characterisation of dystrophic skeletal muscle using

Characterisation of dystrophic skeletal muscle using polarisation-sensitive and needle-based

optical coherence tomography

Xiaojie Yang

Master of Biomedical Engineering

This thesis is presented for the degree of Doctor of Philosophy of The

University of Western Australia

School of Electrical, Electronic & Computer Engineering

October, 2014

Abstract

i

Abstract Characterisation and assessment of skeletal muscle damage resulting from Duchenne muscular

dystrophy is essential for the pharmaceutical and nutritional interventions being investigated as

potential treatments for this disease. The conventional method of examining tissue by

histological analysis requires excision, preservation, sectioning, staining, and evaluation by light

microscopy and is, therefore, time-consuming and laborious. Moreover, preclinical and clinical

research, respectively, require sacrifice of animals, which is costly, and biopsy from human

patients, which is invasive. As importantly, it is not possible to perform a longitudinal study of

the same animal or human tissue over an extended period of time. Biomedical imaging

modalities, such as ultrasound, X-ray computed tomography, magnetic resonance imaging, and

light microscopy, have been extensively studied and applied to muscle imaging. The spatial

resolution provided by these clinical volumetric imaging modalities is typically not fine enough

to resolve the ultrastructure of skeletal muscle, such as individual myofibres, that is required for

full characterisation. Moreover, high radiation dose and low contrast in soft tissues remain

issues for X-ray computed tomography and magnetic resonance imaging requires long

acquisition times and is costly.

Optical coherence tomography (OCT) potentially overcomes many of these limitations. OCT is

a noninvasive, low-cost imaging modality providing volumetric data with spatial resolution of

approximately 10 µm. OCT has been applied to imaging skeletal muscle tissue and has

demonstrated potential for characterising muscle damage within dystrophic muscle in mouse

models. However, OCT does not readily lend itself to automatic quantification of the proportion

of muscle damage within a muscle sample, mainly because of its low contrast. This hampers the

inter-scan or inter-sample comparison of the myopathology of the muscle, which is often

required in assessment of skeletal muscle damage. Moreover, the penetration depth of OCT is

limited to approximately 2 mm beneath the surface of skeletal muscle tissue. Visualisation of

the internal structures of tissue ideally requires a greater penetration depth.

In this thesis, two advancements in imaging skeletal muscle using OCT are presented. The

application of an extension of OCT, polarisation-sensitive OCT (PS-OCT), for characterising

and quantitatively assessing muscle damage within dystrophic mouse muscle is presented.

Birefringence of the muscle samples detected by PS-OCT provides a more objective and

reliable indicator of muscle damage. Two-dimensional parametric images, readily indicating the

volumetric proportion of damage within imaged regions of muscle samples, were automatically

generated by a custom computational algorithm applied to the acquired volumetric PS-OCT

data. The volumetric proportion of muscle damage calculated from the parametric images is in

good agreement with the volumetric values manually assessed by conventional stereology of the

Abstract

ii

corresponding histological sections. This method may provide an efficient and accurate

alternative to conventional approaches to damage assessment in the future.

The second advancement presented in this thesis is the development, fabrication and application

of an ultrathin side-viewing needle-based OCT probe. The probe is the smallest side-viewing

OCT volumetric imaging needle probe to be developed in the world, and is reported here along

with two alternative designs for achieving an extended depth of focus. The ultrathin side-

viewing OCT needle probe was first applied in imaging internal ultrastructures of lung tissue.

The results demonstrated the capability of the needle probe in imaging the internal ultrastructure

of opaque tissue. Subsequently, the ultrathin needle probe was applied to imaging internal

ultrastructures of skeletal muscle. Individual myofibres and other internal structures, such as

connective tissues, that were ~1 cm below the tissue surface were clearly visualised within the

acquired volumetric data. This demonstration of an ultrathin needle probe for muscle imaging

extends the utility of OCT to deep in tissue well beyond the conventional few-millimetre limits.

Contents

iii

Contents

Abstract ........................................................................................................................................... i

Contents ....................................................................................................................................... iii

Acknowledgements ..................................................................................................................... vii

Statement of contribution .............................................................................................................. ix

List of publication ....................................................................................................................... xii

List of figures .............................................................................................................................. xvi

List of tables ................................................................................................................................ xxi

List of abbreviations ................................................................................................................. xxii

Chapter 1 Introduction ........................................................................................................ 1

1.1 Research motivation.......................................................................................................... 1

1.2 Outline of thesis ................................................................................................................ 3

Chapter 2 Background ........................................................................................................ 6

2.1 Preface .............................................................................................................................. 6

2.2 Overview of the structure and function of muscles .......................................................... 6

2.3 Skeletal muscle ................................................................................................................. 8

2.3.1 Myofibres in skeletal muscle ............................................................................... 8

2.3.2 ECM in skeletal muscle ..................................................................................... 13

2.3.3 Contraction of skeletal muscle ........................................................................... 16

2.4 DMD ............................................................................................................................... 18

2.4.1 Phenotype of DMD ............................................................................................ 18

2.4.2 Pathological changes of DMD ........................................................................... 20

2.4.3 The mdx mouse model ....................................................................................... 22

2.5 Techniques for imaging skeletal muscle and muscle damage ........................................ 23

2.5.1 Ultrasonography ................................................................................................. 24

2.5.2 CT ...................................................................................................................... 27

2.5.3 MRI .................................................................................................................... 29

2.5.4 Light microscopy ............................................................................................... 31

Contents

iv

2.6 OCT ................................................................................................................................ 33

2.6.1 Working principle .............................................................................................. 34

2.6.2 Application of OCT in imaging skeletal muscle and muscle damage ............... 37

2.6.3 Challenges of using OCT for assessment of muscle damage and in vivo imaging

of skeletal muscle .............................................................................................. 39

2.7 Chapter summary............................................................................................................ 40

Chapter 3 Characterisation of skeletal muscle damage using PS-OCT ....................... 42

3.1 Preface ............................................................................................................................ 42

3.2 Optical birefringence and polarisation ........................................................................... 42

3.3 Representation of the SoP .............................................................................................. 46

3.4 PS-OCT .......................................................................................................................... 49

3.5 Birefringence of skeletal muscle .................................................................................... 52

3.6 En face parametric imaging of tissue birefringence using polarization-sensitive optical

coherence tomography .................................................................................................... 56

3.6.1 Introduction ....................................................................................................... 56

3.6.2 Method............................................................................................................... 57

3.6.3 Experiment ........................................................................................................ 59

3.6.4 Results ............................................................................................................... 61

3.6.5 Discussion ......................................................................................................... 63

3.6.6 Conclusion ......................................................................................................... 64

3.6.7 Acknowledgements ........................................................................................... 65

3.6.8 References ......................................................................................................... 65

3.7 Quantitative assessment of muscle damage in the mdx mouse model of Duchenne

muscular dystrophy using polarization-sensitive optical coherence tomography .......... 68

3.7.1 Introduction ....................................................................................................... 68

3.7.2 Materials and methods ....................................................................................... 71

3.7.3 Results ............................................................................................................... 76

3.7.4 Discussion ......................................................................................................... 79

3.7.5 Conclusion ......................................................................................................... 82

3.7.6 Acknowledgements ........................................................................................... 82

Contents

v

3.7.7 References .......................................................................................................... 82

3.8 Related works ................................................................................................................. 87

3.8.1 The injected EBD does not significantly affect the detected birefringence ....... 87

3.8.2 Manual estimation of percentage necrosis within histological sections ............ 88

3.9 Chapter summary ............................................................................................................ 92

Chapter 4 Needle probes for OCT .................................................................................... 94

4.1 Preface ............................................................................................................................ 94

4.2 Review of endoscopic OCT probes ................................................................................ 94

4.2.1 Catheter-based OCT probes ............................................................................... 94

4.2.2 Needle-based OCT probes ................................................................................. 95

4.3 Development of ultrathin needle probes for OCT imaging ............................................ 96

4.3.1 Preface ............................................................................................................... 96

4.3.2 Ultra-thin side-viewing needle probe for optical coherence tomography .......... 96

4.3.3 Static and dynamic imaging of alveoli using optical coherence tomography

needle probes ................................................................................................... 102

4.4 Alternative designs of OCT fibre probes for extended depth of focus with maintained

lateral resolution and sensitivity ................................................................................... 118

4.4.1 Preface ............................................................................................................. 118

4.4.2 Ultrathin fiber probes with extended depth of focus for optical coherence

tomography ...................................................................................................... 119

4.4.3 Accurate modeling and design of graded-index fiber probes for optical

coherence tomography using the beam propagation method ........................... 124

4.5 Chapter summary .......................................................................................................... 145

Chapter 5 Imaging skeletal muscle using an ultrathin side-viewing OCT needle probe

......................................................................................................................... 148

5.1 Preface .......................................................................................................................... 148

5.2 Imaging data of mouse skeletal muscle obtained using the 840-nm OCT needle probe

............................................................................................................................................... 149

5.3 Imaging deep skeletal muscle structure using a high-sensitivity ultrathin side-viewing

optical coherence tomography needle probe ................................................................. 152

5.3.1 Introduction ...................................................................................................... 152

Contents

vi

5.3.2 Materials and methods ..................................................................................... 154

5.3.3 Results ............................................................................................................. 160

5.3.4 Discussion ....................................................................................................... 163

5.3.5 Conclusion ....................................................................................................... 164

5.3.6 Acknowledgements ......................................................................................... 164

5.3.7 References ....................................................................................................... 165

5.4 Effect of the relative orientation of the needle insertion and myofibres ...................... 169

5.5 Chapter summary .......................................................................................................... 171

Chapter 6 Conclusion ...................................................................................................... 172

6.1 Significance of the research outcomes ......................................................................... 172

6.2 Research limitations and future work ........................................................................... 174

6.3 Summary of contributions ............................................................................................ 176

Appendix I Theoretical description of OCT ................................................................... 177

Preface ................................................................................................................................... 177

Introduction ........................................................................................................................... 177

A1.1 The incident light .......................................................................................................... 177

A1.2 The reflected and back-scattered light .......................................................................... 178

A1.3 Detection of the signal .................................................................................................. 179

A1.4 Analysis of the signal ................................................................................................... 182

References ................................................................................................................................ 185

Acknowledgements

vii

Acknowledgements First of all, I would like to thank God for helping me to have the chance to pursue an

engineering PhD in a world-class university overseas, which has been a dream since my

childhood. I presume that God has been witnessing me standing on the top of the hill behind my

apartment in Qingdao (Tsingtao) (Shandong, China) and praying towards the sky with the Bible

in early 2009.

I would like to thank my mother, my father, and my grandparents. They are either teachers in

primary and middle schools, or professors in colleges and universities. Therefore, great

demands are required to be their child due to their extremely high expectations for me. As their

only child, I am supposed to be better than any other children that they know, especially in

terms of studying. Whether or not these requirements are acceptable in western culture, I am

propelled to pull through any hardships to pursue the highest qualification. My grandmother on

my mother’s side, unfortunately, passed away in 2010. I hope she has been able to see my

progress from heaven. Special gratitude should be conferred to my mother’s father, my

grandfather. Although he has been probably deprived of the right of seeing my progress because

of Alzheimer’s disease, I will never forget his encouragement to me whilst I was growing up.

It is my real honour to be included in this world-class research group, Optical + Biomedical

Engineering Laboratory (OBEL), and to be admitted to the University of Western Australia

(UWA). My first thanks go to Winthrop Professor David D. Sampson for mentoring me in

2009. David’s warm reply to my inquiry emails in 2008 gave me the most brilliant and glittering

light of hope, when almost all of other universities relentlessly ignored my inquiries about PhD

studies at that time. Associate Professor Robert A. McLaughlin’s very warm welcome and

detailed guidance permeated not only into my research but also into my life. It was my luck to

be supervised by and work with Assistant Professor Dirk Lorenser during my PhD years. Dr.

Lorenser is the best supervisor I have ever met. His patient and considerate guidance helped me

to overcome numerous practical problems during experiments. Winthrop Professor Miranda D.

Grounds is another supervisor for whom I should show my sincere respect. Her comfort and

encouragement rebuilt my confidence constantly. Thus, I could keep walking forward along this

long journey.

Moreover, I would like to thank Dr. Joanne Edmondston, who always provided me with

substantial help and significant support during my whole PhD candidature; thanks to Dr.

Timothy R. Hillman, who was the first friendly colleague in OBEL explaining the principle of

spectral-domain optical coherence tomography (SD-OCT) to me; thanks to Mr. Bryden C.

Quirk, who generously gave me professional guidance in practical operations; thanks to Mr.

Lixin Chin, who came to OBEL perfectly in time to provide me with help in computational

Acknowledgements

viii

programming; thanks to Dr. Yih M. Liew and Mr. Peijun Gong, who were the only people

speaking Mandarin to me in OBEL.

I have suffered many trials and tribulations during my five years of PhD study. I was suffering

from bed bugs in early 2011. Numerous clusters of red bumps covered my body and brought me

unbearable itching. In the middle of 2011, my short-sightedness became worse. The most

serious issue happened in the middle of 2012 when I became a victim of internet violence from

Qingdao (Tsingtao) (Shandong, China). My private information was illegally released and

abused by several lawbreakers in Qingdao. Libel and insult were levelled at me and,

unavoidably, caused me psychological trauma. However, I have overcome all of these

difficulties. For those who expect to see my failure, I will try my best to keep disappointing

you! For those who have plagued me, my payback time will definitely come, sooner or later!

I have been in Australia for almost seven years. I have finished my master’s degree in

Melbourne, and I am finishing my PhD in Perth. I determined to study overseas to pursue my

honour of life, although it is clearer than crystal that this way is deemed to be tough from its

beginning to the end. I am not as lucky as those Chinese students who are sponsored by the

Chinese government (specifically, the Chinese Scholarship Council). Instead, I was self-funding

in Melbourne and then successfully applied for the scholarships from UWA by myself. I am not

a born genius, so I have to devote more time and effort compared with those intelligent or lucky

people. It is true that I am not young anymore at the last stage of my PhD. Thirty, is no longer a

proud age for submitting a PhD thesis. According to Chinese tradition, a 30-year-old man

should already have his own career and family. From this perspective, I am not yet successful.

However, I will go on following my way towards my aim, no matter what dangers and obstacles

are in store for me in the future. I will try my best to raise me up!

Statement of contribution

ix

Statement of contribution This thesis contains seven published journal articles. The candidate, Xiaojie Yang (XY), is the

first author of two of these journal articles and the second author of five other journal articles.

Xiaojie Yang is the sole author for the remainder of this thesis. The journal articles are

presented in the form in which they were published, except the formatting has been adapted to

match the style of the thesis, according to The University of Western Australia’s guidelines on

“Thesis as a series of papers” (http://www.postgraduate.uwa.edu.au/students/thesis/series.

Accessed: 22 March, 2014). The bibliographical details of these articles, the locations where

they appear and the contribution by XY are outlined below. Acronyms for other authors’ names

are BCQ (Bryden C. Quirk), BRK (Blake R. Klyen), DDS (David D. Sampson), DL (Dirk

Lorenser), LC (Lixin Chin), MCS (M. Cather Simpson), ME (Matthew Edmond), MDG

(Miranda D. Grounds), PBN (Peter B. Noble), RAM (Robert A. McLaughlin), RWK (Rodney

W. Kirk), and TS (Tea Shavlakadze).

Lixin Chin, Xiaojie Yang, Robert A. McLaughlin, Peter B. Noble, and David D. Sampson,

“En face parametric imaging of tissue birefringence using polarization-sensitive optical

coherence tomography”, Journal of Biomedical Optics, 18(6), art.066005, 2013.

This publication is presented in Chapter 3, Section 3.6. XY prepared the tissue (tendon) samples

for PS-OCT imaging and provided assistance for the operation of the imaging system. The

sample preparation included excision and cutting of the tendon samples. XY provided assistance

in the experiment for the thermal damage of the samples. The estimated percentage contribution

from XY is 20%.

X. Yang, L. Chin, B. R. Klyen, T. Shavlakadze, R. A. McLaughlin, M. D. Grounds, and D.

D. Sampson, "Quantitative assessment of muscle damage in the mdx mouse model of

Duchenne muscular dystrophy using polarization-sensitive optical coherence

tomography," Journal of Applied Physiology 115(9), pp. 1393-1401, 2013.

This publication is presented in Chapter 3, Section 3.7. XY, under the supervision of RAM,

MDG, and DDS, conducted all the imaging experiments presented in this article, to acquire the

PS-OCT volumetric data and photographs of all the imaged muscle samples. Moreover, XY

conducted the fixation of the samples after imaging in preparation for histology. The

histological sections were imaged by XY. The image coregistration and colocated comparison

between the images of histological sections and the corresponding PS-OCT images were

performed by XY. The manual estimation of the percentage necrosis within the histological

sections was performed by XY. XY provided assistance in the sacrifice of the mice and excision

http://www.postgraduate.uwa.edu.au/students/thesis/series


x

of the muscle samples. XY drafted the journal article, which has been comprehensively

reviewed and edited by all co-authors. The estimated percentage contribution from XY is 40%.

D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin, and D. D. Sampson,

“Ultrathin side-viewing needle probe for optical coherence tomography”, Optics Letters,

36(19), pp. 3894-3896, 2011.

This publication is presented in Chapter 4, Section 4.3.2. XY fabricated the ultrathin side-

viewing OCT needle probe under the detailed supervision by DL. The fabrication included

cleaving, and splicing that were for the fabrication of the optical fibre elements following the

specific design; angle-polishing and fibre probe with accurate control of the removed fibre

lengths; taking microphotograph of the fabricated fibre probe. All of these steps of fabrication

were conducted by XY. XY provided assistance in the metal coating of the fibre probe and the

assembling of the completed needle probe. XY, under the supervision of BCQ, conducted the

electro-chemical etching of the side opening on the employed hypodermic needles.

Furthermore, the beam profiles of the fabricated fibre probes and assembled needle probes were

measured by XY. The estimated percentage contribution from XY is 30%.

R. A. McLaughlin, X. Yang, B. C. Quirk, D. Lorenser, R. W. Kirk, P. B. Noble, and D. D.

Sampson, “Static and dynamic imaging of alveoli using optical coherence tomography

needle probes”, Journal of Applied Physiology, 113(6), pp. 967-974, 2012.

This publication is presented in Chapter 4, Section 4.3.3. XY fabricated the ultrathin OCT

needle probe (the probe presented in the previous journal article by Lorenser et al. published in

2011) used in the experiments that was presented in this article. XY provided assistance in the

imaging experiment. The estimated percentage contribution from XY is 20%.

D. Lorenser, X. Yang, and D. D. Sampson, "Ultrathin fiber probes with extended depth of

focus for optical coherence tomography", Optics Letters, 37(10), pp. 1616-1618, 2012.

This publication is presented in Chapter 4, Section 4.4.2. XY fabricated the designed fibre

probes. This fabrication included cleaving and splicing of the sections of optical fibres with

accurate control of their lengths. The hemispherical refractive lens was generated and appended

by XY to the end of the fibre probe, using optical adhesive and the ultraviolet lamp. The beam

profiles of the fabricated fibre probes were measured by XY. The estimated percentage

contribution from XY is 40%.


xi

D. Lorenser, X. Yang, and D. D. Sampson, "Accurate modeling and design of graded-

index fiber probes for optical coherence tomography using the beam propagation

method", IEEE Photonics Journal, 5(2), art.3900015, 2013.

This publication is presented in Chapter 4, Section 4.4.3. XY fabricated the fibre probes, which

were for the validation of the simulated results, following the design by DL. The beam profiles

of the fabricated fibre probes were measured by XY. The estimated percentage contribution

from XY is 15%.

X. Yang, D. Lorenser, R. A. McLaughlin, R. W. Kirk, M. Edmond, M. C. Simpson, M. D.

Grounds, and D. D. Sampson, "Imaging deep skeletal muscle structure using a high-

sensitivity ultrathin side-viewing optical coherence tomography needle probe," Biomedical

Optics Express, 5(1), pp. 136-148, 2014.

This publication is presented in Chapter 5, Section 5.2. XY fabricated the improved ultrathin

side-viewing OCT needle probes that were presented in the article. The fabrication included

cleaving, and splicing that were for the fabrication of the optical fibre elements following the

specific design; angle-polishing and fibre probe with accurate control of the removed fibre

lengths; and taking a microphotograph of the fabricated fibre probe. All of these steps of

fabrication were conducted by XY. The beam profiles of the fabricated fibre probes and

assembled needle probes were measured by XY. XY operated the customised imaging system

and achieved the imaging experiments under the detailed supervision of DL. The imaged muscle

samples were prepared by XY. After imaging, the acquired OCT data were processed by XY,

using the customised software developed by RWK. The imaged muscle samples were fixed by

XY in preparation for histology. The histological sections were imaged by XY. The colocated

comparison and image coregistration between the images of histological sections and the OCT

data were subsequently performed by XY. The journal article was drafted by XY based on the

analysis of the OCT data. The article draft was comprehensively reviewed and edited by all co-

authors. The estimated percentage contribution from XY is 40%.

Student’s signature: Date:

Co-ordinating supervisor’s signature: Date:

List of publication

xii

List of publication Peer-reviewed journal articles:

1. D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin, and D. D. Sampson,

“Ultrathin side-viewing needle probe for optical coherence tomography”, Optics Letters,

36(19), pp. 3894-3896, 2011.

2. D. Lorenser, X. Yang, and D. D. Sampson, "Ultrathin fiber probes with extended depth of

focus for optical coherence tomography", Optics Letters, 37(10), pp. 1616-1618, 2012.

3. R. A. McLaughlin, X. Yang, B. C. Quirk, D. Lorenser, R. W. Kirk, P. B. Noble, and D. D.

Sampson, “Static and dynamic imaging of alveoli using optical coherence tomography

needle probes”, Journal of Applied Physiology, 113(6), pp. 967-974, 2012.

4. X. Yang, L. Chin, B. R. Klyen, T. Shavlakadze, R. A. McLaughlin, M. D. Grounds, and D.

D. Sampson, "Quantitative assessment of muscle damage in the mdx mouse model of

Duchenne muscular dystrophy using polarization-sensitive optical coherence tomography,"

Journal of Applied Physiology 115(9), pp. 1393-1401, 2013.

5. D. Lorenser, X. Yang, and D. D. Sampson, "Accurate modeling and design of graded-index

fiber probes for optical coherence tomography using the beam propagation method", IEEE

Photonics Journal, 5(2), art.3900015, 2013.

6. L. Chin, X. Yang, R. A. McLaughlin, P. B. Noble, and D. D. Sampson, “En face parametric

imaging of tissue birefringence using polarization-sensitive optical coherence tomography”,

Journal of Biomedical Optics, 18(6), art.066005, 2013.

7. X. Yang, D. Lorenser, R. A. McLaughlin, R. W. Kirk, M. Edmond, M. C. Simpson, M. D.

Grounds, and D. D. Sampson, "Imaging deep skeletal muscle structure using a high-

sensitivity ultrathin side-viewing optical coherence tomography needle probe," Biomedical

Optics Express, 5(1), pp. 136-148, 2014.

Conference proceedings:

Keys: § Domestic; ‡ International; † poster presentation; ¡ oral presentation

1. §† X. Yang, L. Chin, R. A. McLaughlin, B. R. Klyen, H. G. Radley-Crabb, G. J. Pinniger,

M. D. Grounds, and D. D. Sampson, "Quantitative identification of muscle necrosis in an

mdx mouse using high-resolution optical birefringence imaging," presented at Combined

Biological Sciences Meeting (CBSM), Perth, WA, Australia, 2011.

2. ‡¡ X. Yang, R. A. McLaughlin, D. Lorenser, R. W. Kirk, P. B. Noble, and D. D. Sampson,

"In situ 3D imaging of alveoli with a 30 gauge side-facing optical needle probe," presented at

List of publication

xiii

International Conference on Intelligent Sensors, Sensor Networks and Information

Processing (ISSNIP), Adelaide, SA, Australia, 2011.

3. §† L. Chin, X. Yang, R. A. McLaughlin, and D. D. Sampson, "A novel image processing

algorithm for high resolution assessment of tissue damage using polarisation sensitive optical

coherence tomography," presented at Combined Biological Sciences Meeting (CBSM), Perth,

WA, Australia, 2011.

4. ‡¡ X. Yang, D. Lorenser, R. W. Kirk, B. C. Quirk, P. B. Noble, R. A. McLaughlin, and D. D.

Sampson, "In situ 3D imaging of alveoli with a 30-gauge side-facing OCT needle probe,"

presented at BiOS, San Francisco, CA, US, 2012.

5. ‡¡ X. Yang, D. Lorenser, G. J. Pinniger, R. W. Kirk, R. A. McLaughlin, and D. D. Sampson,

“In situ 3D imaging of internal structures of skeletal muscle with a 30-gauge optical needle

probe”, presented at International Conference of APMC-ICONN-ACMM, Perth, WA,

Australia, 2012.

6. ‡† X. Yang, D. Lorenser, R. W. Kirk, G. J. Pinniger, M. D. Grounds, R. A. McLaughlin, and

D. D. Sampson, “3D imaging of internal structures of skeletal muscle with an ultrathin side-

viewing optical needle probe”, presented at International Congress of World Muscle Society

(WMS), Perth, WA, Australia, 2012.

7. §† X. Yang, R. A. McLaughlin, D. Lorenser, B. C. Quirk, R. W. Kirk, P. B. Noble, G. J.

Pinniger, M. D. Grounds, and D. D. Sampson, “3D imaging of biological tissue using a 30-

gauge side-facing OCT needle probe”, presented at Combined Biological Sciences Meeting

(CBSM), Perth, WA, Australia, 2012.

8. §† X. Yang, R. A. McLaughlin, D. Lorenser, B. C. Quirk, R. W. Kirk, P. B. Noble, G. J.

Pinniger, M. D. Grounds, and D. D. Sampson, "3D imaging of biological tissue using a 30-

gauge side-viewing optical needle probe," presented at Postgraduate Electrical Engineering

and Computing Symposium (PEECS), Perth, WA, Australia, 2012.

9. ‡¡ D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin, and D. D. Sampson,

"Ultra-thin 30-gauge needle probe for minimally invasive 3D optical coherence

tomography," presented at BiOS, San Francisco, CA, US, 2012.

10. §† L. Chin, X. Yang, B. R. Klyen, R. A. McLaughlin, T. Shavlakadze, M. D. Grounds, and

D. D. Sampson, “Automated assessment and quantification of muscle necrosis in the mdx

mouse model of Duchenne muscular dystrophy”, presented at Combined Biological Sciences

Meeting (CBSM), Perth, WA, Australia, 2012.

11. ‡¡ L. Chin, X. Yang, R. A. McLaughlin, H. G. Radley-Crabb, M. D. Grounds, and D. D.

Sampson, “Parametric imaging of birefringence in muscle using polarisation-sensitive

optical coherence tomography using polarisation-sensitive optical coherence tomography”,

List of publication

xiv

presented at International Conference of APMC-ICONN-ACMM, Perth, WA, Australia,

2012.

12. ‡† L. Chin, X. Yang, R. A. McLaughlin, B. R. Klyen, H. G. Radley-Crabb, G. J. Pinniger, T.

Shavlakadze, M. D. Grounds, and D. D. Sampson, “Identification of muscle necrosis in mdx

mice using optical birefringence imaging”, presented at International Congress of World

Muscle Society (WMS), Perth, WA, Australia, 2012.

13. ‡¡ D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin, and D. D. Sampson,

“Needle probes for optical coherence tomography: recent advances in technology and

applications”, oral presentation in International Conference Series of Focus on Microscopy

(FOM), Singapore, 2012.

14. ‡¡ D. Lorenser, X. Yang, and D. D. Sampson, “Analysis of fiber-optic probes using graded-

index fiber microlenses with non-ideal refractive index profiles”, presented at International

Conference of Optical Fibre Sensors (OFS), Beijing, China, 2012.

15. ‡¡ X. Yang, D. Lorenser, R. A. McLaughlin, R. W. Kirk, M. Edmond, M. C. Simpson, M. D.

Grounds, and D. D. Sampson, "Robust ultrathin needle probe with high sensitivity for

imaging deep skeletal muscle structure with optical coherence tomography," presented at

Australian and New Zealand Conference on Optics and Photonics (ANZCOP), Fremantle,

WA, Australia, 2013.

16. ‡¡ L. Chin, X. Yang, B. R. Klyen, R. A. McLaughlin, T. Shavlakadze, M. D. Grounds, and

D. D. Sampson, “Automated quantification of birefringence for assessment of muscle

necrosis using polarization-sensitive optical coherence tomography”, presented at BiOS, San

Francisco, CA, US, 2013.

17. ‡¡ L. Chin, X. Yang, R. A. McLaughlin, P. B. Noble, and D. D. Sampson, "Birefringence

imaging for optical sensing of tissue damage," presented at International Conference on

Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Melbourne,

VIC, Australia, 2013.

18. ‡¡ D. Lorenser, L. Scolaro, X. Yang, B. C. Quirk, R. W. Kirk, M. Auger, W. Madore, N.

Godbout, M. Edmond, M. C. Simpson, C. Boudoux, R. A. McLaughlin, and D. D. Sampson,

"Advancements in performance and capabilities of OCT needle probes," presented at

European Conferences on Biomedical Optics (ECBO), Munich, Germany, 2013.

19. §¡ R. A. McLaughlin, D. Lorenser, B. C. Quirk, L. Scolaro, X. Yang, K. M. Kennedy, and

D. D. Sampson, "A microscope in a needle - new techniques to view disease," presented at

Engineering and the Physical Sciences in Medicine conference (EPSM), Perth, WA,

Australia, 2013.

List of publication

xv

20. ‡¡ X. Yang, D. Lorenser, R. A. McLaughlin, R. W. Kirk, M. Edmond, M. C. Simpson, M. D.

Grounds, and D. D. Sampson, "Demonstration of 3D imaging of skeletal muscle at

centimeter depths using a 30-gauge side-viewing optical coherence tomography needle

probe," presented at BiOS, San Francisco, CA, US, 2014.

List of figures

xvi

List of figures

2.1 Light microscopic images of the H&E-stained histological sections of mouse skeletal

muscle, smooth muscle and cardiac muscle ..................................................................... 7

2.2 Diagram to illustrate myogenesis and the formation of skeletal myofibres, with

comparison to cell sizes .................................................................................................... 9

2.3 Structural hierarchy of skeletal muscle .......................................................................... 10

2.4 Different architectures of skeletal muscle ...................................................................... 10

2.5 Distribution of nuclei in mature and regenerated myofibres .......................................... 11

2.6 The interdigitating arrangement of myosin and actin filaments ..................................... 12

2.7 The structure of sarcomeres at the cellular and molecular levels, including the

definitions of A-band, I-band, H-zone, M-line, and Z-line ............................................ 12

2.8 The ECM structure of skeletal muscle ........................................................................... 14

2.9 Tendons attach the ends of skeletal muscle to bones ..................................................... 15

2.10 Schematic representation of the ECM surrounding skeletal muscle .............................. 15

2.11 The arrangement of myofilaments, as well as the definitions of A-band, I-band, H-zone,

M-line, Z-line, within one individual sarcomere when the muscle is stretched, resting

and contracted ................................................................................................................. 17

2.12 Schematic and TEM images revealing that cross-bridges are formed when the state of

muscle changes from resting to contracted..................................................................... 17

2.13 H&E-stained transverse sections of dystrophic mouse quadriceps muscle containing

normal-appearing, necrotic, and regenerated myofibres revealing the changes in

geometry and the locations of nuclei .............................................................................. 19

2.14 TEM image revealing Delta lesion ................................................................................. 21

2.15 Summary of pathological event sequence of DMD ........................................................ 22

2.16 Transverse US images of a normal and a DMD left quadriceps muscle of human

patients ............................................................................................................................ 26

2.17 CT scan of skeletal muscle of a human patient at the lumbar level ............................... 29

2.18 MRI images of dystrophic muscle from mdx mice with and without the contrast agent

M-325 ............................................................................................................................. 31

2.19 SHG images of normal and mdx mouse muscle ............................................................. 32

2.20 Schematic of a generic fibre-optic OCT system ............................................................. 34

List of figures

xvii

2.21 Illustration of the A-scan, B-scan, and C-scan performed by OCT scanning mechanism

........................................................................................................................................ 35

2.22 OCT image of mouse muscle from the whole-muscle autograft model ......................... 38

2.23 OCT image of exercised mdx mouse muscle .................................................................. 39

3.1 Schematic of linear SoP oriented vertical, linear SoP oriented 45˚, and right-hand

circular SoP ..................................................................................................................... 44

3.2 Differential phase retardation between the two orthogonal polarisation components is

introduced by the medium with SoP-dependent refractive index ................................... 45

3.3 Schematic of double refraction within a crystal medium................................................ 46

3.4 Schematic of the Poincaré sphere ................................................................................... 49

3.5 Schematic of a bulk-optic PS-OCT system ..................................................................... 52

3.6 The direction of optic axis within skeletal muscle .......................................................... 54

3.7 Schematic of the employed PS-OCT system .................................................................. 60

3.8 Quadrature demodulation and phase unwrapping applied to a single representative A-

scan ................................................................................................................................. 60

3.9 The mean birefringence of porcine tendon samples after thermal stress ........................ 61

3.10 Phase retardation B-scans of a porcine tendon sample after partial immersion into 69˚C

Krebs solution for 5 min ................................................................................................. 62

3.11 En face OCT intensity images, the corresponding en face parametric PS-OCT images,

and H&E-stained histological section of the same porcine tendon sample depicted in

Fig. 3.10 before and after the partial immersion into 69˚C Krebs solution for 5 min .... 63

3.12 Schematic of PS-OCT imaging system and experimental setup ..................................... 73

3.13 Representative H&E-stained histological sections of mdx muscles revealing normal-

appearing region, necrotic region with fragmentation of sarcoplasm and minimal

evidence of inflammation, and necrotic region with inflammation ................................ 74

3.14 Colocated EBD photograph, H&E-stained histological section, OCT log-scaled en face

intensity image, and parametric birefringence image of dystrophic triceps muscle from a

treadmill-exercised mdx mouse ....................................................................................... 77

3.15 Second representative set of colocated EBD photograph, H&E-stained histological

section, OCT log-scaled en face intensity image, and parametric birefringence image of

dystrophic triceps muscle from a second treadmill-exercised mdx mouse ..................... 78

List of figures

xviii

3.16 Colocated EBD photograph, H&E-stained histological section, OCT log-scaled en face

intensity image, and parametric birefringence image of quadriceps muscle from a C57

wild-type mouse ............................................................................................................. 78

3.17 Comparison of percentage necrosis evaluated using histology and PS-OCT for 11 scans

of selected 4 × 4 mm regions within 7 muscle samples from 5 mdx mice ..................... 79

3.18 Colocated EBD photograph and EBD auto-fluorescence image revealing necrosis

within dystrophic mouse muscle .................................................................................... 88

3.19 Colocated H&E-stained histological section and en face parametric PS-OCT image of

the EBD-free treadmill-exercised mdx mouse muscle.................................................... 88

3.20 Representative histological sections with manual identification and measurement of the

necrosis areas and sample areas inside the images ......................................................... 89

4.1 Side-viewing OCT needle probes with different deflection mechanisms ...................... 96

4.2 Schematic of the ultrathin side-viewing needle probe design, the corresponding

micrographs of the angle-polished fibre probe with the deposition of the metal coating,

and the micrograph of the completed needle probe ........................................................ 98

4.3 Output beam characteristics of the fabricated 30G needle probe ................................... 99

4.4 Schematic of the 840 nm SD-OCT system, and the SNR measurement of the 30G

needle probe immersed in water at 2-µs exposure time ............................................... 100

4.5 OCT images of a lamb lung obtained with the 30G needle probe ................................ 101

4.6 Schematic of OCT needle imaging system................................................................... 105

4.7 Illustration of the functionality of the 2 types of OCT needle probes used in the imaging

of lung tissue ................................................................................................................ 106

4.8 Static OCT images and the colocated H&E-stained histological section of a rat lung

sample ........................................................................................................................... 108

4.9 Static OCT images and the colocated H&E-stained histological section of a fetal lamb

lung sample ................................................................................................................... 108

4.10 Three-dimensional visualisation of fetal lamb lung ..................................................... 109

4.11 Screen shots from animation acquired with the dynamic OCT needle probe .............. 110

4.12 EDOF probe using a GRIN fibre lens and a GRIN fibre phase mask .......................... 120

4.13 EDOF probe using a refractive lens and a GRIN fibre phase mask ............................. 121

4.14 Results for the fabricated EDOF probe ........................................................................ 122

4.15 Results for the fabricated normal refractive-lens probe ............................................... 123

List of figures

xix

4.16 Schematics of a fibre-optic OCT needle probe and the same probe but with an

additional GRIN phase mask ........................................................................................ 125

4.17 Schematic of the BPM simulation geometry ................................................................ 127

4.18 Power-law refractive index profile with central dip and ripple, illustration of the effect

of the power-law exponent α on the profile shape, and the measured index profiles and

power-law fits of several commercial fibres ................................................................. 131

4.19 BPM simulation results of a lensed fibre probe using a GRIN fibre lens with an ideal

parabolic profile but finite core diameter, illustrating the effects of aperture diffraction

on the output beam as function of the fill factor w/a .................................................... 135

4.20 BPM simulation of a GRIN-lensed fibre with α = 2.15 ................................................ 136

4.21 BPM simulation of a GRIN-lensed fibre with α = 1.85 ................................................ 136

4.22 BPM simulation of a GRIN-lensed fibre with α = 2.0 and central index dip with wdip =

1.5 μm and hdip = 0.5 ..................................................................................................... 137

4.23 BPM simulation of a GRIN-lensed fibre with α = 2.0 and ripple with hrip = 0.03 and prip

= 5 μm ........................................................................................................................... 139

4.24 Comparison of BPM simulation to the measured beam profile of a lensed fibre using the

GRIN MMF with the index profile shown in Fig. 4.18(c) ............................................ 140

4.25 BPM simulation of a GRIN fibre probe using a phase mask to increase the DOF ....... 141

5.1 OCT image acquired from the first-generation ultrathin OCT needle probe, showing the

transverse view of a healthy left TA mouse muscle, and the colocated histological

section ........................................................................................................................... 150

5.2 OCT image acquired from the first-generation ultrathin OCT needle probe, showing the

longitudinal view of a healthy right TA mouse muscle, and the colocated histological

section ........................................................................................................................... 151

5.3 A 3D-rendered volumetric OCT image of the healthy right TA mouse muscle ........... 151

5.4 Schematic of the ultrathin OCT needle probe, microscope image of the angle-polished

fiber probe before metallisation, SEM image of the laser-drilled side opening, fully

assembled needle probe showing the laser-drilled side opening .................................. 156

5.5 Beam profile and sensitivity characterisation of the probe, illustration of the

astigmatism introduced by the fibre, resulting in different working distances WDx and

WDy in the x- and y-directions, measured, simulated and fitted FWHM output beam

diameters in water, and calculated normalised on-axis intensity, transverse intensity

profile of the beam in water at the focus of the x-direction, at a distance of 330 µm from

List of figures

xx

the fibre, averaged OCT A-scan of a silica/water interface located at the distance of

maximum SNR ............................................................................................................. 158

5.6 Schematic of the 1300-nm SSOCT needle imaging system ......................................... 159

5.7 Representative images of normal mouse skeletal muscle and the corresponding H&E-

stained histology ........................................................................................................... 161

5.8 Representative images of dystrophic mouse skeletal muscle and the corresponding

H&E-stained histology ................................................................................................ 162

5.9 A 3D-rendered volumetric OCT dataset of normal mouse muscle and three orthogonal

cross sections ................................................................................................................ 162

5.10 Schematic of 3D view of longitudinal and transverse needle insertion; schematic of the

radial B-scans of longitudinal and transverse needle insertion (according to the green

dash lines); schematic of the en face 2D view of longitudinal and transverse needle

insertion (according to the purple dash lines); the corresponding OCT images of the en

face 2D view of longitudinal and transverse needle insertion ...................................... 170

A1-1 Schematic of the field quantities in a typical OCT system ........................................... 179

A1-2 Spectral interferogram of a single reflector and multiple reflectors ............................. 182

A1-3 Fourier transform relationship between the coherence function and the spectrum of the

OCT light source .......................................................................................................... 183

A1-4 Illustration of the spatial-domain A-scan calculated based on the IFT ........................ 184

List of tables

xxi

List of tables

2.1 A summary of dimensions, shape, and nucleus arrangement of skeletal, smooth, and

cardiac muscle cells .......................................................................................................... 8

2.2 A summary of US technical properties corresponding to different incident frequencies

........................................................................................................................................ 25

3.1 Reference values of birefringence in skeletal muscles ................................................... 53

3.2 Changes of muscle birefringence caused by muscle contraction .................................... 55

3.3 A summary of imaged muscles ....................................................................................... 72

3.4 The manually measured and calculated percentage values of each histological section

and histology stack. ......................................................................................................... 91

List of abbreviations

xxii

List of abbreviations 1D one-dimensional

2D two-dimensional

3D three-dimensional

BPM beam propagation method

BWF bound water fraction

CCD charge-coupled device

CT X-ray computed tomography

CW continuous-wave

DMD Duchenne muscular dystrophy

DOF depth of focus

EBA Evans blue dye-albumin conjugate

EBD Evans blue dye

ECM extracellular matrix

EDL extensor digitorum longus

EDOF extended depth of focus

FFT fast Fourier transform

FoV field of view

FS fused-silica

FWHM full-width at half-maximum

G gauge

GRIN graded-index

H&E haematoxylin and eosin

HRCT high-resolution computed tomography

IFT inverse Fourier transform

MCVD modified chemical vapor deposition

MEMS microelectromechanical system

MFD mode field diameter


xxiii

MMF multimode fibre

MPM multiphoton microscopy

MRI magnetic resonance tomography

MZI Mach-Zehnder interferometer

NA numerical aperture

NCF no-core fibre

NIR near infrared

OCS optical coherence system

OCT optical coherence tomography

OD outer diameter

PBS phosphate-buffered saline

PM phase mask

PMF polarisation-maintaining fibre

PS-OCT polarisation-sensitive optical coherence tomography

RI refractive index

RDOF relative depth-of-focus

RMS root mean square

SA spherical aberration

SD standard deviation

SD-OCT spectral-domain optical coherence tomography

SHG second harmonic generation

SMF single-mode fibre

SNR signal-to-noise ratio

SoP state of polarisation

SS-OCT swept-source (spectral-domain) optical coherence tomography

TA tibialis anterior

TD-OCT time-domain optical coherence tomography

TEM transmission electron microscope

TPM two-photon microscopy


xxiv

US ultrasound

WD working distance

WDM wavelength-division multiplexer

Chapter 1 - Introduction

1

Chapter 1

Introduction

1.1 Research motivation

One of the most severe modes of human muscular dystrophy, Duchenne muscular dystrophy

(DMD), occurs at a rate of 1 in 3600 to 6000 male births worldwide [1]. Duchenne muscular

dystrophy is characterised by the progressive degeneration of skeletal and cardiac muscle tissue,

eventually resulting in death from respiratory or cardiac failure [1, 2]. Duchenne muscular

dystrophy is caused by a mutation of a recessive gene located on the X-chromosome that codes

for dystrophin. Dystrophin is a sub-sarcolemmal protein that is vital for preserving mechanical

integrity of the muscle fibres (i.e., myofibres) [3]. Absence of dystrophin results in a fragile

membrane that is easily damaged, activating an inflammatory response that leads to degradation

and fragmentation of myofibres [4-6]. Although there is regeneration of new muscle tissue in

DMD, repeated cycles of muscle damage result in the progressive replacement of functional

tissue with fibrous and fatty connective tissue [7].

To treat the inflammatory response that precedes the loss of functional muscle tissue in DMD,

pharmaceutical and nutritional interventions are currently being investigated as potential DMD

treatments [8-11]. To determine the effectiveness of these potential treatments, it is important to

assess the progression of the disease pathology by morphological analysis of the internal

structure of skeletal muscle at the microscopic level. The conventional method is the visual

analysis of haematoxylin and eosin (H&E)-stained histology sections of tissue samples under

light microscopy [12]. The preparation of H&E histology sections requires excision of tissue,

which has a number of disadvantages. For preclinical research using animal models, H&E

histology requires sacrifice of animals, which is costly. For humans, biopsy samples are

required, which may cause further loss of functional muscle tissue in patients with an already

reduced amount of functioning muscle tissue. Moreover, the method does not allow the

longitudinal study of the same animal or same human tissue over multiple times points.

Furthermore, the preservation, sectioning, staining, and the microscopic evaluation of tissues are

time-consuming and laborious.

Numerous biomedical imaging modalities have been investigated as alternatives or adjuncts to

H&E histology, including ultrasound (US) [13-17], X-ray computed tomography (CT) [18-22],

magnetic resonance imaging (MRI) [23-27], and light microscopy [28-31]. These imaging

modalities have been applied to muscle imaging in preclinical research with animals or routine

clinical use, or both. As a noninvasive imaging modality, US has been widely used in routine

clinical practice because of its low cost and short acquisition time. This methodology is able to


2

differentiate dystrophic from healthy skeletal muscle [15, 32], measure the response of tissue to

pharmacological treatment in vivo [33], and discriminate in longitudinal in vivo studies between

mouse models of DMD with varying severity of dystropathology. Ultrasonography has been

used for the quantitative assessment of skeletal muscle tissue from mouse models of muscular

dystrophy [34]. Conventional US has a large penetration depth [35] and moderate spatial

resolution that is typically coarser than 80 µm [36, 37]. This resolution is usually not enough for

resolving ultrastructure within skeletal muscle, such as individual myofibres. However, the

resolution of micro-US is fine enough (~20 µm) to resolve ultrastructures within skeletal

muscles [13].

X-ray computed tomography generates three-dimensional (3D) images using computer-based

scanning and processing. The spatial resolution of conventional CT is coarser than 100 µm [38],

whilst micro-CT can provide 3D images with ~20-µm resolution [22, 39, 40]. However,

although CT possesses the advantages of simple operability and fast scanning protocols, it is

limited by the high radiation patients are exposed to and relatively low contrast in soft tissues.

Micro-CT has not been applied on clinical imaging, because of the high radiation dose.

Magnetic resonance imaging is able to provide 3D volumetric imaging data noninvasively.

Imaging of canine [41, 42] and murine [27, 43-45] models have demonstrated that MRI is

capable of discriminating between dystrophic and healthy muscle tissue. However, the spatial

resolution (20 to 50 µm) of conventional MRI is still not fine enough to resolve individual

myofibres [46, 47]. Although the resolution of some micro-MRI systems can be as fine as 20

µm [48-50], the long acquisition time and high cost of MRI remain as disadvantages.

Optical coherence tomography (OCT), is an optical imaging technique that offers the potential

for high-resolution (~10 µm), non-invasive 3D imaging [51]. Optical coherence tomography is a

reflectance-mode optical imaging modality which uses low-coherence interferometry to produce

3D images of tissue [52, 53]. Optical coherence tomography operates by detecting depth-

resolved backscattered near-infrared light (typical wavelengths lie in the range 800 nm to 1300

nm) in a way that is analogous to ultrasonic pulse-echo imaging. Several studies have reported

the application of OCT to imaging muscular dystrophy [54, 55]. These studies have

demonstrated that OCT is capable of differentiating damaged muscle tissue from undamaged

tissue. Polarisation-sensitive OCT (PS-OCT), an extension of OCT, has been applied to muscle

imaging [56]. Polarisation-sensitive OCT detects an optical property, birefringence, of the

imaged tissue [57] and, thus, introduces new contrast mechanism to differentiate damaged from

undamaged muscle tissue.

One of the limitations of OCT is that it does not lend itself to automated quantification of the

areas of muscle damage. This is because OCT detects the intensity of the reflected or

backscattered signal. This intensity is dependent on not only the reflectivity of the imaged

reflector inside the tissue, but also the intensity of the incident light, the sensitivity of the system


3

used to detect the light signal, and the position of the imaged tissue. As a result, the inter-scan

comparison of the detected signal intensity is difficult. Another limitation of OCT is its

moderate penetration depth. The penetration depth of the incident light from a free-space OCT

probe is typically less than 2 mm from the surface of opaque tissues. This penetration depth is

not usually adequate to image structures deep inside biological tissues.

The aim of this thesis is to further develop the application of optical imaging techniques to

muscle imaging. As OCT does not lend itself to automated quantification of the areas of

necrosis, PS-OCT is applied to the imaging of muscle damage within dystrophic murine muscle.

Pasquesi et al. did preliminary work by applying PS-OCT to characterising the change of

birefringence in dystrophic muscle and, furthermore, demonstrating the correlation between

remarkably reduced birefringence and the exercised dystrophic muscle (mdx mouse muscle)

[56]. We have presented an extension of this study by correlating low-birefringence regions

with the muscle damage in dystrophic muscles from the acquired 3D PS-OCT data volumes and

the corresponding histological analysis. Moreover, the implementation of a fully automated

algorithm for the quantitative analysis of muscle birefringence and assessment of muscle

damage is another extension. In this thesis, a computational algorithm that enables automated

quantitative analysis and assessment of muscle damage within the imaged dystrophic muscle is

developed for PS-OCT imaging. For each one-dimensional (1D) scan in depth, a birefringence

value is automatically calculated based on the measured PS-OCT data. The two-dimensional

(2D) collection of these birefringence values in the en face plane (the surface perpendicular to

optical beam direction) defines a parametric image of birefringence. Areas with damaged

muscle are, therefore, quantitatively differentiated from the areas with undamaged muscle,

based on variations in the birefringence. Hence, the automatically generated 2D parametric map,

which contains 3D information, illustrates the percentage and distribution of areas with muscle

damage.

To overcome the penetration limitations of OCT, an ultrathin side-viewing OCT needle probe

was developed and applied to imaging internal structures deep inside skeletal muscle. Since the

needle probe can be inserted into tissue, 3D scans can be performed deep inside (tens of

millimetres from the tissue surface) the tissue. As the ultrathin needle probe is the smallest

reported side-viewing OCT needle probe (outer diameter 0.31 mm), the damage caused by

needle insertion is minimised.

1.2 Outline of thesis

Chapter 2 – Background. In Chapter 2 of this thesis, an overview of the background relevant

to the physiology of skeletal muscle, the pathology of DMD, the mdx mouse model, and the

imaging modalities applied to muscular dystrophy are provided. The chapter begins with a

review of skeletal muscle ultrastructure, including myofibres, myofibrils, sarcomeres, myosin


4

filaments, and actin filaments. The genetic basis and pathological effects of DMD in altering

these ultrastructures are subsequently described. The mdx mouse model, as the most widely

used animal model in the preclinical research of DMD, is described. Imaging modalities for the

characterisation of muscular dystrophy, such as US, CT, MRI, and microscopy, are reviewed.

The focus of this thesis, OCT, is then discussed in relation to its physical principles and reported

application to muscle imaging.

Chapter 3 – Characterisation of skeletal muscle damage using PS-OCT. In Chapter 3 of this

thesis, the physical basis of birefringence is described, followed by the working principles of

PS-OCT. This is followed by the application of PS-OCT to quantitative characterisation of

muscle damage in the mdx mouse model of DMD based on the measurement of muscle

birefringence. To our knowledge, this is the first time that PS-OCT has been applied to 3D,

automated characterisation and assessment of muscle damage within DMD muscle. This

research was published in Journal of Applied Physiology. The development of the

computational algorithm that is employed in the automated generation of parametric images and

analysis of tissue damage is described. This research was published in Journal of Biomedical

Optics.

Chapter 4 – Needle probes for optical coherence tomography. In Chapter 4 of this thesis, the

development of an ultrathin side-viewing OCT needle probe is described, followed by the

application of this probe to biological tissue imaging and probe optimisation. Four published

journal papers are presented in this chapter, following a brief review of endoscopic OCT probes

(both catheter-based and needle-based). The first paper (published in Optics Letters) in this

chapter describes the design, fabrication, and validation of the probe. The second paper

(published in the Journal of Applied Physiology) demonstrates the application of the probe to

imaging ultrastructures within biological tissue in situ. The other two journal papers (published

in Optics Letters and IEEE Photonics Journal) describe the depth-of-focus (DOF) optimisation

of a fibre-based OCT probe (which is encased in the OCT needle probe) by accurately modeling

focus optics using computational simulation.

Chapter 5 – Imaging skeletal muscle suing an ultrathin side-viewing OCT needle probe. In

Chapter 5 of this thesis, the application of the improved ultrathin side-view OCT needle probe

to imaging internal structures, such as myofibres and connective tissues, deep inside (tens of

millimetres from the tissue surface) skeletal muscle is described. The use of the improved

needle probe to overcome the limitations of OCT in penetration depth is described. The probe is

shown to offer high-resolution 3D imaging data volumes with minimum invasive tissue damage.

The visualisation of individual myofibres and differentiation of damaged from undamaged

muscle tissue demonstrate the potential of the OCT needle probe to characterise muscular

dystrophy and other myopathies. This research was published in Biomedical Optics Express.


5

Chapter 6 – Conclusions and future research. In the final chapter of this thesis, Chapter 6,

the research findings are summarised and synthesised. Polarisation-sensitive OCT, with the

developed computational algorithm, is shown to quantitatively characterise muscle damage

within dystrophic muscle based on the measurement of tissue birefringence, providing

automated assessment of muscular dystrophy. The developed ultrathin side-facing OCT needle

probe is able to provide high-resolution 3D imaging data showing individual myofibres deep

inside the skeletal muscle tissue up to tens of millimetres from the tissue surface. This suggests

that further development of ultrathin side-viewing PS-OCT needle probes is warranted and may

lead to an automated method for the quantitative assessment of muscular dystrophy inside

skeletal muscle tissue with minimum damage to the muscle.

Chapter 2 - Background

6

Chapter 2

Background

2.1 Preface

This chapter provides some background to the motivation and aims of the presented research.

Moreover, the description of the employed imaging technology, as well as the comparison of

this technology to other available imaging modalities, is given. After an overview of the

structure and function of muscles, the anatomy and physiology of skeletal muscle is described.

An introduction of the targeted myodiseases and the available imaging modalities for the

detection of these myodiseases is subsequently provided, followed by the technical description

of our employed imaging technology, OCT. Previous studies in imaging skeletal muscle using

this technology and their reported challenges, which have led to the research presented here, are

discussed in the final part of this chapter.

2.2 Overview of the structure and function of muscles

Three types of muscles, namely skeletal, smooth, and cardiac muscle, exist within human bodies

and most animals (Fig. 2.1). Skeletal muscles contribute approximately 40% of the human body

weight and the force generated by skeletal muscle contraction causes movements of the skeleton

and other parts of the body involved in various physiological functions (e.g., respiration) [58,

59]. Skeletal muscle consists of muscle cells and extracellular matrix (ECM) with many

interstitial cells. Each mature multinucleated muscle cell is referred to as a muscle fibre (or

myofibre), because of its long, rod-like shape with the diameter typically ranging from 30 to 50

µm [60] (Fig. 2.1a). Myofibres are highly organised in a parallel arrangement to provide the

mechanical basis of muscle contraction. The ECM, providing mechanical support and the

surrounding environment of myofibres, comprises membrane and interstitial connective tissue

that contains blood vessels, nerves and lymphatics [61]. As the main focus of this thesis is

skeletal muscle, the structure and function of skeletal muscle will be discussed in detail in

Section 2.3, but smooth and cardiac muscle are first concisely reviewed.


7

Fig. 2.1 Light microscopic images of the H&E-stained histological sections of mouse (a) skeletal muscle,

(b) smooth muscle, and (c) cardiac muscle. Scale bar indicates 50 µm (adapted from [62]).

Smooth muscles were first described in the mid-nineteenth century [63, 64] and studied based

on electron microscopy in the 1950s [65-67]. Microscope studies have shown that smooth

muscles are mononucleated cells and form muscle layers in most hollow organs, typically in

visceral tissues, such as the intestine and urinary bladder [68], and they are arranged in a spiral

or helical fashion in the walls of blood vessels [69-71]. The diameter of smooth muscle cells in

their nuclear regions ranges from 2 to 12 µm. This variety in diameter is due to the various

shapes (e.g., polyhedral, triangular, ribbon-like, or rod-like) of the smooth muscle cells [64].

Smooth muscle cells in both muscle layers [65, 72-77] and media of blood vessels [78] have

been shown to be arranged in bundles, with the bundles’ diameters of ~100 μm or slightly less

[73, 74, 77, 79-81]. The separation of neighbouring smooth muscle cells is from 50 to 80 μm in

most organs [74, 75, 82]. The extracellular space is filled with basement membrane and other

ECM molecules, including collagens, mucopolysaccharides and elastic tissue, plus blood

vessels, nerves, macrophages, fibroblasts, and Schwann cells [83]. The length of smooth muscle

cells ranges from 30 to 1200 μm [64]. However, this size varies by hundreds of microns

dependent on the specific tissue in which the smooth muscle is located and the degree of muscle

contraction. Tightly packed contractile myofilaments lying approximately parallel to the long

axes of the smooth muscle cells occupy the entire cell area except the terminal zones [67, 83-

87]. The dominant components of these myofilaments are actin filaments (i.e., thin filaments),

which are 3 to 8 nm in diameter and form distinct bundles [74, 86]. Myosin filaments (i.e., thick

filaments) are reported to be present but dispersed as single molecules, with their diameters of 7

to 20 nm (Fig. 2.1b).

Cardiac muscle provides the structural basis of most cardio-vascular functions in heart. In

mammals, ~75% of the total volume of the heart is made up of cardiac myocytes

(cardiomyocytes), which are the mature contractile cells of cardiac muscle (Fig. 2.1c). These


8

cardiomyocytes usually have one or two nuclei in most adult mammalian hearts [88]. Data from

left ventricular myocytes show that the mean length of individual cardiac myocytes is 120 to

150 μm [89]. The mean value of the diameter of individual cardiac myocytes in the adult heart

of mammals ranges from 10 to 25 μm [90], with females being in the lower range and males in

the upper range. This diameter, furthermore, varies depending on the wall stress of the

ventricular chamber [91, 92]. The total number of cardiac myocytes per heart, based on data

from rats, appears to be different between males and females. Males tend to have a larger

number of myocytes due to the effect of larger body mass on heart growth [88]. The

architectural arrangement of cardiac myocytes forms helical muscle wrapping around the

ventricular cavities inside the heart [93]. Branching interconnections occur intensively at the

specialised junctions at the ends of cardiomyocytes, to rapidly transmit electrical signal between

the cardiomyocytes to result in coordinated 3D pumping contractions. Light microscopic studies

have revealed that contractile myofibrils occupying more than 50% of the cytoplasm of

cardiomyocytes. These myofibrils are composed primarily of overlapping myosin and actin

myofilaments organised into sarcomeres, visible by the transmission electron microscope

(TEM). When the myosin and actin filaments slide past one another, contraction results to

provide the pumping action of the heart [88]. A summary of the dimensions, shapes, and

nucleus arrangement of the three types of muscles is given in Table 2.1.

Table 2.1 A summary of dimensions, shape, and nucleus arrangement of skeletal, smooth, and cardiac

muscle cells.

Skeletal muscle Smooth muscle Cardiac muscle

Diameter (µm) 30 to 50 2 to 12 (in nuclear region) 10 to 25

Length (µm) 103 to 106 30 to 1200 120 to 150

Cell shape rod-like polyhedral, triangular,

ribbon-like, rod-like

rod-like

Nucleus

arrangement

multinucleated (mature

cells) or mononucleated

(young or regenerated cells)

mononucleated mono- or two-

nucleated

2.3 Skeletal muscle

2.3.1 Myofibres in skeletal muscle

Multinucleated skeletal myofibres are formed by myogenesis that involves the proliferation of

mononucleated myoblasts that differentiate and fuse together to form small multinucleated

myotubes, which mature into innervated myofibres (Fig. 2.2). Mononucleated muscle precursor

cells (myoblasts) are similar in size to fibroblast, macrophages and many other mononucleated


9

cells (roughly 10-20 µm in diameter). Myoblasts proliferate and then differentiate and fuse to

form thin, multinucleated, immature muscle cells (myotubes) that subsequently mature into

myofibres. Some myoblasts persist as quiescent muscle precursor cells located on the surface of

myotubes and myofibres, between the sarcolemma (muscle cell membrane) and the overlying

basement membrane: these are called satellite cells and are responsible for generation of new

myoblasts and muscle regeneration in response to necrosis of post-natal myofibres. The

basement membrane is a light microscopy term that refers to the complex layer of specialised

ECM molecules adjacent to the sarcolemma; it includes the basal lamina at the cell surface and

others associated layers that are described by electron microscopy. The myotubes continue to

differentiate and enlarge, become innervated (not shown) and expand dramatically in width

(hypertrophy) and especially length during post-natal growth, until adult myofibres stabilise in

length as bone growth ceases (Fig. 2.2). This huge post-natal growth for almost 20 years in

humans is associated with dynamic expansion of cell membranes, specifically sarcolemma.

Only a portion of a mature myofibre is indicated, since the average adult human myofibre can

reach about 60 µm in width and 40 mm or more in length [94].

Fig. 2.2 Diagram to illustrate myogenesis and the formation of skeletal myofibres, with comparison to

cell sizes [94].

The number of myofibres within various skeletal muscles varies from over a million (e.g.,

medial gastrocnemius muscle) to a few hundred (e.g., tensor tympani) [95]. These myofibres are

organised into bundles called fascicles, with each individual fascicle surrounded by ECM called

perimysium, and multiple fascicles are encapsulated within epimysium to form the completed

muscle (the ECM is discussed in detail in Section 2.3.2, see Fig. 2.3). The myofibres are


10

arranged in a parallel style lying obliquely (e.g., pinnate muscle) to, or along, the longitudinal

axis (e.g., strap muscle) of the muscle, depending on the architecture of various skeletal muscle

[95] (Fig. 2.4).

Fig. 2.3 Structural hierarchy of skeletal muscle (adapted from [62]).

Fig. 2.4 Different architectures of skeletal muscle.

The length of an individual myofibre can range from millimetres (mm) to centimetres (cm) in

humans, while the diameter of a myofibre usually ranges from 30 to 50 µm [60]. Each healthy

mature myofibre contains numerous nuclei that are dispersed along its length in a peripheral

location beneath the cell membrane (sarcolemma). When mature muscles are damaged and

undergo necrosis and regeneration, the myonuclei within the newly formed myotubes or

myofibres are initially in a central location. This difference in the distribution of nuclei can be

easily visualised in longitudinal and transverse H&E-stained histological sections of the muscle

sample (Fig. 2.5). This difference is widely used in both pre-clinical and clinical studies for

distinguishing between healthy mature myofibres and recently regenerated myofibres arising

from damage or disease [12].


11

Fig. 2.5 Distribution of nuclei (purple spots) is different in (a) mature myofibres compared to (b)

regenerated myofibres is shown in H&E-stained histological sections of mouse quadriceps muscle. The

location of multiple nuclei of (a) each individual mature myofibre is peripheral to the myofibres; whereas,

in (b) a single nucleus is located at the centre of each myofibre. The scale bar represents 50 µm (adapted

from [96]).

Within the longitudinal axis of the myofibre, the contractile proteins are arranged into parallel

myofibrils. The diameter of an individual myofibril is ~1.0 μm [59]. A myofibril comprises

highly organised cytoskeletal proteins, including myosin filaments (thick filaments, with their

diameters of ~15 nm) and actin filaments (thin filaments, with their diameters of ~7 nm) [97],

arranged in a parallel and interdigitating manner (Fig. 2.6). From the 3D perspective, six actin

filaments, in the hexagonal array, surround the myosin filament located at the centre [98]. This

arrangement of myosin and actin filaments, in combination with other cytoskeletal proteins such

as tropomyosin, troponin, desmin and other molecules organised into sarcomeres, provides a

structural basis for the muscle contraction (discussed in Section 2.3.3).

The organisation of the sarcomeres results in the characteristic striated appearance showing

periodically altered light and dark bands along the axis of each individual myofibril. The dark

bands, A-bands, correspond to the presence of myosin filaments, while the light bands, I-bands,

contain actin filaments only (Fig. 2.7). Because of the interdigitating manner of the molecular

arrangement, the myosin and actin filaments typically overlap each other to some extent. The

overlapping regions belong to the A-bands and form the darker region within the A-band. The

myosin filaments without overlap form the relatively pale region, H-zone, within the A-band. In

the middle of the H-zone, fine, filamentous structures, which run perpendicular to the myosin

filaments, connect the myosin filaments and provide them with a regular spacing from each

other. These filamentous structures form a relatively darker line, M-line, perpendicular to the

length of the molecular filaments. The ends of actin filaments, interfacing the next period of

such bands, form a relatively darker line, Z-line, in the middle of the I-band. These Z-lines are

perpendicular to the length of molecular filaments and thus parallel to the M-lines [95] (Fig.

2.7b and c). This periodic banding structure is visible under both light microscopes (Fig. 2.7a)

and TEMs (Fig. 2.7b). The capability of the contained molecular structure in scattering light or

electrons positively determines the darkness of the band. The periodic molecular structure along


12

one individual myofibril, therefore, causes the periodically altered darkness and thus the striated

appearance. One period of this banding structure, typically from one Z-line to the next Z-line, is

considered to be a sarcomere, which functions as the contractile unit during muscle contraction

(will be discussed in Section 2.3.3; Fig. 2.7b and c). The length of one sarcomere ranges from

2.0 to 4.2 μm depending on the resting/contracting state of the skeletal muscle [99].

Fig. 2.6 The interdigitating arrangement of myosin and actin filaments (adapted from [100]).

Fig. 2.7 The structure of sarcomeres shown at (a) the cellular level (light microscopic image) and (b) the

molecular level (TEM images). Definitions of A-band, I-band, H-zone, M-line, and Z-line, as well as one

individual sarcomere are shown in both (b) transmission electronic microscopic image and (c) schematic

(adapted from [101, 102]).


13

2.3.2 ECM in skeletal muscle

The material between the myofibres is called the ECM or connective tissue, and accounts for

approximately 1 to 10% of the muscle tissue [103, 104]. The ECM of skeletal muscles is very

important for various reasons: firstly, it serves as a scaffold for myofibre formation during

muscle development and to hold the myofibres together in the gross structure of mature muscle;

secondly, to provide a conduit for the blood vessels and nerves; thirdly, to resist excessive

passive stretching of the muscle and minimise myofibre damage; and fourthly, to transfer the

force (generated by the contractile proteins within the myofibres) to move the parts of the body,

especially via tendons connected to the bones [95].

The connective tissue of the skeletal muscle is organised into: the epimysium, perimysium, and

endomysium [105, 106] (Fig. 2.8). The epimysium that encloses the entire muscle is composed

mainly of tightly woven bundles of collagen fibres (600 to 1800 nm in diameter) and is a

particularly tough coat that separates individual muscles. The perimysium is tough and

relatively thick and composed mainly of collagens. The perimysium surrounds the bundles of

myofibres (fascicles) and contains the blood vessels and nerves. Within the coarse perimysial

sheets, each individual myofibre is surrounded by a more complex ECM, the endomysium. The

endomysium consists of a looser and more delicate interstitial network of collagen fibrils (60 to

120 nm in diameter) run in all directions and connected with the basement membrane

(specialised ECM rich in laminin and glycoproteins) that surrounds, and is in intimate contact

with, the surface of each myofibre. The interstitial spaces separating the myofibres are usually

no wider than 1 μm [95] and some of these collagen fibrils are continuous with the fine fibrillar

mesh of the perimysium. The force generated within each myofibre is transferred laterally

directly through the basement membrane to the interstitial collagens to convey part of the

contractile force to the tendon [95, 107] (Fig. 2.8c and d).


14

Fig. 2.8. The ECM structure of skeletal muscle. (a) The organisation of the connective tissue of the ECM.

The epimysium surrounds the entire skeletal muscle. The perimysium surrounds a fascicle, a bundle of

myofibres. The endomysium surround an individual myofibre. (b) The endomysium and embedded blood

vessels (illustrated as red and blue branches) surround individual myofibres. (c) A microscopic view

shows the endomysium (indicated as ECM) between two myofibres. (d) A microscopic view shows the

basement membrane and plasmalemma (indicated as sarcolemma) underneath endomysium, surrounding

one individual myofibre [61].

The tendons, which attach the ends of muscle to bones (Fig. 2.9), are dense specialised

connective tissue structures with much collagen (60 to 85% of dry weight) designed to

withstand tension [104, 108, 109]. The division of tendons into fibrils not only spreads the

potential damage to the entire tendon, but also provides a high total structural strength [104].

The myotendinous junctions on myofibres are specialised areas for force transmission [110].


15

Fig. 2.9 Tendons attach the ends of skeletal muscle to bones (adapted from [111]).

The basement membrane, is specialised ECM that anchors the myofibre to collagens in the

interstitial connective tissue: in mature skeletal muscle it is composed largely of laminins,

glycoproteins, collagens IV and VI, and a wealth of other interacting molecules that form a

complex network on the surface of the myofibre and interact with protein complexes that span

the cell membrane (sarcolemma) and connect to various molecules within the myofibre (Fig.

2.10) [61, 95, 112].

Fig. 2.10 Schematic representation of the ECM surrounding skeletal muscle. Individual molecules are

depicted at their approximate location in relation to the sarcolemma. Well-established molecular


16

interactions between individual ECM molecules are portrayed. Not all possible interactions are indicated

due to the limited space. Names of ECM molecules of which no genetic mutations are associated with

specific myopathies or inherited connective tissue disorders in human, are printed in italic [112].

The muscle cell membrane (also known as plasmalemma or sarcolemma), with its thickness of

7.5 nm, encloses the myofibre contents (termed as cytoplasm or sarcoplasm), such as aqueous

solution (the cytosol), organelles, myofilaments and signaling molecules. The sarcolemma gives

each myofibre its own anatomical identity and importantly transfers the electrical signal that

stimulates contraction over the length of the myofibre to stimulate contraction of the sarcomeric

proteins and the myofibres [95].

2.3.3 Contraction of skeletal muscle

In summary, contraction of skeletal muscle is the physiological basis of the muscle function that

generates mechanical force and movement. Mechanical force is generated by shortening the

length of the sarcomeres and contracting the muscle. Healthy nerves, myofibres, and ECM are

required for the generation and transmission of the mechanical force [61]. The mechanical force

from the contracting sarcomeres within myofibres, is transferred laterally through the basement

membrane, initially to the endomysium and then the force is integrated and transmitted through

the perimysium, epimysium, and tendons, eventually to the bones [61] to result in full muscle

function.

The “sliding theory” is the most widely accepted explanation for the molecular mechanism of

muscle contraction. The myosin and actin filaments aligned in an interdigitating manner slide

relatively to each other along the longitudinal axis of the myofibril. During muscle contraction,

the sliding movement of the myosin and actin filaments performs towards each other and along

the myofibril axis [113]. As a result, the overlapping region between these two types of

filaments becomes larger and thus the length of each sarcomere is shorter. Based on the

arrangement of myosin and actin filaments in sarcomeres, the theory suggests that length of the

I-band will be shortened, while length of the A-band will be maintained during muscle

contraction. However, length of the H-zone, which indicates the presence of myosin filaments

without overlap with actin filaments, will be narrowed and even disappear completely. This has

been experimentally supported by early studies of muscle contraction [99, 114] (Fig. 2.11).

Further insights into the mechanism of muscle contraction expose small projections sticking

from the axis of each myosin filaments. These projections are able to attach the adjacent actin

filaments, forming crossbridges. During muscle contraction, these crossbridges momentarily

change their directions from more parallel to more perpendicular relative to the axis of the

myosin filaments and thus propel actin filaments to new positions [114] (Fig. 2.12). In a single

“working stroke”, a crossbridge moves an actin filament through 5 to 10 nm [115].


17

Fig. 2.11 The arrangement of myofilaments, as well as the definitions of A-band, I-band, H-zone, M-line,

Z-line, within one individual sarcomere when the muscle is (a) stretched, (b) resting, and (c) contracted

(adapted from [101]).

Fig. 2.12 Cross-bridges are formed when the state of muscle changes from (a) resting to (b) contracted.

TEM reveals the formed cross-bridges during muscle contraction in (c) [116, 117].

Muscle function can be impaired by many forms of injury and a wide range of muscle disorders.

In muscle with Duchenne muscular dystrophy, for instance, the absence of the protein of

dystrophin, which plays a vital part connecting the intracellular filaments with the ECM, could

cause abnormal force transmission and distribution that may injure the plasmalemma and thus

lead to muscular necrosis (discussed in Section 2.5) [12]. The central aim of this thesis is to

develop new imaging techniques that can observe changes in muscle structure that affect muscle

function. Of central interest to this thesis is imaging of skeletal muscles in the inherited lethal

muscle disease DMD that is described below.


18

2.4 DMD

2.4.1 Phenotype of DMD

The genetic muscle disease DMD is one of the most severe muscular dystrophies, which was

described by the English physician Edward Meryon in 1851 [118] and affects about 1 in 3600 to

6000 male births worldwide [1]. Muscles of boys with DMD progressively degenerate, leading

to replacement of myofibres by fibrous and fatty connective tissue and dysfunction of the

skeletomuscular system (Fig. 2.13). The pathological loss of muscle mass results in weakness,

loss of function and general locomotion, wheel-chair confinement by 12 years of age. The death

of DMD patients usually occurs in the second to third decade of their life due to respiratory or

cardiac failure. To date, there is no cure for DMD and thus the death from the disease is

inevitable. Current treatment for DMD is administration of steroids (that has variable success)

and interventions to aid quality of life, pain relief, and respiratory assistance [12, 118].


19

Fig. 2.13 H&E-stained transverse sections of dystrophic mouse quadriceps muscle containing (a) normal-

appearing myofibres with multiple peripheral nuclei, (b) necrotic myofibres with infiltration of

inflammatory cells and fragmented sarcoplasm, and (c) regenerated myofibres with single central nuclei.

Scale bars indicate 50 µm (adapted from [96]).

Duchenne muscular dystrophy results from mutations in the gene that is mapped to the Xp21.1

band on the human X chromosome: mutations in this gene result in an altered form or complete

absence of the protein dystrophin [119, 120]. Dystrophin is a cell membrane-associated protein,

which plays a vital role in membrane stability and maintenance, and is found in not only skeletal

muscle but also cardiac and smooth muscle, as well as the brain [119, 121]. In skeletal muscle,


20

the dystrophin protein is located beneath the sarcolemma, and connected with the actin

filaments that link to the sarcomeres, and dystrophin is part of a major transmembrane

dystrophin-dystroglycan complex that connects with laminin and other molecules in the ECM

[112, 120] (Fig. 2.10). In this way, dystrophin links the cytoskeleton (i.e., the molecular

filaments) inside the myofibre to the ECM and, therefore, is involved in force transmission.

Dystrophin protects the sarcolemma from the imposed shear stresses during muscle contraction,

especially eccentric contraction. Myofibres that lack functional dystrophin are very susceptible

to damage of the sarcolemma in response to exercise and muscle contraction. This damage

results in entry of calcium and necrosis (death) of parts of the myofibre: the precise molecular

mechanism that initiate myonecrosis in dystrophic muscles remain unclear. Such necrosis is

associated with inflammation, myogenesis, new muscle formation, and deposition of fibrous

connective tissue [122]. The ongoing repeated cycles of necrosis and regeneration in DMD boys

increase fibrosis that impairs myogenesis, so that regeneration fails and the pathology

progresses as the fatty infiltration and fibrosis replace the muscle. When key muscles involved

in respiratory or cardiac functions are damaged and become dysfunctional, death occurs

eventually [12, 111, 118].

2.4.2 Pathological changes of DMD

Initialised by the absence of dystrophin, a series of pathological changes occur within

dystrophic muscle. Generation of “delta lesions” is the first step. Small tears or lesions occur

even on healthy plasmalemma, especially after exercise. However, these small tears can be

repaired rapidly by the cell with intact molecular structure and normal function [123]. In

contrast, tears and lesions form more easily on the plasmalemma in dystrophic muscle, even by

general locomotion. This is because the dysfunctional cytomechanical network cannot transmit

the contractile force properly and promptly during muscle contraction due to the absence of

dystrophin [124]. Even worse, these tears and lesions are difficult to repair immediately and

thus can be enlarged in further movement by more muscle contraction. As a result, wedge-

shaped defects on the transversal section of plasmalemma, which are termed “delta lesions”,

form from the enlarged tears and lesions [125, 126] (Fig. 2.14).


21

Fig. 2.14 TEM image revealing Delta lesion (arrow). The scale bar indicates 1 µm [125].

The permeability of plasmalemma is subsequently abnormally increased by these delta lesions.

This abnormally high membrane permeability induces a leakage of several micro-agents from

the ECM to the inside of myofibres through the plasmalemma. Particularly the leakage of Ca2+

has been demonstrated to be the trigger resulting in the eventual necrosis of the contractile

structure inside myofibres [125]. Previous studies suggested that high concentration of

intracellular Ca2+ would firstly activate Ca2+-sensitive proteases, which are enzymes

decomposing proteins inside myofibres. The triggered biochemical cascades then result in

segmental hypercontraction of myofibres and inhibiting synthesis of proteins [126-128]. These

abnormalities inside myofibres induce inflammation reactions within fibres, followed by the

fatty infiltration and fibrosis. Regeneration of myofibres is simultaneously activated as another

response of the body environment. The pathological events of DMD initialised by the mutation

in the gene of dystrophin are summarised in Fig. 2.15.


22

Fig. 2.15 Summary of pathological event sequence of DMD.

2.4.3 The mdx mouse model

Research into fundamental principles and the testing of therapeutic hypotheses for treatment

demand to be performed on animal models for human diseases, which exhibit homologous or

analogous human conditions. As a classical genetic and biochemical animal model for DMD,

the mdx mouse was discovered and described by Bulfield et al. in the early 1980s [129]. The

mdx mouse model carries a null mutation of the dystrophin gene, which occurs spontaneously

due to a premature stop codon resulting in an abnormal termination of the gene expression [12].

Therefore, the mdx mice suffer from a similar X-linked form of muscular dystrophy which

results in a complete lack of dystrophin in both skeletal and cardiac muscles [120, 130, 131].

Compared to other animal models for DMD [132, 133], the mdx mouse model has been the

most widely used one during the past decades [8, 134-136] because of its short breeding time

(20 days gestation), large litters (4-8), and low relative cost [131]. These advantages guarantee

the effectiveness of preclinical studies (e.g., histological analysis and ex vivo microscopy) that

require the sacrifice of mdx mice.

In mdx mice, the absence of dystrophin results in Z-line streaming of sarcomeres by 1 day post-

natal [12]. By 10 days after birth, necrosis within skeletal muscles appears evident [137, 138].

An abrupt onset of skeletal muscle necrosis, affecting 20 to 80% of the muscle, occurs around

21 days of age and peaks by 26 days of age, especially in hindlimb muscles [7, 139]. This

abrupt onset of muscular necrosis stimulates muscle regeneration by day 28 [140].

Subsequently, the level of muscular necrosis decreases significantly to stabilise by 8 weeks of

age. The cyclic progression of necrosis and regeneration continues throughout life although

reduces by one year [141]. The exhibited levels of necrosis in different muscles are different.


23

The hindlimb muscles, including tibialis anterior (TA), gastrocnemius, quadriceps, and extensor

digitorum longus, typically show severe necrosis [142, 143], whereas the necrosis within some

muscles of the head and chest region is very mild [12]. Besides the natural biophysical variety

between these muscles, one another possible reason for this difference in the severity of

pathology is that the hindlimb muscles are more involved in the endurance exercises (e.g.,

forced treadmill running) performed on the mdx mice. The endurance exercises are commonly

employed in preclinical research to enhance the level of muscular necrosis within mdx mice [55,

144-148].

The differences between mdx mice and DMD human patients should be noted. Although both

caused by the null mutation of the dystrophin gene, the muscular dystrophy in the mdx mouse

shows milder phenotypes than in DMD human patients. The mdx mouse has an almost normal

lifespan and exhibits only minor clinical dysfunction for most of time [149]. Although the full

explanation to this difference is yet to be elucidated, this difference is possibly due to the much

larger scale of a human patient compared to the mdx mouse. As a result, the mechanical stress

applied on the muscles, which is postulated to be related to the cube of the linear size of the

body [150, 151], is much larger in a human patient than in the mdx mouse. The damage to the

dystrophic muscle, therefore, is more severe in the human patients [149].

2.5 Techniques for imaging skeletal muscle and muscle damage

A wide range of imaging techniques have been employed for assessing and/or revealing the

extent of muscle disease based on their visualisation of muscle composition and structure at

both the macroscopic and the microscopic levels. Ultrasonography, MRI, and CT are clinical

imaging modalities that are used in both preclinical and clinical imaging of skeletal muscle

because these imaging modalities are capable of serial detection and assessment of living

muscle tissue in a noninvasive manner. Microscopic imaging modalities, such as confocal

microscopy, multiphoton microscopy (MPM), and second harmonic generation (SHG)

microscopy, serve as preclinical imaging modalities only since they typically require excision

and preparation of muscle samples. The applications of these modalities in muscle imaging

include: firstly, the development of image-based biomarkers for muscle damage and/or repair;

secondly, the development of an improved understanding in the pathology of skeletomuscular

diseases, based on the acquired information from structural and functional measurement;

thirdly, the studies of candidate drugs and therapeutic interventions, including the assessment of

drug efficacy and the investigation in the mechanism of drug action [25].

In preclinical studies, the noninvasive or nondestructive nature of clinical imaging modalities

enables their exclusive benefits, such as the longitudinal study of living tissue on the same

animal, reduced animals use, and reduced biological variability [25]. However, those preclinical

imaging modalities are able to provide high-resolution images showing structural and/or


24

functional information at the subcellular level. By contrast, the finest spatial resolution that

clinical imaging modalities can reach is tens of microns, which is at the cellular level within

skeletal muscle.

2.5.1 Ultrasonography

After being used in microstructural imaging at the cellular level within biological tissues for the

first time in the 1930s [13] and in medical practice since the early 1950s [152], US has rapidly

developed its widespread use in almost all fields of medicine because of its non-invasiveness

(especially the freedom from ionising radiation), real-time display, low cost, and portability of

equipment [15, 16, 153]. Early US typically provided 2D or B-mode images, until 3D scanning

mechanism was developed and enabled C-mode volumetric images in the mid 1980s [154]. The

physical basis of US is the incident sound waves and their echoes. A sequence of sound-wave

pulses is sent into biological tissues by the pulse transducer. These sound-wave pulses are then

attenuated, due to the reflection, dispersion, and absorption, when transmitting through the

tissue. The reflected sound waves and echoes are received by the same transducer and

computationally analysed for intensity and arrival time. Array transducers have been recently

developed to improve focusing [155] and increase image frame rates [17], compared with the

originally employed single, mechanically scanned transducers. The temporal property of the

echo, that is, the time between sending and receiving the same US pulse, determines the

location of the corresponding reflecting pixel. Moreover, the amplitude of the echo indicates the

acoustic property of the corresponding pixel within the tissue and determines the brightness of

the pixel on the image [156-160]. As the reflection only occurs when the US beam encounters

tissue with different acoustical properties (i.e., acoustical impedance), tissues with small

acoustical impedance (e.g., muscle, fat) show as darker regions on the image and vice versa

(e.g., bone/air interface). Little/no tissue beneath the structure with large acoustical impedance,

as a result, can be detected because of the shadow effect [36, 156, 157].

The axial resolution of US is determined by and proportional to the frequency of the incident

sound, whereas the lateral resolution is limited by the beam width and can be several times

larger than the axial resolution [36]. However, the depth of penetration is inversely correlated

with the frequency [36, 158-160]. The trade-off between the axial resolution and penetration

depth makes the range of 2-20 MHz commonly used for clinical US, mainly including the eye

[14, 161, 162], the skin [163-165], and the intravascular imaging [166-168]. Axial resolution

ranging from 80 to 800 µm can be achieved with adequate depth of penetration (no less than

several mm) [36, 37]. Broadband transducers have been developed recently for combining the

high resolution and deeper penetration using both high and low frequencies. High-frequency

US, which is termed as US biomicroscopy or micro-US, was first demonstrated in the late 1980s

by Sherar et al. [154] in imaging tumour spheroids and mainly for preclinical imaging of small

animals, including developmental biology [169-173], cardiovascular research [174-177], and

cancer imaging [178-182], due to its relatively smaller depth of penetration [183]. Typical


25

frequencies employed by micro-US range from 20 to 70 MHz, resulting in axial resolutions in

the range 20-80 µm [13]. Higher frequencies such as 100 MHz or 200 MHz have also been

reported to be used [13, 154, 184, 185]. Besides very high frequencies, higher resolution can be

achieved by using contrast agents, such as gas bubbles [186] or nano-/micro-sized particles [37],

although the diffusion of the intravenously administrated contrast agents out of vasculature that

are injected into blood vessels is a potential disadvantage. The values of spatial resolution and

depth of field, corresponding to three typical frequencies of US or micro-US are listed in Table

2.2 (adapted from [13]).

Table 2.2 A summary of US technical properties corresponding to different incident frequencies.

30 MHz 60 MHz 100 MHz

Lateral resolution 250 µm 75 µm 60 µm

Axial resolution 62 µm 31 µm 19 µm

Depth of field 2.5 mm 1.6 mm 1.6 mm

Ultrasound was demonstrated to be able to differentiate diseased muscles from healthy muscles

first by Heckmatt et al. in 1980 [187]. As a noninvasive and easily accessible method, US is

suitable for muscle imaging in young children even without sedation [153, 188, 189]. Several

following studies subsequently suggested each type of muscular disorder tends to show specific

appearance on muscle US compared not only controls but also other types of muscle disorders

[16, 189-191]. Healthy muscle tissue, because of its highly organised ultrastructure consisting of

cytoplasm and repeating links of identical structural proteins, shows low echo intensity (i.e., a

darker structure), which makes muscle distinct from surrounding structures such as

subcutaneous fat, bone, nerves, and blood vessels [188, 190, 192-197]. A speckled appearance

in the transverse plane of muscle is caused by the echogenic sheets of connective tissue [15]. In

contrast, dystrophic muscle shows higher echo intensity because of the pathological fatty

infiltration within myofibres and intramuscular fibrosis [15, 187, 198]. Although the age [190,

199], proportion of fibrous tissue (determined by the type of the muscle) [200], and even the

imaged location [16, 187] or direction [188, 201, 202] of the muscle could elevate the muscle

echo intensity, the specific extent and distribution of the increase of echo intensity within

muscle with specific disorders (e.g., DMD) give diagnostic information [189, 203, 204]. For

example, DMD results in a severe, homogenous increase of muscle echo intensity (compared

with that of controls) with normal muscle thickness (Fig. 2.16), whereas spinal muscular

atrophy shows an inhomogeneous increase of echo intensity with severe atrophy [15]. A visual

grading scale for manually evaluating muscle echo intensity, giving that grade I represents

normal muscle and grade IV represents the severest diseased muscle, was developed by

Heckmatt et al. [205]. Quantification of muscle echo intensity based on computer-aided


26

techniques, which is more objective and allows for statistical analysis, has been introduced in

image interpretation nowadays [34, 190, 198, 199, 204, 206-208]. Although early clinical

studies suggested that US has less capable of detecting pathological changes in early or pre-

symptomatic disease, and in metabolic or mitochondrial myopathies, muscle US was showed to

be capable of discriminating between children with and without a neuromuscular disorder with

high predictive values ~90% in children elder than 3 years old [16, 188, 190, 209], as

inflammatory events in advanced stage of muscular dystrophy show remarkable and specific

changes on US [188, 190]. Furthermore, dynamic imaging of muscle movement using US has

been also operated for evaluating muscle diseases [193, 194].

Fig. 2.16. Transverse US image of a normal left quadriceps muscle (a) and of a patient with DMD (b).

Both are 3.5 years of age. The rectus femoris muscle is encircled. The mean echo intensity is measured

for this region, as shown in the histograms below (scale: black = 0; white = 255). The rectus femoris of

the DMD patient has increased muscle echo intensity, with the corresponding histogram being displaced

to the right. Note the fine granular pattern of echo intensity, homogeneously spread among the muscle

with attenuation of the US beam; that is, the echo intensity in deeper areas of the muscle is decreased

compared to the superficial areas. Fascia within the muscle, such as the central fascia in the anterior part

of the rectus femoris (single arrow), are more difficult to recognise in the DMD patient. VM, vastus

medialis; VL, vastus lateralis; VI, vastus intermedius; F, femur; double arrow, subcutaneous tissue. The

quadriceps muscle was measured halfway along the line from the anterosuperior iliac spine to the patella

[15].

In summary, US has the advantages of non-invasiveness, low cost, portability of equipment, and

easy accessibility, which make US routinely employed in clinical imaging. However, the

primary limitation of US in muscle imaging is the moderate spatial resolution that is typically

coarser than 50 µm. Individual myofibres, typically with their diameter of 20 to 50 µm, cannot

be resolved by US. The resolution of micro-US is as fine as ~20 µm with high-frequency

incident sound. With the penetration depth of ~2 mm inside biological tissues, and this fine

spatial resolution, micro-US is promising in imaging ultrastructures in biological tissues.


27

2.5.2 CT

The technology of CT (X-ray CT) produces tomographic X-ray images using computer-based

scanning and processing. Employing digital geometry processing, 3D images showing inside

structure and morphology of the object are generated for diagnostic or therapeutic purposes. The

contrast of CT is typically introduced by attenuation of the incident X-rays in the examined

sample [210]. With lower incident X-ray energy, the attenuation is caused mainly by the

photoelectric effect, which makes the resulting X-ray energy after attenuation anti-proportional

to the 3rd power of the atomic number. With a higher incident X-ray energy, Compton scattering

becomes the dominant cause of the attenuation, leading to an anti-proportional dependency of

attenuated X-ray energy to the atomic number divided by 2 [19]. Some physical methods, such

as K-edge subtraction [211-214], X-ray phase delay contrast [215-217], and X-ray scatter

contrast [218] were employed to further enhance the X-ray contrast. Although widely used in

clinical applications, conventional CT typically provides moderate spatial resolution coarser

than 100 µm, which precludes the capability of conventional CT in visualising microscopic

structures inside biological tissues [38].

Micro-CT is a novel imaging technique which has attracted increasing attention from the early

1980s [219, 220]. Micro-CT is able to provide 3D images with their typical spatial resolution

finer than 50 µm [22, 39] or even 20 µm with contrast-enhanced agents [40]. Recent studies

demonstrated the applications of micro-CT in osseous-structure imaging [221, 222], vascular-

structure imaging [223, 224], cardiothoracic imaging [20, 225], thoracic imaging [226, 227],

cardiac imaging [228, 229], abdominal-organ imaging [21, 230], and cerebral-structure imaging

[231, 232]. However, although micro-CT demonstrates excellent capability in imaging tissue

samples with high atomic number (e.g., bones), the exhibited contrast in soft tissue under micro-

CT is relatively weak. Conventional CT, due to the same contrast mechanism, shows the same

limitation. As a result, the administration of a contrast agent during CT or micro-CT imaging is

desirable or even indispensable when imaging soft tissues [19].

Contrast agents employed in micro-CT imaging are able to transfer in vitro applications to in

vivo ones by elevating soft tissue contrast in preclinical research regarding to the evaluation of

soft tissue structure or morphology. Three types of contrast agents are generally available for in

vivo imaging: first, a conventional iodinated contrast medium; second, a blood-pool contrast

agent; third, a liposome-based contrast agent [19]. Water-soluble, non-ionic, iodine-based

contrast agents are generally used in humans because it can be eliminated from the blood

immediately after injection via the kidneys. Whereas this rapid elimination benefits human

patients, it restricts the use of iodinated contrast agents in small animals such as rodents due to

their very short circulation times [233]. Blood-pool contrast agents consist of molecules that are

able to bind to structural proteins or other macromolecules inside biological tissues. As a result,

longer scanning time lasting up to several hours, or even repeated measurement without

repeated administration of contrast agents, is enabled by blood-pool contrast agents. However,


28

the level of contrast provided by blood-pool contrast agents is generally lower than that

provided by conventional iodinated contrast agents [234, 235]. Liposome-based contrast agents

are novel ones allowing for the measurement of hepatic metastasis and delineation of the liver

and spleen [19]. Moreover, liposome-based contrast agents are suitable for imaging vascular

structures [236].

The application of CT in imaging muscular degradation was in 1938 [237, 238], after the initial

radiological study of neuromuscular pathology starting from 1928 [237, 238]. Muscular

dystrophy can be diagnosed based on the morphological imaging of the diseased muscle.

Skeletal muscles with muscular dystrophy appear to be enlarged or pseudohypertrophic [239].

X-ray computed tomography is able to explicitly detect and measure these morphological

changes [38, 239-241]. Furthermore, damaged areas within dystrophic muscle can be

distinguished by CT imaging from those undamaged areas based on tissue composition and thus

tissue density. The detected tissue density of undamaged regions of dystrophic muscle, as well

as normal muscle, appears to be uniformly high, whereas damaged areas are shown as low-

density areas [18, 242]. This altered density of tissue is caused by the replacement of muscle

tissue by the infiltrating fat and connective tissue (fatty infiltration), which is the principal

feature of many muscular dystrophies (e.g., DMD) [38, 243]. It should be noted that the extent

of fatty infiltration and thus the decrease of tissue density vary among different types of

muscles. Density readings of exactly the same area (on the same muscle), however, enable

quantitative longitudinal study of muscular dystrophy, which can monitor the progress in

severity of the pathology. This is based on the plausible positive correlation between the

decrease of tissue density and the severity of the muscular degradation [244, 245]. In some

recent studies, the muscle volume index was measured as a novel indicator for the severity of

DMD using CT scanning [246]. A typical CT scan of skeletal muscle is shown in Fig. 2.17.

Although muscle CT scans, as well as other preclinical or clinical applications of CT and micro-

CT, have the advantages of permitting non-destructive and painless imaging, simple operability,

fast scanning protocols (up to less than 1 min), and fine spatial resolution (for micro-CT), the

high radiation dosage and relatively low contrast in soft tissues remain to be unavoidable

limitations, compared to other clinical imaging modalities [19].


29

Fig. 2.17 CT scan of skeletal muscle of a human patient at the lumbar level [247].

2.5.3 MRI

Magnetic resonance imaging, as a nonionising imaging modality providing better soft-tissue

contrast than CT [26], has been systemically employed for imaging biological tissue since the

1950s [248]. Recently, MRI has been used for mapping dystrophic lesions of muscle in both

human patients [249] and animal models [41-43, 250, 251]. The contrast mechanism of MRI is

provided by the longitudinal (T1) or transverse (T2) relaxation time of protons on the water

molecules and macromolecules (e.g., proteins, nucleic acids) within the imaged tissues [252].

The measured relaxation time is determined by the quantity and biochemical status of the

molecules and thus sensitive to the modifications of tissue structure and tissue water content

[252-254]. Potential targets for imaging muscle damage in myopathies include the varied intra-

or intercellular water content, fat infiltration, and fibrosis in the regions with inflammatory

response. Early researchers tended to use T1-weighted MRI, detecting either fat infiltration [23,

255-257] or modifications of water content in damaged muscle [251, 252, 256, 257]. More

recent studies have focused on T2-weighted MRI for acquiring detailed information regarding to

not only fat infiltration [46] and modification of water content [256, 258, 259], but also

modifications in the content of bound water, free intracellular water, and free interstitial water.

Furthermore, the measured T2 is affected by interaction between water and macromolecules

[252] and the trans-sarcolemma water exchange [25]. Various levels of magnetic field, from less

than 1 Tesla (T) [260] to more than 17 T [261] (typically 1.5 T [262], ~4 T [255], and ~7 T

[263]) are used for imaging systems. Higher field strength typically provides finer spatial

resolution [43, 250, 255, 261], but possibly lower contrast [250] and sensitivity [260]. MRI

systems with 1.5-T magnetic field are commonly employed in clinical imaging.

The T1 reflects mainly the bound water fraction (BWF) within the muscle: an increase of BWF

leads to a decrease in T1 [256]. Experimental results in both human patients [256, 259] and

animal models [251] demonstrate that T1 is initially higher in dystrophic muscles than in


30

controls due to the decreased BWF (i.e., increased free water content in muscle) and decreases

to a value lower than controls due to the fat infiltration at the advanced stage of pathology [41,

46, 249, 250]. Thus, the change of T1 is negatively correlated to the modification of BWF [256]

and fat content [256, 259]. The quantitative measurement of muscle damage may be enabled by

this negative correlation between the fat and water content and T1 [250, 257]. In contrast, T2 is

measured to be higher in dystrophic muscle than in controls [259]. The main contribution to this

prolonged T2 is considered to be fat infiltration in human dystrophic muscle [46, 250, 259], but

still controversial in the dystrophic muscle of animal models, such as mdx mouse [264-266].

Moreover, the detected T2 signal in MRI contains more complicated information since the

transverse relaxation-time function shows a multiexponential character. Typically, three

exhibited exponentials, indicating three components of the measured T2, correspond to the

transverse relaxation time of bounded water or macromolecules, free intracellular water, and

free interstitial water, respectively [25, 252]. More or less components of T2 were detected and

discussed in other studies [24, 267-271]. Quantitative analysis of T2 components may be used

to assess and monitor the progression of muscular dystrophy [259]. In addition, T2-weighted

MRI can provide functional information of muscle. The measured T2 of mammalian skeletal

muscle would increase by more than 10 ms from resting to contracting status [272, 273].

As expansion of conventional MRI, contrast agent-enhanced MRI has been intensively

development recently for evaluating the localisation, extent, and mechanisms of skeletal muscle

damage in muscular dystrophy. Some of the employed contrast agents are expected to facilitate

assessment of therapeutic approaches in myopathies [44]. Albumin-targeted contrast agent, such

as MS-325 [44] and Gd/DTPA [27], were used to not only identify dystrophic muscle but also

study the mechanisms of myofibre damage (Fig. 2.18). Before imaging, the albumin-targeting

contrast agents would be intravenously injected and form compounds by combining albumin

molecules. The compounds would accumulate within dystrophic muscle, but not enter normal

muscle. As a result, extra contrast leading to localised signal enhancement can be provided [27,

44, 274, 275] (Fig. 2.18). Labeled stem cells are another type of contrast agent. Walter et al.

[261] noninvasively tracked the accumulation and dynamics of magnetodendrimers-labeled

stem cells within dystrophic muscle [261]. In another study, mesoangioblast stem cells labeled

by superparamagnetic iron oxide nanoparticles were tracked using T2-weighted MRI. These

labeled stem cells possess potential to follow the progress of stem cell-mediated repair of

muscle, because the presence of mesoangioblasts indicates the presence of dystrophin and thus

the repair of dystrophic muscle tissue [261, 276-281]. Diffusion MRI is another expansion of

conventional MRI for imaging muscle damage [25]. Diffusion MRI is sensitive to detect

damage to the myofibres because water diffusion within myofibres, which is characterised by a

much greater diffusion coefficient parallel to the length of myofibre than perpendicular to the

length of myofibre, is severely interfered by the lesions on the membrane of myofibres [25, 282,

283]. Micro-MRI, with a small, high-efficiency coil in a high-field imager, is typically used for


31

pre-clinical imaging. Due to the high-level magnetic field employed in micro-MRI, spatial

resolution as fine as ~20 µm can be achieved [48, 49]. Contrast agents, in addition, were

employed in micro-MRI in recent studies [50].

In summary, although MRI is a noninvasive imaging modality providing 3D images with

excellent contrast in soft tissues (e.g., skeletal muscle tissue), the limitation of MRI in spatial

resolution remains. The typical spatial resolution of conventional MRI is ranged from 50 to 100

µm [47] or even coarser [46]. Individual myofibres with their diameter ranging from 20 to 50

µm cannot be resolved. Although some of micro-MRI systems can reach their spatial resolution

of ~20 µm, which is enough for resolving individual myofibres, the cost of such systems is then

very high because of their employed high magnetic field. Long acquisition time during imaging,

in addition, is another disadvantage of MRI in both pre-clinical and clinical imaging.

Fig. 2.18 MRI (3T, field of view = 3.2 cm) of dystrophic muscle from mdx mice reveals (a) homogeneous

signal intensity without the contrast agent M-325, but (b) enhanced signal intensity in necrotic regions 15

min after M-325 administration. Arrows indicate the uptake of M-325 by the muscle damage (adapted

from [44]).

2.5.4 Light microscopy

Microscopy of skeletal muscle typically requires excision and fixation of tissue. Therefore,

microscopy of skeletal muscle is typically ex vivo and thus employed in preclinical applications.

Compared to conventional light microscopy, advanced microscopy imaging modalities, such as

confocal microscopy, MPM, and SHG microscopy, are able to provide 3D images with

excellent spatial resolution, which can be as fine as ~500 nm [284]. As a result, microscopic

structures at the subcellular level [28] or even molecular level [285] are visualised (Fig. 2.19).

With fluorescence labeling (e.g., immunofluorescence staining), fundamental molecular

mechanisms of biological events can be exposed by tracking or showing the distribution of

specific molecules [29, 286].


32

Fig. 2.19 SHG images of (a) normal and (b) mdx mouse muscle (gastrocnemius). The mice are 5-week

old. The rod-like structures are myofibres. The striates on the myofibres indicate sarcomeres. The scale

bar represents 20 µm [30].

After Marvin Minsky built the first confocal microscope in 1955 [287], biomedical imaging has

become one of the main applications of confocal microscopy. Confocal microscopy detects the

fluorescence of the imaged tissue generated by the tissue itself (autofluorescence) or by extra

fluorophores. Depth-resolved (3D) imaging is enabled by the equipped pinhole, which

eliminates the “out-of-focus” flare in the specimen. This confocal-gated spot of light scans

across the specimen to build a 3D image [284]. There are two mechanisms of scanning: stage

scanning, which moves the specimen under a fixed microscope; and laser scanning, which scans

the beam across a stationary specimen. The former one is conventional, while the latter one is

more popular these days because it enables the potential of in situ or in vivo imaging using

confocal microscopy. The first effective digital imaging processing applied to biological

imaging was achieved by Shinya Inuoe and Robert Allen in the 1980s [288, 289]. This digital

imaging processing enables an apparent increase in resolution of structures using digital

enhancement of the images. The application of confocal microscopy in imaging muscular

dystrophy includes both molecular imaging, studying the localisation or distribution of specific

molecules [29], and cellular imaging, studying structural or morphological changes of

myofibres [28] (Fig. 2.19). Endoscopic or needle probes for confocal microscopy have been

developed in recent years [31, 290] to overcome the limited penetration depth (typically several

hundreds of microns), although the moderate field of view remains.

Whereas confocal microscopy, which generates contrast based on a linear (or one-photon)

absorption process, nonlinear optical microscopy employs nonlinear light-matter interaction for

the generation of contrast. This contrast mechanism of nonlinear optical microscopy gives the

incident light a lower sensitivity to tissue scattering, the penetration depth of nonlinear optical

microscopy, therefore, is increased [291]. MPM, particularly two-photon microscopy (TPM), is

the most widely used nonlinear optical microscopy modality. Two photons that arrive at a


33

molecule in the tissue simultaneously (within ~0.5 fs) combine their energies to promote the

molecule to an excited state, which evokes the emission of fluorescence [292]. Similarly, three

or more photons can combine to cause excitation. Another group of modalities of nonlinear

optical microscopy is optical-harmonic generation, in which two or more photon are

simultaneously scattered, generating a single photon of exactly twice (or thrice, and so on) the

incoming quantum energy [293]. Second harmonic generation microscopy is the most widely

used optical-harmonic generation in practice [294, 295]. Nonlinear optical microscopy provides

depth-resolved images based on not the pinhole but a higher threshold of the incident intensity

for excitation. As a consequence, only the incident light at the perifocal region will reach the

excitation threshold and thus be effective in imaging. Similar with confocal microscopy,

applications of nonlinear optical microscopy in imaging muscular dystrophy include the

detection of localisation and distribution of specific molecules, the measurement of structural

and morphological changes, with or without extra fluorescence labeling. The recent

development of endoscopic nonlinear imaging enables in vivo imaging of deep tissue [290].

However, the limitation of nonlinear optical microscopy is still its moderate field of view.

2.6 OCT

Optical coherence tomography was first developed and demonstrated on biomedical imaging by

Huang et al. [51] in 1991. As a relatively new imaging technique, OCT possesses the

advantages of non-invasiveness, low cost, and portability, providing 3D volumetric datasets at

the microscopic level. The most attractive merit of OCT is its spatial resolution, which ranges

from 2 to 20 μm for both the axial and lateral coordinates. Both pre-clinical and clinical

applications of OCT in biomedical imaging, therefore, have been enabled. To date, clinical OCT

has been widely used in ophthalmological imaging [296-298], while pre-clinical OCT, which

also shows its potential in clinical use, has been applied in imaging viscera (e.g., gastrointestinal

tract [299, 300], lung [301, 302], pancreas [303, 304], prostate [305, 306], etc.), cardiovascular

system [307, 308], skin [309, 310], lymph nodes [311, 312], breast cancer [313, 314], and other

biological tissues.

The imaging mechanism of OCT can be considered as an analogue of ultrasonic pulse-echo

imaging. Compared to ultrasonography, which measures the echo times of backscattered

pressure waves from the imaged tissue samples, OCT measures echoes of backscattered light.

The direct measurement of the echo times of backscattered light is impossible based on current

technique of detection because the temporal differentiation of backscattered light from different

depths requires extremely high speed of the detector. As a result, OCT measures the time-of-

flight of the light by interferometry, which employs superposition of electromagnetic waves as

the “coherent-gated” technique. An OCT system, therefore, also refers to as an interferometer


34

(e.g., Michelson interferometer). More details of the components and working principle

employed by an OCT imaging system are discussed in Section 2.6.1.

2.6.1 Working principle

Schematic of a generic OCT system is illustrated in Fig. 2.20. A typical OCT system consists of

a light source, a 2 × 2 fibre-optic coupler (for fibre-optic OCT systems) or beamsplitter (for

free-space OCT systems), a reference arm, a sample arm, and a detector. Incident light from the

light source is directed into the fibre coupler/beamsplitter. An even splitting (50/50 splitting) of

power is the intuitive assumption but not necessarily always the case. However, many practical

OCT system designs, as described theoretically or experimentally, take advantage of unbalanced

power splitting [315, 316]. Light propagating along the reference fibre (i.e., reference arm) is

reflected by the mirror at the end of this arm and returns via the same fibre. Light propagating

along the sample fibre (i.e., sample arm) is directed into the imaged sample under some

computer-controlled focusing and scanning mechanism. The reflected or backscattered light

from the sample is redirected back through the same fibre. This sample-reflected light is mixed

with the reflected light returning from the reference arm in the fibre coupler/beamsplitter. The

combined light is made to interfere and be detected on the surface of the detector. This

interference guarantees the depth-resolved reflectivity profile, A-scan, of the sample at a fixed

lateral position to be acquired from the detected signal. Multiple A-scans can be acquired and

assembled into a 2D cross-sectional image as the scanning mechanism sweeps the position of

the incident light beam across the sample. This 2D image is termed as B-scan. As the scanning

mechanism steps the position of the incident light beam perpendicular to B-scans, multiple B-

scans will be acquired and assembled into a 3D volumetric dataset, which is termed as C-scan

(Fig. 2.21) [317].

Fig. 2.20. Schematic of a generic fibre-optic OCT system. Lines with arrows represent fibre-optic paths;

bare lines indicate electronic signal paths; and redlines indicate optical paths in free space (Figure

reproduced with permission from Dr. R. A. McLaughlin).


35

Fig. 2.21. Illustration of the A-scan (1D), B-scan (2D), and C-scan (3D) performed by OCT scanning

mechanism (Figure reproduced with permission from Dr. D. Lorenser).

Optical coherence tomography systems are divided into time-domain OCT (TD-OCT) and

spectral-domain OCT (SD-OCT). Spectral-domain OCT systems are further subdivided into

spectrometer-based SD-OCT and swept-source SD-OCT. The latter one is sometimes referred

to as SS-OCT. In addition, SS-OCT is alternatively called optical frequency-domain imaging or

OFDI. The key differences among these OCT systems include their employed light source,

photoreceiver/detector, and the scanning mechanism of their reference arms. In the case of TD-

OCT, the employed light source is a low-coherence one with broadband and continuous-wave

(CW), the reference arm delay is repetitively scanned in length. A single-channel photoreceiver

is employed in a TD-OCT system for detecting the envelope of the detected fringe burst pattern

corresponding to interference between the reference arm light and each successive scattering

site in the sample [318, 319]. In the case of spectrometer-based SD-OCT, the employed light

source is also broadband and CW. However, the reference arm length is fixed at a position

instead of changing in length. An array detector (e.g., a photodiode array or charge-coupled

device, CCD) is employed for simultaneously collecting and dispersing the spectral interference

pattern between the reflected light from the reference arm and all depths in the sample. In the

case of SS-OCT, the light source has narrow instantaneous linewidth but is rapidly swept in

wavelength. The spectral interference pattern is correspondingly detected on a single or small

number of photoreceivers as a function of time, based on a reference arm with fixed-length. In

SD-OCT, inverse Fourier transverse is thus employed to obtain the entire depth-resolved

information of the sample from each A-scan based on the analysis of the detected spectral

interference pattern. Additional signal processing steps (e.g., interpolation) may also be required

in SD-OCT to prepare the spectral interferogram for the inverse Fourier transform.


36

A sample under OCT imaging is characterised by its profile of depth-dependent reflectivity,

)( SS zr , where Sz is the sample depth. This reflectivity profile may be defined as a discrete sum

of delta functions spaced arbitrarily closely:

N

nnn zzrzr

1SSSSS )()( (1)

This definition is a discrete approximation of the continuous reflectivity profile in depth in a

practical sample under interrogation. This approximation enables further digital analysis of the

detected signal. The reflected electric fields returning from the sample reflectors, SE , contain

spatial information (i.e., depth-resolved). The interference between this SE and the reflected

field returning from the reference arm, RE , is detected by causing photocurrent response in the

employed detector. Therefore, this photocurrent is proportional to the intensity of interference:

2SRD 2

EEI (2)

Here, DI is the photocurrent. SR EE represents the interference between the two reflected

fields. The intensity of this interference is given by squaring the module of the interference

field. is termed as the responsivity of the detector. The factor of 2 indicates the loss of signal

intensity when passing through the beamsplitter after reflection.

In the case of TD-OCT, the depth of each detected sample reflector is explicitly given by the

corresponding reference pathlength, Rz , since the reflected fields from other sample reflectors

are filtered by the dominated coherent signal intensity (fringe burst) from the sample reflector

located at the depth without pathlength difference compared to the reference pathlength. The

precisely controlled axial change of the reference pathlength over the entire range of imaging

depth guarantees the generation of each depth-resolved reflectivity profile (i.e., A-scan) during

TD-OCT scanning. In the case of SD-OCT, however, the depth of each sample reflector is given

by data analysis. As the spectral signal (spectral interferogram) is acquired by the array detector,

spatial information can be obtained via inverse Fourier transform (IFT) of the spectral

interferogram. Hence, depth-resolved A-scans are generated by an SD-OCT system employing

its reference arm with a fixed pathlength [52, 317-320]. Further theoretical description OCT

(based on SD-OCT) is provided in Appendix I.

The spatial axial resolution of OCT is inversely proportional to the bandwidth of the employed

light source, either the spectral bandwidth of the broadband employed in TD-OCT and

spectrometer-based SD-OCT or the swept range of a narrowband swept source employed in SS-

OCT [319, 321]. A Gaussian-shaped function in spectral domain is a valid approximation of the

source spectrum. This Gaussian-shaped spectrum is characterised by its full-width half-


37

maximum (FWHM) value of source bandwidth, , and its central wavelength, 0 (typically

at ~800 nm or ~1300 nm). The spatial axial resolution is then given by

202ln2

cl (3)

Here, cl is the spatial axial resolution. Spatial transverse resolution, which is defined as the spot

size of the light exiting from the lens at the end of sample arm, is inversely proportional to the

numerical aperture (NA) of the objective lens in the sample arm and, thus, decoupled from the

axial resolution. This conclusion is physically reasonable because a larger NA leads to a more

tightly focused light beam with a smaller spot size and thus a smaller transverse resolution. The

transverse resolution is given by

NAx037.0

[317]. (4)

Notably, a trade-off exists between a fine x and a larger DOF, as the DOF is dependent on the

Rayleigh range for a Gaussian beam and proportional to x . In most pre-clinical and clinical

applications of OCT, the employed imaging systems are designed to generate approximately

isotropic voxels by making the transverse and axial resolutions comparable to each other [317,

318].

2.6.2 Application of OCT in imaging skeletal muscle and muscle damage

The application of OCT in imaging skeletal muscle is relatively later compared to other

biological tissues, although macroscopic structure and morphology of skeletal muscle (e.g.,

muscle layers, fascicles) have been visualised in the demonstration of the developed ultrahigh-

resolution OCT systems [322] or OCT needle probes [323]. In contrast to lung tissue filled with

alveoli, which are microscopic structures providing high-contrast air/tissue interface,

ultrastructures within skeletal muscle typically show moderate contrast and, thus, appear almost

homogeneous under imaging modalities with insufficient spatial resolution or sensitivity [324].

However, investigations in imaging another type of striated muscle, cardiac muscle,

experimentally demonstrated the potential of OCT in resolving cellular structures (i.e., muscle

fibres) and their lesions inside striated muscle by visualising tissue lesions and the orientation of

cardiac fibres inside cardiac muscle [325, 326].

The first OCT image showing individual myofibres was reported by Klyen et al. in 2008 [60]. A

whole-muscle autograft mouse model was employed in the ex vivo study. In the acquired 3D

OCT images, the transverse view of individual myofibres, as distinctive high-intensity circular-

shaped structures, was shown within the healthy muscle samples (host tissue). Moreover, the

grafted tissue containing necrotic tissue and inflammatory cells were differentiated from those

healthy host tissues by showing as featureless and low-intensity regions under OCT imaging


38

(Fig. 2.22). Because the necrosis and inflammation, as well as the subsequent muscle

regeneration, within the grafted tissue represent the key pathological features in human DMD,

the demonstrated capability of OCT in the differentiation between healthy host muscle and

necrotic grafted muscle in this autograft model indicates the potential of OCT in distinguishing

necrotic from normal muscle tissues in DMD. Further investigations by Klyen et al. [55]

experimentally proved this potential. By imaging the exercised dystrophic mouse muscle

samples using OCT, longitudinal views of individual myofibres showed high-sensitivity and

highly organised structures within normal-appearing or undamaged regions without necrosis or

inflammation. Damaged regions with necrosis or inflammation are clearly distinguished based

on their featureless appearance and low intensity of signal (Fig. 2.23). A recent in vivo study

further demonstrated the ability of OCT in differentiating the damaged regions from undamaged

ones in dystrophic muscle by detecting the architectural changes resulting from the muscular

disease [54].

Fig. 2.22. OCT image of mouse muscle from the whole-muscle autograft model. High-intensity circular-

shaped structures indicate the transverse view of individual myofibres in the host muscle, which can be

differentiated from the featureless, low-intensity grafted muscle [60].


39

Fig. 2.23. OCT image of exercised mdx mouse muscle. Longitudinal view of individual myofibres are

visualised within the normal-appearing/undamaged region, which can be differentiated from the

featureless damaged region [55].

2.6.3 Challenges of using OCT for assessment of muscle damage and in vivo imaging of

skeletal muscle

Although the applications of OCT in visualising cellular structures inside skeletal muscle and

assessing necrosis within dystrophic muscle have been reported, several obstacles that preclude

OCT from becoming a routine muscle imaging modality in either preclinical or clinical usage

still remain. Firstly, the detection of necrosis within dystrophic muscle is based on the contrast

generated by the OCT signal intensity. The variance of the detected OCT signal intensity within

one single scan (intrascan variance) indicates different structures or pathological states inside

the imaged muscle sample. However, the intensity variance from scan to scan, or even from

sample to sample (interscan variance), may be caused not only by the structural or pathological

changes within each muscle sample, but also by the type of the muscle samples, the smoothness

of the imaged muscle surface, the incident intensity of the employed light, the sensitivity of the

employed imaging system, and other environmental artefacts during the experimental scans. As

a result, a threshold of the absolute intensity of the detected OCT signal for differentiating

necrosis from undamaged muscle tissue is difficult to define. Hence, quantitative assessment of

muscle damage is difficult to achieve using plain OCT imaging. Secondly, the moderate

penetration depth of OCT confines the imaging within 2 or 3 mm below the surface inside the

muscle tissue. Most muscles in human patients or animal models cannot be fully scanned from

their surfaces using OCT. Furthermore, removal of the skin and fat covering the muscles is

usually required.


40

In the following chapters of this thesis, solutions to these obstacles are addressed and discussed.

In Chapter 3, it is reported that an extension of OCT, PS-OCT, has been employed for the

detection of muscle damage within dystrophic muscle samples. The contrast of PS-OCT is

generated based on the pathological change of an optical property, birefringence, inside the

muscle samples. Since birefringence is less affected by the experimental artefacts just described,

quantitative assessment of muscle damage within dystrophic muscles samples is enabled. In

Chapters 4 and 5, the development of an ultrathin OCT needle probe and the application of this

needle probe in visualising cellular structures and pathological changes deep inside muscle

samples are described. The developed OCT needle probe can be inserted into the imaged muscle

and thus overcome the limitation in penetration depth of OCT. A significant step forward to in

vivo OCT imaging of skeletal muscle with minimum invasion is achieved by this development

of the ultrathin OCT needle probe.

2.7 Chapter summary

Skeletal muscle, as one of the three types of muscle tissue within human bodies and most

animals, possesses highly organised structures from the molecular level (i.e., myofilaments) to

the cellular level (i.e., myofibres). Mature myofibres that are developed from myotubes are rod-

like, multinucleated cells, forming bundles termed fascicles. The myofibres are arranged in

parallel styles, which lie obliquely to, or along, the longitudinal axis. These arrangements

perform as structural basis of the various architectures of skeletal muscles. Each myofibre

consists of hundreds of myofibrils; while each myofibril comprises hundreds of myofilaments.

The myofilaments include myosin (i.e., thick) and actin (i.e., thin) filaments. The interdigitating

arrangement of myosin and actin filaments provides the structural basis of muscle contraction,

which is driven by the relative sliding between these two types of myofilaments.

Duchenne muscular dystrophy, as one of the most severe muscular dystrophies, is caused by

mutations in the gene mapped on the human X chromosome. The genetic abnormality results in

an altered form or complete absence of the protein dystrophin, which subsequently reduces the

stability and maintenance of sarcolemma. The myofibres with the lack of functional dystrophin

are dystrophic myofibres, which are very susceptible to the damage of sarcolemma in response

to muscle contraction during exercise (e.g., general locomotion). The entry of calcium through

the damage (e.g., delta lesions) on the sarcolemma triggers enzyme-involved cascades and leads

to muscle necrosis. The respiratory or cardiac failure resulted from the muscle necrosis results

in the death of DMD patients in the second to third decade of their life.

Several imaging techniques, including US, CT, MRI, and light microscopy, have been applied

to the characterisation and analysis of DMD. Ultrasonography, CT, and MRI typically perform

as clinical imaging modalities. Ultrasonography is a non-invasive, low-cost imaging modality

with real-time display and portable equipment. Three-dimensional data volumes, with the


41

spatial resolution ranging from 80 to 800 μm and the penetration depth of several millimetres,

can be provided by US. The spatial resolution of micro-US, which is typically used for

preclinical imaging, can be as fine as 20 μm. X-ray computed tomography generates 3D data

volumes with the spatial resolution of ~100 μm, although it has been reported that the spatial

resolution of micro-CT that is used for preclinical imaging can reach 50 μm, or even 20 μm with

the contrast-enhanced agents. However, the high radiation dosage and relatively low contrast in

soft tissues remain to be limitations of CT in clinical imaging. Magnetic resonance imaging

provides better soft-tissue contrast without invasiveness or radiation dosage. The spatial

resolution of MRI ranges from 50 to 100 μm. A finer resolution of ~20 μm can be achieved by

micro-MRI, which is typically used for preclinical imaging. Light microscopic imaging

modalities, including confocal microscopy, MPM, SHG, provide high-resolution (finer than 1

μm) 3D images. However, excision and preparation of tissue samples are typically required.

Hence, light microscopic imaging modalities are typically applied to preclinical imaging.

Optical coherence tomography, including TD-OCT and SD-OCT, is a non-invasive imaging

modality providing 3D data volumes with the spatial resolution of ~10 μm. Klyen et al. first

applied OCT to the characterisation of muscle damage within dystrophic muscle samples. The

capability of OCT in differentiating muscle damage from surrounding normal-appearing tissue

within dystrophic mouse muscle samples has been demonstrated. However, OCT does not lend

itself to automatic quantification of the proportion of muscle damage within a muscle sample.

Moreover, the penetration depth of OCT in opaque tissues, which is no more than 2 mm, is

usually not enough for in vivo muscle imaging. Therefore, two solutions respectively according

to these limitations are presented in this thesis. The application of PS-OCT, with a

computational algorithm, enables fully automatic and quantitative characterisation of muscle

damage within dystrophic muscle samples. The moderate penetration depth of OCT in opaque

tissue can be overcome by OCT needle probes, which is presented in Chapter 3 and 4 in this

thesis.

Chapter 3 - Characterisation of skeletal muscle damage using PS-OCT

42

Chapter 3

Characterisation of skeletal muscle damage using PS-OCT

3.1 Preface

This chapter begins with a detailed theoretical explanation of polarisation and optical

birefringence, given its prominence in this thesis. An extension of OCT, namely PS-OCT,

which can characterise and assess the birefringence of imaged samples, is described.

Subsequently, birefringence within skeletal muscle, in terms of the structural origin of muscle

birefringence and the effect of muscle contraction in muscle birefringence, is discussed. Two

published journal papers (with minor modifications in the first paper) are then presented. The

first paper presents our self-developed automated algorithm for the quantitative assessment of

tissue birefringence based on PS-OCT imaging data. The second paper demonstrates the

application of this developed algorithm for the quantitative characterisation and assessment of

muscle damage in dystrophic muscle (mdx mouse muscle) based on PS-OCT imaging data.

Additional work related to the published papers is presented in the last part of this chapter.

Following Azzam and Bashara [327], in the text, bold face symbols are used to represent both

vector and matrix quantities and these may be distinguished by the context in which they are

used.

3.2 Optical birefringence and polarisation

Light propagating in free space is a transverse wave because the local oscillations of a light

wave can be oriented perpendicular to the direction of wave propagation. Therefore, a light

wave cannot be completely described by the parameters of amplitude, frequency, and phase. An

extra freedom, given by the direction of local oscillations, is called the polarisation state or state

of polarisation (SoP) [328]. A generic monochromatic light wave can be described by its

complex electric field ),(C tzE (hereafter, the letters in bold indicate vectors). This ),(C tzE is

defined as )-i(e ωtkzE , where k is known as the wavenumber. This wavenumber, k, is given by

2 , where λ is the wavelength of the light wave. The symbol of is the angular frequency of

the light wave; and i is the unit of imaginary number. The direction of the local oscillations of

this light wave can be decomposed in terms of a pair of othonormal basis vectors: the horizontal

vector (H) and the vertical vector (V). Thus

VVHH ˆˆ ee EE E , (1)

where


43

H-iHH e aE , (2)

and

V-iVV e aE . (3)

Here, He and Ve are unit vectors along the horizontal and vertical directions, respectively; Ha

and Va are amplitude components along the horizontal and vertical, respectively. As the local

oscillations are always perpendicular to the z-axis, which is the propagation direction of the

light wave, the SoP is determined by the change of direction in local oscillation in the xy-plane

[328, 329]. The local oscillations can be performed along the x-axis, y-axis, or any arbitrary

combination of the two. Therefore, if z is set to 0 for simplicity, then the curve traced out by the

tip of the electric field, known as the vibrational ellipse, can be obtained [328]. The shape of this

vibrational ellipse determines the SoP of the light wave. Following the definitions and equations

above, the mathematical expression of this vibrational ellipse is given by [328]

VVVHHHvib ˆcosˆcos e e tatatE . (4)

Here, we define the phase retardation between the horizontal and vertical polarisation

components of the light wave as

VH . (5)

When m , where Zm , the vibrational ellipse collapses to a straight line described by

[328]

ee HVVHHvib cos ˆ1ˆ taat mE . (6)

In this particular case, the SoP is said to be linear. The ratio between Ha and Va determines the

orientation of this straight line [328]. If 0H a or 0V a , the straight line will be oriented

vertically (Fig. 3.1a) or horizontally, respectively. If 0VH aa , the straight line will be

oriented at ±45˚ (Fig. 3.1b). In more general cases, the orientation angle can be calculated by

[328]

V

H1tanaa . (7)

When 0VH aa and

n2

(where Zn ), the vibrational ellipse becomes a circle

described by [328]

VHHHHvib ˆsinˆcos e e ttatE . (8)


44

The handedness of this circle (i.e., whether the circle is left- or right-circular) is determined by

the sign between the two orthogonal polarisation components [328] (Fig. 3.1c). Apart from

these two specific cases, an elliptic SoP will be obtained when the amplitudes and phase

retardation have more general values.

Fig. 3.1 Schematic of (a) linear SoP oriented vertical, (b) linear SoP oriented 45˚ with the horizontal, and

(c) right-hand circular SoP [328].

A medium may be able to change the SoP of a light wave propagating through it if the refractive

index of this medium is SoP-dependent. This light wave, which is a plane wave with angular

frequency , propagates along the z-axis of a medium with complex refractive index

i nN (9)

can be described by [330]

tz

cn

zctz

00i-

C ee, EE , (10)

From this equation, the imaginary part of the complex index, , will only affect the real part of

the complex field and, thus, the amplitude of the light wave; whereas, the real part of the

complex index, n, will affect the imaginary part of the complex field and, thus, the phase of the

light wave. Therefore, if the real part of the refractive index, n, is SoP-dependent, differential

phase retardation will be introduced by changing the phases of the two orthogonal polarisation

components to varying degrees (Fig. 3.2). Hence, a medium is defined to be birefringent if the

real part of its refractive index is SoP-dependent [328].


45

Fig. 3.2 Differential phase retardation between the two orthogonal polarisation components is introduced

by the medium with SoP-dependent refractive index (i.e., birefringent medium) [328].

Birefringent mediums, such as crystals, usually possess one particular direction of optic axis

and, thus, show structural anisotropy [329]. Accordingly, the optical property along the optic

axis is different from the optical property perpendicular to the optic axis. The incident light

wave can be decomposed in terms of two polarisation components with orthogonal directions of

local oscillations to each other: one component with an oscillation direction along the optic axis,

and the other component with an oscillation direction perpendicular to the optic axis. The

parallel polarisation component will experience a smaller n and, thus, exhibit a faster speed

when propagating through a medium. The real part of the refractive index for this faster

component is termed fn ; while the one for the slower component is termed sn . Therefore,

differential phase retardation can be introduced by the difference between the two refractive

indices and increases with the propagation distance of the light wave, following the equation

nzk . (11)

Here, Δφ is the differential phase retardation introduced within the birefringent medium; k is the

wavenumber in vacuum; z is the physical pathlength of propagation within the medium; and Δn

is the difference between fn and sn . This Δn is defined as the birefringence value (or

birefringence) of the medium. The birefringence value is the property of the material and, thus,

a constant for a specific material. However, the detected phase retardation, Δφ, is dependent on

the incident direction. When the incident light is perpendicular to the direction optic axis, Δφ is

maximised. In contrast, when the incident light propagates along the direction of the optic axis,

as all the local oscillations are perpendicular to the optic axis, no phase retardation is detected.

Equation (11) describes the case when the phase retardation is maximised.

In addition, the relationship between the non-zero incident angle, 1, and the refraction angle,

2, is given by the Snell’s law, expressed as [331]

2211 sinsin nn . (12)


46

Here, n1 and n2 represent the refractive indices of the medium in which the incident light

propagates and the medium in which the refractive light propagates, respectively. If the incident

light is a polarised light beam propagating from the air to a birefringent medium, n1 should be

the refractive index of the air and n2 should be the refractive index of the birefringent medium,

which is SoP-dependent. The two polarisation components of the incident light will, thus,

experience different refractive indices and show different refractive angles. As a result, two

refractive light beams, representing these two polarisation components, can be observed inside

the birefringent medium (Fig. 3.3). This phenomenon is called “double refraction”. Calcite is a

classic example of a birefringent medium that exhibits double refraction [328, 329].

Fig. 3.3 Schematic of double refraction within a crystal medium. The optic axis is horizontal. The

horizontal oscillation component and the vertical oscillation component are divided during the refraction

of the incident light.

3.3 Representation of the SoP

The SoPs of light waves are usually represented using the Jones formalism or the Mueller-

Stokes formalism. Because the decomposition of the electric field of a light wave involves two

orthogonal components, the horizontal and vertical components, this electric field can be

intuitively represented by a two-element vector as

V

H

EE

E . (13)

Here, HE and VE represent the scalar electric fields of the horizontal and vertical components,

respectively. This vector is called the Jones vector [328]. The electric field in the Jones vector is

considered to be time-invariant. Hence, the represented electric field is only dependent on the

amplitudes and exact phases of the components, as


47

V

H

iV

iH

V

H

ee

aa

EE

E . (14)

Furthermore, the SoP of the represented electric field is completely determined by the

orientation angle of the local oscillations, , and the phase retardation, Δφ, between the two

polarisation components, since the electric field can be further rewritten as

sinecos

eee

ii

iV

iH

V

H H

V

H

aaa

EE

E , (15)

where a is the total amplitude of the electric field, defined as 2V

2H aaa [328]. A Jones

matrix is a complex 2 × 2 matrix relating two Jones vectors. Therefore, any non-depolarising

optical system can be described by a Jones matrix. The transmitted SoP, E , as a result of a

non-depolarising optical system, thus, can be calculated by Jones matrix, J , acting on an

incident SoP, E , as

EJEE

2221

1211

JJJJ

[328]. (16)

The Jones matrix of any non-depolarising optical system can be deduced by measuring both the

incident and the transmitted SoPs. Furthermore, the combined effect of multiple non-

depolarising optical systems with their Jones matrices 1J , 2J , …, nJ , is described by the

product of their Jones matrices, as

EJJJE 12n ... [328]. (17)

Although intuitive and relatively simple in calculation, the Jones formalism has a disadvantage

that only purely polarised light can be described. The case of non-polarised or partially

polarised light needs is described by the Mueller-Stokes formalism. A Stokes vector is

composed of four elements, I, Q, U, V, which are defined as

VVHH EEEE I , (18)

VVHH EEEE Q , (19)

HVVH EEEE U , (20)

and

HVVHi EEEE V . (21)


48

Here, the angular parentheses indicate an average over a long time interval compared with the

period and E represents the conjugate electric field. The irradiance of the electric field, thus,

can be calculated by EE (The permittivity is omitted for simplicity here) [328]. Therefore, I

and Q intuitively represent the total irradiance and the difference in irradiance between the

horizontal and vertical components, respectively. The elements U and V characterise the phase

and circularity of the components, respectively [328, 332]. The degree of polarisation is

introduced by this Mueller-Stokes formalism, which is described as

2

222

IVUQP

. (22)

This degree of polarisation ranges from 0 for non-polarised light to 1 for purely polarised light

[328]. Corresponding to the four elements involved in a Stokes vector, a Mueller matrix relating

an incident Stokes vector to a transmitted vector is a 4 × 4 matrix. Although more

comprehensive than the Jones matrices, Mueller matrices have the advantage over Jones

matrices of being able to describe depolarisation effects and, thus, depolarising optical systems

[333, 334].

Based on the definition of a Stokes vector, only three elements (Q, U, and V) are adequate to

describe the SoP of the light. The additional element I only provides the degree of polarisation.

Hence, a 3D representation of SoP can be performed by the Poincaré sphere based on the Q-, U-

, and V-coordinates of a 3D space (Fig. 3.4). The centre of the sphere is located at the origin;

and the radius of the sphere can be 1 or I. For any purely polarised light, the SoP corresponds to

a particular point on the surface of the Poincaré sphere [328, 332, 335]. Some particular SoPs

are shown in Fig. 3.4 (the radius here is set as 1): (-1, 0, 0) and (1, 0, 0) represent linear SoPs

with horizontal and vertical oscillations, respectively; (0, -1, 0) and (0, 1, 0) represent linear

SoPs with their oscillations oriented at 45˚ and –45˚, respectively; (0, 0, -1) and (0, 0, 1)

represent left- and right-circular SoPs, respectively. The transition between two SoPs is

represented by a path on the surface of the Poincaré sphere. In addition, when the degree of

polarisation is less than 1 and the light is partially polarised, the SoP of the light can be

represented by a particular point inside the Poincaré sphere. As a result, depolarisation effects

can be represented by a path from the surface to the inside of the Poincaré sphere.


49

Fig. 3.4 Schematic of the Poincaré sphere. VLP: vertical-linear polarisation; HLP: horizontal-linear

polarisation; 45˚LP: 45˚-linear polarisation; -45˚LP: -45˚-linear polarisation; LHCP: left-handed circular

polarisation; RHCP: right-handed circular polarisation [328].

3.4 PS-OCT

Polarisation-sensitive OCT is an extension of OCT. Additional contrast in images can be

provided by PS-OCT based on the SoP information encoded in the interference fringe intensity

of the back scattered signal. The first PS-OCT system applied for the measurement of tissue

(calf coronary artery) birefringence was reported by Hee et al. in 1992 [57], following the

application of laser interferometry to characterisation of the SoP of light in 1973 [336], and the

initial measurement of birefringence using both a low-coherence light source and polarisation

sensitive detection [337, 338]. In 1997, the first 2D images of birefringence, showing changes in

birefringence induced by thermal damage in bovine tendon, were presented by de Boer et al.

[339].

PS-OCT is currently a widely employed tool for the assessment of birefringence and

characterisation of the change in birefringence in various biological tissues [56, 148, 340-343].

Polarisation-sensitive OCT systems can be categorised as bulk-optic systems or fibre-based

systems, both of which are widely used in biomedical imaging. The bulk-optic PS-OCT system

was more commonly used by early researchers. A typical configuration of a bulk-optic PS-OCT

system is shown in Fig. 3.5. The key differences between this bulk-optic PS-OCT system and a

typical OCT system include the linear polariser located between the light source and the beam

splitter, and the quarter wave plates located in the reference arm and the sample arm, oriented at


50

22.5˚ and 45˚, respectively [332]. Jones formalism will be employed in the following

description of the bulk-optic PS-OCT system. The light coming from the low coherence light

source becomes a purely polarised one with linear SoP after propagating through the linear

polariser. For simplicity, the local oscillations of this linearly polarised light are assumed to be

horizontal. So the electric field of the incident light arriving at the beam splitter is given by

01

zEzE . (23)

Since the light source has low temporal coherence, i.e., the light is broadband (non-

monochromatic), a complex analytic function is employed for the description of the electric

field amplitude, as

dkkezEkz)i(

e)(~

[344]. (24)

Here, k is the wavenumber of the light and )(~ ke is the field amplitude in k-space. Assume the

beam splitter has a 50/50 splitting ratio and, thus, the incident light is divided evenly by

amplitude between both arms of the interferometer. Since the beam splitter does not change the

SoP of the light, the electric fields of both the sample arm and reference arm are given by

01

2)(

S0R0zEEE . (25)

Here, R0E and S0E represent the electric fields of the incident light to the reference and sample

arms, respectively. The light propagating within the reference arm passes through the quarter

wave plate oriented at 22.5˚to the incident horizontal polarisation. Following the reflection from

a mirror or retroreflector, the light passes through the same quarter wave plate again. The Jones

matrix of the quarter wave plate is given in Equation (26):

QWP =

/4i-

/4i

e00e

, (26)

and the rotation matrix as Equation (27):

cossinsincos

)(R . (27)

Here, φ = 22.5, corresponding to the rotation angle of the optic axis of the quarter wave plate.

Then the reflected light from the reference arm is given by

11

)2(2122.5-22.5 RR0

2RR zEz EE RQWPR [332]. (28)


51

Here, the dot operator indicates dot product between two vectors. This result indicates that the

light reflected from the reference arm has a linear SoP at an angle of 45˚ to the horizontal. In

other words, the horizontal and vertical amplitudes of this reference-arm light are identical and

free of phase retardation. Hence, no extra difference will be introduced by this reference-arm

light during the following interference with the light reflected from the sample arm. In the

description of the sample-arm light, the sample is assumed to be equivalent to a homogenous

linear retarder with a constant orientation of the optic axis. Then the Jones matrix of the sample

can be written as a product of average phase delay within the sample, rotation matrices with the

rotation angle of the sample, and the Jones matrix of a linear retarder with its horizontal optic

axis. So the Jones matrix of the sample is

RR 2/i

2/ii

e00e

e,, nkz

nkznkznzB [332]. (29)

Here, nkz is the average phase delay of the light wave propagating to the depth z inside the

sample with its average refractive index n . This n is defined as 2

sf nnn

, where fn and sn

are the refractive indices of the polarisation components with the local oscillations parallel ( fn )

and perpendicular ( sn ), respectively, to the optic axis of the sample.

2/i

2/i

e00e

nkz

nkz

is the

Jones matrix of a linear retarder. n is the difference between the two refractive indices fn and

sn . The angle involved in the rotation matrices is the angle of the sample optic axis to the

horizontal. Therefore, the Jones vector of the light reflected from the sample arm is given by

sss 45-,,,,45 EBBE QWPQWP nzzRnzzz . (30)

Here, zR is a scalar that describes the reflectivity at depth z inside the sample; while zs is the

optical pathlength of the arm up to the surface of the sample. Using the equations for the light

waves reflected from reference and sample arms, and the assumption of Gaussian power

spectral density for the light source, the amplitudes of the horizontal and vertical polarisation

components are calculated to be

2

-

00H e22cossin,

lz

zknzkzRzzA (31)

and

2

-

00V e2coscos,

lz

zknzkzRzzA , (32)


52

respectively, where k0 is the wavenumber based on the central wavelength of the light source;

and Δz is the difference in optical pathlength between sample and reference arms. After

demodulation, the term of 2k0Δz can be eliminated and, thus, the detected irradiances in the

horizontal and vertical polarisation channels are given by

nzkzRzAzI 022

HH sin (33)

and

nzkzRzAzI 022

VV cos . (34)

The phase retardation as a function of depth is given by [332]

nzkzIzIz

0

H

Varctan . (35)

Description of the fibre-based PS-OCT system is more complicated because the optical fibres

would introduce an unknown and variable SoP [345-347]. Mathematical and theoretical analysis

of the fibre-based PS-OCT system is presented by Makita using Jones formalism [348], and

Park and de Boer using Mueller-Stokes formalism [328].

Fig. 3.5 Schematic of a bulk-optic PS-OCT system. L: lens, Pol: polariser, QWP: quarter wave plate, BS:

beam splitter, PBS: polarising beam splitter [328].

3.5 Birefringence of skeletal muscle

Skeletal muscle has been found to be birefringent since Brucke’s report in 1858 [349]. Previous

investigations suggest that the birefringence value of skeletal muscle is typically less than 3.0 ×


53

10-3 but larger than 1.0 × 10-3 (Table 3.1). The exhibited birefringence value of skeletal muscle

is similar among muscle species, for instance, between quadriceps and triceps. This is because

of the similar ultrastructure at not only the subcellular level but also the molecular level of these

different species of muscles, which forms the physical basis of the birefringence of skeletal

muscle (discussed later in this section). The birefringence of skeletal muscles is dependent on

the state of muscle contraction (discussed later in this section). Muscular pathology, such as

DMD or other muscular dystrophies, in addition, will destroy the ultrastructure of skeletal

muscle and, thus, remarkably reduce the muscle birefringence. This pathological change in

birefringence provides a novel contrast mechanism to distinguish necrotic or damaged muscle

from undamaged muscle using PS-OCT imaging.

Table 3.1 Reference values of birefringence in skeletal muscles.

Tissue Birefringence Researcher and year

Rodent muscle 1.4 × 10-3 de Boer et al. (1999) [350]

Rat muscle 2.2 × 10-3 de Boer et al. (1999) [351]

Murine muscle (1.90 ± 0.06) × 10-3 Pasquesi et al. (2006) [56]

The structural origin of muscle birefringence is the highly organised arrangement, leading to

structural anisotropy, within the skeletal muscle from the molecular level (myofilaments) to the

macroscopic level (fascicles). The molecular basis of muscle birefringence was first studied by

von Muralt and Edsall in 1930 [352]. Myofilaments, including myosin filaments and actin

filaments, play principal roles in muscle birefringence. The optic axis within skeletal muscle is

along the length of myofibres and the contained myofilaments [353] (Fig. 3.6). Both myosin and

actin filaments have a rod-like shape, and contain α-helical protein molecules and are, thus,

anisotropic. However, because the percentage of the α-helical protein molecules is lower in

actin filaments than in myosin filaments, the actin filaments are less birefringent than the

myosin filaments. Colby, a pioneering researcher in measuring birefringence of molecular

filaments extracted from skeletal muscle, reported that the ratio of birefringence between the

myosin filament and the actin filament is 3.1 ± 0.2, since the measured birefringence value was

10.1 × 10-3 ± 1.4 for the individual myosin filament and 3.3 × 10-3 ± 0.3 for the individual actin

filament [354]. As a result, I-bands in myofibrils that consist of actin filaments only, show

lower birefringence than A-bands that consist of both myosin and actin filaments.


54

Fig. 3.6 The direction of optic axis within skeletal muscle. Green arrows represent the direction of optic

axis, which is always along the length of myofibres, and the contained myofilaments (adapted from

[355]).

The total birefringence within skeletal muscle is divided into two types: firstly, intrinsic

birefringence, which is caused the anisotropic molecular structure of individual filaments; and

secondly, form birefringence, which is caused by the highly organised, parallel arrangement of

the elongated molecular filaments [356, 357]. Intrinsic birefringence typically accounts for 30 to

40% of the total birefringence, while form birefringence typically accounts for 60 to 70% [349,

353, 356-360].

Form birefringence within skeletal muscle is dependent on the state of muscle contraction. As

discussed in Section 2.3.3, crossbridges form between myosin and actin filaments. During


55

muscle contraction, these crossbridges momentarily change direction from more parallel to

more perpendicular relative to the axis of the myosin filaments, driving the relative sliding

between myosin and actin filaments. As a result, the angle between each crossbridge and the

myosin filament increases by some degree during muscle contraction (Fig. 2.11). Hence, the

anisotropy provided by the parallel arrangement will be decreased by these perpendicular

crossbridges, which structurally disturb the parallel arrangement and significantly reduce the

birefringence (Table 3.2) [98, 349, 358, 360-363]. Irving has shown that this decrease in

birefringence is roughly proportional to the degree of overlap between the actin and myosin

filament molecules during muscle contraction [364]. This decrease is reversible and

birefringence returns when the skeletal muscle comes to its relaxed state [98, 360]. However,

when muscle contraction is excessive and the crossbridges over rotate, causing the angle

between each crossbridge and the myosin filament to exceed 90˚, the parallel organisation of

myosin molecules is reinstated. In this case, birefringence increases again after reaching the

minima [360, 365].

Table 3.2 Change of muscle birefringence caused by muscle contraction.

Resting birefringence Contracting birefringence Muscle Researcher(s) and year

1.92 ± 0.03 × 10-3 8.2 ± 1.2% lower frog myofibre Eberstein and Rosenfalck

(1963) [366]

1.67 ± 0.05 × 10-3 1.46 ± 0.08 × 10-3 rabbit psoas Taylor (1975) [98]

20% lower Fischer (1936) [358]

2.80 ± 0.59 × 10-3 8.4% ± 6.4% lower Burton et al. (1990) [367]

As discussed in Section 2.4.1, muscular dystrophies, such as DMD, introduce structural damage

within diseased muscles by necrosis and inflammation of myofibres. This significantly disorders

the parallel arrangement of myofilaments, myofibrils, and myofibres (Fig. 2.14). Therefore, the

structural anisotropy and, subsequently, the birefringence of the muscle are reduced. Pasquesi et

al. have shown that the birefringence is remarkably reduced in exercised mdx mouse muscle

[56]. The following sections in this chapter present two published papers (with minor

modifications in the first paper) which demonstrate the ability of PS-OCT to quantitatively

assess the damage within dystrophic muscle (mdx mouse muscle) using an automated algorithm

expressly developed for this purpose.


56

3.6 En face parametric imaging of tissue birefringence using polarization-sensitive optical

coherence tomography

[Lixin Chin, Xiaojie Yang, Robert A. McLaughlin, Peter B. Noble, David D. Sampson; Journal of

Biomedical Optics, 18(6), 066005, 2013]

Abstract We present a technique for generating en face, parametric images of tissue birefringence from scans

acquired using a fiber-based polarization-sensitive optical coherence tomography (PS-OCT) system

utilizing only a single incident polarization state. The value of birefringence is calculated for each A-scan

in the PS-OCT volume using a quadrature demodulation and phase unwrapping algorithm. The algorithm

additionally uses weighted spatial averaging and weighted least squares regression to account for

variation in phase accuracies due to varying OCT signal-to-noise-ratio. The utility of this technique is

demonstrated using a model of thermally induced damage in porcine tendon, and validated against

histology. The resulting en face images of tissue birefringence are more useful than conventional PS-OCT

B-scans in assessing the severity of tissue damage, and in localizing the spatial extent of damage.

3.6.1 Introduction

Many types of tissue exhibit birefringence, such as those of the musculoskeletal system –

muscle, cartilage, ligaments and tendon [1, 2]. Birefringence in biological tissue results from the

presence and arrangement of anisotropic ultrastructures. Disease and other processes can disrupt

these structures and reduce the degree of birefringence. Quantification of birefringence is, thus,

a potential metric for quantifying tissue damage [1, 2]. The shape, extent, and distribution of the

damaged regions are also informative in pathological assessment, and an en face view of

birefringence could provide additional spatial information about the damaged tissue.

Polarization-sensitive optical coherence tomography (PS-OCT) is a noninvasive imaging

modality that can quantify the birefringence in tissue by measuring the changes in the

polarization of back-scattered light [3]. Local estimates of birefringence are calculated from PS-

OCT scans using the rate of change of phase retardation with axial depth [4]. Computing this

parameter for each A-scan in the volume generates a two-dimensional (2-D) map of

birefringence. We refer to this map as a parametric image [5], where the pixel intensity at each

(x, y) location is indicative of an optical parameter, birefringence, calculated from the

underlying PS-OCT data. Such an image gives a visual representation of the changes in

birefringence, and hence the extent of tissue damage.

Sakai et al. presented a method for generating parametric images of birefringence from PS-OCT

scans of human skin [6]. However, skin possesses relatively low levels of birefringence, ≈10%

of the birefringence of tendon, or 20% of that of skeletal muscle [1, 6-8]. Highly birefringent

tissue presents the additional complication of phase wrapping [9].

One method of overcoming the problem of phase wrapping is to calculate the local phase

retardation from cumulative Jones matrix measurements. This requires calculating the local


57

change in the tissue’s optic axis, which in fiber-based PS-OCT systems is typically

accomplished by sampling the tissue using multiple incident polarization states [9, 10].

Alternatively, Stifter et al. adopted a signal processing technique to unwrap the cumulative

phase retardation based on a 2-D quadrature transformation [11]. They demonstrated its use in

imaging the cross-sectional (B-scan) view of the birefringence of polymer materials under stress

[11]. However, the accuracy of the phase retardation signal is related to the signal-to-noise ratio

(SNR) of the OCT signal (OCT SNR) [4, 12]. Previously reported methods have not accounted

for this reduction in accuracy in areas of low signal, such as in the troughs of OCT speckle, or

with increasing depth into the tissue.

We propose a fully automated signal processing algorithm to quantify the birefringence of a

sample accounting for differing phase accuracies due to varying OCT SNR and utilizing a

quadrature transformation to account for highly birefringent materials. In addition, we extend

the algorithm to generate an en face parametric OCT image of birefringence capable of

highlighting areas of tissue damage in biological samples. This method is usable on scan

volumes acquired with fiber-based PS-OCT systems possessing only a single incident

polarization state. The algorithm is demonstrated on porcine tendon; the degree of measured

birefringence is compared to the degree of thermally induced tissue damage, and validated

against colocated histological sections.

3.6.2 Method

Generating parametric images of birefringence from PS-OCT scan volumes requires separating

the value of birefringence from the other polarization altering properties of both the tissue and

of the PS-OCT system itself. The recorded signal from each voxel in the scan volume can be

expressed as a real-valued Stokes vector, TVUQI ],,,[S , which describes the polarization

state of light [13,14]. PS-OCT detects a fully polarized signal, so the Q, U, and V components

fully describe the polarization state. The normalized, reduced Stokes vector (hereafter, “Stokes

vector”), TVUQ ]ˆ,ˆ,ˆ[ˆ S , is obtained by dividing the Q, U, and V components by

I = (Q2 + U2 + V2)1/2. It is common to treat the polarization changes due to the PS-OCT system

as both lossless and constant during imaging [4]. The birefringence of the tissue sample can,

thus, be extracted from the relative difference between Stokes vectors in an A-scan.

The phase retardation, or phase angle φr(zi), is the angle between the Stokes vectors refS (at the

surface of the tissue) and )(ˆizS (at a depth zi into the tissue. That is, ii zz SS ˆˆ)(cos refr ,

where is the three-dimensional (3-D) vector dot product and the subscript i represents the

discretization of the OCT signal in the z-dimension. The measurement accuracy of φr(zi) is

affected by the OCT SNR, which varies due to speckle, and decreases with depth into the tissue.

In the shot-noise limit, noise can be modeled as a circularly symmetric complex Gaussian

random variable [zero mean, phase uniformly distributed over (-π, π)] added to the complex


58

electric field describing light backscattered from the sample. With high OCT SNR, this gives

the variance of φr(zi) as approximately twice the inverse OCT SNR at zi, )(SNR/2)(2r ii zz

[4, 12]. The effects of varying OCT SNR due to speckle can be decreased by averaging the

Stokes vectors over distances larger than the coherence length of the source [14-16]. The

relationship between OCT SNR and the accuracy of φr(zi) implies that the Stokes vectors should

be weighted by 2/)(SNR)(/1)( 2r iii zzzw during spatial averaging. The variance of the

angle calculated from the weighted, spatially averaged Stokes vectors is then given by

av2av SNR/2SNR)/(2 K , where denotes the convolution operation, K the kernel

used for spatial averaging, and SNRSNR av K the “spatially averaged” SNR.

In a noise-free model, the angle, φr(zi), between Stokes vectors is a function of the polarization

state of light incident on the tissue (hereafter “incident polarization”), the diattenuation of the

tissue, the birefringence of the tissue, and the orientation of the tissue’s optic axis [16]. If the

tissue’s optic axis changes minimally within an A-scan, its effects on φr(zi) will be limited and

can be modeled as a low-frequency modulation allowing φr(zi) to be measured using a single-

incident polarization state. The incident polarization should ideally be circular or linearly

polarized at 45˚ to the tissue optic axis. Misalignment of the incident polarization away from

these target polarization states degrades the effective SNR of φr(zi) [16].

The effects of incident polarization, diattenuation, and changing optic axis with depth into the

tissue can be modeled as modulations of the amplitude, A(zi), of the cosine-phase signal with

depth [11,16],

)(cosˆˆcinref iiii zzAzCz SS . (1)

This leaves φc(zi), the continuous-phase retardation with depth, as a function of tissue

birefringence. The amplitude modulations, A(zi), can be removed using the quadrature

component, )(sin cquad iii zzAzC , determined using the Hilbert transform, H, to the in-

phase signal Cin(zi). That is, ))(H( inquad ii zCzC [11]. This gives the demodulated, wrapped,

phase retardation,

)()( quadinw iii ziCzCz . (2)

As φw(zi) is discretized in zi, it can be unwrapped by considering the difference between

successive values, 1wwdiff iii zzz . Phase wrapping is considered to occur at the

values of zi for which |φdiff(zi)| exceeds a threshold, and phase unwrapping is performed by

interpolating φdiff(zi) at these locations. Calculating the cumulative sum of φdiff(zi) with depth

gives the unwrapped double-pass phase retardation

i

j ji zz0 diffu )( . The

birefringence, Δn, in each A-scan is then calculated as


59

4RI 0u n , (3)

where RI is the bulk refractive index of the tissue sample, λ0 is the mean wavelength of the PS-

OCT system, and δφu is the slope of φu(zi) [14]. The slope of phase retardation with depth, δφu,

is obtained using weighted least squares linear regression, with the weight at each point equal to

half of the spatially averaged OCT SNR at that point (SNRav/2). Figure 3.8 shows this process

on a single representative A-scan.

3.6.3 Experiment

(a) PS-OCT imaging

The algorithm described here was applied to scans acquired using a fiber-based, swept-source

PS-OCT system (PSOCT-1300, Thorlabs, New Jersey) [17]. A schematic of the PS-OCT

system is shown in Fig. 3.7. When comparing this system to similar fiber-based systems

published in the literature, one notices that it does not contain a polarization modulator for

generating two orthogonal (in a Poincaré sphere representation) incident polarization states in

alternate A-lines [18]. This is normally required in order to retrieve sufficient information to

compensate for the unknown incident polarization state on the sample in fiber-based systems.

Polarization modulators add substantial cost and complexity to the hardware and software of

such systems, which is undesirable in a commercial product. For this reason, this system uses a

very simple approach to circumvent this problem which appears to work quite well in practice

for samples that exhibit a certain amount of birefringence. Before every measurement, the

polarization controller in the sample arm is optimized for optimum contrast in the real-time

display of the phase retardation image (maximum amplitude of the “banding pattern”). For a

birefringent sample, the highest contrast will be obtained for input polarization states that will

be rotated on a grand circle in the Poincaré sphere representation after returning from different

depths in the sample [18]. In this way, the phase retardation can be determined correctly by

comparing the Stokes vectors from different depths in the sample to the Stokes vector of the

sample surface reflection. This system has a manufacturer specified mean wavelength/spectral

bandwidth of 1325 nm/100 nm and a measured axial/lateral resolution of 17 µm/16 µm in air

[full-width-at-half-maximum (FWHM) of intensity]. The sensitivity of the system is ~97 dB

according to the manufacturer specifications (the PS-OCT system consists of an OCS1300SS

1300-nm swept-source OCT base unit with a specified sensitivity of 100 dB, together with a

polarization-diversity detection module that will introduce a sensitivity penalty of

approximately 3 dB.). The incident polarization was manually adjusted before scanning to

maximize the SNR of the phase retardation signal. Scan volumes were acquired measuring

4 × 4 × 2.8 mm (832 × 832 × 512 pixels). The Stokes vectors within each B-scan were spatially

averaged using a 2-D Gaussian kernel with FWHM in z/x equal to twice the OCT axial/lateral

resolution. After demodulation using the Hilbert transform, φw(zi) was unwrapped using a

threshold on |φdiff(zi)| of 0.5 rad/pixel (≈ 0.091 rad/µm). The slope of φu(zi) was calculated using


60

weighted least squares regression over a range of 300 µm, starting approximately at 175 µm

from the surface of the tissue, and the en face parametric image of tissue birefringence was

calculated using Eq. (3) for each A-scan.

Fig. 3.7 Schematic of the employed PS-OCT system (PSOCT-1300, Thorlabs, New Jersey). AO: analog

output card, AL: alignment laser, BD: balanced detector, C: collimator, CCD: charge-coupled device

camera, CIR: circulator, D: detector, DAQ: data acquisition board, FC: fiber coupler, M: mirror, MS:

microscope, MZI: Mach-Zehnder interferometer, OBJ: objective, P: horizontal polarization state, PBS:

polarized beam splitter, PC: polarization controller, S: vertical polarization state, SD: XY scanner driver,

SS: swept laser source, TRIG: trigger, VA: variable attenuator,

Fig. 3.8 Quadrature demodulation and phase unwrapping applied to a single representative A-scan. From

the angle between the weighted, spatially averaged, Stokes vectors, (a) cos(φr(zi)) and (b) φr(zi), (c) is the

wrapped, double-pass, demodulated phase retardation, φw(zi), and (d) is the unwrapped, double-pass,

demodulated phase retardation, φu(zi), along with a linear fit (in red) over a 300 µm range (length

exaggerated for visibility).

(b) Thermally damaged porcine tendon

Scans were acquired of porcine tendon that had its birefringence decreased through thermal

stress. Fresh tendon is highly birefringent; however, once heated above an activation


61

temperature (≈ 62 °C for these samples), the collagen in the tendon denatures. This leads to a

decrease in birefringence with the rate of decrease being a function of both temperature and

heating time [2, 8]. This model was used to both quantify birefringence and to generate en face

parametric OCT images of birefringence.

Three castrated-male pigs (≈ 8 to 10 weeks, 30 kg) were euthanized by exsanguination under

barbiturate anesthesia in accordance with institutional ethics requirements. Tendons were

extracted from the posterior side of the hind limbs and cut into strips measuring approximately

10 × 10 × 5 mm. The samples were clamped between aluminum blocks and fully immersed in

heated physiological Krebs solution. After 2.5 min, the samples were removed from solution

and imaged on the PS-OCT system. The samples were then replaced in the heated Krebs

solution for a further 2.5 min, and the process repeated until each sample had been heated for a

total of 15 min. En face parametric birefringence images of each sample were generated using

the described algorithm, taking the bulk refractive index of porcine tendon, RI, as 1.4 [8, 19].

3.6.4 Results

Fig. 3.9 shows the mean birefringence for six tendon samples at temperatures ranging from

61 °C to 67 °C. The birefringence of fresh tendon prior to thermal stress (t = 0 min) was

4.0 × 10-3 ± 0.4 × 10-3 (mean ± standard deviation), comparable with previously reported values

of 4.2 × 10-3 ± 0.3 × 10-3 [8]. As anticipated, the mean birefringence decreased with time, as the

period of thermal stress increased, and the rate at which the birefringence decreased was

observed to increase with temperature. Tendon birefringence was generally unchanged by

heating at 61°C, but had mostly dissipated after 7.5 min at 67 °C. This agrees with previous

studies, which showed that porcine tendon was unaffected by heating at 60 °C, but rapidly

denatured at 65 °C [20].

Fig. 3.9 The mean birefringence of porcine tendon samples (S1-S6) after thermal stress. Samples were

immersed in heated Krebs solution at the indicated temperatures. Total heating time refers to the duration

of the applied thermal stress.


62

Additionally, one tendon was cut to 2 cm in length then suspended such that one end was

immersed in heated Krebs solution (69 °C for 5 min), while the other end was left in air

(≈ 60 °C). PS-OCT scans were acquired both before and after heating. The sample was then

fixed in formaldehyde, embedded in paraffin wax, sectioned, and stained with haematoxylin and

eosin (H&E). Figure 3.10 shows three phase-retardation B-scans from regions of the sample

after heating. Figure 3.11 shows the en face parametric images of the sample birefringence

before and after heating, and the corresponding histological section and OCT intensity images.

The mean birefringence of the sample prior to heating was 4.5 × 10-3, which is within the

expected range. After heating, there is a visible difference in the phase retardation B-scans from

the immersed region (Fig. 3.10a) compared to the nonimmersed region (Fig. 3.10c), although

the boundary between the two regions is more difficult to discern in the B-scan (Fig. 3.10b). By

contrast, the en face parametric image shows a clear boundary between the low- and high-

birefringence regions (Fig. 3.11d), corresponding to the liquid-air interface during the heating

protocol. The boundary in the parametric image is also more apparent than in the corresponding

en face OCT intensity image (Fig. 3.11c). The mean birefringence after heating was 6.1 × 10-4

in the immersed region, and 3.2 × 10-3 in the non-immersed region. This is comparable with the

mean birefringence after 5 min of the samples heated to 67 °C (6.8 × 10-4) and 61 °C (3.5 × 10-

3), respectively. The liquid-air boundary is also evident in the histological section (Fig. 3.11e).

The damaged region stains a deep purple, and the collagen weave has lost its fine structure and

fused together. The large tears are artifacts resulting from the weakened tissue breaking during

histological processing. There is a clear correspondence between the en face parametric image

of tissue birefringence (Fig. 3.11d) and the colocated H&E stained histological section (Fig.

3.11e).

Fig. 3.10: Phase retardation B-scans of a porcine tendon sample after partial immersion into 69 °C Krebs

solution for 5 min. (a) is a B-scan from a section of the sample which was immersed into solution. (b) is

from the boundary between the immersed (right) and non-immersed (left) regions. (c) is from the non-

immersed region.


63

Fig. 3.11: En face OCT intensity images of the same porcine tendon sample depicted in Fig. 3.10, (a)

before and (c) after partial immersion into 69 °C Krebs solution for 5 min. (b) and (d) are corresponding

en face parametric OCT images of tissue birefringence. (e) is a H&E stained histological section

corresponding to the region shown in (c) and (d). The dashed lines indicate the location of the liquid-air

boundary during heating.

3.6.5 Discussion

Results presented here demonstrate the ability of an en face parametric OCT image of

birefringence to improve differentiation of tissue damage. Compared to the B-scan images of

phase retardation (Fig. 3.10), the en face parametric images of birefringence (Fig. 3.11) show a

clearer view of the lateral extent of the tissue damage, as well as presenting the same orientation

as conventional polarized light microscopy. We note that the parametric OCT image of

birefringence has compressed the 3-D PS-OCT volume into a more concise 2-D representation

showing areas of tissue damage.

This study used an empirically chosen range of 300 µm over which to calculate tissue

birefringence. From Eq. (3), the precision of the calculated birefringence is proportional to the

precision of the slope of the phase retardation with depth. The standard deviation of the slope of

the phase retardation can be modeled as the standard deviation of the slope parameter of a

weighted least squares linear estimator [21]. Using a single-scattering model of OCT, taking the

attenuation coefficient of tendon as 0.24 mm-1 [22], and an initial OCT SNR of 30 dB, the

300 µm fitting range corresponds to an estimated standard deviation on the slope of phase

retardation of 0.072 rad/mm, leading to a standard deviation on the birefringence estimate of

1.1 × 10-5. Halving this range to 150 µm would increase the standard deviation of the

birefringence estimates by a factor of ≈ 3. Similarly, doubling the range to 600 µm would

decrease this standard deviation by a factor of ≈ 3. However, increasing the fitting range also


64

increases the possibility of errors due to aggregating birefringence over different tissue types.

The optimal fitting length will be application specific, depending on the anticipated

homogeneity of the tissue.

The current implementation assumes tissue homogeneity within the section of the A-scan used

to calculate the birefringence. This is likely to be the case when imaging musculoskeletal tissue,

such as tendon or muscle, which consist mostly of a single tissue type, but may not be the case

in complex biological structures such as airways. In this situation, a segmentation algorithm

(e.g., as shown by van Soest et al. [23]) will be necessary to identify homogenous regions of

tissue, so that the birefringence of each tissue type can be calculated separately.

The presented method has been demonstrated on ex vivo tissue samples. The low penetration

depth of PS-OCT (≈ 1 to 2 mm in tissue) presents a challenge to extending this work to in vivo

imaging. In addition, the method works best if the incident polarization state is manually

optimized before imaging, but such adjustments also complicate potential in vivo imaging

scenarios. To overcome the challenge posed by the low penetration depth of OCT-based

imaging modalities, several groups have shown that OCT imaging probes can be miniaturized

and encased within hypodermic needles [24-27] and endoscopes [23, 28-30]. OCT needle

probes capable of acquiring 3-D scans have been reported to be as small as 30-gauge (outer

diameter 310 µm) [25, 31], significantly smaller than standard biopsy needles. PS-OCT needle

probes could be used interstitially to image birefringent tissues such as tendon, muscle, or

cartilage in situ. OCT endoscopic probes have been demonstrated capable of in vivo imaging of

human airways [28] and arteries [23], and PS-OCT endoscopic probes have been demonstrated

on ex vivo human arteries [29]. Additionally, as one method of addressing the challenge posed

by the optimization of the incident polarization state, it has been shown that fiber-based PS-

OCT systems may be constructed using polarization-maintaining fibers (PMFs) [32, 33]. PMF-

based systems keep the use of a single incident polarization state, but do not require tuning of

the incident polarization before each scan [32]. In combination with the technique presented,

PS-OCT needle and endoscopic probes and PMF-based PS-OCT systems could enable the

generation of parametric OCT images of tissue birefringence in vivo.

3.6.6 Conclusion

In summary, we have demonstrated an automated method to quantify birefringence in PS-OCT

volumes and have used this to define a novel en face parametric image. This method accounts

for variances in phase accuracy due to differing OCT SNR, improving performance compared to

conventional mean filtering, and accounts for highly birefringent tissue by utilizing quadrature

demodulation and phase unwrapping. In addition, this method is useable with fiber-based PS-

OCT systems possessing only a single-incident polarization state. When compared against OCT,

the en face parametric image of birefringence gave clear visualization of the damage in

birefringent tissue and enabled automated quantification of the degree of tissue damage.


65

3.6.7 Acknowledgments L. Chin is supported by a Robert and Maude Gledden postgraduate research scholarship from the

University of Western Australia. R. A. McLaughlin is supported by a fellowship from the Cancer Council

Western Australia. P. B. Noble is supported by a career development fellowship from the NHMRC of

Australia (1045824).

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Liu, J. G. Fujimoto and M. E. Brezinski, "Assessment of coronary plaque collagen with

polarization sensitive optical coherence tomography (PS-OCT)," International Journal of

Cardiology 107(3), 400-409 (2006)

[30] P. B. Noble, A. R. West, R. A. McLaughlin, J. J. Armstrong, S. Becker, P. K. McFawn, J.

P. Williamson, P. R. Eastwood, D. R. Hillman, D. D. Sampson and H. W. Mitchell, "Airway

narrowing assessed by anatomical optical coherence tomography in vitro: dynamic airway wall

morphology and function," Journal of Applied Physiology 108(2), 401-411 (2010)

[31] D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin and D. D. Sampson,

"Ultrathin side-viewing needle probe for optical coherence tomography," Optics Letters 36(19),

3894-3896 (2011)

[32] E. Götzinger, B. Baumann, M. Pircher and C. K. Hitzenberger, "Polarization maintaining

fiber based ultra-high resolution spectral domain polarization sensitive optical coherence

tomography," Optics Express 17(25), 22704-22717 (2009)


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[33] M. K. Al-Qaisi and T. Akkin, "Swept-source polarization-sensitive optical coherence

tomography based on polarization-maintaining fiber," Optics Express 18(4), 3392-3403 (2010)

The paper presented above describes the development of the computational algorithm that

enables fully automated quantification of the birefringence value from each OCT A-scan. The

en face parametric birefringence map, a 2D image containing 3D information can be generated

by this algorithm from the acquired volumetric data of PS-OCT. The application of this

algorithm to the quantification of the change in birefringence of tendon tissue with thermally

induced damage provided the validation of this algorithm. The paper presented in the next

section (Section 3.7), will describe the application of this algorithm to the characterisation and

quantitative assessment of the muscle damage in the exercised dystrophic muscle samples based

on the volumetric data acquired from PS-OCT imaging is described. Image coregistration and

numerical comparison between the generated en face parametric images of the muscle samples

and the corresponding histological sections showed fairly good agreement. The results

demonstrate the potential significance of PS-OCT imaging in clinical use.

3.7 Quantitative assessment of muscle damage in the mdx mouse model of Duchenne

muscular dystrophy using polarization-sensitive optical coherence tomography

[Xiaojie Yang, Lixin Chin, Blake R. Klyen, Tea Shavlakadze, Robert A. McLaughlin, Miranda D.

Grounds, and David D. Sampson; Journal of Applied Physiology, 115(9): 1393-1401, 2013]

Abstract Minimally invasive, high-resolution imaging of muscle necrosis has the potential to aid in the assessment

of diseases such as Duchenne muscular dystrophy. Undamaged muscle tissue possesses high levels of

optical birefringence due to its anisotropic ultrastructure, and this birefringence decreases when the

tissue undergoes necrosis. In this study, we present a novel technique to image muscle necrosis using

polarization-sensitive optical coherence tomography (PS-OCT). From PS-OCT scans, our technique is

able to quantify the birefringence in muscle tissue, generating an image indicative of the tissue

ultrastructure, with areas of abnormally low birefringence indicating necrosis. The technique is

demonstrated on excised skeletal muscles from exercised dystrophic mdx mice and control C57BL/10ScSn

mice with the resulting images validated against co-located histological sections. The technique

additionally gives a measure of the proportion (volume fraction) of necrotic tissue within the three-

dimensional imaging field of view. The percentage necrosis assessed by this technique is compared

against the percentage necrosis obtained from manual assessment of histological sections, and the

difference between the two methods is found to be comparable to the interobserver variability of the

histological assessment. This is the first published demonstration of PS-OCT to provide automated

assessment of muscle necrosis.

3.7.1 Introduction

Duchenne muscular dystrophy (DMD) is a lethal, X-chromosome linked muscle wasting

disorder affecting mainly boys that is caused by a defect in the gene that encodes for the


69

structural subsarcolemmal protein dystrophin [54]. Initial muscle damage in boys with DMD

can progress to myofiber necrosis, because absence or impaired functioning of the dystrophin

protein leads to increased susceptibility of dystrophic myofibers to contractile damage after

exercise [36]. In DMD, repeated cycles of myofiber necrosis over many years leads to

replacement of muscle tissue with fibrous connective tissue and fat [30, 37], resulting in

progressive loss of muscle mass and function and early death, often due to cardiac or respiratory

failure [4, 12]. The dystrophic mdx mutant mouse (C57BL/10ScSnmdx/mdx) is a model for DMD

that is widely used in preclinical research [15, 16, 50]. Assessment of disease progression in the

mouse typically involves death of the animal for tissue sampling and histological analysis to

identify muscle necrosis [15]. Such analysis is both very time-consuming and its invasive nature

precludes the possibility of longitudinal assessment of disease progression over time in a single

animal, increasing experimental uncertainty and cost.

In whole living animals, noninvasive imaging techniques such as magnetic resonance imaging

(MRI) [2, 25, 26, 31, 43, 47], ultrasonography [11, 42, 46] or X-ray computed tomography (CT)

[39, 40, 44, 53], have shown potential for imaging muscle necrosis in vivo, with the option of

repeated measurements over time on the same subject. MRI is able to provide three-dimensional

(3-D) imaging data from tissue volumes and discriminate between healthy and dystrophic

muscle in canine [25, 26] and murine [2, 31, 43, 47] animal models. Use of MRI contrast agents

enables quantitative assessment of the permeability of dystrophic myofibers and improves

imaging contrast [2, 43]. However, the imaging resolution of MRI is insufficient to visualize

individual myofibers. Furthermore, the cost and long acquisition time of scans remain a

challenge for employing MRI in either clinical imaging or preclinical studies. Ultrasonography,

due to its lower cost and shorter acquisition time, is preferable for routine clinical use. The

imaging resolution of ultrasonography, however, is also not capable of differentiating individual

myofibers [11, 42, 46]. CT is employed in clinical studies of myopathies, and a resolution of 40

to 50 µm can be reached with high-resolution micro-CT imaging of small animals [39, 53].

With iodinated contrast agent, the imaging resolution of micro-CT can be as fine as 16 µm [40]

under ideal conditions. However, the disadvantages of lower soft tissue contrast, and very high

radiation dosage, remain impediments in micro-CT imaging [39]. The challenge is to provide a

minimally invasive imaging technique that can view a wide area of tissue with deep penetration,

combined with high resolution [38], and ideally with the potential to be applied in situ in living

animals.

Recently developed optical imaging techniques, such as optical coherence tomography (OCT),

offer the potential for high-resolution, minimally invasive imaging methodologies [10, 13].

OCT is a reflectance-mode optical imaging modality that uses low-coherence interferometry

combined with point beam scanning to produce 3-D images of tissue structure. OCT operates by

detecting depth-resolved backscattered near-infrared light (typical operating wavelength bands

lie in the vicinity of 800 nm and 1,300 nm) in a way that is analogous to ultrasonic pulse-echo


70

imaging [21]. OCT imaging has been demonstrated to be capable of displaying the changes in

myofibers due to necrosis in whole ex vivo murine muscles [23, 24]. Although OCT has

demonstrated an ability to display myofibers, it does not lend itself to automatic quantification

of the proportion (volume fraction) of necrotic tissue within a muscle sample [23, 24].

Polarization-sensitive optical coherence tomography (PS-OCT) is an extension of OCT that

measures the optical birefringence of tissue by analyzing the polarization of the backscattered

light [19]. Birefringence is an optical property of an anisotropic material whereby the

propagation speed (and hence refractive index) of light traveling through the material depends

on the polarization state of the light. In linear birefringence, which is the property of interest

here, light polarized linearly parallel to the optic axis of the uniaxial, birefringent material

experiences a different refractive index than light polarized linearly orthogonal to the optic axis.

The difference between these two refractive indices is the amount of linear birefringence of the

material [3]. Healthy skeletal muscle tissue exhibits high linear birefringence (hereafter

“birefringence”), arising from the highly organized anisotropic cellular structure and

arrangement of myofibers. The detected birefringence is a maximum for light incident

orthogonal to the fiber axis, which is the optic axis in this case, and is zero for coaxial

illumination. Previous studies have shown that birefringence in normal skeletal muscle is due

both to the anisotropic arrangement of subcellular structure within myofibers [18], and the

anisotropic molecular structure of the filament molecules contained in the myofibers [6, 52]. By

contrast, damaged or necrotic muscle loses its anisotropic ultrastructure, and possesses

correspondingly low birefringence [22]. Although collagen and other filamentous,

nonmyofibrillar proteins also exhibit birefringence [45], muscle birefringence is mostly a result

of myofiber structures [6, 18]. We therefore postulate that it is possible to use PS-OCT to

identify regions of necrosis within skeletal muscle by calculating the birefringence across the

muscle, and locating the regions of abnormally low birefringence. A previous study suggests

that PS-OCT can detect the damage induced by exercise in dystrophic mdx mouse muscles by

determining the decrease in birefringence. However, the study did not extend to visualization of

the areas of necrosis, nor to quantification of the proportion of necrotic tissue within the mdx

muscles [33].

In this paper, we present a novel imaging and analysis technique that uses PS-OCT to quantify

the proportion of necrotic tissue in fresh (unfixed) skeletal muscle tissue. The technique

quantifies the level of birefringence in muscle tissue, generating an image that is indicative of

the tissue structure. The technique is demonstrated on ex vivo skeletal muscles from both

dystrophic mdx mice, and wild-type C57BL/10ScSn mice. The resulting birefringence images

are validated against colocated histological sections. Automated segmentation of the

birefringence image additionally provides a measure of the proportion (volume fraction) of

necrotic tissue within the imaging field of view (FoV). The proportion of muscle necrosis


71

assessed by this technique is favorably compared against the proportion of muscle necrosis

obtained from manual assessment of the histological sections.

3.7.2 Materials and methods

(a) Animal handling. All mice were obtained from the Animal Resources Center, Murdoch,

Western Australia. Experiments conformed to the guidelines of the National Health and Medical

Research Council Code of Practice for the Care and Use of Animals for Scientific Purposes

(2004) and the Animal Welfare Act of Western Australia (2002) and were approved by The

University of Western Australia Animal Ethics Committee. Six mdx mice

(C57BL/10ScSnmdx/mdx) (male, 9-10 wk old) were exercised on a horizontal treadmill for 30 min

at a speed of 12 m/min to increase the amount of necrosis in their skeletal muscles [36].

Immediately after exercise, five of the mdx mice were injected with 1% (wt/vol) Evans Blue

Dye (EBD; Sigma, St. Louis, Missouri) in phosphate-buffered saline (PBS) (pH 7.5) by

intraperitoneal injection at a dose of 100 µL per 10 g body wt [17, 41]. The remaining mdx

mouse was imaged without EBD injection as a control sample. EBD has been shown to be a

useful marker for identifying the onset of muscle damage by binding to serum albumin and

readily diffusing only into myofibers with a permeable (damaged) membrane [15]. The

damaged EBD-positive myofibers could be identified macroscopically by their dark blue

staining. This in situ staining was used to guide the subsequent imaging. In addition, four wild-

type normal mice (C57BL/10ScSn) (male, 8-10 wk old) were sampled and imaged without

exercise or EBD injection to provide necrosis-negative control (healthy) muscle samples. The

C57 mice were not exercised because it is well documented that even strenuous exercise does

not induce necrosis in normal wild-type mouse muscles [36].

(b) Sample collection. All mice were anesthetized using 2% (vol/vol) isoflurane (Bomac,

Australia), N2O, and O2 and then killed via cervical dislocation. This occurred in the mdx mice

24 h after completing the treadmill running exercise. Skeletal muscles from both the forelimbs

and hindlimbs were excised and immediately placed in PBS on ice. Muscles were excised by

severing muscle-tendon and muscle-bone attachments; subsequent PS-OCT imaging was

performed away from muscle-tendon junctions and muscle-bone attachment points to avoid any

effect of excision-induced muscle trauma on the PS-OCT images. Muscles were selected for

PS-OCT imaging on the basis of observation of EBD accumulation, indicating leaky myofibers

and an increased likelihood of a necrotic lesion. These muscles were preferentially dissected and

scanned during the time period available. Scanning of the muscle samples began within 2 h of

excision. A total of 11 muscles were imaged from six mdx mice (7 from five mdx mice injected

with EBD; 4 from one mdx mouse that was not injected with EBD), and 15 muscles were

imaged from four C57 wild-type mice (that were not injected with EBD), as shown in Table 3.3.


72

Table 3.3: A summary of imaged muscles

Mouse type Number of mice

/ muscles / scans

EBD

injection

Exercised

Mdx mice

(dystrophic)

Necrosis positive 5 / 7 / 11 Yes Yes

EBD-negative control 1 / 4 / 4 No Yes

C57 mice (healthy) Necrosis-negative

control

4 / 15 / 34 No No

EBD, Evans blue dye

(c) PS-OCT imaging. PS-OCT acquires images of tissue by illuminating a biological sample

with a weakly focused beam of polarized, near-infrared light and detecting the polarization of

light that is backscattered (reflected) from the sample [9, 19]. The backscattered light from a

range of depths is detected simultaneously by the system, giving a narrow one-dimensional

measurement into the tissue along the path of the light beam. The signal at each individual depth

is acquired through a process referred to as low-coherence interferometry [19, 21]. A 3-D data

volume of polarization and backscatter by depth is acquired by scanning the beam in two

directions across the surface of the sample. The polarization state at each depth is compared

with that measured at the surface of the tissue, and the rate of change of polarization (phase

retardation) with depth gives a measure of the birefringence of the tissue. For PS-OCT systems

(such as the one used to conduct these experiments) that use a single polarization state incident

on the sample (the incident polarization), the dynamic range of the detected phase retardation is

maximized when the incident polarization is circular, or linear at 45˚ to the sample’s optic axis.

The optic axis of muscle tissue runs along the muscle fibers [18], and is approximately constant

over the PS-OCT FoV, so light of linear incident polarization ≈ 45˚ to the optic axis was

sufficient for this study. The incident polarization state was manually adjusted before each scan

to achieve the maximum dynamic range of the detected phase retardation.

All samples were imaged using a fiber optics-based PS-OCT imaging system (PSOCT-1300;

Thorlabs, NJ) as shown in Fig. 3.12. Each intact muscle sample was placed on a glass coverslip

and imaged through the coverslip from below. This minimized imaging artifacts by flattening

the imaging surface and by reducing the refractive index mismatch when the light enters the

tissue [28]. Samples were kept hydrated using PBS during imaging. Three-dimensional PS-OCT

scans were acquired, each covering a 4 × 4 (lateral) × 3 mm (depth) volume, with a resolution

of ≈ 16 µm [5, 27]. Typically, two to three adjacent scans were required to cover the majority of

each muscle. For muscle samples from the EBD-injected mdx mice, the presence of the dye

provided an indication of areas of muscle damage. This was used to guide imaging towards

regions that included a boundary between damaged and undamaged areas of muscle. For muscle


73

samples from the non-EBD-injected mdx mouse, regions for imaging were selected using a real-

time display of the PS-OCT phase retardation signal. For muscle samples from the C57 wild-

type mice, the regions for imaging were selected to cover the whole muscle.

Fig. 3.12. Schematic of PS-OCT imaging system and experimental setup. The imaging beam is weakly

focused into the muscle sample by the objective lens setup to a depth of 300 to 400 µm (depending on the

region of interest) from the coverslip. The beam is raster-scanned over the sample surface by the xy-

galvanometer mirror scanner. The PS-OCT system guides light using a single-mode optical fiber (blue

line in the schematic).

(d) Post PS-OCT imaging histology. Immediately after imaging, the muscle samples were

carefully moved onto cork boards to preserve their orientation. The samples were fixed to the

cork with tragacanth gum or pins to prevent any movement, before being preserved either by

freezing in liquid nitrogen-cooled isopentane, or fixed in formaldehyde solution (Confix Clear

pH 7.0, AB1020.1000C; Australian Biostain) for future histological analyses. This ensured as

much as possible that the subsequent histological sections were obtained parallel to the plane of

the PS-OCT birefringence images. Histologic preparation was carried out on a series of 8-µm-

thick sections that were obtained on a cryomicrotome with 120-µm intervals between adjacent

sections throughout the depth of tissue, and stained with hematoxylin and eosin (H&E).

Histological sections were digitally photographed at 20× magnification (Scanscope XT; Aperio

Technologies, Vista, CA). Muscle regions in H&E-stained histological sections were classified

as either normal-appearing or necrotic, on the basis of visual inspection of the photographed

sections. Examples of normal-appearing muscle histology and two stages of necrotic muscle

histology are shown in Fig. 3.13.


74

Fig. 3.13. Representative H&E-stained histological sections of mdx muscles sectioned longitudinally. A:

normal-appearing region. The myofibers possess intact sarcolemma and nonfragmented sarcoplasm. The

muscle region exhibits a clear anisotropic structure. B: necrotic region with fragmentation of sarcoplasm

and minimal evidence of inflammation (early stage necrosis). The myofibers have begun to degenerate,

and thus the arrangement of myofibers is disordered. Compared with A, the anisotropic structure of the

muscle is clearly degraded. C: necrotic region with inflammation, marked by numerous blue-stained

nuclei. The myofibers are degenerated with fragmented sarcoplasm. The muscle structure is highly

degraded compared with A.

(e) Generation of parametric PS-OCT birefringence images and calculation of percentage

necrosis. The method of generating parametric PS-OCT images of birefringence is described

fully by Chin et al. [5], but is summarized here for completeness. Each voxel in the acquired 3-

D PS-OCT data set was converted into a 4-element Stokes vector, S = [I, Q, U, V]T, representing

the polarization state of light backscattered from that location in the tissue [1]. A standard OCT

image was formed using the I component of the Stokes vector, and because PS-OCT detects

only the fully polarized component of the light backscattered from tissue, Ŝ = [Q, U, V]T, the

reduced Stokes vector (hereafter, Stokes vector) was sufficient to fully describe the polarization.

The Stokes vectors were smoothed to reduce noise through convolution with a Gaussian kernel

of width equal to twice the resolution of the PS-OCT system. Any changes in polarization due

to the components of the PS-OCT system were treated as lossless and constant during imaging,

so the birefringence of the tissue could be extracted from the rate of change of the phase angle,

or phase retardation, of the smoothed Stokes vectors with depth into the tissue [1, 34]. The

phase retardation with depth, φr(zi), in radians, between the smoothed Stokes vectors Ŝref at the

tissue surface and Ŝ(zi), at a depth zi into the tissue, is given by

φr(zi) = cos-1( (Ŝref • Ŝ(zi))/(||Ŝref||×||Ŝ(zi)||) ), where • is the 3-D vector dot product, and the

subscript i denotes the discretization of the PS-OCT signal in the z dimension. The Hilbert

transform, H, along the z dimension was used to demodulate φr(zi) to yield the wrapped phase

φw(zi) = tan-1(H(cos(φr(zi))) / cos(φr(zi))), which in turn was unwrapped to give

φu(zi) = unwrap(φw(zi)). The birefringence, Δn, at each lateral (x, y) location across the surface of

the tissue sample, was calculated as Δn = δφu × λ0/(4π), where λ0 is the mean wavelength of the

PS-OCT system (1325 nm), and δφu is the slope of φu(zi), obtained using linear regression on


75

φu(zi) over a physical range of 50 µm to 550 µm from the tissue surface (determined from the

OCT signal by taking the tissue refractive index as 1.4) [9].

The resulting 2-D collection of values was used to define a parametric image of birefringence,

where each value specified the image intensity at a corresponding lateral (x, y) location, and is

represented graphically using a false-color map, as shown in Figs. 3.14D, 3.15D, and 3.16D.

Blue indicates a high birefringence value; red indicates low birefringence. At locations where

there was insufficient signal to calculate the fitting over the full 500-µm range, the

corresponding region in the parametric image is encoded as white. The resulting color-coded

parametric image was then compared against colocated H&E-stained histological sections.

(f) Coregistration of images. As mentioned previously, a 3-D OCT data set was generated

from the I component of the Stokes vector form of the 3-D PS-OCT data set. The two data sets

are thus automatically coregistered. The 3-D PS-OCT data set was used to generate the

corresponding 2-D PS-OCT birefringence image, and on the basis of size, geometry, and

features of interest shown in the birefringence image, the colocated 2-D OCT slice in the x-y

plane with the best correlated features was chosen from the 3-D OCT data set. The OCT data

were presented as log-scaled signal-to-noise-ratio intensity with an approximate dynamic range

of 40 dB.

From the stack of H&E-stained histological sections (8 µm thick, 120 µm apart), a single

representative section was chosen from the first nine sections in the stack. This representative

section was selected on the basis of a visual correlation of features between the histological

sections, photographs of the sample taken during the imaging experiment, the 2-D OCT image,

and the 2-D PS-OCT birefringence image. It should be noted that there are small discrepancies

between the PS-OCT birefringence image and the corresponding OCT image or H&E-stained

histological section because the PS-OCT birefringence image contains 3-D information,

whereas the OCT image and H&E-stained histological section contain only 2-D information.

These 2-D images were used for visual comparison of the discernible features using the

different methods. The calculation of muscle necrosis was performed using multiple histological

sections.

(g) Automated calculation of the percentage of muscle necrosis from PS-OCT

birefringence images. The birefringence measurements were thresholded to automatically

distinguish normal-appearing tissue from necrotic tissue. The threshold was empirically

calculated from four training data sets with matching histology, and then applied to all

remaining PS-OCT data sets, giving an estimate of the percentage of muscle necrosis within

each imaging region. Birefringence values above 0.5 × 10-3 were deemed to indicate normal-

appearing/healthy tissue regions, and birefringence values below this threshold were deemed to

indicate necrotic tissue. The relative areas of necrotic muscle and normal-appearing/healthy

muscle were automatically calculated by counting the number of pixels in the birefringence


76

images that lay below or above the threshold value, respectively. The percentage of muscle

necrosis in each PS-OCT data set was then automatically calculated as the ratio of the area of

necrotic muscle to the total area of muscle tissue in that data set. These percentage values were

subsequently compared with the corresponding percentage values, which were manually

estimated from histological sections of the volume of tissue represented by the PS-OCT images.

(h) Manual estimation of the percentage of muscle necrosis from histological sections.

Reference estimates of the percentage of necrotic tissue were obtained by manually delineating

necrotic areas in the regions of the histological sections corresponding to the regions of the PS-

OCT scans of the mdx mouse muscles. Photographs of the H&E-stained histological sections

were manually segmented into necrotic and normal-appearing regions to a granularity of

individual myofibers. Because PS-OCT scans a volume of tissue, each scan corresponds to a

stack of histological sections through the depth of the sample. For each stack of histological

sections, the percentage volume of muscle necrosis was calculated on the basis of the first nine

sections (8 µm thick, 120 µm apart) from the top of the sample to ensure that the stack covered

the range measured by PS-OCT. For each histological section the region corresponding to the

area within the PS-OCT imaging FoV was located by visual coregistration of the section with

the PS-OCT birefringence image, the OCT images, and the preceding histological sections in

the stack. The areas of necrotic and normal-appearing tissue were then marked and calculated

by manual assessment.

A relative measure of the amount of necrotic tissue within the PS-OCT imaging volume was

estimated from the histological sections as the sum of the area of necrotic tissue from the FoV

of the first nine sections. Similarly, a relative measure of the amount of muscle tissue, both

necrotic and normal appearing, within the imaging volume was estimated as the sum of the area

of both necrotic and normal-appearing tissue from the FoV of the nine sections. The percentage

of necrotic tissue within the imaged volume was then calculated as (summed necrosis area) /

(summed necrosis area + summed normal-appearing area) × 100%, and compared with the

corresponding percentage value calculated from the PS-OCT birefringence image. To assess

interobserver variability in this manual scoring, a test set comprising of 10 histological sections

photographed at 20× magnification was blindly scored by two trained observers. The test set

consisted of 10 randomly selected H&E-stained sections taken from 7 different muscles from 4

of the EBD-injected mdx mice. The interobserver variability was calculated as the mean

absolute difference of the percentage necrosis as assessed by these two observers.

3.7.3 Results

Three representative sets of images are shown in this section. Two of them (Figs. 3.14 and 3.15)

are of dystrophic muscles that were taken from two exercised mdx mice, and display areas of

necrosis. The third set of images (Fig. 3.16) is a control set from healthy muscle tissue from a

C57 wild type mouse. Each set contains four colocated images – a photograph of the excised


77

muscle, an H&E-stained histological section, an OCT image, and the calculated PS-OCT

birefringence image showing corresponding features of interest.

Figure 3.14 A shows a photograph of an EBD-stained, excised, mdx mouse triceps muscle. The

necrotic region is visible by its darker blue staining relative to the rest of the muscle. The

corresponding H&E histology is shown in Fig. 3.14B, with areas of necrosis identified by

fragmented muscle fibers and the appearance of purple-stained, basophilic inflammatory cells

(with examples marked by * symbols). Figure 3.14, C and D shows the colocated OCT image

and the parametric birefringence image computed from the PS-OCT data acquired on the intact,

fresh (prefixation) tissue. The OCT image shows striations corresponding to intact myofibers

and an area of low (dark) signal in the region of necrosis, in agreement with previously

published findings (23, 24). The parametric birefringence image demonstrates a clear distinction

between the high birefringence of the region of undamaged tissue (blue and green) and the

region of necrosis (red). The corresponding values for the birefringence extracted from the PS-

OCT signal are indicated by the color bar to the right of Fig. 3.14D.

Fig. 3.14. Colocated images of dystrophic triceps muscle from a treadmill-exercised mdx mouse. A:

photograph of the whole muscle showing EBD staining. B: H&E histology of a frozen tissue section from

within the tissue volume imaged by PS-OCT. C: OCT log-scaled en face intensity image of intact whole

muscle, 0.73 mm from the top surface of the sample. D: parametric birefringence image. * indicates

necrotic regions with inflammation, which correspond to the low-birefringence regions within the

parametric birefringence image D.

Figure 3.15 shows a large region of necrosis present in a triceps muscle from a different mdx

mouse, enclosed on either side by normal-appearing muscle tissue. There is a clear

correspondence between the region marked by EBD (Fig. 3.15A), areas of inflammatory cells

and degraded myofibers in the histology (Fig. 3.15B), and the region of low birefringence

observed in the PS-OCT image (Fig. 3.15D). These regions are notably less well differentiated

in the standard OCT image (Fig. 3.15C), with faint striations still visible in the area of necrosis.


78

Fig. 3.15. Second representative set of colocated images of dystrophic triceps muscle from a second

treadmill-exercised mdx mouse. A: photograph of the whole muscle showing EBD staining. B: H&E

histology of a frozen tissue section from within the tissue volume imaged by PS-OCT. C: OCT log-scaled

en face intensity image of intact whole muscle, 0.52 mm from the top surface of the sample. D:

parametric birefringence image. * indicates regions with necrosis, including inflammation and fragmented

myofibers. Both of these regions correspond to the low-birefringence regions within the parametric

birefringence image D.

Figure 3.16 shows colocated images of healthy muscle taken from a C57 wild-type mouse. The

H&E histology (Fig. 3.16B) shows all myofibers to be intact and well organized. The OCT

image (Fig. 3.16C) shows a generally consistent striation pattern over the entire imaging region.

Similarly, the parametric birefringence image of Fig. 3.16D measured a high birefringence

(healthy/normal-appearing muscle) across the entire imaging field (blue and green). Some

localized artifacts of low birefringence are present, due primarily to hairs and surface dirt

obstructing and distorting the imaging light beam. Such small particles proved difficult to

remove from the surface of the fresh tissue without risking damage to the samples.

Fig. 3.16. Quadriceps muscle from a C57 wild-type mouse. A: photograph of the whole muscle showing

Evans blue dye staining. B: H&E histology of a frozen tissue section from within the tissue volume

imaged by PS-OCT. C: OCT log-scaled en face intensity image of intact whole muscle, 0.57 mm from

the top surface of the sample. D: parametric birefringence image. Small patches of unusually low

birefringence are believed to be caused by occasional hairs and small particles of nontissue substances on

the surface of the tissue distorting the PS-OCT measurements.

Figure 3.17 shows the comparison between the manually estimated (from H&E histology) and

automatically calculated (from PS-OCT) percentage of necrotic tissue within corresponding

regions of dystrophic mdx mouse muscle samples. This comparison involves the 11 scans (with

matching histology) from 7 different muscle samples from 5 different EBD-injected mdx mice.


79

Although histology covers the entire muscle, this comparison is calculated only for the areas of

the muscle samples that lay within the 4 × 4 mm FoV of the PS-OCT scans. The mean

difference between the percentage necrosis calculated from PS-OCT and from histology was ≈

2%. The error bars indicate the calculated interobserver variability for manual scoring of the

H&E histology; 4.1% ± 4.7%, mean ± SD (standard deviation), calculated from the 10 test

sections.

Fig. 3.17. Comparison of percentage necrosis evaluated using histology (white bars) and PS-OCT (black

bars) for 11 scans of selected 4 × 4 mm regions within 7 muscle samples from 5 mdx mice. Scans 1 and 2

are two different regions from the left quadriceps of mdx mouse 1. Scans 3 and 4 are two different regions

from the right triceps of mdx mouse 1. Scans 5, 6, and 7 are three different regions from the right

quadriceps of mdx mouse 2. Scan 8 is a region from the right triceps of mdx mouse 2. Scan 9 is a region

from the right triceps of mdx mouse 3. Scan 10 is a region from the right tibialis anterior of mdx mouse 4.

Scan 11 is a region from the right gluteus of mdx mouse 5. Error bars indicate the calculated interobserver

variability for manual scoring of the H&E histology. The mean difference between the percentage

necrosis calculated from PS-OCT and from histology is ≈ 2%. The interobserver variability for manual

scoring of the H&E histology is 4.1% over all 10 test sections, with an SD of 4.7%.

3.7.4 Discussion

We have presented a new technique for the automated quantification of the amount of necrosis

in fresh (unfixed) muscle tissue on the basis of a method for calculating birefringence from 3-D

PS-OCT scan volumes. Visual assessment of the extent of necrosis may be made by inspection

of the generated parametric birefringence images, and automated quantification of the

proportion of necrotic tissue may be performed by thresholding of the birefringence values. We


80

suggest that this technique has the potential to complement current histological and imaging

methods.

The optical birefringence of muscle tissue is primarily a result of the anisotropic structural

organization of the myofibrils, and not of their genetic encoding [6, 18]. For this reason, healthy

muscle tissue, regenerated muscle tissue, and regions of normal-appearing tissue in dystrophic

muscle exhibit comparable birefringence, allowing this technique to distinguish between

normal-appearing and necrotic tissue in dystrophic muscle. Similarly, we noted that muscle

tissue loses its birefringence at an early stage of the necrosis process, as seen for example, in the

center right in Fig. 3.15, B and D. The histological section in Fig. 3.15B shows the myofibers in

this region to be still relatively intact, although starting to fragment, but the birefringence in Fig.

3.15D is comparable to the regions in the center left of the image, which consist of highly

fragmented myofibers.

We used systemic injection of EBD to guide imaging toward those muscle regions likely to

contain necrosis. EBD stains necrotic regions dark blue due to the enhanced permeability of

damaged myofibers. Note that whereas EBD was used to aid in the validation, it is not required

in general usage of the technique. The imaging of a control, EBD-free mdx mouse was used to

confirm that PS-OCT imaging is not affected by the presence or absence of EBD (data not

shown). Treadmill exercise of mdx mice is also not required to perform PS-OCT imaging, but

has been used here simply to increase the proportion of necrotic tissue assessed within these

experiments.

Examination of individual histological sections provides a detailed 2-D assessment of the

integrity of individual myofibers; however, the parametric birefringence images provide a more

concise representation of the amount of necrosis within the 3-D volume. Differences in the

estimated percentage (≈ 2%) of necrotic tissue between an observer manually scoring H&E-

stained histological sections and the proposed automated method were found to be comparable

to the interobserver variability (4.1 ± 4.7%, mean ± SD). In general, the parametric

birefringence images show good visual correspondence to the H&E-stained sections. However,

we note small discrepancies between the parametric birefringence images and specific H&E-

stained histological sections. This is due in part to the histological sections being 8 µm thick,

whereas the birefringence image aggregates information over a 500-µm-thick volume of the

tissue. For example, the band of low birefringence to the left of the birefringence image in Fig.

3.14D is not visible in the corresponding histologic image, Fig. 3.14C; however, an examination

of subsequent and preceding histological sections reveals a region of fragmentary myofibers

corresponding to this band of low birefringence. Additionally, tissue is subject to shrinkage and

deformation during freezing and histological staining [20, 48], and this has the potential to

affect both the location and relative size of areas of necrosis and normal-appearing tissue. It is

also extremely difficult in practice to obtain a histological section in precisely the same


81

orientation as the plane of the birefringence image, and this could further increase the

discrepancy between features visible in the histological sections and in the birefringence

images. We have conservatively attributed features visible in the PS-OCT birefringence images,

but not in the histological sections, to imaging artifacts; for example, the band of higher

birefringence to the right in Fig. 3.14D, or the small regions of low birefringence in Fig. 3.16D.

However, such imaging artifacts make only a small contribution to the estimates of the

proportion of necrotic tissue, accounting for the good correspondence between the manual and

automated estimates of the percentage volume of muscle necrosis.

Furthermore, we note that the measured birefringence of the muscle is dependent upon the

orientation of the myofibers with respect to the optical beam. The maximum birefringence will

be measured when the PS-OCT beam is oriented perpendicular to the longitudinal axis of the

myofibers. In this case, the generated birefringence image will correspond to a histological

section that cuts longitudinally across the myofibers. When the PS-OCT light beam is parallel to

the longitudinal axis of the myofibers, no birefringence will be detected even in healthy or

normal-appearing regions of the muscle sample. If the sample contains myofibers oriented in

multiple directions, then PS-OCT imaging will tend to underestimate the birefringence of

myofibers that are not oriented parallel to the plane of the birefringence image. However, the

expected orientation of the myofibers is typically well understood from the morphology of the

muscle, allowing optimization of the direction of PS-OCT scanning.

Muscle samples often exhibit regional variations in the severity of necrosis, as illustrated by the

range of values for the proportion of necrotic tissue shown in Fig. 3.17 (i.e., for the same muscle

from the same mouse, when acquired over a 4 × 4 mm subset of the muscle). This may cause

difficulties in estimating the overall necrosis within dystrophic muscle when employing a PS-

OCT system with a limited FoV (less than 10 × 10 mm). Within this study, scans were guided

by the use of EBD as a marker of necrosis. In practice, multiple acquisitions across the muscle

would be required during the assessment. However, recent improvements in OCT image

acquisition rates (49) could potentially allow larger scans to be acquired in real time.

One challenge in extending the use of PS-OCT to an in vivo setting is its limited penetration

depth in tissue, typically 1-2 mm. However, it has been shown that an OCT probe may be

miniaturized and encased in a medical needle [8, 32, 35, 51]. OCT needle probes capable of

acquiring 3-D data volumes have been reported down to a size of a 30-gauge needle (outer

diameter 0.31 mm) [29, 32], substantially smaller and less invasive than standard biopsy

needles. Such an imaging probe could be used interstitially to image muscle structure in situ. A

single needle scan, because it can image a greater area of muscle tissue, may be as informative

as tissue removal, sectioning, and histological analysis. Insertion of a fine needle at several

locations within one large muscle is potentially far more informative (and less invasive) than a

single biopsy.


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3.7.5 Conclusion

This paper presents a new technique that utilizes PS-OCT to image dystrophic skeletal muscle

in a mouse model to estimate the proportion (volume fraction) of necrosis using a fully

automated algorithm. PS-OCT detects the optical birefringence in skeletal muscle tissues with

high birefringence values (> 0.5 × 10-3) indicative of healthy skeletal muscle tissue and normal-

appearing regions in dystrophic muscle tissue. Low birefringence values (< 0.5 × 10-3) are

indicative of necrotic (damaged) regions of myofibers (both early and later stage damage

indicated by inflammation) within dystrophic muscle. This report presents the first 3-D PS-OCT

data volumes from both dystrophic and healthy mouse skeletal muscle samples, as well as the

first quantitative color-coded parametric images differentiating normal-appearing from necrotic

regions within skeletal muscle on the basis of calculated optical birefringence values. The

percentage of necrotic tissue within the imaged locations on whole muscles was calculated and

found to correspond well (mean difference of ≈ 2%) to manual assessment of H&E-stained

histological sections. This technique has the potential to provide a complementary, minimally

invasive modality for analyzing and assessing the pathology of muscular dystrophy in situ.

3.7.6 Acknowledgements We thank Dr Gavin J. Pinniger, School of Anatomy, Physiology & Human Biology, The University of

Western Australia, and Dr Hannah Radley-Crabb, Curtin University, for discussions and suggestions

relating to muscle physiology. We thank Ms Leonie Khoo, CELLCentral, The University of Western

Australia, for the preparation of the H&E-stained histological sections. The authors acknowledge the

facilities, and the scientific and technical assistance of the Australian Microscopy & Microanalysis

Research Facility at the Centre for Microscopy, Characterization & Analysis, The University of Western

Australia, a facility funded by the University, State and Commonwealth Governments.

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3.8 Related works

3.8.1 The injected EBD does not significantly affect the detected birefringence

Evans blue dye has been widely used as a non-toxic in vivo marker of myofibre damage in

muscle imaging [55, 368]. EBD can be administrated via intravenous or intraperitoneal

injection, and specifically binds to serum albumin forming EBD-albumin conjugate (EBA). As

the sarcolemma of a necrotic or damaged myofibre within dystrophic muscle is abnormally

permeable, serum albumin and EBA can penetrate through the abnormal sarcolemma into the

myofibres. This allows damaged myofibres to be macroscopically identified due to EBD’s

striking blue colour [368, 369] (Fig. 3.18a), and microscopically visualised with fluorescence

microscopy due to EBD’s red fluorescence emission [368-371] (Fig. 3.18b). We employed EBD

in the quantitative assessment of muscle damage as an indicator of regions with high potential

for necrosis, which are required for further PS-OCT imaging. We hypothesised that the presence

of EBD, as well as the form of EBA, would not significantly affect the detected birefringence of

the tissue, because both EBD and EBA are small and homogeneous molecules. This hypothesis

can be expressed as followed: the detected low birefringence from the necrotic regions within

exercised dystrophic muscle is caused by the muscle damage instead of the injected EBD or

formed EBA. To test this hypothesis, an mdx mouse (dystrophic) muscle sample that had not

been administered with EBD was imaged using PS-OCT.

The acquired parametric birefringence map from PS-OCT and the colocated H&E histology of a

frozen tissue section from within the same tissue volume are shown in Fig. 3.19 a and b,

respectively. The red regions (labeled with *) in the birefringence map indicate those regions

with low birefringence (< 0.5 × 10-3). These regions show fairly good correspondence with the

necrotic regions within the H&E histological section (labeled with *). This suggests that the

absence of EBD hardly affect the loss in birefringence caused by necrosis within the dystrophic

muscle. Loss of birefringence detected under PS-OCT resulted from the disorder of muscle

ultrastructure that was caused by muscle damage or necrosis and, thus, has no large relevance to

the presence or absence of EBD.


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Fig. 3.18 EBD shows as (a) striking blue colour in necrotic regions within dystrophic muscle, which can

be identified macroscopically and (b) red auto-fluorescence in necrotic regions within dystrophic muscle,

which can be observed via fluoresence microscopy [55].

Fig 3.19 (a) The corresponding histological section of the EBD-free treadmill-exercised mdx mouse

muscle. Colocated necrotic regions are labeled with *, exhibiting low birefringence (red) in the

parametric birefringence map and (b) the parametric birefringence map.

3.8.2 Manual estimation of percentage necrosis within histological sections

In Section 3.8.2 (h), the percentage necrotic area for each stack of histological sections was

calculated manually using the first nine sections (8-µm thick, 120-µm apart). For each of these

nine sections, the imaged region (4 mm × 4 mm) was manually chosen based on the image co-

registration with the birefringence map. We assumed that the PS-OCT imaging depth was

strictly perpendicular to each histological section surface within the corresponding histology

stack. The histological sections with selected imaged regions were imported into the analysis

software, Image-Pro Plus (MediaCybernetics®). Both the area of the sample and the area of the

necrosis within the selected imaged region were manually identified and measured. Fig. 3.20

shows 11 representative histological sections (from 11 stacks, one section each) and their


89

corresponding measurements. The percentage area of necrosis was calculated by dividing the

total area of necrosis of the first nine histological sections within one stack by the total sample

area. The 11 acquired percentage values are listed in Table 3.4, according to the values shown in

Fig. 3.20.


90


91

Fig. 3.20 Representative histological sections with manual identification and measurement of the necrosis

areas and sample areas inside the images. The necrotic regions, as well as the region of the sample within

the section, were manually selected and marked by the black or yellow lines. Then the areas of these

regions are automatically measured by the software. The percentage of the necrosis area is calculated by

dividing the sum of the necrosis area by the sample total area. The green words are labels of the selected

regions (e.g., PG11 indicates the 11th polygonal region). Representative sections of (a) to (k) are from the

imaged histology stacks 1 to 11, respectively. Scale bars indicate 100 µm.

Table 3.4 The manually measured and calculated percentage values of each histological section and

histology stack. *Because of the different employed slicing protocol, 8 sections were measured within the

11th stack.

Section level 1 2 3 4 5 6 7 8 9 Average

Stack 1

Stack 2

Stack 3

Stack 4

Stack 5

Stack 6

Stack 7

Stack 8

Stack 9

Stack 10

Stack 11

25.4 31.7 35.3 35.9 16.4 21.5 16.5 14.4 12.4 22.8

2.4 22.2 14.9 12.4 6.8 6.6 5.4 5.8 6.4 8.7

94.7 95.5 77.3 51.2 36.3 34.7 32.7 41.0 29.6 49.9

85.9 95.2 72.5 60.0 61.1 63.6 34.2 38.7 49.8 58.9

6.6 17.2 26.0 30.3 31.2 25.6 29.9 41.2 59.7 31.1

12.6 9.9 10.9 13.8 12.1 19.9 19.1 14.2 16.2 14.6

5.9 8.0 7.8 12.2 5.8 9.9 4.5 7.5 5.4 7.5

60.3 68.5 70.4 69.0 65.7 61.7 65.0 61.5 60.8 64.6

54.7 46.3 35.6 37.5 33.4 38.2 29.5 33.2 23.1 37.1

34.7 31.5 24.9 28.0 27.8 16.5 15.5 26.1 12.0 24.4

37.8 45.3 48.6 55.6 50.5 46.8 38.6 42.4 N/A* 46.16


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3.9 Chapter summary

The birefringence of skeletal muscle tissue provides a new contrast mechanism that can be used

for the quantitative analysis and assessment of muscle necrosis within dystrophic muscle. PS-

OCT is able to measure tissue birefringence and, thus, can be used to quantify the amount of

necrosis within exercised mdx mouse muscle.

In this chapter, a theoretical overview and discussion of optical polarisation and birefringence

has been presented. The polarisation of a light beam is specified using the SoP, which can be

described by either the Jones formalism (comprising Jones vectors and Jones matrices) or

Mueller-Stokes formalism (comprising Stokes vectors, Mueller matrices; Stokes vectors can be

additionally represented as points on the Poincaré sphere). A theoretical description of a generic

bulk-optic PS-OCT system has been provided using the Jones formalism in this chapter.

Following the description of polarisation theory in this chapter, birefringence of skeletal muscle

has been discussed. A literature review of the measured birefringence of various skeletal

muscles, as well as a discussion of the physiological basis of muscle birefringence, has been

given. Birefringence in skeletal muscle can be divided into intrinsic birefringence and form

birefringence. Intrinsic birefringence is caused by the anisotropic structure of each individual

myofilament (i.e., a myosin or actin filament), whilst form birefringence is caused by the highly

organised arrangement of these myofilaments. Moreover, previous studies have demonstrated

that the form birefringence is dependent on the state of muscle contraction.

In this chapter, two published journal papers (with minor modifications in the first paper) on the

subject of PS-OCT are presented. The first one, “En face parametric imaging of tissue

birefringence using polarization-sensitive optical coherence tomography”, demonstrates a newly

developed computational algorithm to measure the birefringence in PS-OCT scans, which

generates a 2D parametric image, and maps the birefringence measured at every point on the

surface of a tissue sample. This algorithm was validated by using a model of thermally induced

damage in porcine tendon. The second paper, “Quantitative assessment of muscle damage in the

mdx mouse model of Duchenne muscular dystrophy using polarization-sensitive optical

coherence tomography”, presents the first application of this algorithm on the analysis of PS-

OCT imaging data of dystrophic muscle. This study shows that en face birefringence maps

generated from PS-OCT can be used to identify areas of necrosis, as validated against H&E-

stained histology, and can additionally be used to automatically quantify the amount of muscle

necrosis in mdx mouse muscle samples, to an accuracy of within 2% when compared to manual

quantification using the standard of H&E-stained histology.

In the last part of this chapter, additional work related to the PS-OCT scanning of muscle tissue

has been presented. Additional experimental results showed that EBD, used to visually locate

areas of probable necrosis, had no discernible impact on the measurement of birefringence


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within muscle samples using PS-OCT. Finally, the manual procedure for calculating the

percentage necrosis within the imaged muscle samples has been described in detail.

Chapter 4 - Needle probes for OCT

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Chapter 4

Needle probes for OCT

4.1 Preface

As a high-resolution optical imaging modality, conventional OCT has been restricted in clinical

and in vivo pre-clinical imaging applications due to its limited penetration depth of 2 - 3 mm

within opaque tissue [323, 372]. The limited penetration depth is due to its reliance on the

reflectance measurements using low-power, nonionising near infrared (NIR) light [317, 373],

which is significantly scattered and to a lesser extent absorbed when propagating within opaque

tissue.

The limited penetration depth of OCT can be overcome by using endoscopic OCT probes,

including catheter-based and needle-based probes. Mechanical insertion of these probes allows

them to deliver incident light into hollow tissues, such as the gastrointestinal tract [299, 374-

376] and airways [377-380], and also solid tissues such as the lungs [301, 302] and skeletal

muscle [381]. Mechanical insertion of the needle-based OCT probes into the solid tissue,

however, leads to tissue damage. As a result, there is a demand for highly miniaturised probes

that minimise the damage caused to tissues during scans.

In this chapter, we review endoscopic OCT probes, specifically catheter-based and needle-based

probes. In Section 4.3, two published papers are presented describing the development of an

ultrathin side-viewing OCT needle probe, and the application of this probe to imaging animal

lung tissue in situ. In Section 4.4, two additional published papers are presented. The first

describes the design of two optical-fibre-based OCT probes that have an extended depth of

focus, overcoming a basic restriction of miniaturisation, that the beam depth of focus is limited.

The other paper provides an accurate modeling of the light propagation within the OCT probes

involving graded-index optical fibres.

4.2 Review of endoscopic OCT probes

4.2.1 Catheter-based OCT probes

Catheter-based OCT probes are used to image natural lumens, such as the gastrointestinal tract,

airway, and blood vessels. Hence, almost no trauma will be caused by the insertion of such

probes. A generic catheter-based OCT probe typically consists of core optics assembled with

optical fibres, which are encased in a protective plastic catheter. Focusing optics are involved at

the distal end of the probe, which focus the beam using a length of graded-index fibre [382] or a

small graded-index (GRIN) lens [383]. Most catheter-based OCT probes are side-viewing, and


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deflect the light beam perpendicular to the length of the probe. Deflection is achieved by either

a micro-prism [384-387] or a mirror [388, 389]. More recently, forward-imaging probes have

been developed to scan using a microelectromechanical system (MEMS) mirror [390, 391], or a

piezoelectric cantilever that deflects the fibre over the scanning range [392].

Catheter-based OCT probes can scan linearly or radially. A linearly scanning probe will use a

translation stage at the proximal end to move the probe back and forth. This allows the

construction of a 2D image based on a sequence of radial A-scans [393]. This linear scanning

mechanism has been employed in imaging the urinary tract (e.g., bladder), larynx and uterine

cervix [394]. Compared to linear scanning, which can only generate 2D images, radial scanning

can generate 3D images by combining a sequence of 2D images generated by rotating the probe

and translating it (usually backwards, termed “pullback”). This allows a more complete view of

the lumen and has been applied to scanning the gastrointestinal tract [374], colon [395], cardiac

blood vessels [396] and airways [377, 397]. Catheter-based OCT probes for imaging large

lumens (e.g., gastrointestinal tract) are often large. The diameter of such probes can be 2 mm

[387] or more [386, 398]. The diameter of intravascular probes, however, is restricted to ~1 mm

[383, 384] or less [382] by the size of blood vessels.

4.2.2 Needle-based OCT probes

Although widely employed in visualising ultrastructures within lumens, catheter-based OCT

probes are not able to image areas deep inside solid tissues. Instead, needle-based OCT probes

(i.e., OCT needle probes) are required. These needle probes consist of focusing optics encased

in a hypodermic needle and can be inserted and positioned deep in the solid tissues to image the

area of interest [372]. However, during the insertion of OCT needle probes, there is often some

trauma caused to the tissue. This trauma can be minimised by miniaturising the probe. The

reported sizes of OCT needle probes, corresponding to the size of the used hypodermic needles,

range from 19 gauge (G) to 31G, with outer diameter ranging from 1.067 mm to 0.254 mm.

These sizes are smaller than the typical size of biopsy needles [399].

A forward-imaging OCT needle probe was used by Iftimia et al. to image biological tissues

[400, 401]. The optics were inserted through the bore of a 23G needle and aspiration of the

tissue during imaging was achieved by the suction created by an attached syringe. However,

because focusing optics were not incorporated into this OCT needle probe, the imaging depth

was limited by the diverging light beam.

A more widely used OCT needle probe is the side-viewing one. The optics of a side-viewing

OCT needle probe consist of a length of single-mode fibre (SMF) that transports light from the

scanner to the probe. Focusing optics, usually involving a length of no-core fibre (NCF) and a

length of GRIN fibre, are spliced to the end of the SMF. A deflection mechanism is employed to

redirect the light beam perpendicular to the axis of the needle tubing (Fig. 4.1), and can include

an angle-polished ball lens [402, 403], microprism [323], or mirror [301, 404] at the proximal


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end of the probe. Creating an angle-polished surface at the end of the optics is another

mechanism used to achieve the deflection [314, 405, 406]. The pullback rotation, which

combines both radial and linear scanning mechanisms is widely employed in scans using these

side-viewing OCT needle probes and allows the generation of 3D data volumes [372].

An in depth discussion of the design and fabrication challenges inherent in OCT needle probes

is given in [319].

Fig. 4.1 Side-viewing OCT needle probes with different deflection mechanisms: (a) angle-polished ball

lens [403]; (b) microprism [323]; (c) angle-polished mirror [301]; and (d) angle-polished surface at the

end of the optics [314].

4.3 Development of ultrathin needle probes for OCT imaging

4.3.1 Preface

Two published journal papers are presented in this section. To minimise the trauma caused by

the insertion of an OCT needle probe into tissues, we have developed the smallest side-viewing

OCT needle probe ever known that has an outer diameter of 0.31 mm (corresponding to a 30G

hypodermic needle). The design and fabrication of this ultrathin side-viewing OCT needle probe

is presented in the first paper. The second paper describes the application of two types of OCT

needle probes, including this ultrathin needle probe, to the in situ imaging of lung tissue.

4.3.2 Ultra-thin side-viewing needle probe for optical coherence tomography

[Dirk Lorenser, Xiaojie Yang, Rodney W. Kirk, Bryden C. Quirk, Robert A. McLaughlin, and David D.

Sampson; Optics Letters, 36(19): 3894-3896, 2011]

OCT needle probes [1] are an enabling technology for minimally invasive interstitial imaging of

solid tissues and organs. To minimize trauma resulting from needle insertion in applications

such as imaging of small animals or delicate organs, it is desirable to use very thin needle sizes.

Non-scanning forward-viewing needle probes using gradient-index (GRIN) fiber lenses [2,3]

have been demonstrated with sizes down to 31G (outer diameter (OD) 0.26 mm) [3]. However,

2D or 3D imaging is only practical with side-viewing needle probes which are significantly


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more challenging to miniaturize, as they require a micro-mirror to deflect the beam. The

smallest demonstrated side-viewing needle had a size of 27-gauge (OD 0.41 mm) [1], limited in

size by the necessity to insert and align a micro-prism inside the needle. A higher level of

miniaturization can be achieved with all-fiber designs employing an angle-polished fiber tip as a

beam deflector. Whilst this concept has been partially realized in early work [1-3], no validated

working prototypes of such needle probes with OCT imaging results have been reported. Angle-

polished fiber tip reflectors pose two substantial challenges. Firstly, the output beam acquires

significant astigmatism as it exits the fiber cladding, which acts as a cylindrical lens. Secondly,

the application of a metallic or dielectric reflective coating to the polished end face is

problematic, as the simultaneous coating of the beam output window must be avoided.

Therefore, this concept has only been employed in catheter-type probe assemblies which allow

the use of an uncoated reflector under total internal reflection [4], or the elimination of the

astigmatism with index matching fluid [5]. However, this results in larger probe diameters due

to the enclosing catheter lumen.

In this Letter, we show that all-fiber probes incorporating angle-polished fiber tip reflectors can

be designed to yield probe beams with sufficient depth-of-field and sensitivity for practical

imaging applications. We describe the fabrication and optical characterization of a 30G (OD

0.31 mm) needle probe based on this design, which we believe is the smallest side-viewing

OCT needle probe demonstrated to date, and validate its performance by acquiring 3D OCT

images of lamb lungs. A schematic of our probe is shown in Fig. 4.2a. The distal focusing

optics consist of a 290-µm section of no-core fiber and a 126-µm section of GRIN fiber

(GIF625, Thorlabs, USA) spliced to the end of a single-mode fiber (SM800, Fibercore, UK). An

additional section of no-core fiber is added after the GRIN section, and polished at an angle of

45° using a fiber connector polishing machine (SpecPro 4L, Krelltech, USA). A metal coating

consisting of a 10-nm chrome adhesion layer and a 300-nm gold layer is applied to the angle-

polished fiber tip using a thermal vacuum deposition machine (see Fig. 4.2c). The Cr/Au

combination was chosen because of its good adhesion properties and because it is a reliable and

well-established process in our facility. The coating had a measured reflectivity of ~50%,

indicating that the chrome layer introduces significant losses. A reflector material such as

aluminium (R = 87% at 840 nm), which can be deposited directly without an adhesion layer,

should yield better reflectivities. The thermal vacuum deposition process is ideal since the metal

atoms travel on a line-of-sight trajectory from the source to the sample and therefore the beam

output window of the probe can be protected by orienting it to face away from the source. After

coating, the fiber probe is mounted inside a 30G needle with an output window that is fabricated

via electrochemical etching (see Fig. 4.2d) using a custom-made setup.


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Fig. 4.2. (a) Schematic of the needle probe design. NCF: no-core fiber; GRIN: gradient-index fiber; SMF:

single-mode fiber (b) Illustration of the astigmatism induced by the fiber cladding. (c) The angle-polished

fiber probe after deposition of the metal coating. (d) Close-up view of the tip of the assembled 30G needle

probe, showing the electrochemically etched side-window.

The output beam of the fabricated probe was measured with a beam profiler (SP620U, Ophir-

Spiricon, USA). The Gaussian fit diameters agree well with the simulated diameters obtained

from paraxial ray matrix theory for Gaussian beams [2], as shown in Fig. 4.3a (the gradient

parameter g of the GRIN fiber was 5.75 mm-1). The strong cylindrical lens effect at the glass-air

interface focuses the output beam in the x-direction and produces an astigmatism ratio (ratio of

the y and x waist diameters) of 3.9. However, when the needle probe is inserted into biological

tissue, the fiber is either adjacent to solid tissue or immersed in aqueous tissue fluids, which

reduces the astigmatism due to the lower refractive index contrast. The simulation shows that

for immersion in water (n = 1.329), the astigmatism ratio is reduced to 1.8, with waist diameters

of 7.7 µm and 13.6 µm in the x- and y-directions, respectively (Fig. 4.3b). The calculated on-

axis intensity of the elliptical beam (Fig. 4.3b) exhibits a pronounced peak close to the focus of

the x direction at a distance of ~300 µm from the fiber, which can be considered as the working

distance of the probe, with a full width at half-maximum (FWHM) of 275 µm. The maximum

diameter of the probe beam stays smaller than 30 µm over a distance of 550 µm, making it

suitable for OCT imaging at good-to-moderate resolutions over this entire range. For 3D OCT

imaging, the 30G needle probe was mounted on a rotation/pullback mechanism and interfaced

with a fiber-based 840-nm spectral-domain OCT (SD-OCT) system as shown in Fig. 4.4a. The

SD-OCT system incorporates a wavenumber-linear spectrometer (Hyperion 830, Thorlabs HL

AG, Germany) and a superluminescent diode source with 50-nm bandwidth and 23-mW output

power (S-840-B-I-20, Superlum, Ireland). The measured axial resolution after spectral

reshaping and numerical dispersion compensation is 9.3 µm in air (7 µm in water).


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Fig. 4.3. Output beam characteristics of the fabricated 30G needle probe. (a) Simulated and measured

beam diameters in air. (b) Simulated beam diameters in water (n = 1.329), as well as the calculated on-

axis intensity of the astigmatic probe beam.

The sensitivity of the needle-based SD-OCT system was compared to that of a standard galvo-

scanning sample arm configuration (collimator, x/y galvanometers, scan lens). At 2 µs exposure

time and a reference arm power of 4.7 µW, the galvo-scanning sample arm configuration had a

measured sensitivity of 91 dB, whereas the needle-based configuration had a measured

sensitivity of 84 dB. The theoretical shot-noise-limited sensitivity is 99 dB. For the needle-

based configuration, the sensitivity was determined for the water-immersed needle probe by

measuring the SNR of a reflection from a fused-silica (FS) prism surface (n = 1.453), resulting

in a -27 dB Fresnel reflection (see Fig. 4.4b). The solid line shows the averaged A-scan signal

obtained when the water/FS interface (peak 5) is at a distance of 488 µm from the fiber. Peak 1

is due to backscattering from imperfections of the angle-polished fiber-tip reflector and peak 2

is the backreflection from the fiber/water interface. Peaks 3 and 4 are autocorrelation artifacts of

peak 5 with peaks 1 and 2, respectively, appearing broadened after numerical dispersion

compensation. The maximum SNR of 57 dB, corresponding to a sensitivity of 84 dB, is

obtained at a distance of ~300 µm from the fiber, which is consistent with the output beam

profile simulation in water (Fig. 4.3b).


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Fig. 4.4. (a) Schematic of the 840 nm SD-OCT system. PC: polarization controller; A: attenuator; M:

mirror. (b) SNR measurement of the 30G needle probe immersed in water at 2-μs exposure time. Solid

line: A-scan showing the reflection from a water/glass interface (peak 5). Peak 2 is the fiber/water

interface, see text for peaks 1, 3, 4. Dashed line with markers: SNR of the water/glass reflection peak

versus distance from the fiber.

The difference in the sensitivities of the two configurations can be explained by examining the

round-trip loss RT of the sample arm, defined as the fraction of the returning power from a unity

reflector placed in the probe beam. For a given exposure time and reference arm power, the

system sensitivity will be proportional to S, defined as the fraction of the source input power

returning to the spectrometer via the sample arm for a unity reflector [6], with S being

proportional to RT of the sample arm. For the galvo-scanning sample arm, we measured RT = -

2.7 dB, whereas we obtained RT = -10 dB for the needle sample arm (using a silver mirror

reflector under water immersion). The difference of 7.3 dB closely matches the 7 dB difference

of the measured sensitivities. The relatively high RT of the probe is mainly due to the low

coating reflectivity (~6 dB double-pass loss), with the remaining ~4 dB attributable to non-ideal

back-coupling of the probe beam into the SMF due to astigmatism.

Fig. 4.5 shows a 3D OCT scan of preterm lamb lung (excised) filled with amniotic fluid and

further inflated with saline, imaged with the 30G needle at an exposure time of 13 µs. Radial B-

scans, each comprising 800 A-scans were acquired by counter-rotating the needle over a range

of 360 degrees at a rate of 1 Hz. The needle was translated in steps of 5 µm between B-scans.

The images resolve the extensive network of alveoli as well as bronchioles, with a useful

imaging range of ~600 µm, which is consistent with our probe beam characterization. In this

scan, the zero delay was located between peaks 1 and 2 of Fig. 4.4b. This resulted in a mirror


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image of peak 1 which obscured the central portion of the image and which had to be

suppressed via a fixed-pattern-noise removal algorithm [7]. This is not an intrinsic limitation of

our probe, however, as it can be avoided by adjusting the reference arm delay to locate both

peaks 1 and 2 in the positive half-space of the image. The very thin 30G needle caused very

little tissue damage and deformation during insertion and rotation compared to the 23G

(diameter 0.64 mm) needles used in previous work [8], and no deflation or leakage of the lung

was observed after the needle was retracted.

Fig. 4.5. OCT images of a lamb lung obtained with the 30G needle probe. (a) A single radial B-scan. (b)

Cutaway view of a rendered volume consisting of 400 B-scans. The length of the cylindrical volume is 2

mm and the diameter is 1.66 mm. A: alveoli; B: bronchiole.

In conclusion, we have fabricated and fully optically characterized a 30G side-viewing OCT

needle probe. When immersed in aqueous tissue fluids, the astigmatic probe beam has a

working distance of 300 µm, with beam diameters below 30 µm over a depth of field of

550 µm. With low-loss reflection coatings of the angle-polished reflector, needle probes of this

type should allow imaging with sensitivities well in excess of 90 dB with state-of-the-art SD-

OCT systems at exposure times on the order of 10 µs. Imaging of a lamb lung was performed at

840 nm with an imaging range of ~600 µm, showing delineation of individual alveoli and

bronchioles, demonstrating that the ultra-thin probe is capable of generating useful 3D

interstitial OCT images of biological tissue whilst achieving the smallest probe size yet reported

for a side-facing OCT needle probe.

References

[1] X. Li, C. Chudoba, T. Ko, C. Pitris, and J. G. Fujimoto, Opt. Lett. 25, 1520 (2000).

[2] Y. Mao, S. Chang, S. Sherif, and C. Flueraru, Appl. Opt. 46, 5887 (2007).

[3] W. A. Reed, M. F. Yan, and M. J. Schnitzer, Opt. Lett. 27, 1794 (2002).

[4] H. Li, B. A. Standish, A. Mariampillai, N. R. Munce, Y. Mao, S. Chiu, N. E. Marcon, B. C.

Wilson, A. Vitkin, and V. X. D. Yang, Laser. Surg. Med. 38, 754 (2006).


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[5] M. S. Jafri, S. Farhang, R. S. Tang, N. Desai, P. S. Fishman, R. G. Rohwer, C. M. Tang, and

J. M. Schmitt, J. Biomed. Opt. 10, 051603 (2005).

[6] R. Leitgeb, C. Hitzenberger, and A. Fercher, Opt. Express 11, 889 (2003).

[7] S. Moon, S. W. Lee, and Z. Chen, Opt. Express 18, 24395 (2010).

The paper presented above describes the design and fabrication of the ultrathin side-viewing

OCT needle probe. The application of this probe in imaging the biological tissue will be

presented in the paper in the following section. In the next paper, two types of OCT needle

probes, the ultrathin side-viewing OCT needle probe and a dynamic OCT probe, were applied to

imaging samples of animal lung tissue. In the ultrathin side-viewing OCT needle probe, the

focusing optics is rigidly encased within the needle, allowing a high degree of miniaturisation.

In the dynamic OCT needle probe, a more complex scanning mechanism is utilised, which

comprises a small OCT needle encased within a larger needle. This reduces the miniaturisation

possible for the larger, enclosing needle. A range of designs were available for the internal OCT

needle. We chose to use the design first published in [301]. Smaller internal needles are feasible.

However, our goal within this chapter is to provide a proof-of-principle of the operation of a

dynamic OCT needle probe, which is achieved using the design from [301]. Microscopic

structures, such as alveoli, were clearly visualised from the acquired imaging data.

4.3.3 Static and dynamic imaging of alveoli using optical coherence tomography needle

probes

[Robert A. McLaughlin; Xiaojie Yang; Bryden C. Quirk; Dirk Lorenser; Rodney W. Kirk; Peter B. Noble;

David D. Sampson; Journal of Applied Physiology, 113(6): 967-974, 2012]

Abstract

Imaging of alveoli in situ has for the most part been infeasible due to the high resolution

required to discern individual alveoli and limited access to alveoli beneath the lung surface. In

this study, we present a novel technique to image alveoli using optical coherence tomography

(OCT). We propose the use of OCT needle probes, where the distal imaging probe has been

miniaturized and encased within a hypodermic needle (as small as 30-gauge, outer diameter

310 µm), allowing insertion deep within the lung tissue with minimal tissue distortion. Such

probes enable imaging at a resolution of ~12 µm within a three-dimensional cylindrical field of

view with diameter ~1.5 mm centered on the needle tip. The imaging technique is demonstrated

on excised lungs from three different species: adult rats, fetal sheep, and adult pigs. OCT needle

probes were used to image alveoli, small bronchioles, and blood vessels, and results were

matched to histological section. We also present the first dynamic OCT images acquired with an

OCT needle probe, allowing tracking of individual alveoli during simulated cyclical lung

inflation and deflation.


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(a) Introduction

For the study and assessment of lung physiology, both in healthy tissue and in the presence of

respiratory disease, lung imaging is a particularly informative approach. Imaging of lung tissue

has the potential to reveal structural, functional and anatomical abnormalities that may occur in

disease or following acute lung injury. For example, thickening or degradation of alveoli walls

in chronic disease [1, 23], changes in lung elastance [7, 13, 47, 48] and the innate heterogeneity

of disease processes are all properties that can be assessed by an appropriate in vivo imaging

device. The development of new, more effective ways to image the lung is an important area of

respiratory science.

Unlike airway passages (i.e., bronchi) which are accessible by high resolution computed

tomography (HRCT), an approach utilized routinely in clinical research [6, 24, 38, 39], imaging

of alveoli presents particular challenges. The high resolution required to discern individual

alveoli and the depth of the tissue being imaged has, for the most part, prevented real-time

visualization of alveoli. X-ray micro-computed tomography has been used to image fixed lung

samples from mice [43], rats [27], pigs [30] and humans [52]. Such imaging provides exquisite

anatomical detail, but is restricted to ex vivo samples, which are subject to tissue shrinkage and

distortion as a result of the fixation process. Intravital [26] and confocal microscopy [44] have

been used with some success to image alveoli in rats. However, this is restricted to imaging

alveoli at the very surface of the lung due to the limited penetration depth of these imaging

modalities, in the latter case to a depth of 30 µm. Other more indirect approaches have also been

applied, notably 3He diffusion magnetic resonance imaging (MRI) [18] which provides

estimates of alveolar volume and surface area by characterizing the pattern of 3He diffusion

through the lungs and combining this with geometrical models of idealized alveolar ducts.

These techniques are non-invasive and lend themselves to dynamic studies, although the limited

spatial resolution of the underlying MRI acquisitions means that these measurements are not

able to image individual alveoli.

Optical coherence tomography (OCT) is a high-resolution optical imaging modality, based on

reflectance measurements using low power, non-ionizing near-infrared light [11, 12]. It has

been used to quantify airway size in both animal models [41, 42] and in vivo in humans [35, 54-

57]. Ex vivo studies have also shown that OCT may be used to image individual alveoli [4, 19],

and in vivo OCT imaging using a thoracic window has been demonstrated in both mouse and

rabbit models [3, 36, 37]. While conventional OCT has a tissue penetration depth of only 2-

3 mm, this limitation can be overcome by use of OCT needle probes [8, 31, 46, 59], wherein the

optics have been miniaturized and encased within a hypodermic needle. Needle OCT facilitates

access to deeper regions of the target tissue with an acquisition time sufficient to provide

information on dynamic tissue properties.


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In this paper, we examined the utility of a new lung imaging technique using OCT needle

probes, allowing high-resolution static and dynamic visualization of parenchymal structures

deep within the lung. We present two OCT needle probes designed by our group: the first,

encased within a 30-gauge needle, is designed to minimize tissue distortion and damage; and the

second, encased within a larger 18-gauge needle, is optimized for dynamic imaging and tracking

of individual alveoli. In the present study, the needle probes were used to image ex-vivo lung

lobes from three different species: adult rats, fetal sheep, and adult pigs. Our findings

demonstrate the capacity for OCT needle probes to image alveoli, small peripheral airways and

blood vessels deep within lung tissue. We show the first co-registered OCT-histology image

pairs acquired with a 30-gauge OCT needle probe. This probe is half the size of that used in the

acquisition of previously published comparable lung images [46], resulting in substantially less

trauma-induced artifact. In addition, this paper presents the first published dynamic OCT needle

images of alveoli during lung inflation and deflation.

(b) Materials and methods

(i) Animal Handling

All animal experiments conformed to the American Physiological Society’s Guiding Principles

in the Care and Use of Animals. Animal tissue was obtained from animals sacrificed as part of a

different research project approved by the University of Western Australia Animal Ethics

Committee, and tissue was utilized under institutional tissue sharing protocols. Three different

species were used: rats, sheep and pigs. Adult rats (Wistar, n = 2) were euthanized by CO2

inhalation. One pre-term fetal merino lamb (144 days gestation, term = 150 days) was delivered

by caesarian section and overdosed by pentobarbitone (250 mg/kg IV). Rats and sheep were

exsanguinated prior to removal of lung lobes. One adult White Landrace pig was sedated with

tiletamine/zolazepam (4.4 mg/kg IM) and xylazine (2.2 mg/kg IM) and exsanguinated under

pentobarbital sodium anesthesia (30 mg/kg IV).

(ii) Excised lung lobes

Animals were sacrificed on the day of experiment and dissection was performed immediately

post mortem. Scans were acquired between 1 and 4 hours after dissection. During this period

lungs were kept moist with Krebs solution to prevent tissue dehydration. Rat and sheep lung

lobes were used for static OCT needle imaging, and pig lobes for dynamic OCT needle imaging.

Rat and pig lobes were excised and allowed to deflate passively for 1-2 hr. Following tracheal

cannulation, lungs were inflated by a syringe filled with Krebs solution or isotonic saline. The

pre-term lamb lung containing amniotic fluid was clamped at the trachea prior to excision to

prevent fluid drainage. The trachea was subsequently cannulated and inflated as above. Prior to

scanning, lungs were laid horizontally with the anterior surface facing downwards and cycled

several times between 0 and 30 cmH2O (tracheal pressure) as determined from a fluid-filled

column connected in series with the trachea. Static imaging was performed under a fixed


105

positive distending pressure. For dynamic imaging, pressure was cycled between 0 and

20 cmH2O to simulate cyclical lung inflation and deflation. The external surface of the lungs

was kept moist throughout the duration of the experiments.

(iii) OCT imaging

OCT, described in detail in [11, 12], acquires images of tissue by illuminating a biological

sample with a focused beam of near-infrared light, and detecting the component of this light that

is backscattered (reflected). Backscattering from different depths within the tissue is separated

through a process referred to as interferometry, giving a narrow, one-dimensional depth scan

focused into the tissue at a specific location. A schematic of the imaging set-up is shown in Fig.

4.6. The OCT scanner is interfaced to an OCT needle probe [8, 29, 34, 46, 59] through a length

of optical fiber. The OCT needle probe contains miniaturized optics to focus the light beam and

a small mirror to redirect the light beam perpendicular to the needle shaft. The light beam is

emitted through a small imaging window etched near the distal end of the needle, and is able to

image tissue up to 2-3 mm from the needle tip. The inset of Fig. 4.6 shows a photo of a probe

encased within a 30-gauge needle (outer diameter 310 µm).

Fig. 4.6. Schematic of optical coherence tomography (OCT) needle imaging system. Inset: photo of a 30-

gauge OCT needle probe. Units on ruler shown in inset are mm.

Within this study, we utilized a spectral domain OCT scanner developed in-house. With a

spectral domain system, reflections of the near infrared light beam are acquired simultaneously

from all depths in the sample. The detected signal is combined with a reference light beam using

interferometry, and the strength of backscattered light at each depth is extracted through a

Fourier analysis, as described in [11], giving a single depth scan. The light source used in our

setup has a central wavelength of 836 nm, and a spectral bandwidth of 50 nm giving a measured


106

axial resolution (along the length of the depth scan) of 9.3 µm in air (7 µm in water). Two

different OCT needle probe designs were utilized, illustrated in Fig. 4.7 and described below.

Fig. 4.7. Illustration of the functionality of the 2 types of OCT needle probes used in this work. A: the

static probe uses a counter-rotation/pull-back scan motion that enables acquisition of full 3-dimensional

(3-D) data sets but that is limited in image acquisition speed. B: the dynamic probe uses a fast-oscillating

linear scan motion that is capable of acquiring rapid sequences of 2-D image frames.

(iii) Static OCT Needle Probe

The static OCT needle probe was developed to acquire 3D OCT volumetric data sets. The small

caliber 30-gauge needle (outer diameter 310 µm) reduces tissue damage and can be used in

small animal models. This is the smallest caliber side-facing OCT needle probe reported to date.

Its design has been detailed elsewhere [31] but is briefly summarized here. To attain the

smallest possible probe diameter, the focusing optics consist of a miniaturized lens and side-

reflecting mirror constructed from different types of optical fiber. Counter-rotation of the probe

at 1 Hz provides a 2D image disc, centered on the OCT needle probe and with a radius of

approximately 600 µm. Serial consecutive 2D images are acquired as the probe is pulled back in

small steps of 5 µm to produce a 3D cylindrical volumetric dataset, as illustrated in Fig. 4.7A.

The average transverse resolution of the probe is 12 µm in tissue over a range of 600 µm.

(iv) Dynamic OCT Needle Probe

The dynamic OCT needle probe has been developed to acquire a rapid sequence of 2D OCT

images, allowing imaging of dynamic physiological processes, such as alveoli dynamics during

lung inflation/deflation. The probe consists of an inner imaging needle (outer diameter 720 µm)

that translates back and forth within an enclosing outer needle (outer diameter 1.27 mm). Details

of the focusing optics are given in [46]. In brief, light is transported from the scanner to the


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inner imaging needle probe along a length of single-mode optical fiber. Fused to the distal end

is a 270 µm length of GRIN fiber. Within the GRIN fiber, the refractive index of the fiber core

varies approximately quadratically, causing the light beam to converge and diverge periodically.

By cleaving the GRIN fiber at an appropriate length [32], it is possible to control the focal

length of the emitted light beam. The GRIN fiber was then terminated with a small copper

mirror, polished at an angle of 45°, to redirect the light beam at right angles to the needle axis.

The light beam is emitted through a slit window (length 20 mm) ground into the outer needle, as

illustrated in Fig. 4.7B. Each stroke of the inner probe acquires a 2D rectangular image, with the

long axis oriented along the needle. The linear motion has a rate of 3 Hz and a stroke of 12 mm,

allowing acquisition of a time sequence of 2D images. The average transverse resolution of the

probe is 15 µm in tissue, over a range of 700 µm. Image data was over-sampled, acquiring

1,600 axial depth scans (A-scans) per stroke, to allow for resampling of the image to account for

the sinusoidal probe translation.

(v) Post-imaging Histology

After scanning, 1 × 1 cm-wide sections were excised along each needle trajectory. The excised

tissue was fixed (4% formaldehyde), embedded in paraffin, and sectioned at 100 µm intervals in

accordance with standard laboratory procedures, and haematoxylin and eosin (H&E) sections

prepared. The histological sections were manually co-registered to the OCT data. The co-

registration utilized in-house visualization software to perform multiplanar reformatting of the

OCT data, allowing the extraction of arbitrary oblique slices. For each histological section, the

optimal oblique OCT slice was selected based on visual identification of multiple distinct

anatomical features, such as bronchioles and blood vessels.

(c) Results

(i) Static OCT Needle Probe

Fig. 4.8-4.9 show the first OCT needle probe images with matching histology in the small

animal models of rat and fetal lamb. The static OCT needle probe was used to successfully

visualize individual alveoli, small bronchioles and blood vessels.

Fig. 4.8 shows representative OCT images acquired on rat lungs. A radial image, constructed

from one full rotation of the OCT needle probe, is shown in Fig. 4.8A. The needle hole (labeled

n) is located at the center of the image, surrounded by alveoli and a small blood vessel (labeled

v1) to the left of the image. Each alveolar space presents as a small region of low backscatter

(dark gray), incompletely delineated by the more highly backscattering alveoli walls (light

gray).

Fig. 4.8B highlights the value of 3D imaging, showing the relative position of multiple vessels

and bronchioles not visible in a single radial image. A longitudinal OCT image was extracted

from the data volume, perpendicular to the radial image. Its location is indicated by the dashed

green line in Fig. 4.8A, and its horizontal axis was aligned along the direction of the needle


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retraction. A bronchiole (labeled b) and three vessels (labeled v1, v2, v3) are visible, showing

the correspondence with the matching H&E histology section in Fig. 4.8C. Orthogonal views of

vessel v1 are visible in both radial and longitudinal OCT images (Fig. 4.8A and Fig. 4.8B).

Fig. 4.8. Static OCT images of rat lungs. A: radial OCT image acquired from 1 rotation of the static OCT

needle probe. Dashed green vertical line shows location of the longitudinal image shown in B. B:

longitudinal reconstructed OCT image showing a bronchiole and multiple vessels, with the horizontal

axis aligned with the direction of needle retraction during scanning. Dashed cyan vertical line shows

location of the radial image shown in A. C: corresponding hematoxylin and eosin (H&E) section. n,

Needle hole; b, bronchiole; v1, v2, and v3, blood vessels.

Fig. 4.9 shows representative images acquired from a fetal sheep lung. Both radial (Fig. 4.9A)

and longitudinal (Fig. 4.9B) OCT images are shown, with matching histology for the latter.

Multiple matching bronchioles (labeled b1, b2) and vessels (labeled v1, v2, v3) are visible in

both the OCT and histological images, allowing manual co-registration of the images. The

needle tract (labeled n) is also visible in the histology image.

Some distortion of alveoli is apparent in the top left corner of Fig. 4.9A, which can be accounted

for by precession of the OCT needle probe and compression of the alveoli. The longitudinal

image of Fig. 4.9B was extracted from this region (location indicated by dashed green line in

Fig. 4.9A). Even with this needle-induced distortion, multiple bronchioles and vessels are

visible in the OCT imaging plane shown in Fig. 4.9B.

Fig. 4.9. Static OCT images of a fetal lamb lung. A: radial OCT image. Dashed green vertical line shows

location of the longitudinal image shown in B. B: longitudinal reconstructed OCT image. Dashed cyan

vertical line shows location of the radial image shown in A. C: corresponding H&E section. n, Needle

tract; b and b2, bronchioles; v1, v2, and v3; blood vessels.


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A 3D OCT rendered visualization of the fetal lamb lung is shown in Fig. 4.10. A video of the

3D rendered volume is available as Supplementary Video 1, which shows the first published

animated 3D volume rendering of data acquired with an OCT needle probe. Part of the

cylindrical data volume has been cropped to reveal the bifurcation of a pair of bronchioles. By

manipulating the rendered volume, it is possible to explore the complex 3D structures present in

the image data.

Fig. 4.10. Three-dimensional visualization of fetal lamb lung, showing alveoli and bifurcation of

bronchioles. This image is a frame from Supplemental Video 1. The length of the cylindrical data volume

is 2 mm.

(ii) Dynamic OCT needle probe

The dynamic OCT needle probe was used to track changes in anatomical features during a

period of simulated inflation and deflation of a pig lung. A video showing the multiple ‘breath’

cycles is available as Supplementary Video 2. Fig. 4.11A shows a still frame extracted at

maximum deflation, while Fig. 4.11B shows a frame extracted at maximum inflation. These

images are acquired parallel to the needle shaft (illustrated in Fig. 4.7B) as the internal imaging

needle is translated over a range of several millimeters. In Fig. 4.11, the OCT needle probe is

positioned along the top of the image, with the light beam orientated downwards. The void at

the top of the image shows a narrow saline-filled region immediately adjacent to the needle.


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Fig. 4.11. Screen shots from animation acquired with the dynamic OCT needle probe, showing simulated

deflation A and inflation B in a pig lung. See Supplemental Video 2 to view the dynamic sequence.

In the supplementary video, the apparent displacement of the parenchyma is influenced by

movement of the needle in response to the inflationary and deflationary forces. For this reason,

proximal alveoli appear to move little, while more distant alveoli are displaced a greater

amount. Alveoli displacement visualized with an OCT needle probe is relative to the position of

the needle.

(d) Discussion

Static and dynamic imaging of alveoli with OCT needle probes opens new possibilities for the

assessment of lung physiology in health and disease. The results presented here demonstrate a

high level of structural detail visible with an OCT needle probe, allowing visualization of

alveoli, bronchioles and vessels in situ. Furthermore, for examination of dynamic tissue

properties, the OCT needle probe has the capability to track the movement of individual alveoli

over a breath cycle.

In this proof-of-principle study, an excised lung model was utilized which provided direct

access to lung tissue structures, although for in vivo application, insertion through the chest wall

is feasible (see below). To maximize OCT image penetration depth, we chose to use liquid-

perfused lungs, i.e., saline or Krebs solution, or in the case of the fetal lung, amniotic fluid. Our

early experimental work with air-filled lungs found that strong optical reflections at each air-

tissue interface rapidly attenuated the OCT signal. The introduction of a liquid medium into the

lungs reduces the optical refractive index mismatch at each air-tissue interface, allowing the

near infrared light beam to penetrate through multiple alveolar spaces. In addition, this

prevented tissue dehydration and the associated distortion of structural and mechanical lung

properties [17]. The use of a liquid medium removes the air-liquid interface and reduces

alveolar surface tension [58], altering the forces exerted on cells in the alveolus and increasing

the degree of lung distension for a given pressure. It is, therefore, likely that in the present study

alveoli are larger than they may be in an air-filled lung. However, this approach may afford


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some advantage in that tissue displacements measured reflect the intrinsic mechanical properties

of the parenchymal tissue. In vivo extensions of these measurements are feasible through the use

of bronchoalveolar lavage [9, 51] or whole lung lavage [2]. Notably, other exogenous refractive

index-matching liquids are available and could be used to optimize imaging depth. Imaging is

certainly possible in air-filled lungs, although with present probe designs, the imaging depth is

reduced to alveoli immediately adjacent to the OCT needle probe.

Translation from the excised lung model to the in vivo scenario is possible by inserting the

needle probe through the chest wall. As with transthoracic lung biopsies and fine-needle

aspiration biopsies, the use of OCT needle probes carries a risk of pneumothorax, or tissue

trauma due to the relative movement of the lung surface and the chest wall. In the present study,

introduction of the OCT needle probe was found to cause some local trauma to pulmonary

structures. Our development of a small caliber 30-gauge OCT needle probe, which is

significantly smaller than the needles currently used for lung biopsies, is an important step

forward in reducing these complications.

Earlier work [46] has shown the use of static OCT needle probes in larger animal models (pig).

The present study has demonstrated the first use of static OCT needle probes in small animal

models (rat, fetal lamb). Miniaturization of the OCT needle probe (outer diameter 310µm) has

been critical in extending the range of animal models for this imaging technique, with the needle

used in the current studies being less than half the outer diameter of the probe used in [46]. The

reduction in probe size has been possible by redesigning the distal focusing optics. The small

copper mirror present in earlier designs [34, 46], used to redirect the light beam at right angle to

the needle axis, has been replaced in the static probe with a gold-coated angle polished length of

no-core fiber [31].

Correlations were demonstrated between OCT needle probe images and matching H&E

sections. However, some differences were observed, due to imaging artifacts in both the H&E

preparation and the OCT image acquisition. In this study, the tissue adjacent to the OCT needle

probe was excised immediately after imaging, to assist in colocation of histology and OCT. The

difference in inflation between OCT imaging of the fresh tissue, and fixation of the excised

sample will have contributed to discrepancies between the OCT and histology images. Tissue

samples have also been shown to undergo shrinkage and deformation during histological

preparation [20, 33], with different tissues affected to different degrees [60]. Because of such

inhomogeneous distortion, there will be additional disparity between the optimal OCT imaging

plane and each histological section. Rotation of the needle probe during 3D imaging also

resulted in some tissue drag. Alternative OCT needle probe designs have been proposed to

minimize this by enclosing the imaging probe within a stationary catheter [29].

Of further consideration is the impact that breathing movements may have on the positioning of

the probe. During lung inflation and deflation, the needle will move with the surrounding


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parenchyma. As can be seen in Supplementary Video 2, distant alveoli appear to move more

than alveoli that are adjacent to the needle, as the displacement is visualized relative to the

needle position. However, by tracking the movement of the OCT probe [28, 61], it is possible to

calculate absolute displacement of the alveoli walls.

A feature of the present probe design is the capacity for assessment of lung viscoelastic

properties, which can be achieved by tracking the displacement of individual alveoli in response

to pressure fluctuations. Similar measurements have been performed with ex vivo tissue samples

using light microscopy and multi-photon microscopy [10, 15], and these small-scale

measurements have been correlated against whole lung measurements of elastance [5]. OCT is

capable of performing highly localized measurements of the viscoelastic properties of tissue, a

technique referred to as optical coherence elastography [21, 22, 49]. We note that dynamic OCT

needle probes may present the opportunity to perform such measurements in situ at different

locations and depths within the lung, which may be useful in the scenario of lung disease or

injury that is inherently heterogeneous.

In addition to the possible assessment of lung pathologies by needle OCT, there are number of

physiological questions that could be addressed by use of an OCT needle probe. For instance,

the mechanisms of lung volume expansion have been widely discussed in the literature [14, 47],

yet no established unifying model of alveolar mechanics has been accepted. A key question is

whether alveoli are recruited during respiration, or do they follow some model of expansion.

Different models of expansion include isotropic growth; growth which changes the shape of the

alveoli; or expansion through the folding and unfolding of the alveoli walls [16]. Techniques to

perform dynamic imaging of fresh (not fixed) or in vivo tissue are providing new insights into

these mechanisms. Endoscopic confocal microscopy [50] has been used to track alveolar

expansion in mouse lungs, and has shown evidence of alveolar recruitment driven by airflow

between alveoli via the pores of Kohn (40). 3He diffusion MRI studies of healthy human lungs

suggest inflation occurs primarily through recruitment in conjunction with anisotropic

expansion of the alveolar ducts [18]. We propose that OCT needle probes provide an alternative

imaging modality to explore the specific mechanisms of lung inflation (i.e., alveoli expansion

versus recruitment). In the present study, the excised lung lobe model was subject to alveoli

collapse, not only during the process of dissection but also as a result of deflation to 0 cmH2O

tracheal pressure (0 cmH2O transpulmonary pressure). We note that this is below the normal

physiological lung volume present at functional residual capacity, and that under these

experimental conditions inflation of the excised lung lobe likely involves considerable lung

recruitment. During the inflationary maneuver, alveoli recruitment as well as expansion of

individual alveoli was detected (see Supplementary Video 2). These observations provide proof-

of-concept that OCT needle probes have the potential to discern alveoli expansion and

recruitment. The dynamic OCT probe used in this study has a greater imaging field of view than

is possible in endoscopic confocal microscopy, and higher resolution than can be achieved with


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MRI. For measurements which require a higher resolution, our group has recently published a

confocal needle probe with a lateral resolution of 700 nm [45].

Methods for analysis of OCT needle probe data need further development; however,

quantification of 2D OCT images could be achieved through the use of stereological methods

for estimation of characteristics such as lung surface density and number of alveoli in a given

region [53]. By defining a number of random test lines spanning the 2D image and recording the

distance between adjacent intercepts with the alveoli walls, it is possible to accumulate an

estimate of the distribution of intra-alveoli chord lengths. The arithmetic mean and other

moments of this distribution provide a quantification of both average alveoli size and size

variation, as described in [25]. The high image contrast between the alveoli walls and the

enclosed airspace visible in the OCT images lends itself to analysis with image processing

techniques to discern the extent of each alveolus and allow automated stereological analysis of

OCT needle probe scans. Static OCT needle probes scans may be acquired in both deflated and

inflated states, provided that a constant lung pressure is maintained during each individual

acquisition. This would allow the use of stereological techniques to contrast lung characteristics

between these states.

(e) Conclusion

This paper describes the use of a new technique for pulmonary imaging using OCT needle

probes. These probes may be optimized for a range of applications, and we have described

specific designs for minimal caliber needle imaging of lung tissue in small animals models, and

for dynamic imaging of alveoli during simulated inflation and deflation. This paper has

presented the first published dynamic images acquired with an OCT needle probe, and the first

co-registered OCT-histology images acquired with a 30-gauge OCT needle probe. Individual

alveoli, bronchioles and blood vessels were visualized, and 3D rendering of the data allowed the

exploration of features such as bronchiole bifurcations. This technique has the potential to offer

new insight into a range of physiological properties, including alveolar mechanics and

morphometric analysis of parenchymal structures.

(f) Acknowledgements

The authors wish to acknowledge Prof. J. Pillow, UWA, Centre for Neonatal Research and

Education, for provision of the lung tissue used in this research.

(g) Grants

R. A. McLaughlin is supported by a fellowship from the Cancer Council Western. P. B. Noble

is supported by an NHMRC of Australia Biomedical Fellowship (513921). This project has

been supported by the Raine Medical Research Foundation and the National Breast Cancer

Foundation, Australia.

(h) Disclosure

The authors have no conflicts of interest.


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[60] Yeap BH, Muniandy S, Lee S-K, Sabaratnam S, and Singh M. Specimen shrinkage and its

influence on margin assessment in breast cancer. Asian J Surg 30: 183-187, 2007.

[61] Yeo BY, McLaughlin RA, Kirk R, W., and Sampson DD. Enabling freehand lateral

scanning of optical coherence tomography needle probes with a magnetic tracking system.

Biomed Opt Express 3: 1565-1578, 2012.

4.4 Alternative designs of OCT fiber probes for extended depth of focus with maintained

lateral resolution and sensitivity

4.4.1 Preface

Two published journal papers are presented in this section. In the first paper, two alternative

designs of ultrathin OCT needle probes that have an extended depth of focus (EDOF) whilst

maintaining lateral resolution and sensitivity are presented. Although these two designs are

forward-viewing, they have the potential to be used in side-viewing OCT needle probes if a

deflection mechanism, such as a microprism or mirror, is added. However, as mentioned in this

paper, attempts to fabricate the probe showed that the beam profile is sensitive to deviations of

the refractive index profile of the GRIN lens section from the ideal parabolic shape. We

confirmed this by computational simulation of the beam propagation within the GRIN lens. The

simulation results and the supporting experimental data are presented in the second paper.

All non-Gaussian beams with extended DOF exhibit a certain amount of sidelobe structure as

well as a resulting loss of signal in the main lobe. To illustrate this phenomenon, the relative

sidelobe intensity levels have been quantified in some specific examples presented in the two

papers (in percent of the central lobe peak intensity). Furthermore, the second paper introduces

the Strehl ratio as a quantitative measure of the loss of signal in the central lobe of aberrated and

wavefront-shaped beams.


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4.4.2 Ultrathin fiber probes with extended depth of focus for optical coherence

tomography

[Dirk Lorenser, Xiaojie Yang, and David D. Sampson; Optics Letters, 37(10): 1616-1618, 2012]

Ultrathin fiber-optic probes delivered via hypodermic needles enable imaging deep within

biological tissue using optical coherence tomography (OCT) [1, 2]. Using state-of-the-art

broadband light sources, such probes can image with high axial resolutions of a few

micrometers. However, it is not straightforward to increase their transverse resolution to similar

values without severely compromising the useful imaging depth range due to the strong

divergence of the tightly focused beam. This problem has been addressed in bulk-optic OCT

scanners by generating focal regions with an extended depth of focus (DOF) using axicons [3,

4] or pupil phase masks [5]. Unfortunately, it is not possible to simply scale down the bulk-optic

solutions to the dimensions of ultrathin fiber probes with diameters on the order of 125 µm, as

in the latter case the formation of the focal region takes place in a regime of Fresnel diffraction

where the optical design methods and approximations used in [3-5] are no longer valid. A first

demonstration of an ultrathin OCT probe using a fiber-tip micro-axicon [6] has shown that

pseudo-Bessel beams can still be generated from such structures at low Fresnel numbers, but

with a very short working distance and reduced DOF gain compared to their bulk-optic

counterparts. Rather than trying to mimic bulk-optic axicons, we have explored the use of phase

mask structures in the regime of low Fresnel numbers using numerical simulations based on the

beam propagation method (BPM). As a result of this, we demonstrate an extended-depth-of-

focus (EDOF) fiber probe design that uses a very simple phase mask consisting of a short

section of overfilled graded-index (GRIN) fiber, which can yield a DOF gain around 2.

The concept is illustrated in Fig. 4.12a. A normal lensed fiber is made by using a section of no-

core fiber (NCF) to expand the beam emitted by the single-mode fiber (SMF), and a section of

GRIN fiber to focus it with the desired NA. In order to make an EDOF probe, a phase mask

consisting of an additional short section of GRIN fiber with a smaller core diameter is appended

to the lensed fiber. The rays traced in Fig. 4.12a show that the effect of this arrangement can be

intuitively understood as a “double-focus” lens, with the small core of the phase mask affecting

only the central portion of the converging wavefront (see Fig. 4.12b). The output beam from

such a probe was simulated at a wavelength of 820 nm using a split-operator BPM algorithm

[7], where the propagation operator is applied in the spatial frequency domain after fast Fourier

transform (FFT) of the transverse field amplitude. The EDOF probe has design lengths of

LNCF = 300 µm, LGRIN = 190 µm and LPM = 14 µm, connected to SMF with a mode-field

diameter of 5.6 µm. The lens section is a 100-µm core diameter GRIN fiber with a gradient

parameter of g = 4.5 mm-1, and the phase mask is a 32-µm core diameter GRIN fiber with

g = 10 mm-1. The simulated output beam intensity in water (refractive index n = 1.33) is shown

in Fig. 4.12c. The full width half maximum (FWHM) beam diameter and the normalized on-


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axis intensity are shown in Fig. 4.12d. The minimum FWHM beam diameter (which

corresponds to the maximum OCT resolution) is 6 µm and the DOF is 874 µm. Compared with

an ideal Gaussian beam of the same minimum FWHM diameter (dotted curves in Fig. 4.12d), a

DOF gain of 1.9 is obtained at the cost of a 4.8-dB reduction of the peak signal-to-noise ratio

(SNR). The sidelobes visible in Fig. 4.12c have an intensity below 5% of the peak over most of

the DOF. In this work, we have chosen to define the DOF as the region over which the FWHM

beam diameter is smaller than twice its minimum value. This definition allows more tolerance

for beam width fluctuations in the focal region of non-Gaussian beam profiles than the Rayleigh

range criterion. We believe that this is justified since the Rayleigh range underestimates the

perceived useful imaging depth range in OCT. A 40% (factor of 2 ) change in transverse

resolution is hardly visible due to the effects of logarithmic compression of the images and

speckle.

Fig. 4.12. EDOF probe using a GRIN fiber lens and a GRIN fiber phase mask. (a) Schematic of the

design: PM, phase mask. (b) Illustration of the index profiles of the GRIN lens (green; upper line) and the

phase mask (blue; middle line) relative to the Gaussian beam intensity profile (red; bottom line): nclad,

cladding index. (c) Simulated output beam intensity distribution in water. (d) Simulated FWHM diameter

and normalized on-axis intensity of the output beam in water. The dotted lines show the values for an

ideal Gaussian beam. The vertical green lines indicate the boundaries of the extended DOF.

An alternative EDOF probe design is shown in Fig. 4.13a, in which a GRIN phase mask is used

in conjunction with a refractive lens.

The simulated output beam in water at 820 nm wavelength is shown in Figs. 2b and 2c for a

structure with lengths of LNCF = 340 µm, LPM = 20 µm and a hemispherical lens with RLens =


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80 µm and n = 1.7 (a typical value for photoresist). The GRIN phase mask has a 32-µm core

diameter and g = 10 mm-1. The minimum FWHM beam diameter is 6.5 µm and the DOF is

1060 µm. Compared with an ideal Gaussian beam of the same minimum FWHM diameter

(dotted curves in Fig. 4.13c), a DOF gain of 2 is obtained at the cost of a 5.2-dB reduction of the

peak SNR. The sidelobe intensity is below 5% of the peak over most of the DOF.

Fig. 4.13. EDOF probe using a refractive lens and a GRIN fiber phase mask. (a) Schematic of the design.

(b) Simulated output beam intensity distribution in water. (c) Simulated FWHM diameter and normalized

on-axis intensity of the output beam in water. The dotted lines show the values for an ideal Gaussian

beam. The vertical green lines indicate the boundaries of the extended DOF.

The EDOF probe designs presented in Figs. 4.12 and 4.13 are both tolerant of length errors of

up to ~20% in the GRIN phase mask section, and our fabrication method which uses a

micrometer translation stage mounted to the fiber cleaver can achieve this level of accuracy

(fabricated lengths are validated by inspection under a phase-contrast microscope). However,

attempts to fabricate designs of the type shown in Fig. 4.12 revealed that the beam profile is

sensitive to deviations of the refractive index profile of the GRIN lens section from the ideal

parabolic shape (which is often the case in commercial GRIN fibers [8]), and we were able to

confirm this in simulations (results not shown here). To experimentally validate our EDOF

probe concept, we therefore chose to fabricate a probe of the type shown in Fig. 4.13, which

avoids the use of a GRIN lens section, and we modified the design to use a phase mask

consisting of 50-µm core diameter GRIN fiber (GIF50, Thorlabs, USA) with g = 6.2 mm-1 (g

was obtained from fits of beam profiles of test structures). In order to overfill this GRIN fiber,

the beam from the SMF (SM800, Fibercore, UK) had to be expanded to a relatively large 1/e2

diameter of 52 µm, which resulted in a noticeable degradation of the beam quality due to the


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spherical aberration of the refractive lens. The achievable DOF gain in the simulation was,

therefore, limited to ~1.7. The fabricated structure is shown in Figs. 4.14a and 4.14b. It has

dimensions of LNCF = 400 µm, LPM = 32 µm and RLens = 68 µm, and the lens was made by

dipping into UV optical adhesive (Norland 81, Thorlabs, USA) with n = 1.56. The beam profile

was measured using a beam profiler (Ophir Spiricon, USA) and is shown in Fig. 4.14e (since

the refractive lens was designed for water immersion, the probe tip was immersed in a drop of

water on a microscope cover slip, and the profile was measured in air behind the coverslip). The

horizontal axis for the measured beam profile in Fig. 4.14e is rescaled by the refractive index of

water for comparison with the simulated beam profile in water. The simulation is in fairly good

agreement with the measured values, but the measured DOF of 980 µm is slightly lower than

the simulated one. The maximum resolution is 7 µm.

Fig. 4.14. Results for the fabricated EDOF probe. (a) Fiber probe before formation of the refractive lens.

The red arrow indicates the splice between the NCF and GRIN phase mask. (b) After formation of the

lens. (c) and (d) OCT images of lemon pulp, log scale with 35 dB dynamic range. (e) Measured and

simulated beam profile in water. The horizontal axes of plots (c), (d), and (e) are identical. The vertical

green lines indicate the boundaries of the DOF.

In order to demonstrate the achieved DOF gain, a normal refractive-lens fiber probe with the

same resolution as the EDOF fiber probe was fabricated, again using the process of dipping into

optical adhesive. Its dimensions are LNCF = 504 µm and RLens = 65 µm. The measured beam


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profile is shown in Fig. 4.15c, with the simulated curves showing good agreement with the

measured values. The asymmetric axial intensity distribution is caused by the spherical

aberration of the refractive lens. The DOF is 630 µm and the maximum resolution is 7 µm.

The measured DOF gain of the EDOF probe compared to the normal probe is therefore 1.55.

The question remains whether this DOF gain results in a visible improvement in the OCT

imaging performance. This was tested by interfacing both probes with an 840-nm SDOCT

system which has been described previously [2], with an axial resolution of 7 µm in water. OCT

images of a lemon pulp sample were acquired with an exposure time of 5.8 µs. The sample was

imaged through a microscope coverslip whilst the water-immersed fiber probe was scanned

laterally in 1-µm steps using a motorized stage. The results are shown in Figs. 4.14c and 4.14d

for the EDOF probe and in Figs. 4.15a and 4.15b for the normal probe. Two images are shown

for each probe, where the second image shows the same sample region as the first image, but

with the distance from the probe tip to the coverslip increased by ~800 µm in order to allow

clear imaging in the far range of the probe’s DOF without the effects of attenuation at depth due

to sample scattering. The regions of good image resolution correspond well with the measured

and simulated DOF of the two probes, indicated by the vertical green lines. We therefore

conclude that the DOF gain of 1.55 is a practically useful and visible improvement.

Fig. 4.15. Results for the fabricated normal refractive-lens probe. (a) and (b) OCT images of lemon pulp,

log scale with 35 dB dynamic range. (c) Measured and simulated beam profile in water. The horizontal

axes of plots (a), (b), and (c) are identical. The vertical green lines indicate the boundaries of the DOF.

In summary, we have presented a simple and power-efficient technique for extending the DOF

of ultrathin fiber probes for OCT using GRIN fiber phase masks which are spliced in series with


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the distal focusing optics and thereby require no additional fabrication processes. A DOF gain

of 1.55 compared to a conventional lensed fiber probe was demonstrated in a prototype device

with a lateral resolution of 7 µm. Using GRIN fibers with suitable parameters, our simulations

show that a DOF gain of 2 can be obtained at the cost of a modest reduction in peak SNR of

about 5 dB. Since modern preform fabrication processes can produce custom GRIN fibers with

high optical quality [8], this approach could facilitate the development of high-transverse-

resolution extended-DOF ultrathin needle probes for OCT.

References

[1] X. Li, C. Chudoba, T. Ko, C. Pitris, and J. G. Fujimoto, Opt. Lett. 25, 1520 (2000).

[2] D. Lorenser, X. Yang, R. W. Kirk, B. C. Quirk, R. A. McLaughlin, and D. D. Sampson, Opt.

Lett. 36, 3894 (2011).

[3] Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, Opt. Lett. 27, 243 (2002).

[4] R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, Opt. Lett. 31,

2450 (2006).

[5] L. Liu, C. Liu, W. C. Howe, C. J. R. Sheppard, and N. Chen, Opt. Lett. 32, 2375 (2007).

[6] K. M. Tan, M. Mazilu, T. H. Chow, W. M. Lee, K. Taguchi, B. K. Ng, W. Sibbett, C. S.

Herrington, C. T. A. Brown, and K. Dholakia, Opt. Express 17, 2375 (2009).

[7] M. D. Feit and J. A. Fleck Jr, Appl. Opt. 17, 3990 (1978).

[8] W. A. Reed, M. F. Yan, and M. J. Schnitzer, Opt. Lett. 27, 1794 (2002).

As mentioned in the paper presented above, for the design using an additional GRIN lens, there

was a discrepancy between the measured beam profile and the simulated one. It was

hypothesised that this discrepancy is due to the deviation of the refractive index profile of the

additional GRIN lens section from the ideal parabolic shape, which occurs in commercial GRIN

fibres fabricated by using modified chemical vapor deposition method. The measured beam

profile is sensitive to this deviation and, thus, interfered. In the paper presented in the next

section, this hypothesis is presented to be validated by accurately simulating the beam

propagation along the designed fibre probe with the additional GRIN lens section by means of

using the beam propagation method instead of ABCD matrix transformations.

4.4.3 Accurate modeling and design of graded-index fiber probes for optical coherence

tomography using the beam propagation method

[D. Lorenser, X. Yang, and D. D. Sampson; IEEE Photonics Journal 5(2): art. 3900015, 2013]

Abstract

Fiber-optic probes for sensing and biomedical imaging applications such as optical coherence

tomography (OCT) frequently employ sections of graded-index (GRIN) fiber to re-focus the

diverging light from the delivery fiber. Such GRIN fiber microlenses often possess aberrations

that cause significant distortions of the focused output beam. Current design methods based on


125

ABCD matrix transformations for Gaussian beams cannot model such effects and are therefore

inadequate for the analysis and design of high-performance probes that require diffraction-

limited output beams. We demonstrate use of the beam propagation method (BPM) to analyze

beam distortion in GRIN-lensed fibers resulting from ripples or a central dip. Furthermore, we

demonstrate the power of this method for exploring novel probe designs that incorporate GRIN

phase masks to generate wavefront-shaped output beams with extended depth-of-focus (DOF).

We present results using our method that are in good agreement with experimental data. The

BPM enables accurate simulation of fiber probes using non-ideal or custom-engineered GRIN

fibers with arbitrary refractive index profile, which is important in the design of high-

performance fiber-based micro-imaging systems for biomedical applications.

(a) Introduction

Miniaturized fiber-optic probes that can be delivered to deep-tissue locations via hypodermic

needles or catheters are an enabling technology that allows minimally invasive optical

biomedical imaging far beyond the normal depth penetration of light into biological tissues

using techniques such as optical coherence tomography (OCT) [1]-[3]. Fig. 4.16(a) shows a

schematic of a fiber-optic OCT imaging probe, consisting of an assembly of a single-mode fiber

(SMF) terminated with focusing optics and a side-deflecting micromirror inside a hypodermic

needle with a side opening, allowing the generation of 3-D images by rotation and pullback of

the needle after its insertion into the tissue region of interest [4]. In order to eliminate the need

for alignment of discrete micro-optical components, there has been a trend toward all-fiber

probe designs using no-core fiber (NCF) spacers for beam expansion and sections of graded-

index (GRIN) fiber that act as microlenses to focus the beam into the biological tissue for

imaging at high resolution [2], [5]-[7]. Such highly miniaturized all-fiber probes are amenable

to fabrication using established fusion-splicing technology, which is reproducible and self-

aligning, and which also ensures minimal losses and back reflections. Furthermore, we have

recently shown that this all-fiber probe concept includes the possibility of adding a GRIN phase

mask section after the GRIN lens section in order to generate a wavefront-shaped output beam

with extended depth-of-focus (DOF) [8], as illustrated in Fig. 4.16(b).

Fig. 4.16. (a) Schematic of a fiber-optic OCT needle probe. The focused output beam has a Gaussian

transverse intensity profile. SMF, single-mode fiber; NCF, no-core fiber; GRIN, graded-index fiber;

DOF, depth-of-focus. (b) Schematic of the same imaging probe as in (a), but with an additional GRIN


126

phase mask (PM), which generates an output beam with a non-Gaussian transverse intensity profile that

has similar transverse resolution but extended DOF compared to (a).

For high-performance OCT imaging, it is important that the probe optics introduces minimal

aberrations since the characteristics of the output beam determine the transverse resolution and

also directly impact on the sensitivity of the system (as the signal level obtained from a point-

like scattering object will depend on the peak intensity of the focused probe beam). One of the

current limitations of fiber-optic OCT probes lies in the optical quality of the GRIN fiber lenses,

as the probe designer is typically forced to choose from a finite range of commercially available

multimode fibers (MMFs), which are optimized for optical telecommunications rather than for

imaging. It was already recognized in early work that the refractive index profiles of such GRIN

MMFs can exhibit significant deviations from the parabolic shape required for them to act as

ideal GRIN lenses, which results in aberrations and sub-optimal optical performance [5], [9].

Improved preform fabrication methods [5], [10] have led to a new generation of high-bandwidth

GRIN MMFs with smooth refractive index profiles, which are free of the central index dip that

plaques legacy GRIN MMFs. However, these modern high-bandwidth GRIN MMFs are only

available with small core diameters of 50 and 62.5 μm, limiting their use to probe designs with

relatively low numerical aperture (NA) and working distance (WD). Furthermore, their index

profiles tend to exhibit a more or less pronounced deviation from the ideal parabolic shape that

is purposely introduced by the manufacturer in order to minimize intermodal pulse broadening

in the targeted operating wavelength band [11], [12]. Thus, large-core-diameter fibers drawn

from preforms of such high-bandwidth GRIN MMFs [5] will not necessarily behave as ideal

GRIN lenses.

The aberrations introduced by index profiles with non-parabolic shapes and central dips cannot

be modeled by current design methods based on ABCD matrix transformations for Gaussian

beams [13], as these assume a perfect square-law refractive index profile of the GRIN fiber.

ABCD matrix modelling has proven to be a useful framework for basic probe design and

analysis [2], [6], [7], [14], [15] and as a simple tool for calculating approximate values for the

GRIN fiber and NCF spacer section lengths, which can then be experimentally optimized to

yield the desired output beam characteristics [7]. However, for the development of next-

generation, high-performance OCT fiber probes, a more sophisticated numerical modeling

technique is required for two reasons. First, in order to achieve diffraction-limited resolution

and maximum sensitivity, it is necessary to quantify how imperfections of the GRIN fiber

profile influence the beam quality and focal spot intensity (Strehl ratio), particularly in probe

designs with high NA or long WD that may require the use of large-core-diameter GRIN fibers

of sub-optimal quality. Secondly, the development of novel probe designs of the type shown in

Fig. 4.16(b), which make use of GRIN fiber phase masks to generate non-Gaussian, wavefront-

shaped output beams with increased DOF, requires a rigorous diffraction modeling method that

can accommodate GRIN elements with arbitrary refractive index profiles.


127

Fig. 4.17. (a) Schematic of our BPM simulation geometry. (b) The N × N simulation grid with dimension

L sampled with increments Δx = Δy = L/N and with an absorbing boundary of radius Rabs. (c) The N × N

simulation grid in the spatial frequency domain sampled with increments Δfx = Δfy = 1/L with a guard

band of radius fguard.

In this paper, we demonstrate the application of advanced numerical modeling based on the

beam propagation method (BPM) [16], [17] to fiber-optic probes using GRIN lenses and phase

masks. The BPM can be used to simulate light propagation through GRIN fibers with arbitrary

refractive index profiles and to calculate the true 3-D diffracted field in the focal region of the

probe, from which the designer can extract a wealth of advanced performance metrics beyond a

rudimentary characterization in terms of WD and “spot size”, including Strehl ratio and DOF.

One of the great strengths of the BPM is its validity for systems of arbitrary Fresnel numbers

(The Fresnel number N = a2/(λL)) determines whether the imaging system operates in the “near

field” or in the “far field” of the diffraction pattern generated by the system aperture of radius a,

where L is the distance of the focal region from the aperture, and λ is the wavelength [18].).

Miniaturized fiber-optic probes for OCT are near-field systems with Fresnel numbers on the

order of unity, and for this reasons, it is difficult to extend their DOF by a straightforward

application of schemes developed for bulk-optic microscopes (e.g., pupil plane phase masks

[19] or axicons [20], [21]) since these are all derived under the assumption of large Fresnel

number. Thus, the BPM is a necessary tool for studying schemes for creating focal regions with

extended DOF in low-Fresnel-number systems such as fiber-optic probes.

The remainder of this paper is divided into three main sections. In Section 2, we describe our

implementation of the BPM algorithm and its application to the problem of GRIN fiber probes,

including a brief discussion of its numerical accuracy. In Section 3, we use the BPM to analyze

beam distortions resulting from index profile aberrations that are common in commercial GRIN

fibers, and we demonstrate good agreement with experimental data. In Section 4, we explore the

performance of a novel probe design incorporating an axicon-like GRIN phase mask to generate

a Bessel-like output beam with extended DOF.

(b) Numerical modeling technique

The general simulation geometry used in this paper is illustrated in Fig. 4.17(a) [22]. The

launched fundamental mode from the SMF is treated as an ideal Gaussian beam with a 1/e2


128

waist diameter equal to the mode field diameter (MFD) of the SMF, and its complex field

amplitude at the location of the NCF/GRIN interface is used as the input to the BPM simulation.

In the GRIN fiber lens, in the (optional) GRIN fiber phase mask, and in the sample medium, the

field is numerically propagated with BPM step sizes Δzlens, Δzpm, and Δzout, respectively (the step

sizes are not necessarily identical as the BPM accuracy constraints differ in the various

sections.). The field is sampled on a N × N Cartesian grid of dimension L, as illustrated in Fig.

4.17(b). As the BPM algorithm switches back and forth between the spatial and spectral

(spatial-frequency) domains, the field is also represented by its discrete Fourier transform on an

N × N spectral grid of dimension N/L, as shown in Fig. 4.17(c). In order to prevent the sampled

wave amplitude from exceeding the boundaries of the spatial and spectral grid during the

numerical propagation, we have implemented two simple but effective measures. First, we

apply an “absorbing boundary” (a 2-D window function) to the field amplitude in the spatial

domain at every BPM step in order to prevent large-angle diffracted light from reaching the

edges of the grid and causing artifacts in the fast Fourier transform (FFT) [see Fig. 4.17(b)]. We

have chosen a Tukey window, which smoothly tapers to zero at the grid boundary for radii

exceeding a radius Rabs, which is chosen to lie within the cladding region of the fiber. During the

simulation, we monitor the integrated beam power and can therefore detect when a significant

amount of light reaches the boundary. Second, in the spectral domain, we define a “guard

band”, which covers all spatial frequencies that exceed a frequency of fquard, which we choose to

be 90% of the spectral grid half-width N/2L. At every BPM step, we compute the relative

integrated spectral power in the guard band to check that it remains negligible (below 10-6).

We closely follow the implementation of the BPM in [17]; therefore, we review it only briefly

here with a view toward some aspects that are important for its application to light propagation

in GRIN fiber lenses and phase masks. Our BPM code is implemented in MATLAB, and the

simulations presented in this paper took between 8-16 s on a basic desktop computer with a 2.4-

GHz CPU and 4 GB of memory.

(i) Beam propagation method

The BPM is a numerical technique for solving the scalar Helmholtz equation in a weakly

inhomogeneous medium with a spatially dependent refractive index n(r) [16]:

022 Uk , (1)

where k = n(r)k0 is the spatially dependent propagation constant, with k0 = 2π/λ0 and λ0 denoting

the vacuum values of the propagation constant and wavelength, respectively. In optical fibers,

the refractive index variation is on the order of a few percent, and therefore, the refractive index

can be expressed as n(r) = yxnn , , where n is a constant background refractive index

(e.g., the index of the silica cladding), and n(x, y) is a small transverse index variation. The

complex scalar wave amplitude U can be written as zkzyxAzyxU -ie,,,, , where 0knk


129

is the propagation constant in the background medium. Note that in [17], it is not assumed that

A(x, y, z) is a slowly varying amplitude (although this assumption is often made in the BPM,

leading to a simplified paraxial version). From Equation (1), we can obtain a differential

equation for the amplitude A, which is first order in the propagation coordinate z:

ANDAyxnkkk

AkkzA ˆˆ,iii 02/122

trans

2trans2/122

trans

, (2)

where 2trans is the Laplacian in the transverse coordinates, D is the diffraction operator in a

homogeneous medium with refractive index n , and N is an operator that accounts for the

inhomogeneity of the refractive index. A formal solution to Equation (2) can be written as

zNzDzND zyxAzyxAzzyxA ˆˆˆˆ ee,,e,,,, . (3)

As D and N are noncommutating operators, the last approximate equality is only valid for

small index variations and sufficiently small step sizes Δz [16]. However, it enables

implementation of an intuitive numerical solution where the propagation in the inhomogeneous

medium can be approximated by a repeated step-wise application of phase screen

znkzN 0iˆ ee followed by free-space propagation in homogenous material with the

background refractive index n . For computational efficiency, the free-space propagation

operator D is applied in the spectral domain after performing a 2-D FFT of the field amplitude.

The propagated field amplitude after a single step of size Δz is therefore

znkkkkk

kkz

x,y,zAzzyxA yx

yx

02/1222

22

i-

i

1 eFFTeFFT,,, (4)

where yxyx ffkk , 2 , are the spatial frequency coordinates. As explained in [17], the

spectral-domain diffraction operate in Equation (4) is valid for high spatial frequency

components in the propagating field (e.g., due to the sharp central dip). Inspection of the square-

root term in Equation (4) shows that the diffraction operator approaches the paraxial (or Fresnel)

diffraction operator

kkkz yx

2i 22

e in the limit of small spatial frequencies 22yx ff << 0/n and

that it ensures exponential decay of sub-wavelength wavefront modulations with spatial

frequencies that exceed the physical cutoff frequency 0/n of free-space propagation [23].


130

(ii) Refractive index profile model

For the GRIN fiber lens, we use a power-law profile of the type widely used in the fiber-optic

telecommunications literature, which has been modified to allow for the optional inclusion of a

Gaussian central index dip or a sinusoidal “ripple” term [see Fig. 4.18(a)] [12]

rp

nhharnrn

wr

ripripdip1

2sine21

2

dip

(when ar ) (5)

2112 nnrn (when ar ) (5)

where a is the core radius, and 21

22

21

2nnn

is the relative index difference between the core

and cladding refractive indices n1 and n2 (for small index differences, we can write 1nn

,

where 21 nn ). The central index dip is characterized by its relative depth n

nh

dipdip and

1/e – radius wdip. The sinusoidal ripple is characterized by its relative amplitude n

nh

riprip and

its period prip. The dip and ripple are index profile errors commonly encountered in GRIN fibers

fabricated using the modified chemical vapor deposition (MCVD) method, where the dip results

from “burnoff” of dopant during the high-temperature collapse of the preform, and the ripples

result from the deposition of a finite number of layers of changing composition as well as

gradients within these layers caused by dopant evaporation from the layer surface during

vitrification [24]. The effect of the power-law exponent α on the profile shape is illustrated in

Fig. 4.18(b).

Some example index profiles of commercial GRIN fibers, together with their best-fit power-law

profiles, are shown in Fig. 4.18(c)-(e). Fig. 4.18(c) shows a 100-μm core-diameter GRIN MMF

(100/140 MMF, POFC, Taiwan), which was profile on an EXFO NR-9200 fiber analyzer at a

wave-length of 655 nm. The fiber has an α-parameter of 2.1 and a central index dip with wdip =

1.8 μm and hdip = 0.12. This GRIN fiber produces significant beam distortion, as we will show

in Section 3.3. Fig. 4.18(d) shows a 62.5-μm core-diameter GRIN MMF (GIF625, Thorlabs,

USA), which we have used extensively in our recent work [2], [7] because probes fabricated

using this fiber have exhibited very good Gaussian-like beam quality and shown fairly good

agreement with ABCD matrix calculations. This observation is not surprising when one

considers the index profile, which has no measurable dip in the center, and a near-parabolic

shape with α = 1.96. The 50-μm core-diameter GRIN MMF shown in Fig. 4.18(e) (GIF50,

Thorlabs, USA) also has a very clean index profile with no central dip. However, its profile


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deviates markedly from the ideal parabolic shape with an α-parameter of 2.17, which is most

likely due to its optimization for use with 850-nm lasers (Ge-doped GRIN fibers have optimum

values of α > 2 in the 850-nm telecommunications band [25]). The index profiles of GIF625 and

GIF50 shown here were provided by the supplier (Thorlabs) and can be assumed to be

representative of the characteristics of these particular products, but the reader should be aware

that the profiles can vary slightly between manufacturing runs.

Fig. 4.18. (a) Power-law refractive index profile with central dip and ripple. (b) Illustration of the effect

of the power-law exponent α on the profile shape. (c, d, e) Measured index profiles and power-law fits of

several commercial fibers (the cladding index n2 of all fibers is set to the refractive index n = 1.453 of

pure silica at 800 nm). (c) 100-μm core-diameter GRIN MMF (100/140 MMF, POFC, Taiwan). (d) 62.5-

μm core-diameter GRIN MMF (GIF625, Thorlabs, USA). (e) 50- μm core-diameter GRIN MMF (GIF50,

Thorlabs, USA).

(iii) Numerical accuracy of the BPM

in this section, we investigate the conditions that dictate the required sizes of the transverse

sampling intervals Δx = Δy of the computational grid and of the propagation increment Δz of the

BPM. Due to the use of the discrete Fourier transform in the transverse dimensions, the Nyquist

criterion applies, which requires that the transverse sampling interval must be smaller than half

the period p = 1/fmax of the highest spatial frequency component fmax of the propagating field,

i.e.,

2px . (6)

We can estimate the value of fmax using the fiber NA, where 2NA 122

21 nnn (This

equation is normally derived for a step-index profile, but it can also be shown to hold true for

GRIN fibers with a parabolic index profile.). The sine of the propagation angles of the angular


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spectral will, therefore, be bounded by 1max /NAsin n , which corresponds to a spatial

frequency of fmax = 0max0 /NAsin /n . Therefore, we obtain the condition

NA20x . (7)

Typical GRIN MMFs have NAs around 0.3 or less; therefore, we obtain a maximum sampling

interval of ~1.7λ0, which means we will have to sample on the scale of the wavelength. When

simulating propagation in GRIN MMFs that have index profile features with very high spatial

frequencies such as central index dips or high-frequency ripple, we need to re-examine the

sampling requirements because the resulting wavefront modulations may result in angular

spectral components that exceed the fiber NA. The Gaussian-shaped dip in our index profile

model [see equation (5)] has a Gaussian spatial frequency spectrum that is approximately

bounded by dip

max1w

f

(this is the 1/e2 radius of the power spectral density), and therefore,

we obtain

2dipw

x

. (8)

Consequently, this condition will take precedence over Equation (7) when wdip becomes smaller

than the wavelength (however, the influence of the dip will start to diminish at this point

because sub-wavelength wavefront modulations cannot propagate, as mentioned in Section (i)).

The conditions that govern the choice of the BPM propagation step size Δz depend in a non-

trivial way on the spatial-frequency content of the propagating wave as well as that of the

inhomogeneous refractive index medium. a thorough analysis has been presented in [16],

leading to a set of five conditions [16, eqs. (41)-(43), (46), and (47)]. For our fiber NA and

index profile model, we have found the most restrictive ones to be (46) and (47) (where we have

used Θmax instead of α to demote the upper bound of the angular spectrum, in order to avoid

confusion with the power-law exponent), i.e.,

maxtan

pz , and (9)

maxmax

0

tan2 npz

. (10)

The upper bound of the spatial frequency content of the propagating wave can again be

estimated using the relation Θmax ≈ sin-1(NA/n1). Let us first consider a power-law index profile

with core radius a and no central index dip. The highest spatial frequencies of this index profile

will have a period p ≈ a. For a 0.3-NA, 50-µm core-diameter fiber at a wavelength of 800 nm,


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Equation (10) turns out to be the most restrictive condition, with a maximum step size of Δz =

23 µm. If this fiber additionally has a central index dip of radius wdip = 1 µm, then Equation (9)

becomes the most restrictive condition, yielding a maximum step size of Δz = 5 µm.

In practice, these numbers can be used as an orientation, and the optimum step size will become

evident by running repeated simulations with decreasing Δz until the results converge to a

steady state. Consistent with [16], we have found that the point of diminishing returns for

decreasing Δz is of the same order as the limits calculated via Equation (9) and (10). Therefore,

in the context of the simulation tasks described in this work, there is no need to stay an order of

magnitude below the calculated limits as the “<<” in Equation (9) and (10) might imply.

We have compared the results of our BPM code with ABCD matrix simulations of simple

NCF/GRIN fiber probes with ideal parabolic refractive index profiles and found the relative

errors of the values of focal spot diameter and ED to be less than 1%.

(c) Analysis of beam distortions caused by index profile aberrations

In this section, we utilize our BPM code to analyze the effects of index profile variations from

the ideal on the output beam of a lensed fiber probe. When we analyze distorted or wavefront-

shaped output beams in the following, we will measure the “quality” of the focal region by two

parameters that are of relevance to the performance of the probe for OCT imaging, namely,

Strehl ratio and relative depth-of-focus (RDOF). The Strehl ratio of an aberrated system is

defined as the ratio of its focal spot peak intensity to that of an equivalent diffraction-limited

system [18]. Similarly, we define the RDOF as the ratio of the DOF of the simulated beam to

that of an equivalent diffraction-limited system. In this context, we represent the equivalent

diffraction-limited system by a suitably defined “reference” Gaussian beam. In the case of the

weakly aberrated power-law profiles considered in this section, we define the reference

Gaussian as the output beam produced by the corresponding aberration-free power-law profile

with α = 2.0 of infinite extent (not truncated at the core radius a, in order to eliminate aperture

diffraction effects). For very strongly aberrated or wavefront-shaped systems, where an

equivalent aberration-free system cannot be inferred in a straightforward manner, we define the

reference Gaussian as the ideal Gaussian beam that has the same full-width at half-maximum

(FWHM) focal spot diameter and integrated power as the simulated beam. We choose to use the

FWHM rather than the more commonly used 1/e2 criterion because the former yields more

meaningful values for the central lobe diameters of non-Gaussian output beams with sidelobes

or pedestals, which often exceed relative levels of 1/e2.

Thus, the Strehl ratio is given by Gaussˆ/ˆ IIS , with I denoting the peak intensity at the focus of

the simulated beam, and GaussI the peak intensity of the reference Gaussian

2FWHM

2Gauss

Gauss)2ln(42ˆ

dP

wPI

, (11)


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where P is the integrated beam power, Gaussw is the 1/e2 waist radius of the reference Gaussian,

and FWHMd is the FWHM focal spot diameter of the simulated beam.

For calculation of the RDOF, we have chosen to define the DOF as the region over which the

FWHM beam diameter is smaller than twice its minimum value (for the reference Gaussian, this

yields a DOF that is 3 times larger than the Rayleigh-range DOF defined as DOFR = 2zR,

where 02Gauss /wnzR , and n is the refractive index of the sample medium). Similar to our

reasoning regarding the choice of FWHM beam diameters, this definition allows more tolerance

for beamwidth fluctuations in the focal region of non-Gaussian beam profiles than the Rayleigh-

range criterion. We believe that this is justifiable because the Rayleigh range underestimates the

perceived useful imaging depth range in OCT (A 40% (factor of 2 ) change in transverse

resolution is hardly visible in an OCT image due to the effects of logarithmic compression and

speckle.).

Our example probe in this section is designed for high-resolution OCT imaging at a center

wavelength of 800 nm with a FWHM transverse resolution of 5 μm. The probe design uses a

100-μm core-diameter GRIN MMF with Δ = 2% and cladding index n2 = 1.453 (NA ≈ 0.3),

which is initially assumed to have a perfect parabolic profile with α = 2.0 (or a gradient

parameter of ag /2 = 4 mm-1 in the equivalent ABCD matrix). The fundamental mode

emitted from the SMF with a MFD of 5 μm is expanded in a 275-μm-long section of NCF so

that its maximum 1/e2 beam radius w inside the GRIN fiber lens section equals half the core

radius a. For a GRIN fiber length of 280 μm, an ABCD matrix simulation yields the desired

output beam characteristics, with a 1/e2 focal spot diameter of 8.5 μm (FWHM diameter of 5

μm) at a WD of 390 μm (Fresnel number N = 8). This ideal Gaussian beam is used as the

reference Gaussian in the examples discussed in the following subsections.

The BPM simulation of the probe using the aberration-free GRIN fiber with α = 2.0 is

consistent with the ABCD matrix result, but it reveals that the finite core diameter of the GRIN

fiber results in some slight aperture diffraction effects on the beam, as shown in Fig. 4.19(a)

(There is no measurable degradation of the beam quality, however, as the calculated Strehl ratio

and RDOF are both still equal to 1.0.). We have intentionally chosen a relatively small fill factor

w/a = 0.5 of the GRIN fiber core in order to minimize the influence of aperture diffraction on

the beam profile as this would make the effects of the index profile aberrations that are

introduced in the following subsections more difficult to interpret. To illustrate this point, we

have also simulated our example probe with larger fill factors (obtained by reducing the core

radius a of the GRIN fiber while keeping the gradient parameter g and the input beam

parameters constant). The result are shown in Fig. 4.19(b) and (c), demonstrating that aperture

diffraction starts to have a significant influence on the output beam profile even if only a small

fraction of the total power in the beam is clipper. For example, if one uses a fill factor of 2/π =


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0.64 corresponding to the “aperture diameter = πw” rule [13] (This is the aperture size that

transmits just over 99% of the Gaussian beam power.), noticeable diffraction ripple and “focal

shift” (a characteristic feature of focusing at low Fresnel numbers [26]) begin to appear, as can

be seen in Fig. 4.19(b). Finally, for a fill factor of unity (86.4% of the Gaussian beam power

passes the aperture.), the ripple and the focal shift are so pronounced that the ABCD matrix

simulation is no longer a useful approximation [see Fig. 4.19(c)]. These results highlight the

limitations of the ABCD matrix approach for realistic modelling of fiber probes using GRIN

fiber lenses, even for the case of aberration-free refractive index profiles.

Fig. 4.19. BPM simulation results of a lensed fiber probe using a GRIN fiber lens with an ideal parabolic

profile but finite core diameter, illustrating the effects of aperture diffraction on the output beam as

function of the fill factor w/a. The ABCD matrix simulation result for the case of an unbounded parabolic

profile is shown for comparison (dotted curves). (a) Simulation of the example probe discussed in Section

3 with GRIN core radius a = 50 μm and fill factor of 0.5. (b), (c) Modified versions of the example probe,

where the core radius a has been reduced to 39 (b) and 25 μm (c), increasing the fill factor to 2/π = 0.64

and 1.0, respectively.

In the BPM simulations presented in this section, we use a 256 × 256 grid with size L = 150 μm

(Δx = 0.59 μm), and the background index n is set equal to the cladding index n2.

(i) Influence of the power-law exponent

A deviation of the refractive index profile from the ideal parabolic shape in a GRIN lens is

equivalent to spherical aberration (SA) in a refractive lens, with α > 2 producing positive SA

and α < 2 producing negative SA. Figs. 4.20 and 4.21 show our BPM simulation results for the

lensed fiber described above when we “de-tune” the power-law profile to values of α = 2.15 and

α = 1.85, respectively, with all other parameters remaining unchanged (these values of α are

representative of the maximum deviations from the ideal that one encounters in real GRIN

MMFs). The BPM step size in the GRIN fiber is 2.4 μm. Figs. 4.20(d) and 4.21(d) show the

FWHM beam diameters and on-axis intensities compared to the curves for the reference

Gaussian. The on-axis intensities exhibit an asymmetric shape, which is characteristic of

Gaussian beams focused with SA at low Fresnel numbers [27]. The de-tuning of α from the

value of 2.0 does not just introduce SA, but it also changes the paraxial focusing power of the

GRIN lens. These two effects shift the focal position in opposite directions, with the latter

outweighing the former. Hence, there is a difference in the sign of our observed focal shift


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compared to [27] and other optics texts, where pure primary SA is added to an ideal lens of

fixed focal length.

Fig. 4.20. BPM simulation of a GRIN-lensed fiber with α = 2.15. (a) Index profile of the GRIN fiber

compared to an ideal parabolic profile. (b) E-field amplitude in the entire simulated region. (c) Output

beam intensity. (d) FWHM beam diameter and on-axis intensity of the simulated output beam (solid

lines) compared to the reference Gaussian (dotted lines).

Fig. 4.21. BPM simulation of a GRIN-lensed fiber with α = 1.85. (a) Index profile of the GRIN fiber

compared to an ideal parabolic profile. (b) E-field amplitude in the entire simulated region. (c) Output

beam intensity. (d) FWHM beam diameter and on-axis intensity of the simulated output beam (solid

lines) compared to the reference Gaussian (dotted lines).

For the case of α = 2.15, we obtain a significantly reduced Strehl ratio of S = 0.77 and a slight

increase of the DOF (RDOF = 1.1). In the case of α = 1.85, the index profile begins to approach

a triangular shape [see Fig. 4.21(a)], resulting in an axicon-like effect on the wavefront. As a

result of this, the output beam starts to show features of a Bessel-like profile with sidelobes and

an elongated focal region with RDOF = 1.44 obtained at the cost of a slightly reduced Strehl

ratio of S = 0.96. We exploit this effect in Section 4 to design a GRIN phase mask with axicon-

like properties in order to maximize the RDOF.

(ii) Influence of the central index dip and index ripple

The effects of the central index dip and index ripple on the bandwidth of GRIN MMFs have

been studies extensively in the fiber-optic telecommunications literature from the viewpoint of

modal analysis [12], [24]. However, these studies provide little insight into the wavefront

distortions that result when using short sections of such GRIN MMFs as lenses. Our aim here is

to gain an intuitive understanding of the beam distortions resulting from central index dips and


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index ripples and to gauge the order of magnitude of their effect on the beam quality in terms of

Strehl ratio and RDOF.

Fig. 4.22 shows the simulation of our example probe for α = 2.0 and a central index dip with hdip

= 0.5 and wdip = 1.5 μm (These values are representative of such dips in measured profile shown

in the literature.). The BPM step size in the GRIN fiber is 1.2 μm. The index dip behaves as a

strong localized negative lens that directs light away from the optical axis, producing a

characteristic hole in the center of the output beam profile in the region immediately adjacent to

the GRIN fiber end face, as can be seen in Fig. 4.22(b). We have indeed experimentally

observed such “donut”-like output beams when using GRIN fibers with central index dips.

Interestingly, the Strehl ratio and the DOF suffer only minimally, with S = 0.97 and RDOF =

0.99. This can be explained by considering that the input beam to the GRIN fiber has been

expanded in the NCF section such that the index dip affects only a small fraction of the incident

beam wavefront. The output beam can, therefore, be described as a superposition of two

components. The first and main component is an aberration-free wavefront (with a small central

“hole”), which has propagated in the outer regions of the core that are not affected by the central

dip and which converges normally to form the focal region of the probe. The second component

is a large-angle diffracted wave, which is generated near the beginning of the GRIN fiber and

which cannot be refocused within the short (0.18-pitch) GRIN section. It therefore exits the

GRIN fiber as a diverging wave, which interferes with the converging main component but

rapidly diminishes in amplitude so that its effect on the focal regions is negligible. Fig. 4.22(c)

is a plot of the integrated beam power versus propagation distance, showing that the diverging

wave generated by the dip begins to strike the absorbing boundary at a distance of ~300 μm

from the probe and is gradually absorbed. When changing the dip parameters, it is not surprising

that the width of the dip turns out to be most critical as it determines the fraction of the incident

beam power that is intercepted by the dip. Doubling the dip radius to wdip = 3 μm decreases the

Strehl ratio to 0.88, whereas doubling the dip depth to hdip = 1 only causes a minimal further

reduction in the Strehl ratio to 0.96.

Fig. 4.22. BPM simulation of a GRIN-lensed fiber with α = 2.0 and central index dip with wdip = 1.5 μm

and hdip = 0.5. (a) Index profile of the GRIN fiber compared to an ideal parabolic profile. (b) E-field

amplitude in the entire simulated region. (c) Normalized power of the propagating beam. (d) Output beam


138

intensity. (e) FWHM beam diameter and on-axis intensity of the simulated output beam (solid lines)

compared to the reference Gaussian (dotted lines).

Next, we have investigated the effect of index ripple on the output beam. Our intuitive

expectation is that, during every BPM step, the superimposed ripple behaves as a thin sinusoidal

phase grating, which diffracts power out of the propagating beam at angles in the vicinity of

rip01 /sin pn [23]. This is confirmed by our simulations, as illustrated by the example

shown in Fig. 4.23 for the case of our example probe, where the index profile with α = 2.0 is

modulated by ripple with hrip = 0.03 (6% peak-to-peak) and prip = 5 μm. The BPM step size in

the GRIN fiber is 1.2 μm. Fig. 4.23(b) shows that the output beam can again be interpreted as

consisting of a superposition of an aberration-free and a large-angle diffracted component. The

aberration-free component converges normally to an essentially un-altered focal spot with S =

0.94 and RDOF = 0.98, whereas the large-angle diffracted component diverges at the GRIN

fiber end where it interferes with the aberration-free component but quickly propagates away

from the optical axis. The plot of integrated beam power versus propagation distance in Fig.

4.23(c) shows that the large-angle diffracted component, which carries ~5% of the beam power,

strikes the absorbing boundary at a distance of ~400 μm from the probe end. The amplitude of

the ripple encountered in real fibers is typically lower than in this example. Therefore, our

conclusion is that index ripple introduces negligible power loss (reducing the amplitude to hrip =

0.01 restores the Strehl ratio to unity) and has practically no impact on the beam profile in the

focal region. A more accurate modeling of the index ripple of real fibers would take into

account that the typical spatial frequencies of the ripple are higher than shown in this example

and that the ripple tends to be “chirped”, increasing to very high spatial frequencies (submicron

periodicity) near the edges of the profile [24]. However, this does not change our conclusion as

higher spatial frequencies will simply diffract outward at even larger angles (and eventually

become “invisible” to the wavefront when they exceed the physical cutoff frequency of 0/n of

free-space propagation). When performing simulations for different ripple periods, we found

that the most noticeable effects are caused by low-frequency ripple with only 1-3 periods in the

core radius, as these produce beam distortions in the focal regions of the probe and can cause

degradation or enhancement of Strehl ratio and RDOF on the order of 10% even for very small

amplitudes of 1% peak-to-peak. Even though such low-frequency ripple is not an inherent

feature of the MCVD process, it can represent a systematic low-frequency deviation of the

profile shape from the power-law model, which has indeed been observed in practical fibers

[12].


139

Fig. 4.23. BPM simulation of a GRIN-lensed fiber with α = 2.0 and ripple with hrip = 0.03 and prip = 5 μm.

(a) Index profile of the GRIN fiber compared to an ideal parabolic profile. (b) E-field amplitude in the

entire simulated region. (c) Normalized power of the propagation beam. (d) Output beam intensity. (e)

FWHM beam diameter and on-axis intensity of the simulated output beam (solid lines) compared to the

reference Gaussian (dotted lines). The sharp minima of the FWHM diameter curve near the probe end

face should not be interpreted as intermediated foci because the FWHM is not a good measure of the

transverse extent of the beam in the presence of strong modulations caused by interference.

(iii) Comparison with experimental results

To demonstrate the accuracy of the BPM code, we have fabricated a lensed fiber using the

100/140 GRIN MMF with the measured index profile shown in Fig. 4.18(c), with lengths of 480

μm of NCF and 170 μm of GRIN fiber, which is spliced to SMF with a MFD of 5.6 μm at 830

nm (SM800, Fibercore, UK). The GRIN fiber used for this probe was from the same reel from

which the sample for the index profile measurement was taken. The output beam was profiled as

a function of distance from the probe at a wavelength of 820 nm using a commercial near-field

beam profiler (SP620U, Ophir-Spiricon, USA). Fig. 4.24 shows the comparison of the

simulation with the beam profiling results. The BPM step size in the GRIN fiber was 1.2 μm.

Using the power-law index profile fit with central dip shown in Fig. 4.18(c), we are able to

correctly model the beam diameter and on-axis intensity distribution in the focal region, as

shown in Fig. 4.24(a). However, in the region immediately adjacent to the probe end face, there

remains some disagreement between the simulated and measured curves. Based on the

assumption that this is caused by subtle features of the index profile that are not correctly

represented in our model, we have empirically found that adding a small amount of low-

frequency sinusoidal ripple to the index profile in the BPM simulation reproduces the fine

structure of the measured beam profile in this region with surprising fidelity, as shown in Fig.

4.24(b). The best agreement was obtained with hrip = 0.008 and prip = 35 μm. Due to the very

small relative amplitude of 1.6% peak-to-peak and the long period, this ripple is difficult to

discern with the eye in the measured index profile of Fig. 4.18(c), but adding the ripple term to

the fit curve reduces the RMS (root mean square) error of the fit from 8.2·10-6 to 6.4·10-6. The

good overall agreement between the measured and simulated beam profile when using the

rippled index profile is evident when comparing the plots of the E-field amplitude shown in Fig.

4.24(c) and (d). This result confirms our finding in Section 3.2 that even very small low-spatial-


140

frequency deviations from the power-law shape on the order of 1% can have a noticeable effect

on the output beams of lensed fibers.

Fig. 4.24. Comparison of BPM simulation to the measured beam profile of a lensed fiber using the GRIN

MMF with the index profile shown in Fig. 4.18(c). (a) Simulated vs. measured FWHM beam diameter

and on-axis intensity, where the simulation uses the index profile fit shown in Fig. 4.18(c). (b) Same as

(a), but with modified index profile including sinusoidal ripple (see text). (c) Measured output beam E-

field amplitude (square root of measured intensity profile). (d) Simulated output beam E-field amplitude.

The BPM simulation accurately predicts the WD and focal spot diameter of the probe. It yields a

Strehl ratio of S = 0.85 and RDOF = 1.0, and it reveals the asymmetric intensity distribution of

the focal region, which is due to the combined effects of positive SA resulting from the non-

parabolic profile (α = 2.1) and aperture diffraction at the GRIN fiber core boundary (the fill

factor in this design is ~0.7). Furthermore, it predicts the characteristic “donut”-like transverse

intensity profile at the end face of the GRIN fiber, which is caused by the central index dip.

(d) Extending the DOF using GRIN fiber phase masks

Even when diffraction-limited focal regions can be achieved by using high-quality GRIN fibers,

the straightforward lensed fiber probes with Gaussian output beams suffer from the problem of

very low DOF at high transverse resolutions (as an example, for 5-μm FWHM transverse

resolution, we have a DOF of only 246 μm in air or 344 μm in tissue with average refractive

index n = 1.4 when using our DOF criterion of beam expansion to twice the focal spot

diameter). We have recently demonstrated that the DOF of lensed fiber probes can be extended

by a factor of ~2 using a simple phase mask consisting of a short section of overfilled GRIN

MMF [8]. Here, we use our BPM code to explore the possibility of achieving even greater DOF

gains by using a custom-designed axicon-like GRIN phase mask to generate a Bessel-like

output beam. We begin our design with a standard lensed fiber for a wavelength of 800 nm

using SMF with 5-μm MFD, a 400-μm-long NCF spacer, and a 135-μm-long section of 100-μm

core-diameter GRIN MMF with α = 2.0, Δ = 2%, and cladding index n2 = 1.453. This

spacer/lens combination produces a collimated beam with a 1/e2 diameter of 66 μm, which is

used as the input to a 95-μm-long, 100-μm core-diameter GRIN fiber phase mask section with

the index profile shown in Fig. 4.25(a). Such axicon-like GRIN fibers are not commercially

available, but their production is feasible using existing preform fabrication techniques.


141

Fig. 4.25. BPM simulation of a GRIN fiber probe using a phase mask to increase the DOF. (a) Index

profile of the axicon-like GRIN phase mask. (b) E-field amplitude in the entire simulated region. (c)

Output beam intensity. (d) FWHM beam diameter and on-axis intensity of the simulated output beam

(solid lines) and an ideal Gaussian beam with the same focal spot diameter (dotted lines). The apparent

discontinuity of the FWHM diameter of the simulated beam (solid red line) near the end of the DOF is

caused by the sidelobes of the beam, which begin to exceed 50% of the central lobe peak intensity beyond

that point.

Identical BPM step sizes of 2.4 μm were used in the GRIN lens and GRIN phase mask section.

The plots of the simulated field amplitude and intensity in Fig. 4.25(b) and (c), respectively,

show that the output beam of this probe exhibits the characteristic features of Bessel-like beams

generated by low-Fresnel-number axicons [28], with a small number of sidelobes and an axial

intensity distribution that is shifted toward the axicon. Fig. 4.25(d) shows that the FWHM

diameter of the central lobe stays approximately constant around 5 μm over a large distance of

~800 μm in air, yielding a substantial DOF gain (RDOF ~3.3) compared to the reference

Gaussian [dotted lines in Fig. 4.25(d)], which is obtained at the cost of a reduced Strehl ratio of

S = 0.56 (The exact value of the useful DOF of this beam will be determined by the acceptable

relative intensity of the sidelobes, which gradually increases to 50% of the central lobe intensity

at the far end of the DOF.). The central lobe carries 36% of the total beam power in the middle

of the Bessel-like region at ~400 μm from the probe end, which is significantly higher than in

the case of bulk-optic axicons used at large Fresnel numbers in benchtop OCT systems, where

the central lobe carries only a few percent of the total beam power [21]. A tolerance analysis of

this probe design using the BPM showed that the Bessel-like structure of the focal region is

quite robust against fabrication errors in the lengths of the NCF, GRIN, and phase mask

sections. For well-calibrated splicing and cleaving setups, a repeatability of ±5 μm can be

achieved. The most sensitive lengths are those of the GRIN and phase mask sections, where

errors of 5 μm cause changes in the central lobe diameter and DOF on the order of 10%;

whereas, a variation of the NCF length by the same amount only causes changes in the output

beam parameters of a few percent.

(e) Conclusion

In summary, we have demonstrated the usefulness of the BPM for accurate modeling of GRIN

fiber probes for future needle-based or micro-endoscopic OCT applications where optimum


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resolution and sensitivity will be crucial for enabling minimally invasive imaging with quality

comparable to state-of-the-art benchtop microscopes.

Our simulations have revealed a number of new insights about GRIN fiber lenses, which cannot

be obtained using established ABCD matrix modeling techniques. The most significant finding

is that low-spatial-frequency features of the index profile (such as deviation of the power-law

exponent α from the ideal value of 2.0 or low-spatial-frequency variations of the profile about

the power-law shape) are much more critical for the output beam quality than high-spatial-

frequency features such as central index dips and short-period ripples, which are often

encountered in fibers drawn from preforms fabricated using the MCVD process. This finding is

important for specifying the fabrication tolerances of customized preforms for high-quality

GRIN fiber lenses. It was also found that the negative SA introduced by profiles with α < 2.0

can be used to enhance the DOF, whereas the positive SA introduced by values of α > 2.0

produces less favourable output beam distortions that result in a significantly reduced Strehl

ratio.

Furthermore, we have demonstrated the power of the BPM for studying advanced probe designs

incorporating novel optical elements such as GRIN phase masks with arbitrary refractive index

profiles to engineer the 3-D diffracted field in the focal region. We would like to point out that

the BPM naturally also includes the possibility of multiplying the propagating wavefront with a

“thin” phase or amplitude mask (which could, for example, represent a diffractive optical

element created by microstructuring the fiber tip). The BPM has also successfully been used to

model refractive surfaces such as waveguide lenses [29] and hemispherical lenses [8]. This

capability is important for studying the effects of enclosing catheters, capillaries, or other

transparent protective sheaths on the output beams of side-facing lensed fiber probes (The

analysis of astigmatism introduced by such cylindrical interfaces is obviously an important

aspect of any realistic side-facing probe design, and it has been studies extensively using ABCD

matrix simulations for the case of probes with Gaussian output beams [2], [7], [14], [15].).

In this paper, we have neglected wavefront distortions that the output beams incur as they

propagate in biological tissue. However, the BPM can be used to study these effects if the tissue

is modelled as an inhomogeneous dielectric medium, and such simulations have provided

important insights regarding optimum beam shapes for microscopy in dense scattering media

[30], [31].

In this paper, we have focused on GRIN fiber probes for OCT imaging, but the methods

described here can also be applied to other imaging systems incorporating GRIN elements, such

as microendoscopes for confocal fluorescence [32] or multiphoton microscopy [33], which use

very thin fiber-like GRIN relay rods and lenses with diameters down to 350 μm at moderate

NAs in the range 0.3-0.5, where scalar diffraction theory (which is the underlying framework of

the BPM) is still very accurate. Some elements of the work presented here could also be useful


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for non-biomedical applications of GRIN fiber microlenses, such as analysis and design of

fiber-to-freespace or fiber-to-fiber coupling assemblies in photonic devices and interconnects

[9], [34].

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4.5 Chapter summary

The moderate penetration depth of OCT in opaque tissues can be overcome by the use of

endoscopic OCT probes, which are able to deliver the incident light deep inside the imaged

tissue after the insertion. The endoscopic OCT probes can be divided into catheter-based and

needle-based OCT probes. Catheter-based OCT probes are typically of larger size and are used

to image the lumens (e.g., gastrointestinal tract, cardiac blood vessels, and airways). Catheter-

based OCT probes perform linear or radial scans. In contrast to the linear scans, which only

provide 2D images, the radial scans give a more completed view of the imaged lumen.


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Needle-based OCT probes, which typically miniaturise focusing optics within hypodermic

needles, are able to scan deep inside solid tissues because they can be inserted into the imaged

tissue. Because the size of needle-based OCT probes is usually small (outer diameter less than 2

mm), the tissue trauma caused by the probe insertion can be minimised. Needle-based OCT

probes can be divided into two categories, forward-viewing and side-viewing ones. Three-

dimensional data volumes can be generated by the side-viewing probes via radial scans (with

pullback rotation). The deflection mechanisms employed by side-viewing probes include angle-

polished ball lens, microprism, angel-polished mirror, and angle-polished surface at the end of

the optics.

The ultrathin side-viewing OCT needle probe developed by us is presented. The deflection

mechanism of angle-polished surface (with the metal coat deposited on the polished surface) at

the end of optics was employed in the design. Therefore, the extremely miniaturised focusing

optics are small enough to be encased in a 30G hypodermic needle, with its outer diameter 0.31

mm. Tissue trauma caused by the insertion, therefore, can be significantly minimised. A side

opening that performs as the output window of the light was fabricated on the needle via

electrochemical etching. This design generates astigmatism because the output beam propagates

through the curved surface on the side of the optical fibre. However, this astigmatism can be

significantly reduced (astigmatism ratio from 3.9 to 1.8) by the aqueous interstitial fluids after

inserted into biological tissues. Interfacing with a fibre-based 840-nm SD-OCT system, the

measured working distance (FWHM) is 275 μm and the beam waist stays smaller than 30 μm

over a distance of 550 μm (in water). The axial resolution and sensitivity measured in water are

7 μm and 84 dB, respectively. Acquired 3D images of lamb lung tissue demonstrate the

capability of this probe in visualising the individual alveoli and bronchioles over a depth of

~600 μm.

A more rigorous application of both this developed ultrathin side-viewing needle probe and a

dynamic OCT needle probe in imaging animal lungs is presented in the second paper. Individual

alveoli and bronchioles are clearly visible in the obtained volumetric OCT data. The dynamic

OCT needle is able to track changes in anatomical features during a period of time. In the

experiment, periodic inflation and deflation of a pig lung simulated the multiple “breath” cycles.

The motion of individual alveoli and bronchioles inside the lung tissue during these cycles was

characterised by the dynamic OCT needle probe.

Two alternative designs of the focusing optics with EDOF, which can be used for making

needle-based OCT probes with EDOF, are presented in the third paper. An additional GRIN

lens section with a smaller core diameter is appended to the end of the focusing optics in the

first design. Based on the computational simulation using the BPM, this design is able to yield a

DOF gain ~2, because the central portion of the converging wavefront is “double focused” by

both the original and the additional GRIN lens sections. With the DOF gain, the transverse


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resolution of this designed probe is slightly compromised by the generated non-Gaussian beam

profile. However, this compromise in the transverse resolution is hardly visible after the

logarithmic compression of the images and speckle. The fabrication of the probe following this

design was proved to be difficult. We hypothesised that this difficulty was because the

measured beam profile of the fabricated probe is sensitive to the deviation of the refractive

index profile of the additional GRIN lens section from the ideal parabolic shape. The validation

of this hypothesis is presented in the fourth paper. The computational simulation using the

BPM, instead of ABCD matrix transformation, provides an accurate description of the beam

profile generated using the GRIN lens with imperfect parabolic refractive index profile. The

simulating results were supported by the acquired experimental data.

In the second design of the probe with EDOF, the original GRIN lens section with a larger core

diameter is removed. The additional GRIN lens section with a smaller core diameter is directly

appended to the NCF. A hemispherical refractive lens is further added to the additional GRIN

lens section. The DOF gain of this designed probe in the simulation is limited to ~1.7 due to the

degradation of the beam quality caused by the spherical aberration of the refractive lens. The

experimentally measured values of the fabricated probe following this design showed fairly

good agreement with the simulated ones.

Chapter 5 - Imaging skeletal muscle using an ultrathin side-viewing OCT needle probe

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Chapter 5

Imaging skeletal muscle using an ultrathin side-viewing OCT

needle probe

5.1 Preface

The successful development of ultrathin OCT needle probes enables the application of these

needle probes in the visualisation and characterisation of microscopic structures inside small

animals in a minimally invasive manner. The first-generation 30G side-viewing OCT needle

probe presented in Chapter 4 [407] has been successfully applied in imaging alveolar structures

inside animal lungs [302]. In this chapter, this first-generation 30G side-viewing OCT needle

probe has been applied to imaging skeletal muscle. The acquired results, which are presented in

Section 5.2, reveal information with moderate quality and quantity. This is deemed to be caused

by the low sensitivity of the probe. An improved second-generation 30G side-viewing OCT

needle probe is subsequently presented in Section 5.3. In addition to longer wavelength

operation and better mechanical integrity due to the laser-drilled side-opening, a higher

sensitivity (108 dB) is achieved by this second-generation ultrathin OCT needle probe and its

combined OCT imaging system. The combination of small size and high sensitivity has

benefited the characterisation of ultrastructures deep inside mouse skeletal muscle.

A published journal paper (with minor modifications) is presented in Section 5.3. This paper

demonstrates the first successful application of an ultrathin side-viewing OCT needle probe in

the detection of ultrastructures inside skeletal muscle. The results demonstrate the visualisation

of internal structures, such as individual myofibres and connective tissues, of mouse skeletal

muscle samples. In addition, pathological features, such as the necrotic regions, were

characterised within dystrophic mdx mouse muscle samples.

In addition, we have noted that the needle insertion orientation relative to the myofibre

orientation affects the imaging results. We define the transverse view of the myofibres as the

view showing cross-sections of individual myofibres. The longitudinal view of the skeletal

muscle is defined to be perpendicular to this transverse view. Imaging results revealed that the

longitudinal view contained more resolved ultrastructures than the transverse view. This finding

is presented and we hypothesise possible mechanisms for this in Section 5.4.

The paper presented in Section 5.3 has been published in Biomedical Optics Express vol. 5(1),

pp. 136-148, 2014. All citations in this paper are listed in the chapter bibliography (Section

5.2.7) rather than the thesis bibliography.


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5.2 Imaging data of mouse skeletal muscle obtained using the 840-nm OCT needle probe

The muscle imaging results acquired from our first-generation 30G OCT needle probe are

presented. As described in Section 4.3.2 in Chapter 4, the sensitivity of the first-generation 30G

OCT (with the 840-nm OCT imaging system) needle probe was measured to be 84 dB. The

results revealed that this sensitivity was barely sufficient to resolve the internal ultrastructure,

such as individual myofibres, of skeletal muscle.

The OCT image acquired using the first-generation ultrathin OCT needle probe, showing the

transverse view of a left tibialis anterior (TA) muscle is shown in Fig. 5.1a. The colocated

histological section is shown in Fig. 5.1b. From the OCT image, the connective tissue is

characterised (indicated by the arrow) due to its different reflectivity and relatively large

dimension. However, circular features representing the cross-sections of individual myofibres

cannot be clearly identified, although a few reflective spots (indicated by the arrow heads) are

occasionally visualised. The OCT image and its colocated histological section illustrating the

longitudinal view of a right TA muscle are shown in Fig. 5.2a and b, respectively. The tendon is

clearly visualised in the OCT image as a reflective structure with a relatively large dimension

(indicated by the arrow). Some striated structures (indicated by the arrow head) following the

running directions of myofibres can be identified. However, these structures are faint.

Moreover, the compacted multiple striated structures in a regular pattern, as shown in the

corresponding region of the histological section, are not observed in the OCT image. A view of

the 3D rendered visualisation of the OCT image of the same right TA muscle is shown in Fig.

5.3. Although the tendon structure is clearly visualised (indicated by the arrow), individual

myofibres cannot be fully resolved. The occasionally appeared striated structures demonstrate

the difficulty in the characterisation of individual myofibres using the first-generation ultrathin

OCT needle probe with low sensitivity.


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Fig. 5.1 (a) OCT image acquired from the first-generation ultrathin OCT needle probe, showing the

transverse view of a healthy left TA mouse muscle. (b) Colocated histological section. The structure of

connective tissue (arrow) can be observed in both the OCT image and the histological section, whereas

the cross-section of individual myofibres cannot be fully resolved in the OCT image appearing as a few

reflective spots in the OCT image (arrowheads).


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Fig. 5.2 (a) OCT image acquired from the first-generation ultrathin OCT needle probe, showing the

longitudinal view of a healthy right TA mouse muscle. (b) Colocated histological section. The structure of

tendon (arrow) can be observed in both the OCT image and the histological section; whereas, individual

myofibres cannot be fully resolved in the OCT image appearing as a few occasionally observed striated

structures (arrowheads).

Fig. 5.3 A 3D-rendered volumetric OCT image of the healthy right TA mouse muscle. The tendon

structure is identified as a reflective structure (arrow). Some occasionally appeared striated structures can

be observed (arrow heads). The 3D scale bar represents 200 µm in each direction.


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5.3 Imaging deep skeletal muscle structure using a high-sensitivity ultrathin side-viewing

optical coherence tomography needle probe

[Xiaojie Yang, Dirk Lorenser, Robert A. McLaughlin, Rodney W. Kirk, Matthew Edmond, M.

Cather Simpson, Miranda D. Grounds, and David D. Sampson; Biomedical Optics Express,

5(1): 136 – 148, 2014]

Abstract: We have developed an extremely miniaturized optical coherence tomography (OCT)

needle probe (outer diameter 310 µm) with high sensitivity (108 dB) to enable minimally

invasive imaging of cellular structure deep within skeletal muscle. Three-dimensional

volumetric images were acquired from ex vivo mouse tissue, examining both healthy and

pathological dystrophic muscle. Individual myofibers were visualized as striations in the

images. Degradation of cellular structure in necrotic regions was seen as a loss of these

striations. Tendon and connective tissue were also visualized. The observed structures were

validated against co-registered hematoxylin and eosin (H&E) histology sections. These images

of internal cellular structure of skeletal muscle acquired with an OCT needle probe demonstrate

the potential of this technique to visualize structure at the microscopic level deep in biological

tissue in situ.

5.3.1. Introduction

Skeletal muscle comprises multiple myofibers, which are long, columnar cells capable of

contraction through the binding of the rod-like protein molecules, actin and myosin. Collections

of parallel myofibers are encased within a connective sheath to form fascicles; and multiple

fascicles are sheathed within a tough layer of connective tissue, the epimysium, to form an

entire muscle. This connective layer is attached to tendons, and, in turn, is anchored to bone [1].

Skeletal muscle is subject to numerous fatal pathologies that compromise this structure and

impair function. For example, Duchenne muscular dystrophy (DMD) is an X-chromosome

linked muscle disorder that affects 1 in 3600-6000 live male births [2], caused by a defect in the

gene that encodes for the structural sub-sarcolemmal protein dystrophin [3]. Pathological

necrosis of myofibers leads to replacement of the muscle tissue with sclerotic tissue and fat,

resulting in progressive muscle loss and eventual death [2].

Assessment of new pharmaceutical and nutritional interventions for such diseases is made

difficult by a lack of techniques to assess muscle structure. Biopsy and subsequent

morphological analysis of histological sections is the gold standard, but requires excision and

fixation of the tissue [4]. In small animal models, such as mouse models, this will typically

involve sacrificing the animal, which precludes the possibility of longitudinal study. In human

studies, the use of large-gauge biopsy needles can be undesirably invasive in patients who

already suffer compromised muscle function.

In vivo biomedical imaging methodologies, such as ultrasonography [5-7], magnetic

resonance imaging (MRI) [8-15] or X-ray computed tomography (CT) [16-18], have been


153

applied to muscle imaging. Ultrasonography is in both routine clinical use (for human patients)

[6] and preclinical use (for animal models) [7] because of its lower cost, shorter acquisition time

and avoidance of ionizing radiation. The imaging resolution, however, limits ultrasonography in

resolving individual myofibers, which are typically 30 to 50 µm in diameter [4]. Although

recently studies report that micro-ultrasonography [19, 20], which is applied in imaging small

animals, can reach spatial resolution as fine as 30 µm [19], its capability in imaging skeletal

muscle is yet to be established.

MRI has been used to provide three-dimensional (3D) imaging of dystrophic muscle not

only in human patients [8, 9] but also in canine [10, 11] and murine [12-15] models. High-field

strength micro-MRI has been reported to achieve a reconstructed resolution of ≈30 µm in

imaging the cat visual cortex [21], but access, cost and the long acquisition times of this

imaging modality still impede its uptake for resolving the microstructure of skeletal muscle.

CT has been used in both clinical assessment of muscular diseases in human patients [16],

as well as in preclinical characterization and analysis of muscle in animal models with iodine

contrast agents [17, 18]. Micro-CT has been also used in preclinical imaging of small animals

[22]. However, the radiation exposure of CT limits its use in longitudinal human studies; and

the limited bore-size of micro CT scanners precludes its extension to in vivo human work.

Optical imaging techniques, such as confocal [23], multi-photon [24], and second harmonic

generation microscopy [25, 26], allow much higher resolution imaging of muscle structures.

These techniques are able to resolve individual myofibers, but typically require ex vivo tissue

samples. A needle probe for confocal microscopy has been developed and demonstrated to be

capable of visualizing ultrastructure of skeletal muscle [27]. In vivo imaging of sarcomeres

within mouse and human skeletal muscle tissues using optical endomicroscopy has also been

reported to achieve penetration depths of a few hundred micrometers [28]. These

endomicroscopic imaging modalities, however, are of limited sub 100-µm field of view.

Optical coherence tomography (OCT) [29], an interferometric technique based on the

backscatter of near infrared light, provides the potential for non-destructive, high-resolution

imaging of muscle structure. Previous studies have demonstrated that OCT can visualize

cellular structures (e.g., individual myofibers) of skeletal muscle [30-32]. However, in common

with other optical imaging methods, OCT is restricted to superficial imaging of muscle (≈2

mm).

Recent work has advanced the use of OCT needle probes for imaging deep within tissue,

including in three dimensions [33-39]. In an OCT needle probe, the distal focusing optics are

miniaturized and encased within a hypodermic needle [40]. The focusing optics typically

comprise either a GRIN lens [33]; a ball lens [41, 42]; or a length of GRIN fiber [34, 36, 39,

43]. By redirecting the light beam perpendicular to the longitudinal axis of the needle probe and

rotating the needle probe, it is possible to acquire a 2D radial scan (radial B-scan). By


154

simultaneously inserting or retracting the needle probe, 3D imaging (C-scan) may be performed.

OCT needle probes have previously been demonstrated in many tissues, including lung [35, 38],

breast [37], prostate [44], and brain [45], amongst others [40].

Although minimally invasive, OCT needle probes cause some trauma to the tissue, which

has driven work to minimize their diameter. This is particularly critical when imaging small

animal tissues, such as those of mouse models. We have previously described a probe encased

within a 30-gauge needle (30G, outer diameter of 310 µm), the smallest published side-viewing

OCT needle probe [36]. However, this preliminary design presented a number of limitations

when utilized to image muscle tissue. Developed for an 840-nm OCT system, the light beam

achieved only a limited image penetration depth in muscle tissue. Furthermore, losses

introduced by the side-deflecting mirror coating reduced the overall system sensitivity to a level

that was insufficient for imaging of tissue structures with relatively weak contrast such as

muscle fibers. In addition, the manufacturing method used to chemically etch an imaging

window into the shaft of the extremely thin 30G needle significantly reduced the robustness and

durability of the probe.

In this paper, we address these limitations in the design and manufacture of an improved,

high-sensitivity, ultrathin, side-viewing 30G OCT needle probe. We adapt the optical design to

a 1300-nm OCT system, achieving an improved imaging depth. The optical losses in the mirror

coating are substantially reduced, leading to a high sensitivity. We utilize laser drilling to

construct an imaging window in the needle shaft, allowing more reproducible needle production

without compromising the structural integrity of the needle. We present a detailed

characterization of the sensitivity and beam characteristics of the probe. Using this improved

OCT needle probe, we present the first published histology-matched images of muscle structure

at the microscopic scale, at a depth of approximately one centimeter below the tissue surface,

visualizing myofibers, tendon and connective tissue; and observing a loss of structure in areas of

muscle necrosis.

5.3.2. Materials and methods

(a) Design and fabrication of the ultrathin needle probe

The schematic of the improved ultrathin needle probe is shown in Fig. 5.4(a). This second-

generation ultrathin OCT needle probe is designed for the 1300-nm operating wavelength band.

The distal focusing optics consists of a 260-µm section of no-core fiber (NCF) and a 120-µm

section of graded-index (GRIN) fiber (GIF625, Thorlabs, USA) spliced to the end of single-

mode fiber (SMF-28, Corning, USA). An additional section of NCF is added after the GRIN

section and polished at an angle of 45˚ using a fiber connector polishing machine (SpecPro 4L,

Krelltech, USA). By simulating the output beam of the probe using the ABCD matrix method

[46], the lengths of the NCF and GRIN fiber sections were chosen such that a full-width at half-

maximum (FWHM) resolution of 20 µm or better is maintained over a depth range of several


155

100 micrometers in water, taking into account the astigmatism resulting from the cylindrical

output window, as discussed in more detail in the following subsection. The beam propagation

method (BPM) is particularly useful in cases where GRIN fibers with non-parabolic index

profiles are used, or when analyzing the effects of phase masks [47]. In the case of this

particular probe, we used a very high quality GRIN fiber which has a nearly perfect parabolic

profile. Hence, the ABCD method was sufficiently accurate to design the probe and it is faster

and simpler than a rigorous BPM simulation.

A metal reflection coating consisting of a 3-nm chrome adhesion layer and a 300-nm gold

layer is applied to the angle-polished fiber tip using a thermal vacuum deposition machine.

After metallization, the fiber probe is mounted inside a 30G hypodermic needle with a 140-µm

diameter side opening (as shown in Figs. 1(c) and 1(d)). In the first-generation ultrathin OCT

needle probe, the side opening was fabricated via electrochemical etching using a customized

setup [36]. Neither the size nor the geometry of the opening could be precisely controlled and

erosion of the hypodermic needle tubing near the imaging window led to a reduction in

structural integrity of the needle.

In the second-generation ultrathin OCT needle probe, the side opening was fabricated by

laser ablation with a femtosecond laser micromachining system based upon a commercial

Ti:Sapphire amplified femtosecond laser (Mantis (oscillator) and Legend Elite (amplifier),

Coherent Inc., USA). The 800-nm, 100-fs pulsetrain with a repetition rate of 500 Hz was

directed to a micromachining stage (IX-100C, JPSA, Inc. USA). The laser focal spot at the

workpiece had a flat-top intensity profile and a diameter of 50 µm, and pulse energy ranged

from 15 to 40 µJ. The spot was scanned in a circle of radius 45 µm, with 0.5-µm spacing

between successive laser pulses. 20 to 30 passes were required to drill through the needle wall.

As can be seen in the scanning electron microscope (SEM) image of the side opening in Fig.

5.4(c), the non-thermal ablation in the femtosecond regime eliminates problems resulting from a

heat-affected zone surrounding the hole that would otherwise compromise the structural

integrity of the very thin hypodermic needle.


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Fig. 5.4 (a) Schematic of the ultrathin OCT needle probe. (b) Microscope image of the

angle-polished fiber probe before metallization. (c) SEM image of the laser-drilled side

opening. (d) Fully assembled needle probe showing the laser-drilled side opening. In

the photo, red light from the aiming laser is visible.

(b) Optical characterization of the ultrathin needle probe

The simplicity and robustness of the side-viewing ultrathin OCT needle probe design of

Fig. 5.4(a) is obtained at the cost of some astigmatism in the output beam. The initially circular

beam acquires astigmatism as it is emitted sideways from the fiber, which acts as a cylindrical

lens, as illustrated in Fig. 5.5(a). In the y-direction, the beam is unaffected and comes to a focus

at a working distance WDy. In the x-direction, however, the beam comes to a focus at a shorter

distance WDx. In air, the high refractive-index contrast produces very strong astigmatism that

renders this probe design unsuitable for use under such conditions. However, when the probe is

inserted into biological tissue, it is always immersed in interstitial fluids with a refractive index

similar to that of water (n = 1.321 at 1.3 µm), thereby reducing the refractive-index contrast at

the silica fiber interface (n = 1.447 at 1.3 µm) to a level where the residual astigmatism of the

beam is tolerable for many applications, as previously demonstrated [36].

Since a direct measurement of the beam profile in water is difficult, we used a setup that

allows an indirect measurement of the output beam when the probe is immersed in water. The

probe was placed in direct contact with a thin coverslip (thickness 150 µm) and immersed in a

drop of water. The beam was then profiled in air behind the coverslip. This measurement

procedure is valid because planar interfaces between homogenous dielectric media do not

change the transverse profile of paraxial beams but simply result in a change of scale of the

propagation axis [46]. The measurement was performed using a commercial near-field beam

profiler that images the transverse intensity profile onto a CCD sensor using an objective lens

with 12× magnification (SP620U, Ophir-Spiricon, USA). Fig. 5.5(b) shows the FWHM beam

diameters, dx and dy, in the x and y directions, respectively, plotted versus the distance in water


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from the fiber/water interface. The diameter values were obtained from fitting Gaussian profiles

to the transverse intensity distributions.

The measured beam profile (solid lines in Fig. 5.5(b), x-direction in blue, y-direction in red)

is consistent with an ABCD matrix simulation [46] of the output beam after the cylindrical

fiber/water interface (dashed lines). The complex beam parameter of the output beam in the y-

direction was obtained from a curve fit to the measured data (dashed red line in Fig. 5.5(b)) and,

using ABCD matrix transformations, the complex beam parameters of the circular beam within

the fiber, as well as of the refracted output beam in the x-direction (dashed blue line in Fig.

5.5(b)), were calculated. The tight focus in the x-direction dominates the resolution and

sensitivity characteristics of the probe and its location at a distance of ≈330 µm from the probe

can be assumed to define the approximate working distance in water. This is also apparent when

looking at the normalized on-axis intensity in Fig. 5.5(b) (dashed black curve), which was

calculated from the measured beam diameters dx and dy using the relation Ion-axis ∝ 1/(dx dy)

under the assumption that the beam can be well approximated by an astigmatic Gaussian beam.

The transverse intensity distribution of the elliptical spot at a distance of 330 µm from the

probe is shown in Fig. 5.5(c), demonstrating that the probe beam has a nearly diffraction-limited

Gaussian-like profile. The elliptical output beam allows imaging with a FWHM transverse

resolution below 20 µm over a distance of ≈700 µm from the probe in water (or ≈740 µm in

tissue with an average refractive index of n = 1.4), with peak resolutions of 8.8 µm and 16.2 µm

in the x- and y-directions, respectively.

The sensitivity of the ultrathin OCT needle probe was measured in combination with a

1300-nm swept source OCT (SSOCT) scanning system (see Fig. 5.6) which has a theoretical

shot-noise-limited sensitivity of ≈117 dB. The sensitivity of the probe was determined by

measuring the signal-to-noise ratio (SNR) of the backreflection from a silica/water interface

(Fresnel reflectivity of -26.8 dB). The results are displayed in Fig. 5.5(d), which shows an

averaged (1000×) A-scan of the silica/water interface (Peak 4) positioned at the point of

maximum backreflection, as well as the SNR of Peak 4 at a range of distances from the probe in

water. Also visible in the A-scan are some of the internal backreflections of the probe, where

Peak 1 is the splice between the GRIN fiber and the angle-polished NCF section; Peak 2 is

believed to be backscattering from imperfections of the angle-polished and metalized NCF end

facet; and Peak 3 is the NCF/water interface. Peak 5 is a spurious signal from the SSOCT

system that is not fully suppressed by the fixed-pattern noise removal algorithm. The highest

SNR is obtained at a distance of 346 µm from the probe, which is in good agreement with the

beam profile measurement results of Fig. 5.5(b) that lead us to expect the point of maximum

sensitivity to be in close vicinity of the tight focus of the x-direction at ≈330 µm. The peak SNR

of 56.1 dB translates into a sensitivity of 108 dB, taking into account the -26.8-dB reflectivity of

the silica/water interface and an additional attenuation of 25 dB, which was introduced by


158

loosening the FC-APC connection of the sample arm fiber. The additional 25-dB attenuation

was necessary to prevent saturation of the detector.

The high sensitivity of the ultrathin OCT needle probe can be attributed to its low round-trip

loss of only ≈2.5 dB, which was determined by measuring the returning signal from a silver

mirror aligned at the working distance under water immersion. This is a significant

improvement compared to the first-generation ultrathin OCT needle probe, which had a

relatively high round-trip loss of ≈10 dB, primarily caused by the absorption of the metal

reflection coating in the 840-nm operating wavelength band [36]. Apart from benefiting from

the lower absorption in the 1300-nm operating wavelength band, this second-generation

ultrathin OCT needle probe also uses a thinner chrome adhesion layer (3-nm thickness

compared to 10-nm in the first-generation needles) in order to minimize its detrimental effect on

the optical properties of the gold reflection coating.

Fig. 5.5 Beam profile and sensitivity characterization of the probe. (a) Illustration of the

astigmatism introduced by the fiber, resulting in different working distances WDx and

WDy in the x- and y-directions. (b) Measured, simulated and fitted FWHM output beam

diameters in water, and calculated normalized on-axis intensity (see text for details). (c)

Transverse intensity profile of the beam in water at the focus of the x-direction, at a

distance of 330 µm from the fiber. (d) Averaged OCT A-scan of a silica/water interface

(Peak 4) located at the distance of maximum SNR. The SNR of Peak 4 over a range of

distances from the probe is also shown (circles). See text for discussion of the

remaining peaks.

(c) 1300-nm OCT imaging system and data acquisition

The OCT needle probe was interfaced to an SSOCT system (Fig. 5.6). The light source is a

wavelength-swept laser (Axsun, USA) with an average power of 40 mW, a sweep rate of


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50 kHz, and a full sweep bandwidth of 100 nm centered at 1310 nm. The source power is

approximately constant within the sweep bandwidth, resulting in a flat-top spectral shape. For

this reason, a Hann window (also known as Hanning window) is applied to the spectral data

prior to the Fourier transform in order to reduce the sidelobes in the axial point spread function.

The resulting FWHM axial resolution in air, after application of the Hann window, is 21 µm.

The source provides a clock output that is generated using a Mach-Zehnder interferometer

(MZI), allowing equidistant sampling in frequency space and eliminating the need for

computationally intensive resampling of the spectral data. The 50-kHz trigger pulses from the

source are gated by a synchronization signal from the needle motion controller which counter-

rotates and retracts the needle during scanning. The motion controller outputs 1600 trigger

pulses per 360 degree rotation of the needle, and it performs a full counter-rotation (360 degrees

clockwise and anticlockwise) every second, resulting in an effective scan rate of ≈3200 A-scans

per second. The OCT signal is sampled with a 12-bit, 500-MS/s digitizer card (ATS9350,

Alazar Technologies, Canada).

The rotation-scanning principle employed acquires A-scans at constant angular intervals,

which inherently results in a circumferential spatial sampling interval that linearly increases as a

function of distance from the needle axis. For this reason, a high angular sampling density of

1600 A-scans per 360 degree rotation was chosen to ensure that, at any given distance from the

needle, the circumferential sampling is always finer than the FWHM transverse resolution of the

beam (see Fig. 5.5(b)). For example, at the maximum expected useful imaging depth in

scattering tissue of 2 mm, the circumferential sampling interval has a size of 8 µm, which is

smaller than the transverse resolution at that depth.

Fig. 5.6 Schematic of the 1300-nm SSOCT needle imaging system. MZI, Mach-

Zehnder interferometer; WDM, wavelength-division multiplexer; VOA, variable optical

attenuator; SYNC, synchronization signal; PC, polarization controller.


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(d) Skeletal muscle imaging experiments

All the animal work conformed to the guidelines of the National Health & Medical Research

Council (Australia) Code of Practice for the Care and Use of Animals for Scientific Purposes

(2004) and the Animal Welfare Act of Western Australia (2002), and was approved by the

University of Western Australia Animal Ethics Committee. To demonstrate the ability of the

needle probe to image the structure of skeletal muscle, normal and dystrophic mouse skeletal

muscle samples, from either forelimbs or hindlimbs, were excised as intact muscles by an

experienced physiologist. Immediately after excision, the samples were stored at room

temperature in phosphate-buffered saline. Imaging experiments were carried out within six

hours of sample collection. We imaged five normal mouse muscles and five dystrophic mouse

muscles (in each case two triceps, two quadriceps, and one tibialis anterior muscle). The

ultrathin OCT needle probe was inserted ≈10 mm deep at one location on each muscle sample.

This location was marked by a piece of surgical thread penetrating the muscle sample

perpendicularly to the needle tract to aid in its identification in subsequent histology. OCT C-

scans were acquired as the needle probe was counter-rotated at 1 Hz and retracted over a

distance of 4 – 6 mm at a speed of 5 µm/s in discrete steps of 5 µm.

After scanning, the intact muscle samples were immediately fixed in formalin solution. The

samples were embedded in paraffin and sectioned into 5 µm-thick sections at 90-µm intervals in

accordance with standard histological procedures. Using the surgical thread as the indicator of

the imaged area, these sections were taken parallel to the needle trajectory. Sections were

stained with haematoxylin and eosin (H&E) and digitally photo-micrographed (Scanscope, XT,

Aperio Technologies Inc., Vista, California, USA). The 3D OCT data volumes were visualized

using in-house visualization software (OCTView) and oblique views were visualized to match

the histological sections by correlating multiple structural features over a range of depths of

both the 3D-OCT volumetric dataset and H&E-stained histological sections.

5.3.3. Results

Figure 5.7 shows a 2D OCT image extracted from a 3D data volume acquired on a mouse

quadriceps muscle, and the matching H&E histology. To obtain corresponding images, an

oblique longitudinal image was extracted from the 3D OCT data volume and orientated so as to

be parallel and adjacent to the needle probe, thus, the needle shaft is not visible. In this oblique

OCT image slice, each horizontal row of the image intersects a different radial B-scan. The

reduced signal strength (darker tones) on the left and right of the image correspond to areas of

muscle tissue that are the most distant from the needle probe. Myofibers (see examples labelled

by arrowheads and MF) in the OCT image appear as a characteristic striated pattern, with the

boundary of the fascicle marked by highly backscattering connective tissue (labelled C) or

tendon (labelled T). Good correspondence is observed in the orientation of the myofibers

between the OCT needle images in fresh tissue and the matching fixed histological section.


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Fig. 5.7 Representative images of normal mouse skeletal muscle. (Left) OCT oblique

slice taken from the 3D OCT volumetric dataset. The striated appearance indicates the

highly organized arrangement of the myofibers (MF and/or arrowhead). Several

structures with higher signal intensity indicate tendon (T) and connective tissue (C).

(Right) Corresponding H&E histology.

Figure 5.8 shows representative images obtained from a dystrophic muscle sample taken

from the quadriceps muscle of an mdx mouse [4]. As with Fig. 5.7, a longitudinal image was

extracted from the 3D OCT volume and matched against histology. The characteristic striated

pattern of myofibers can be seen in the left most area of the image (see examples labelled by

arrowheads and MF), correlating with myofibers visible in the matching histology. An area of

necrosis is visible in the middle section of the histology image, marked by the appearance of

purple-stained, basophilic inflammatory cells, and a “broken” appearance in the adjacent

myofibers. This presents in the OCT image as a loss of striated texture of myofibers (labelled

Necrosis). The normal and necrotic regions are clearly delineated by connective tissue (labelled

C), visible in both images. The appearance of both healthy and necrotic regions of skeletal

muscle imaged with the OCT needle probe are consistent with earlier results obtained with a

standard, external-scanning benchtop OCT system [30, 31]. The OCT image, however, does not

show a structure corresponding to the connective tissue in the right-hand-side of the histological

slide. This is probably because of insufficient signal intensity within that corresponding region

in the OCT image.

Several views of a 3D rendered visualization of the mouse skeletal muscle OCT image are

shown in Fig. 5.9, and the associated video is available as Supplementary Video 3. During each

scan, a 3D cylinder of OCT data is acquired, with the central axis located along the needle

trajectory (labelled N), and the radius of the cylinder corresponding to the image depth from the

needle shaft. Fig. 5.9(a) shows the uncropped data set, with the dashed lines indicating the

different cropping planes used in Fig. 5.9(b)-(d). Note that Fig. 5.9(d) is cropped to show the

imaging plane that was histology matched in Fig. 5.7. Cropping of the 3D data allows

inspection of the 3D structure of the muscle fibers. Connective tissue and tendon are also

visible, labelled C and T, respectively, from different orientations.


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Fig. 5.8 Representative images of dystrophic mouse skeletal muscle. (Left) OCT

oblique slice taken from the 3D OCT volumetric dataset. The striated appearance

indicates the highly organized arrangement of myofibers (MF and/or arrowhead). The

structure with higher intensity indicates connective tissue (C). Muscle necrosis is

visible as a region without striated appearance (Necrosis). (Right) Corresponding H&E

histology.

Fig. 5.9 A 3D-rendered volumetric OCT dataset of normal mouse muscle at an

approximate depth of 10 mm in a) and three orthogonal cross sections in b), c) and d).

The cross section in d) shows the same image plane as that of Fig. 5.7, but the

brightness and contrast in the visualization software were adjusted differently in this 3D

view to enhance the appearance of the full dataset, yielding a slightly different dynamic

range on the color bar compared to Fig. 5.7. B, birefringence artifacts; C, connective


163

tissue; MF, myofibers; N, needle tract; T, tendon. The 3D scale bar in a) represents 500

µm in each direction (Supplementary Video 3).

Healthy skeletal muscle tissue is highly birefringent, arising from the highly organized

anisotropic cellular structure and arrangement of myofibers [48-50]. This results in a banding

pattern in the OCT image. The banding pattern is visible in the 3D visualization (see examples

labelled by double arrow heads and B). It has been demonstrated that polarization-sensitive

OCT (PS-OCT) is able to differentiate exercised dystrophic mouse muscle from healthy muscle

by detecting their different levels of birefringence [51]. In separate research, we have shown

that quantitative analysis of birefringence in a PS-OCT scan may be used to automatically

identify areas of necrosis in skeletal muscle tissue [52].

5.3.4. Discussion

The images presented here demonstrate the potential of OCT needle probes to visualize the

microstructure of mouse skeletal muscle at a depth of approximately one centimeter below the

tissue surface, and discern differences between tissue types. Regions of healthy mouse muscle

presented with a characteristic striated appearance, consistent with the alignment of the

individual myofibers. This was shown to be different for an area of necrosis, wherein the

destruction of the myofibers gave rise to areas of non-textured, more homogeneous backscatter.

Regions of mouse muscle tissue were well delineated by the higher backscatter of tendon and

connective tissue.

While earlier studies have demonstrated the ability of OCT to image mouse skeletal muscle

tissue [30-32], the shallow image penetration depth restricts the utility of such methods.

Deployment through a needle probe represents a significant step forward in the utility of OCT,

providing one solution to address the limited image penetration depth. Assessment of larger

areas of muscle tissue, involving multiple acquisitions, would provide a sampling of tissue

integrity throughout the muscle. An open question remains as to the number of such acquisitions

required to provide a statistically robust characterization of structure within a larger muscle.

This number will depend upon the pathology, with more homogeneous pathologies likely to be

sufficiently characterized by more sparsely distributed imaging acquisitions. Optimal needle

placement may also be guided by a complementary imaging modality such as ultrasound, as

demonstrated in [53].

The ultrathin OCT needle probe described in this paper has several technical improvements

over our earlier design [36], leading to the good image quality reported here. The sensitivity

gain was achieved by adapting the design for operation at 1300 nm in combination with an

SSOCT system with substantially higher baseline sensitivity than the previously used 840-nm

SDOCT system, and by reducing the optical losses of the probe through improvements in the

fabrication process. Operation at 1300 nm, furthermore, was observed to improve the image

penetration depth due to the reduced scattering at longer wavelengths [54, 55]. In addition,


164

improved mechanical robustness was obtained by using non-thermal ablation with femtosecond

laser pulses to fashion the imaging window. This also provided improved control over the

dimensions of the window and improved structural integrity of the adjacent sections of the

needle shaft. Such improvements in the OCT needle manufacturing process are important steps

to transition these probes from an optics research environment to the larger-scale production

required for pre-clinical and clinical usage.

The 2D OCT images of Figs. 4 and 5 exhibit some horizontal striations (perpendicular to

the needle axis), caused by variation in the SNR of individual B-scans. We observed this to be

due to small, isolated pieces of tissue being temporarily lodged in the needle hole through which

imaging occurs. Such tissue debris is typically cleared within one or two rotations of the needle

probe. The effects of such tissue debris could be reduced by increasing the spatial sampling

density in the pullback direction and performing spatial averaging along that axis in post-

processing.

The utility of OCT needle probes in the diagnostic assessment of muscle pathology could be

enhanced by employing quantitative image analysis for identifying regions of diseased tissue.

We note that a range of such techniques is under development, quantifying the distinction

between diseased and healthy tissue using optical properties such as the optical attenuation

coefficient [56, 57] or birefringence [52, 58].

5.3.5. Conclusion

In this paper, a highly optimized, high-sensitivity, ultrathin, side-viewing OCT needle probe has

been presented. With an outer diameter of 310 µm, the needle probe presents a minimally

invasive means of performing OCT imaging deep within tissue. We have presented the first

published 3D OCT data volumes of mouse skeletal muscle obtained by an OCT needle probe of

significantly improved performance and validated against co-registered H&E histology sections.

Results demonstrated the ability of such needle probes to distinguish the appearance of healthy

and necrotic mouse muscle tissue, and differentiate such areas from connective tissue and

tendon. These preliminary findings demonstrate the potential of OCT needle probes to provide a

new way to visualize in situ, deep within the tissue, the structure and integrity of skeletal

muscle.

5.3.6 Acknowledgements

The authors acknowledge Dr. Gavin J. Pinniger for providing the skeletal muscle tissue

samples. The authors acknowledge the facilities, and the scientific and technical assistance of

the Australian Microscopy & Microanalysis Research Facility at the Centre for Microscopy,

Characterisation and Analysis, The University of Western Australia, a facility funded by the

University, State and Commonwealth Governments. We also wish to acknowledge

CELLCentral, University of Western Australia, for the preparation of histological slides. We

acknowledge the support from the Western Australian node of the Australian National


165

Fabrication Facility for vacuum deposition of the metal reflection coatings in the OCT needle

fabrication, and we especially thank Nir Zvison. We also thank Peijun Gong for his help in the

generation of the video. Robert A. McLaughlin is supported by a fellowship from Cancer

Council Western Australia and this research is supported in part by funding from the National

Breast Cancer Foundation, Australia.

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5.4 Effect of the relative orientation of the needle insertion and myofibres

The orientation of the imaging needle relative to the direction of the myofibres was observed to

have an effect on the ability to discern the myofibre striations. Two possible orientations are

illustrated in Fig. 5.10. The imaging view (transverse or longitudinal) is constructed by rotating

and retracting the needle, and extracting a 2D image plane that is parallel to the direction of

retraction of the needle. Figure 5.10(a) shows the needle inserted into a section of muscle, with

the needle orientated along the muscle fibres. The radial B-scan (c) is orientated perpendicular

to the myofibres, and the longitudinal view is generated by taking an imaging plane parallel to


170

the direction of needle retraction/insertion as shown in (d). An example of the corresponding

OCT image acquired with a needle probe is shown in (e), where the striations of myofibres are

visible. Similarly, (b) shows the needle inserted perpendicular to the myofibres, with the radial

B-scan (f) orientated along the myofibres. In the transverse image (g), the light beam from the

rotating needle will extend across myofibres when the beam is orientated up or down. However,

as the needle continues to rotate (such that is orientated into or out of the page), the light will

travel along myofibres. The representative OCT image shown in (h) lacks the characteristic

striations visible in the transverse image. Small circular features are evident, corresponding to

the cross-sectional view of some myofibres.

Fig. 5.10 Schematic of 3D view of (a) longitudinal and (b) transverse needle insertion; schematic of the

radial B-scans of (c) longitudinal and (f) transverse needle insertion (according to the green dash lines);

schematic of the en face 2D view of (d) longitudinal and (g) transverse needle insertion (according to the

purple dash lines); the corresponding OCT images of the en face 2D view of (e) longitudinal and (h)

transverse needle insertion. M: myofibres; N: needle probe. The red regions indicate the fields of view.

The myofibres are indicated by the arrow head in (e) the longitudinal view and by the arrows in (h) the

transverse view. The scale bars in (e) and (h) both represent 100 µm.

During the imaging experiments using the second-generation ultrathin OCT needle probe, it was

noted that muscle striations were more evident in the longitudinal view (Fig, 5.4-01(e)) than in

the transverse view (Fig, 5.4-01(h)). Two hypotheses are presented to explain this phenomenon.

Firstly, we note that OCT typically shows a strong reflection at changes in the refractive index

of the tissue, most commonly occurring at the interface of tissue structures. We propose that, in

the longitudinal view, the light beam is always orientated across the myofibres, and undergoes a

change in refractive index as it enters and leave each myofibre (Fig. 5.10c), giving rise the

regular striations evident in the longitudinal view. Such structures are less evident in the

transverse view (Fig. 5.10h), as the light beam is coupled along the myofibres (not across them)

at some orientations of the needle (in 5.10g, this is when the light beam is orientated into or out


171

of the page). In such orientations, the light does not intersect the boundary of the myofibres,

thus shows less discernible backscatter.

Secondly, we hypothesise that, as the needle is inserted across and through many myofibres to

acquire the transverse view (Fig. 5.10b), it may damage the myofibres. The resulting optical

interface between the needle and adjacent, severed myofibres will present a rough optical

surface which may backscatter light in many directions, only some of which will be detected by

the needle probe.

The relationship between imaging geometry and the detection of anatomical features warrants

additional study, which lies outside of the scope of this thesis. However, our results have

established that the imaging geometry does have an impact of clarity with which features such

as the striations of myofibres may be discerned.

5.5 Chapter summary

The first-generation of ultrathin (30G) side-viewing OCT needle probe was applied to imaging

skeletal muscle. However, the moderate sensitivity (84 dB) makes the needle probe bare enough

to resolve the internal ultrastructure, such as individual myofibres, of skeletal muscle. The

second-generation of ultrathin side-viewing OCT needle probe possesses an improved

mechanical integrity and, more importantly, sensitivity (108 dB). The application of this

second-generation OCT needle probe in imaging skeletal muscle has been successfully

performed on both healthy and dystrophic mouse muscles. Compared with the colocated

histological sections, individual myofibres and other internal structures, such as connective

tissue and tendon, were clearly visualised from the acquired imaging data. From the imaging

data of the dystrophic mouse muscle, muscle damage was differentiated from surrounding

undamaged tissue. This differentiation was validated by the colocated histological sections.

Therefore, the capability of the second-generation ultrathin side-viewing OCT needle probe in

resolving ultrastructure (e.g., individual myofibres) and differentiating pathological muscle

damage deep inside skeletal muscle has been experimental demonstrated.

It was noted from the acquired OCT imaging data that the longitudinal view of skeletal muscle

contained more evident ultrastructures, striated pattern of myofibres, compared to the transverse

view. This phenomenon was hypothesised to be resulted from several mechanisms. One of the

possible mechanisms is that the incident light will experience multiple changes in refractive

index when acquiring the longitudinal view of myofibres. However, such experience will not

occur when acquiring the transverse view of myofibres due to the optical isotropy along the

length of each myofibre. Another possible mechanism is that the irregular interfaces between

the needle and the myofibres, which are created by the disruption and cut of the myofibres

operated by the needle insertion, will reduce the amount of backscattered light. Therefore, the

signal intensity is less in the transverse view of myofibres than in the longitudinal view.

Chapter 6 - Conclusion

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Chapter 6

Conclusion

6.1 Significance of the research outcomes

This thesis has focused on overcoming the impediments of OCT in skeletal muscle imaging.

Specifically, the imaging modality of PS-OCT, an extension of OCT, was applied to the

measurement of muscle birefringence and quantitative assessment of muscle damage within

dystrophic muscle based on the correlation between muscle damage and low birefringence. This

application was able to overcome the limitation of OCT by automatically quantifying the

proportion of muscle damage within a dystrophic muscle sample, which is important for inter-

scan and inter-sample comparisons of the extent of muscle damage. An ultrathin side-viewing

OCT needle probe was developed for minimally invasive in situ or in vivo imaging of

ultrastructures deep inside skeletal muscle. This OCT needle probe overcame the penetration

depth limitations of OCT when imaging opaque tissue samples.

The birefringence of skeletal muscle is the physical and physiological basis of PS-OCT muscle

imaging. From the cellular level to the molecular level, the highly organised structural

arrangement inside skeletal muscle, as described in Chapters 2 and 3, leads to optical anisotropy

of skeletal muscle. Whilst studies of the muscle birefringence have been performed for several

decades [349-354, 357, 359, 366], measurement of muscle birefringence using PS-OCT only

began in the 1990s [350, 351]. Earlier studies usually employed polarised light microscopy.

The mathematical representation (the Jones or the Mueller-Stokes formalisms) of the SoP of

each reflector in an imaged muscle sample can be obtained from PS-OCT data. Based on the

change of SoP along each A-scan, a specific birefringence value can be automatically calculated

using the computational algorithm developed by Chin et al. [408] (see Chapter 3). Therefore,

each PS-OCT volumetric dataset is collapsed to a single value of birefringence along the depth

or A-scan direction.

The optical anisotropy of dystrophic muscle is disrupted by the structural disorder, induced by

the pathological muscle damage associated with the disease. Exercise of the dystrophic muscle

elevates this muscle damage. As a result, the birefringence of damaged muscle tissue is

significantly reduced due to the loss of optical anisotropy. Using PS-OCT imaging, Pasquesi et

al. in 2006 first demonstrated experimentally that exercised dystrophic muscle from mdx mice

had remarkably lower birefringence compared with healthy muscle samples and non-exercised

mdx muscle [56].


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In Chapter 3, the research by Pasquesi et al. was extended by applying PS-OCT to the

characterisation of the SoP of each voxel in imaged muscle samples. The computational

algorithm was used to generate the 2D en face parametric images from each acquired volumetric

PS-OCT dataset. The volumetric proportion of muscle damage was then automatically assessed

from the generated en face parametric images. The measured and calculated birefringence of

each pixel on the en face parametric image is represented by an absolute value, which is

determined only by the extent of optical anisotropy and, thus, the extent of structural anisotropy

of the corresponding A-scan. This distribution of muscle damage, as well as the calculated

volumetric proportion of muscle damage using this method is, therefore, more objective and

reliable than the characterisation of muscle damage offered by OCT, which is based on signal

intensity that is not only determined by the reflectivity of the tissue reflector but also by the

irradiance of the incident light, the sensitivity of the imaging system, and imaging artefacts

induced by the sample itself. Hence, inter-scan and inter-sample comparison of the distribution

and proportion of muscle damage, which is important in both preclinical and clinical studies of

muscular dystrophy, can be achieved by the characterisation and quantitative assessment of

muscle damage using PS-OCT. Moreover, the 2D en face parametric image generated by PS-

OCT gives a more intuitive visualisation of the volumetric proportion of muscle damage.

The development of an ultrathin side-viewing OCT needle probe and the application of this

probe to the characterisation of structures deep inside skeletal muscle samples are described in

Chapters 4 and 5, respectively. Endoscopic OCT probes, including catheter-based [384, 387,

389, 390, 394] and needle-based ones [301, 314, 323, 372, 403, 404], have been intensively

developed to overcome the limited penetration depth of OCT when imaging opaque biological

tissues. In contrast to the catheter-based OCT probes that are typically used to image cavities or

lumens inside animals or human patients, needle-based OCT probes enable deep imaging inside

solid tissues based on needle insertion. For the side-viewing OCT needle probes, which are able

to provide 3D imaging data from the radial scans achieved by pullback rotation, several designs

have been reported [301, 314, 323, 372, 403]. However, the ball lens, microprism, or mirror in

these designs, hamper the extreme miniaturisation of the optics. Therefore, we chose to design a

probe with an angle-polished surface at the end of the optics, which makes the optics small

enough to be encased in a 30G hypodermic needle (OD 0.31 mm). This is the smallest reported

functional side-viewing OCT needle probes and for this reason, tissue damage as a result of the

needle insertion is minimised.

When this fabricated ultrathin side-viewing OCT needle probe was applied to the in situ

imaging of animal lung tissue, this probe was able to image the internal structures of solid

biological tissues. The ultrastructures inside the lung tissue, such as individual alveoli and

bronchioles, were clearly visualised from the acquired volumetric OCT data. However, further

application of this probe to skeletal muscle imaging revealed that the sensitivity of the

employed probe, which is 84 dB, was not enough to resolve muscle ultrastructures, such as


174

individual myofibres. This is probably because the contrast provided from the interface between

air and tissue inside lungs is higher than the contrast provided by the individual myofibres and

their surrounding tissue.

An improved version of the ultrathin side-viewing OCT needle probe, as well as its application

to the characterisation of internal ultrastructures of skeletal muscle, is presented in Chapter 5.

Interfaced to a newly customised 1300-nm SS-OCT system, the sensitivity measured from this

second-generation needle probe was increased to 108 dB. The mechanical integrity of this probe

was improved by including a laser-drilled side opening on the hypodermic needle. The acquired

volumetric data of OCT, which were obtained using this improved probe, were able to visualise

the individual myofibres and differentiate muscle necrosis from the surrounding undamaged

tissue within dystrophic muscle.

By delivering the incident light at a depth of ~1 cm below the tissue surface, the ultrathin side-

viewing OCT needle probe offers a solution to the problem of limited penetration depth of

traditional OCT (with a free-space probe) in imaging opaque biological tissue. In vivo imaging

of the ultrastructures inside solid tissue, especially from small animals, such as mice, can be

achieved with minimal invasion. The capability of the OCT needle probe to characterise the

internal ultrastructures, such as individual myofibres, and differentiate muscle necrosis from the

surrounding undamaged tissue, enables the longitudinal study of animal models and, potentially,

human patients with myopathies, such as muscular dystrophy. This will significantly benefit

pharmaceutical and nutritional intervention studies of myopathies, which require in vivo

monitoring of pathological tissue damage.

In Chapter 4, two alternative designs of the optics are presented that can be potentially

employed in the side-viewing OCT needle probes and extend the DOF. Following one of these

designs, a DOF gain of more than 1.5 was obtained experimentally with acceptable compromise

in the lateral resolution and sensitivity. The other design showed experimental problems in the

demonstration. These problems were hypothesised to be due to the imperfect index refractive

profile of the commercially available GRIN fibre. Further computational simulation based on

BPM validated this hypothesis. Validation of the fabricated probe following one of these

alternative designs demonstrated that the design of the probe was practically useful and

improved the visualisation of tissue.

6.2 Research limitations and future work

The studies presented in this thesis extend the traditional OCT imaging of skeletal muscle in

two ways. The extension of PS-OCT imaging with the automated algorithm offers a more

reliable means for the automatic characterisation and quantitative assessment of muscle damage

within dystrophic muscle tissue. The ultrathin side-viewing OCT needle probe offers access to

the internal structures of solid biological tissues, which enables in vivo imaging of muscle


175

damage inside dystrophic muscle with minimal invasion. Future research may combine these

two extensions by developing needle-based PS-OCT probes. These PS-OCT needle probes will

be able to provide 3D PS-OCT images of the internal structures inside biological tissue. Muscle

damage within dystrophic muscle tissue can then be visually characterised and quantitatively

assessed (with the developed automated algorithm), perhaps at multiple locations, due to

minimal trauma induced by needle insertion (as compared with removal of a small segment of

tissue from a single site as occurs in muscle biopsy that is then analysed by conventional

histology).

The automated algorithm for the calculation of birefringence and assessment of muscle damage,

which is presented in Chapter 3, is not able to provide depth-resolved birefringence profiles.

Each birefringence value calculated using this algorithm represents the birefringence of the

corresponding A-scan, which over a physical range of 50 µm to 550 µm from the tissue surface

(determined from the OCT signal by taking the tissue refractive index as 1.4). Therefore, the

current implementation of the developed algorithm hypothesises that the birefringence of the

tissue is a constant along each A-scan. This occurs because the algorithm calculates the

birefringence by evaluating the slope of the unwrapped phase retardation obtained from each A-

scan over some range. The hypothesis of a constant birefringence along each A-scan is usually

valid for the relatively homogeneous tissues, such as tendon. However, complex structures

inside skeletal muscle, such as connective tissue, may introduce change of birefringence along

tissue depth. In this case, segmentation of the tissue into several homogenous regions may be

required to enable the separate calculation of the birefringence of each homogeneous region.

Hence, a segmentation algorithm, such as the algorithm proposed by van Soest et al. [409], is

likely to represent an improvement over the current algorithm.

There are about 600 different skeletal muscles that represent about 40-50% of the mass of the

human body and an overview of the distribution and proportion of muscle damage can be

problematic because the FoV of each generated en face parametric image is relatively small,

typically less than 10 × 10 mm and individual muscles need to be assessed. A PS-OCT system

with a larger FoV or multiple scans will be required if an overview of the muscle damage in the

whole body of a large animal or human patient is needed. Another potential solution to the

problem of larger scale imaging is to operate random partial scans with the current FoV, which

would give an estimation of the total distribution and proportion of muscle damage.

The small FoV, furthermore, limits needle-based OCT imaging. The FoV of the volumetric

datasets acquired using the ultrathin side-viewing OCT needle probe developed in this study is a

cylinder with an approximate radius of 2 mm and a length of 4 to 6 mm. The length is

determined by the pullback distance of the probe during scans and, thus, can be enlarged at the

expense of longer scan duration. In contrast, the radius of the cylindrical dataset is determined

by the penetration depth of OCT and, thus, cannot be readily changed. Therefore, multiple scans


176

are still likely to be required for imaging of the muscle damage in several muscles from the

animals or human patients.

The multiple scans require repeated needle insertion in needle-based OCT imaging, which is

challenging to manage. Minimal repetition of needle insertion is always preferred as long as a

statistically robust characterisation of the structure within the imaged tissue can be provided.

Hence, the homogeneity and size of the imaged tissue will determine the required number of

needle insertions. For tissues with homogenous internal structures, a relatively small number of

data acquisitions and, thus, needle insertions will be statistically sufficient for the

characterisation of the structural information of the tissue; whilst a large number of needle

insertions will be required if the tissue contains various structures inside. A distribution of the

needle insertions is required to cover the range of structural variety inside the imaged tissue.

Furthermore, different muscles are affected in the various muscular dystrophies. The

distribution of the needle insertions, therefore, should be focused within the most affected

muscles. This distribution can be optimised by the guidance provided by some complementary

imaging modality with larger FoV, such as US, as demonstrated in [410].

6.3 Summary of contributions

In summary, the contributions of this thesis include:

1. Demonstration of the capability of PS-OCT to characterise and quantitatively assess muscle

damage within dystrophic muscle. This is the first report to describe the generation of the en

face parametric images in this application, illustrating the distribution and proportion of muscle

damage within a region of dystrophic muscle from acquired 3D PS-OCT data using an

automated algorithm.

2. Development of an ultrathin side-viewing OCT needle probe. This probe is the smallest (OD

0.31 mm) reported functional side-viewing OCT needle probe. The capability of this probe to

image internal ultrastructures of solid biological tissue was demonstrated by imaging animal

lung samples in which individual alveoli and bronchioles were clearly visible. Two additional

alternative designs potentially useful for OCT needle probes with an extended depth of focus are

presented.

3. Demonstration of the first application of the improved ultrathin side-viewing OCT needle

probe to imaging internal ultrastructures of skeletal muscle and differentiating muscle necrosis

from surrounding undamaged muscle tissue. Individual myofibres were clearly visible in the

acquired 3D OCT images.

The advances reported in this thesis pave the way for future clinical applications of OCT to the

characterisation and quantitative assessment of muscle damage for muscular dystrophies and

other muscle disorders.

Appendix I - Theoretical description of OCT

177

Appendix I

Theoretical description of OCT

Preface

In this appendix, a theoretical description of OCT principles is provided. Since we employed

spectral domain OCT (SD-OCT) as our imaging technology, this description is based on a

generic SD-OCT system. However, we note that the technical development of SD-OCT was not

the focus of this thesis.

Introduction

For a generic OCT imaging system, the incident light comes from the light source to a

beamsplitter, typically with 50/50 splitting ratio. At the beamsplitter, half of the light intensity is

deflected to the mirror at the end of the reference arm, while the other half propagates through

the beamsplitter and illuminates the sample after exiting from the sample arm. The light in the

reference arm will be back-reflected from the reference mirror, whilst the light in the sample

arm will be back-scattered from the sample. Both of these signals will return to the beamsplitter

via the same paths. The light reflected from the reference arm will mix and, subsequently,

interfere with the light reflected from the sample arm at the beamsplitter. The interference signal

between these two light beams is detected by the detector, and a depth-resolved reflectivity

profile (A-scan) at the illuminated position on the imaged sample can be extracted from the

detected signal using Fourier analysis. By incorporating a beam scanning mechanism, B-scans

and C-scans can be acquired by extracting multiple A-scans.

A1.1 The incident light

We use iE to represent the electric field of the incident light exiting from the light source (Fig.

A1-1). This electric field is characterised by its wave number k and angular frequency ,

according to

)(ii e),( tkzksE

, (1)

where z and t are spatial position and time, respectively. The wave number k is defined as

2k , where is the wavelength of the light; while the angular frequency is defined as


178

2 , where is the frequency. The wavelength and frequency are coupled following

the relationship

nc

, (2)

where c and n are vacuum speed of light and refractive index of the medium in which the light

propagates, respectively.

The typically employed 50/50 beamsplitter will deflect half intensity of the incident light to the

reference arm and let the other half intensity of light propagate through (Fig. A1-1). The electric

field intensity is defined as the square modulus of the electric field. As a result, the electric

fields distributed by the beamsplitter to the reference arm and sample arm are both 2iE

.

Because the length of the reference arm is fixed in a typical SD-OCT, we set the optical

pathlength (one way) of the reference arm as Rz (Fig. A1-1). Before hitting the mirror at the end

of the reference arm, the electric field of the incident light propagating through the reference

arm is given by

RiiR e

2kzEE

, (3)

where i in the exponent is the unit of imaginary number. Similarly, the electric field of the

incident light along the sample arm, hitting some reflector inside the imaged sample is

nkzn

EE SiiS e

2

, (4)

where nzS is the total optical pathlength of the incident light from the beamsplitter to the specific

sample reflector [317]. Different sample reflectors at different depths refer to different nES and

nzS (Fig. A1-1).

A1.2 The reflected and back-scattered light

The electric field of the reflected light is dependent on the field reflectivity of the corresponding

reflector. The reflectivity of the mirror at the end of reference arm is fixed, and defined as Rr .

The reflected field from the reference arm at the beamsplitter is given by

R2iR

iR e

2kzrEE

. (5)

The employed factor of 2 indicates the round-trip pathlength of the field (Fig. A1-1).


179

The field reflectivity of the imaged sample is more complicated because it is continuously

varying with depth. However, the key features of the process can be illustrated using a

discretised sample reflectivity defined by a series of weighted delta functions to define the

reflectivity as a function of depth:

N

nnn zzrzr

1SSSSS )()(

. (6)

As a result, the total reflected field returning from the sample arm at the beamsplitter is given by

S2iSS

iS e

2kzzrEE

, (7)

where represents convolution, and the factor of 2 reflects the round-trip pathlength of the

reflected field returning from the sample. By substitution into the above with the definition of

SS zr , this sample reflection can be written as

nkzN

nnrEE Si2

1S

iS e

2

. (8)

The reflected field from the reference arm passes through the beamsplitter again and, thus,

interferes with the field back-scattered by the sample. This interference is subsequently detected

by the detector (Fig. A1-1).

Fig. A1-1 Schematic of the field quantities in a typical OCT system [317].

A1.3 Detection of the signal

The detector generates a photocurrent DI that is proportional to the total intensity of the

reflected and back-scattered light. This total intensity is the square of the sum of the reflected


180

fields. Hence, the photocurrent arising from the reflected fields from both the reference arm and

sample arm is given by

2

2SR

DEE

I

, (9)

where is the responsivity of the detector with units of Amperes/Watt. The factor of 2

indicates the second pass of each field through the beamsplitter. Furthermore, the angular

brackets denote the integration over the response time of the detector. If we replace the reflected

fields with their equivalent expressions involving the incident field, field reflectivities, and the

travelled optical pathlengths, the photocurrent can be rewritten as

2

1

2iS

i2iR

iD

SR e2

e22

N

n

kzn

kz nrErEI

. (10)

With the replacement of iE with )(ii e),( tkzksE , setting 0z at the surface of the

beamsplitter, the detected photocurrent can be fully expressed as

2

1

)2i(S

)2i(RD

SR e2

),(e2

),(2

N

n

tkzn

tkz nrksrksI

. (11)

The expansion of this squared expression eliminates the temporal-dependent terms, which

include 2 . From physical perspective, it is reasonable to eliminate these temporal-

dependent terms because oscillates too fast compared with the response time of any practical

detector. The detected photocurrent, therefore, is only dependent on the temporally invariant

terms:

N

mn

zzkzzkmn

N

n

zzkzzkn

mnmn

nn

RRkS

RRkS

RRRkSI

1

)(2i-)(2iSS

1

)(2i-)(2iSR

S2S1RD

SSSS

SRSR

ee)(4

ee)(4

...))((4

. (12)

Here, )(kS is the substitute of 2),( ks , indicating that the detected photocurrent is

independent of the angular frequency . RR and SR are termed the power reflectivities of the

reference mirror and sample reflector, defined as 2Rr and 2

Sr , respectively. Using Euler’s rule

to rewrite this equation, the detected photocurrent can be expressed as a real function of the

wavenumber, k :


181

N

mnmnmn

N

nnn

zzkRRkS

zzkRRkS

RRRkSkI

1SSSS

1SRSR

S2S1RD

)(2cos)(4

)(2cos)(4

...))((4

)(

. (13)

This function is commonly known as the “spectral interferogram” [317] (Fig. A1-2).

The function includes three components. The first one, ...))((4 S2S1R RRRkS ,

indicates a pathlength-independent offset to the photocurrent, which is referred to as “constant”

or the “DC” component. This component is proportional to the intensity of the incident light and

the sum of power reflectivities from both the reference arm and sample arm. Because the power

reflectivity of the reference arm typically dominates the sample power reflectivity, this

component is typically larger than the other two components. In the spectral interferogram of a

single reflector, this DC component determines the amplitude of the envelope (Fig. A1-2a). The

second component,

N

nnn zzkRRkS

1SRSR )(2cos)(

4

, indicating the interference

between the reflected light beams from both the reference arm and sample arm reflectors, is

termed the “cross-correlation” component, because it involves the power reflectivities of both

the reference mirror and the sample reflectors. The embedded pathlength difference between the

two reflected light beams, nzz SR , guarantees that depth-resolved information is contained by

this component. Therefore, this cross-correlation component is the desired one in OCT imaging.

In the spectral interferogram of a single reflector, this cross-correlation component determines

the amplitude riding on top of the DC-component amplitude or envelope amplitude (Fig. A1-

2a). The third component,

N

mnmnmn zzkRRkS

1SSSS )(2cos)(

4

, indicating the

interference between the different sample reflectors, is the “auto-correlation” component. This

component generates artefacts in the OCT image and is, thus, undesired. Because the power

reflectivities of sample reflectors are typically smaller than that of the mirror in the reference

arm, this auto-correlation component, which does not contain RR , is typically smaller than the

cross-correlation one. Minimisation of this auto-correlation component can be achieved by

properly choosing the reference reflectivity [315, 316]. The information encoding the depth of

the reflector is contained in the wavenumber period of the spectral interferogram of a single

reflector (Fig. A1-2a) and is shown as a superposition of cosinusoids in the spectral

interferogram of multiple reflectors (Fig. A1-2b). This information will be extracted during the

following analysis of the signal.


182

Fig. A1-2 Spectral interferogram of (a) a single reflector and (b) multiple reflectors. The envelope

amplitude, 2

S1R RR , is determined by the DC component (factors of )(kS are omitted for clarity).

The amplitude of S1RRR , superimposed on the DC component amplitude, is determined by the cross-

correlation component. The wavenumber period S1R zz

is determined by the depth of this single

reflector. The spectral interferogram of multiple reflectors is a superposition of cosinusoids with different

amplitudes and wavenumber periods [317].

A1.4 Analysis of the signal

As mentioned above, the cross-correlation component of the spectral interferogram contains the

depth-dependent sample structure encoded in the interference fringe frequencies. Therefore, it is

possible to retrieve the sample structure from the spectral interferogram via an IFT, where

),( kz are a Fourier transform pair. Here, z indicates the depth, which is in the spatial domain;

whilst k indicates wavenumber (defined as

2k ), which is in the spectral domain.

Before going into the details of the signal analysis, it is instructive to review the definition of

the axial resolution of the OCT system based on the given light source spectrum. An OCT

source spectrum is characterised by the central wavenumber 0k and wavenumber bandwidth

k (Fig. A1-3). Here, 0 indicates the central (mean) wavelength, and indicates the

bandwidth of the OCT light source. An OCT source spectrum, )(kS , is often approximated by

a Gaussian function:

20

e1)(

k

k-k

kkS

. (14)

After IFT, one obtains in the spatial domain:


183

22-ze)( kz . (15)

This spatial-domain function is called the “coherence function”. Here, z is the sample depth.

The FWHM of this coherence function, cl (Fig. A1-3), indicating the axial spatial resolution of

the OCT system, is an explicit function of the light source bandwidth:

202ln22ln2

klc

. (16)

This cl is termed the “coherence length” [317]. Hence, a broadband light source or a

monochromatic source that scans over a broad band is typically employed in OCT systems to

achieve a finer axial resolution.

Fig. A1-3 Fourier transform relationship between the coherence function )(z and the spectrum )(kS of the OCT light source [317].

Using the IFT, we can now retrieve the depth-resolved sample structure [317]. Convolution

appears after IFT due to the fact that the product of two original functions will become the

convolution of the two transformed functions. The calculated expression of the acquired spectral

interferogram based on IFT is:

N

mnmnmn

N

nnn

zzzRRz

zzzRRz

RRRzzi

1SSSS

1SRSR

S2S1RD

)(2)(8

)(2)(4

...))((8

)(

. (17)

Taking advantage of the sifting property of the delta function, the convolutions can be carried

out and the function rearranged as:


184

N

mnmnmnmn

N

nnnn

zzzzRR

zzzzRR

RRRzzi

1SSSSSS

1SRSRSR

S2S1RD

)(2)(28

)(2)(24

...))((8

)(

. (18)

This is the acquired signal amplitude, )(D zi , along the sample depth, z , which is commonly

referred to as the “A-scan” signal in OCT imaging. From both forms of the )(D zi function, the

DC component, cross-correlation component, and auto-correlation component, are still distinct

(Fig. A1-4). It should be noted that for each given )( SD nzi , there are two corresponding

pathlength difference values, nzz SR and RS zz n , that are symmetric about Rz (Fig. A1-4).

This is the mathematical explanation of the appearance of “mirror images” in OCT imaging

performed by SD-OCT systems.

Fig. A1-4 Illustration of the spatial-domain A-scan calculated based on the IFT. The A-scan contains

multiple reflectors. The DC component, cross-correlation component, and auto-correlation component are

distinct. Mirror image artefacts are illustrated [317].

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