novel mri tools for focused ultrasound surgery a dissertationsv207hm8865/kaye_elena_thesi… ·...

NOVEL MRI TOOLS FOR FOCUSED ULTRASOUND SURGERY

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Elena Kaye

December 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/sv207hm8865

© 2011 by Elena Aleksandrovna Kaye. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/sv207hm8865

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Kim Rosemary Pauly, Primary Adviser


Brian Hargreaves


John Pauly

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

Magnetic resonance imaging (MRI) guided focused ultrasound (MRgFUS) is a promis-

ing non-invasive and non-ionizing therapy in which the acoustic energy penetrates to

the target through the intact surrounding tissue without causing any significant bioef-

fects and without any incisions. At the target, ultrasound energy is converted to heat,

causing tissue coagulation and necrosis. MRI guidance is used with FUS to provide

high quality tumor margin definition as well as the ability to monitor the temper-

ature of the tissue and assess the treatment. Among the MRgFUS applications are

treatments of tumors in the prostate, breast, uterine fibroids, liver and brain. To

make these applications widely acceptable and available to patients, improvement of

image guidance is essential. The goal of this work was to develop novel MRI tools for

visualization of the focal spot and for adaptive focusing of ultrasound.

Visualization of the ultrasound focus is performed to confirm that the beam’s

focus is placed on the target anatomy. Currently, it is achieved by producing a small

temperature rise in a test spot, which is detected using MRI temperature monitoring

techniques. Focus localization often relies on multiple applications of ultrasound, the

cumulative effects of which can lead to potentially irreversible changes in healthy

tissue. In addition, visualization of the temperature rise with MRI is problematic in

tissue with high fat content such as breast. The thesis addresses the challenges of

focus visualization by introducing novel imaging methods, that image displacement

of tissue due to acoustic radiation force: 2D Fourier Transform (2DFT) spin-echo and

single-shot echo planar imaging (EPI) MR guided acoustic radiation force imaging

(MR-ARFI). The new pulse sequences are demonstrated ex vivo and optimized for

in vivo brain applications.

iv

One of the challenges of using FUS to treat brain pathology is overcoming the

phase aberrations of ultrasound caused by heterogeneous acoustic properties of the

skull bone. These aberrations result in partial or complete destruction of the focal

spot, and therefore prevent the delivery of sufficient energy to the targeted volume,

and cause heating where it was not intended. The current correction method es-

timates the aberrations from the thickness and density of the skull bone obtained

from pre-operative computerized tomography (CT) images of the patient’s head. Re-

cently introduced alternative methods use adaptive focusing approach combined with

MR-ARFI. The transducer elements’ emissions are manipulated until the acoustic

intensity, which is proportional to tissue displacement, is maximized. Promising, but

very time consuming, these methods do not offer a practical solution. In this work, it

is shown how using Zernike polynomials, actively utilized in optics, can increase the

efficiency of MR-ARFI-based adaptive focusing, making it a more suitable technique

for clinical applications.

v

Acknowledgements

It is my great pleasure to thank all the colleagues, collaborators and friends who made

this thesis possible.

The number one person to whom I owe my deepest gratitude is my adviser, Dr.

Kim Butts Pauly. I met Kim in March of 2005. After learning about her group’s

research, I was really eager to join. Thankfully, the interest was mutual and in the

end of the meeting Kim offered me a small project for that quarter, and soon invited

me to join the group. Since then, Kim not only has guided my research work, but

also has been a supportive mentor and an excellent role model. I owe to her the

independence and confidence I developed over the years, and it is fair to say that

meeting Kim was one of the most important events in my life.

Next, I would also like to express my gratitude to the other members of my

Ph.D. oral examination committee: Sami Tantawi, John Pauly and Brian Hargreaves.

While Kim is the reason I stayed at Stanford, Sami is the reason I came. Sami and

I met when I was working at Stanford Linear Accelerator Center. I was one of the

technicians helping Sami test the accelerator components he designed. He was the

first person to suggest I apply to Stanford. He really encouraged me and wrote one

of the recommendation letters. I will always be obliged to his support during that

time, and also for serving as a chair of my oral defense committee years later. After

Kim, John and Brian played the second most active roles in my research work. It is

in John’s class I learned the MRI “ABC’s,” and in his other courses, I made my first

RF pulse and leaned about numerous reconstruction techniques. I am very fortunate

to have had John not only as a teacher but also as my co-adviser. His expertise and

fantastic ideas helped me successfully navigate through all of my research projects. I

vi

am endlessly grateful to Brian for teaching me how to design and build my own pulse

sequences. Seeing my first pulse sequence work during one of the Brian’s classes was

a memorable and quite empowering experience. Particularly, I want to thank Brian

for his consistent support of my work, his readiness to help with trouble-shooting

whether it requires looking at the image artifacts or the pulse sequence code. My

accomplishments would not have been possible without the guidance of these people.

There are other colleagues and collaborators whose role in my work can not be

overlooked. I thank InSightec Ltd. for providing focused ultrasound technology as well

as complete technical support. Many thanks go to Yoav Medan and Yoni Hertzberg

with whom I had the pleasure to discuss with and work on many ideas. Other members

of InSightec’s team who I want to acknowledge are Eyal Zadicario, Gilat Schiff and

Fred Kusumoto. I also would like to thank Beat Werner of Children’s hospital in

Zurich for providing the clinical data that not only inspired some of my work but

also enabled me to test my ideas. Another person whose input into this thesis was

very valuable is Marc Levoy. His deep knowledge of optics helped me shape my final

focused ultrasound projects, and I am thankful for this. Implementing any of my ideas

would not have been possible without numerous discussions I had with my Stanford

colleagues: Gary Glover, Ron Watkins, Bruce Daniel, Dan Spielman, Peji Ghanouni,

Stefan Skare, Graig Scott, Adam Wang, Michael Marx, Sam Mazin, Priti Balchandani,

Pauline Waters, Kyunghyun Sung, Anne Sawyer, Donna Cronister, Donna Boulay,

Wendy Baumgardner, Tom Brosnan.

During my time at Stanford I attended many wonderful engineering courses, how-

ever, two of them I would like to acknowledge specifically. Introduction into Fourier

Transforms by Brad Osgood and Introduction into Linear Systems by Stephen Boyd

were both the most memorable and the most influential courses, and the concepts I

learned from them have been a part of my everyday research work.

I also would like to make a special reference to Vioal Rieke and Rachelle Bitton for

the valuable discussion of MRI and ultrasound as well as their mentorship, support

and friendship. I would like to acknowledge separately three other Ph.D. students

whom I had a privilege of meeting at Stanford: Kristin Granlund, Sonal Josan and

Andrew Holbrook. With them I shared the excitement, the stress, the happiness, the

vii

fears, the pride, the regrets, the flights, the hotel rooms and lots and lots of fun that

filled my time at Lucas Center during the last six years. My graduate experience

would not have been as smooth and enjoyable without these people.

In addition to the above mentioned members of Lucas Center and MRSRL, I

would like to thank many others whom I enjoyed getting to know and working with

during my graduate career. I’d like to express my appreciation to the former and

the current members of Kim’s group: Aiming Lu, Jean Chen, Will Grissom, Randy

King, Juan Plata, Michale Marx and Urvy Vyas. In addition to Kim’s group, I would

like to thank the rest of my MRI and CT friends: Ernesto Staroswiecki, Caroline

Jordan, Rebecca Rakow-Penner, Tao Xu, Jared Starman, Catie Chang, Christine Law,

Samantha Holdsworth, Murat Aksoy, Prasheel Lillaney, Erin Girard, Laura Pisani,

Julie di Carlo, Angel Pineda, Rexford Newbould, Uche Monu, Andy Nnewihe, Joelle

Barral, Kim Schultz, Okai Addy, Monica Sigovan and Valentina Giannini.

I offer my regards and blessings to the family and friends who supported me in any

respect during my years at Stanford: my brother Lev, my friends Natasha Belkova,

Asya Yevdokimova, Jenya Karpenko and the Artemiev family in Russia, my uncle’s

family in Minnesota, the Kaye family, Katya Gladysheva and Natasha Lavryshina in

California. I especially would like to thank Francisco Godoy, who provided me with

moral support, love and encouragement during my graduate career.

Lastly, I would have not been here today if my grandparents Lev and Paulina

Gromov and Alexander and Antonina Golubev did not give their youth defending

Russia in World War II. To their sacrifices I owe my life. I feel the endless gratitude

to my parents, Marina and Alexander Gromov. They have supported my interests in

science and languages, and always provided help when I needed it, be it tutoring me

in Algebra or finding resources to pay for my English lessons. I know that they are

proud and happy for me. For the rest of my life I will work hard in order to have the

time and means to help them and be by their side when they need me.

viii

Contents

Abstract iv

Acknowledgements vi

1 Introduction 1

2 Overview of MRI guided Focused Ultrasound 6

2.1 Basic Concepts of Focused Ultrasound . . . . . . . . . . . . . . . . . 6

2.1.1 Ultrasound Propagation . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Focusing and Steering of Ultrasound . . . . . . . . . . . . . . 10

2.2 Effects of Ultrasound on Tissue . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Non-Thermal Effects . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2.1 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2.2 Acoustic Radiation Force . . . . . . . . . . . . . . . 14

2.3 Imaging of Ultrasound Effects on Tissue with MRI . . . . . . . . . . 17

2.3.1 MR Thermometry . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1.1 PRF-based Temperature Mapping . . . . . . . . . . 18

2.3.1.2 T1-based Temperature Mapping . . . . . . . . . . . 20

2.3.2 MR Acoustic Radiation Force Imaging . . . . . . . . . . . . . 22

2.3.2.1 MRI Spatial Encoding . . . . . . . . . . . . . . . . . 22

2.3.2.2 Early Work in MR-ARFI . . . . . . . . . . . . . . . 26

2.4 Generalized MRgFUS Protocol and Specific Challenges . . . . . . . . 29

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

ix

3 2DFT MR-ARFI for Focal Spot Localization 34

3.1 2DFT Spin-echo MR-ARFI Pulse Sequence . . . . . . . . . . . . . . . 35

3.1.1 2DFT MR-ARFI in Ex V ivo Brain Tissue . . . . . . . . . . . 37

3.1.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.2 Focal Spot Visualization in Fatty Tissue . . . . . . . . . . . . 42

3.1.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.1.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Imaging Temperature and Displacement . . . . . . . . . . . . . . . . 46

3.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4 Adapting 2DFT MR-ARFI for In V ivo Brain MRgFUS 51

4.1 Comparing Bipolar Encoding Configurations in Spin-echo MR-ARFI . 53

4.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Optimization of Encoding Duration for MR-ARFI in the Presence of

Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3 Measuring Tissue Response with MR-ARFI. Optimal Encoding Timing. 59

4.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Novel Adaptive Focusing Algorithms 68

5.1 Introduction to Adaptive Focusing . . . . . . . . . . . . . . . . . . . 70

5.2 Adaptive Focusing using the Partitioning Algorithm . . . . . . . . . . 71

5.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

x

5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.3 Adaptive Focusing Using Non-Iterative Algorithms . . . . . . . . . . 79

5.3.1 Analysis of Skull-Based Aberrations . . . . . . . . . . . . . . . 83

5.3.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.3.2 Simulation of Non-iterative Adaptive Focusing Algorithm Based

on Zernike Polynomials . . . . . . . . . . . . . . . . . . . . . . 87

5.3.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.3.3 Experimental Validation of Non-iterative Adaptive Focusing

Algorithm based on Zernike Encoding . . . . . . . . . . . . . . 92

5.3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.4 Zernike-encoded Adaptive Focusing: Discussion . . . . . . . . 93

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6 Echo Planar Readout for Rapid MR-ARFI 97

6.1 Single-Shot EPI MR-ARFI . . . . . . . . . . . . . . . . . . . . . . . 98

6.1.1 Displacement vs. Intensity . . . . . . . . . . . . . . . . . . . . 100

6.1.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.1.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.1.2 Measuring Temperature with Modified EPI-based MR-ARFI . 101

6.1.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.1.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.1.3 Comparison of EPI and 2DFT Spin-echo MR-ARFI . . . . . . 103

6.1.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.1.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

xi

7 Summary 108

7.1 Focal Spot Visualization . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.2 Adaptive Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Bibliography 113

xii

List of Tables

4.1 2DFT MR-ARFI imaging parameters used in four different experiments 52

6.1 MR imaging parameters used in EPI and 2DFT MR-ARFI acquisitions. 99

xiii

List of Figures

1.1 Schematic of FUS treatment. . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Hemispherical Phased-Array Ultrasound Transducer. . . . . . . . . . 2

2.1 Vibrating Piezoelectric Crystal. . . . . . . . . . . . . . . . . . . . . . 7

2.2 Single-element and Phased-array transducers. . . . . . . . . . . . . . 11

2.3 Focusing Phased-array Transducer to Compensate for Inhomogeneity . 12

2.4 llustration of Acoustic Radiation Force. . . . . . . . . . . . . . . . . . 15

2.5 Tissue Response to Acoustic Radiation Force. . . . . . . . . . . . . . 16

2.6 llustration of PRF Thermometry. . . . . . . . . . . . . . . . . . . . . 19

2.7 llustration of MR Flow Encoding Scheme. . . . . . . . . . . . . . . . 23

2.8 Illustration of MR Elastrography Encoding Scheme. . . . . . . . . . . 25

2.9 Unipolar Line-Scan MR-ARFI . . . . . . . . . . . . . . . . . . . . . . 27

2.10 Unipolar Line-Scan MR-ARFI Results . . . . . . . . . . . . . . . . . . 27

2.11 Unipolar and Repeated Bipolar Displacement Encoding Schemes. . . 28

2.12 Displacement SNR for Unipolar and Repeated Bipolar Encoding Con-

figurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.13 MRgFUS Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1 2DFT Spin-echo MR-ARFI Pulse Sequence Diagram. . . . . . . . . . 36

3.2 Experimental Setup with UF Transducer and Ex V ivo Brain Tissue . 37

3.3 2DFT MR-ARFI Images of Ex V ivo Brain . . . . . . . . . . . . . . . 39

3.4 Displacement Phase of Ex V ivo Brain Using Four Different Levels of

Acoustic Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

xiv

3.5 Displacement Phase Images in Ex vivo Brain Using Four Different

Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6 Schematic of the Ex V ivo Breast Experimental Setup . . . . . . . . . 43

3.7 MR-ARFI vs FSE Images in Ex V ivo Breast . . . . . . . . . . . . . . 44

3.8 Plot of the SNR at the Focal Spot of the FSE Magnitude Difference

Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.9 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.10 Simultaneous Temperature and Displacement Monitoring in Ex V ivo

Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1 Diagram of Displacement Encoding Configurations . . . . . . . . . . 54

4.2 Repeated vs Inverted Bipolar Encoding . . . . . . . . . . . . . . . . . 55

4.3 MR-ARFI at Different Encoding Durations . . . . . . . . . . . . . . . 58

4.4 Partial Diagram of MR-ARFI Pulse Sequence, Modified for Measure-

ment of Tissue Time Constants . . . . . . . . . . . . . . . . . . . . . 60

4.5 Tissue Constant Measurements . . . . . . . . . . . . . . . . . . . . . 63

4.6 Plot of the Normalized Displacement Phase . . . . . . . . . . . . . . 64

5.1 Schematic of adaptive processing process . . . . . . . . . . . . . . . . 69

5.2 llustration of Continuous and Partitioning Algorithms. . . . . . . . . 71

5.3 Illustration of the transducer and aberrator positions. . . . . . . . . . 72

5.4 Effect of acrylic aberrator and numerically added aberrations on the

quality of the focus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.5 Displacement Phase during single iteration. . . . . . . . . . . . . . . . 75

5.6 Displacement Profiles After Each Iteration. . . . . . . . . . . . . . . . 76

5.7 MRgFUS Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.8 Intensity during the 400 iterations of the partitioning and continuous

algorithms with and without noise. . . . . . . . . . . . . . . . . . . . 77

5.9 Zernike Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.10 Hemispherical Transducer Experimental Setup . . . . . . . . . . . . . 83

5.11 Patient skull data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.12 Patient aberration data . . . . . . . . . . . . . . . . . . . . . . . . . . 86

xv

5.13 Graphic presentation of the correlation coefficients between phase aber-

ration data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.14 Orthonormalization of Zernike Polynomials . . . . . . . . . . . . . . . 90

5.15 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.16 Experimental Validation of Non-iterative Adaptive Focusing Algorithm 93

6.1 EPI MR-ARFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2 EPI MR-ARFI Images in a Phantom . . . . . . . . . . . . . . . . . . 101

6.3 Temperature Rise during EPI MR-ARFI acquisitions . . . . . . . . . 102

6.4 EPI vs 2DFT Spin-echo MR-ARFI . . . . . . . . . . . . . . . . . . . 104

6.5 EPI and 2DFT Displacement Images during Transducer Defocusing . 105

xvi

Chapter 1

Introduction

Magnetic resonance imaging (MRI) guided focused ultrasound (MRgFUS) is a promis-

ing non-invasive alternative to conventional surgery. In this approach the acoustic en-

ergy penetrates through the intact skin and through the tissue surrounding the target

of the treatment without causing any significant bioeffects and without any incisions.

The deposition of the ultrasonic energy is limited mainly to the focal spot where it

is absorbed by the tissue and converted to heat, therefore accomplishing localized

treatment of the targeted tissue only (Figure 1.1). MRI guidance of ultrasound ther-

apy provides high quality tumor margin definition as well as the ability to monitor

and assess the treatment. In addition, unlike radiation therapy, MRgFUS presents no

toxicity risk, which is particularly beneficial for pediatric patients and the patients

who have already exceeded their safe radiation dose [1].

Initially, FUS therapy was proposed for the destruction of brain tissue [2] in 1942.

In the 1950’s, William and Francis Fry developed a FUS system to treat Parkin-

son’s disease non-invasively [3, 4]. For more detailed description of these and other

historical milestones of therapeutic ultrasound, the reader is referred to the review

by Kremkau [5]. While the first tests of the FUS system were successful, FUS was

not immediately used outside of the research setting due to the high complexity of

the procedure. Technological advancements were required in the area of transducer

design and medical imaging to bring FUS therapy into clinical use. Today, most of the

FUS systems rely on sophisticated phased-array transducers of up to several hundred

1

CHAPTER 1. INTRODUCTION 2

Figure 1.1: A schematic representation of high intensity focused ultrasound treatment.

(a) (b)

Figure 1.2: (a) Photograph of a 1024-channel hemispherical transcranial phased-arraytransducer filled with degassed water. The radius of the hemisphere is 15 cm. (b)Photograph of the transcranial MRgFUS system showing a patient on the scannertable with his head positioned inside the hemispherical transducer. (This was providedcourtesy of InSightec Inc.)


independent channels. A 1024-channel hemispherical phased-array transducer, devel-

oped for transcranial FUS therapy, is shown in Figure 1.2. In order to enable accurate

targeting of the ultrasound treatments as well as to monitor the effect of ultrasound

on tissue, the modern FUS systems are combined with diagnostic ultrasound imaging

or MRI. Ultrasound guidance offers less expensive and more real-time guidance of

FUS therapy than MRI. In turn, MRI provides outstanding soft tissue constrast and

tumor definition, and most importantly can monitor the temperature of the tissue

during ultrasound ablation.

The successful development of FUS therapy led to a continuously increasing num-

ber of the FUS applications, both ablative and non-ablative. Among the ablative

applications are treatments of tumors in the prostate [6, 7], breast [8, 9], uterine fi-

broids [10], liver [11, 12], brain [13, 14] and eye [15, 16]. The non-ablative procedures

include targeted drug delivery [17], focal blood-brain barrier disruption [18], and gene

therapy [19,20]. To make these MRgFUS applications widely acceptable and available

to patients, improvement of image guidance is essential. One aspect of MRI guidance

in need of improvement is localization of the focal spot. Another area of active devel-

opment is correction of phase aberrations caused by heterogeneous speed of sound in

tissue.

Localization of the ultrasound focal spot is important as it allows confirmation

that the beam’s focus is placed on the target anatomy. Currently, the first step of

any ultrasound procedure is to test whether the focal spot is at the intended location.

If not, the focusing of the transducer is adjusted. Focus visualization is achieved

by producing a small temperature rise in a test spot. This is detected using MRI

temperature monitoring techniques. Unfortunately, accurate focal spot localization

remains difficult to perform well in practice. It relies on multiple applications of

ultrasound, the cumulative effects of which can lead to potentially irreversible changes

in healthy tissue.

When ultrasound is applied to treat organs such as the liver and brain, the ultra-

sound has to pass through the ribs or skull bone, whose speed of sound is approxi-

mately 2.5 times greater than in soft tissue. This interference causes phase aberrations

of the ultrasound beam. If not corrected, these aberrations can result in partial or


complete destruction of the focal spot. Phase aberrations not only prevent the delivery

of sufficient energy to the targeted volume, but they also may lead to the appearance

of erroneous foci in other locations where heating was not intended. Therefore, in

applications like these, phase aberration correction has to be performed before focal

spot localization can even be started. The correction approach, used in ongoing clini-

cal trials of transcranial MRgFUS treatments, is based on estimating the transducer’s

phase aberration. This uses information about the thickness, shape and density of the

skull bone, which is obtained from high resolution pre-operative computerized tomog-

raphy (CT) images of the patient’s head. After phase correction, the intensity at the

focal spot is significantly increased compared to the uncorrected case. However, due

to potential errors during registration between CT and MRI images and due to ap-

proximations used in the phase correction algorithm, the intensity after correction

remains suboptimal. Typically this results in approximately 80% - 85% of the ideal

case value.

In this thesis, novel imaging tools are developed to address focal spot localization

and phase correction challenges of MRgFUS therapy. The outline of the chapters of

the thesis is presented below.

Chapter 2 is an overview of the basic concepts of ultrasound and MRI methods

that are used to guide FUS. First, the theory of the propagation and focusing of

sound waves is presented. Then, the biological effects of FUS, thermal and nonther-

mal, are summarized and put into the context of imaging. Discussion of MR temper-

ature monitoring is focused on proton resonant frequency shift (PRF)- and T1-based

thermometry. MR Acoustic Radiation Force Imaging (MR-ARFI) is presented as an

emerging technique to measure tissue displacement due to ultrasound. The technical

introduction is followed by a description of a generalized FUS treatment protocol and

a more detailed discussion of the current challenges.

Chapters 3 and 4 are devoted to development and optimization of the MR-ARFI

methods for high-image-quality visualization of the focal spot. Chapter 3 introduces

a 2DFT-based spin-echo MR-ARFI pulse sequence. The sequence is tested in ex vivo

brain and breast tissue. A study aimed to demonstrate the advantage of this MR-

ARFI method over a T1-weighted Fast Spin Echo (FSE) method to localize a focal


spot in fatty breast tissue is reported here. In Chapter 4, the existing displacement-

encoding configurations are carefully studied using simulation and experimentally in

normal volunteers and in ex vivo tissue. The effect of patient motion on the level of

ghosting artifacts is analyzed for two encoding gradient configurations with and with-

out cardiac gating. The duration of encoding is then optimized taking into account

not only T2 and diffusion effects, but also patient motion.

In Chapters 5 and 6, a new approach to skull phase aberration correction is de-

scribed. To address the need for rapid displacement imaging, a single-shot-EPI-based

MR-ARFI pulse sequence is demonstrated. This method is tested in ex vivo brain

tissue and compared to the 2DFT MR-ARFI. Chapter 6 deals with MR-ARFI-based

adaptive focusing algorithms for phase aberration correction. First, the existing ap-

proaches are explained in detail, and then, new non-iterative algorithm is presented.

Chapter 7 summarizes the thesis and proposes the potential direction of future

work in this area.

Chapter 2

Overview of MRI guided Focused

Ultrasound

In the context of medical imaging, both MRI and ultrasound play an important role

as modalities that do not rely on ionizing radiation. Ultrasound also has non-imaging

biomedical applications. Among these applications are therapeutic ultrasound abla-

tion, lithotripsy, and targeted drug delivery. This chapter describes the fundamental

principals of ultrasound that make it an excellent therapeutic medium as well as a

very versatile tool. Selected MR imaging methods that enable image guidance of FUS

therapy are discussed with priority given to the techniques most relevant to the work

described in this thesis. More in-depth discussion of MRI-guided FUS can be found

in Refs. [1, 21].

2.1 Basic Concepts of Focused Ultrasound

2.1.1 Ultrasound Propagation

Ultrasound is sound of frequency greater than 18 - 20kHz, which is considered the

upper limit of the audible range for humans. Like any type of sound, ultrasound is

produced by a mechanical motion that causes the particles in the medium to oscil-

late about their rest position. This oscillation results in the medium’s compression

6

CHAPTER 2. OVERVIEW OF MRI GUIDED FOCUSED ULTRASOUND 7

Figure 2.1: Schematic representation of a vibrating piezoelectric crystal disc posi-tioned at x = 0 and emitting an ultrasound plane wave propagating along x .

and rarefaction over time, which is commonly described by a traveling pressure wave.

Generation of ultrasonic pressure waves was not feasible until the discovery of piezo-

electric crystals. These crystals expand and contract with the frequency of the applied

radiofrequency (RF) voltage. Figure 2.1 shows a schematic representation of the ul-

trasound pressure field produced by the vibrations of the disc crystal source of radius

a, placed at location x = 0. The crystal’s sinusoidal vibration leads to the sinusoidal

displacement of the medium at its surface with time, given by

d = d0 sin(2πft), (2.1)

where d0 is displacement amplitude, f is the frequency of applied voltage signal and

t is time. The velocity of the surface motion can be found as the derivative of the

displacement:

u = u0 cos(2πft), (2.2)

where u0 is the amplitude of velocity. Assuming a planar circular source, the form

of pressure field it emits depends on the ratio of the source aperture radius to the

acoustic wavelength a/λ. If the radius a is smaller than the quarter wavelength λ/4,

a hemispherical wave is emitted. If the ratio is larger, the ultrasound field near the

source propagates as a plane traveling wave. In a plane wave, the velocity of a particle


in the ultrasound field is a function of position x and time t. It changes harmonically

with time and decreases exponentially with distance according to attenuation coeffi-

cient α:

u(x, t) = u0 cos(2πft− kx)e−αx. (2.3)

Here, k = 2π/λ is the wave number and α is the attenuation coefficient. This equation

represents an ultrasound wave that moves away from the source with a speed of sound

c = fλ [22]. The average speed of sound in most soft tissues is 1550 m/sec. In fatty

and lung tissue, ultrasound travels slower with respective velocities 1480 m/sec and

600 m/sec. Bone has a speed of sound ranging between 1800 and 3700 m/sec [23]. In

soft tissue, the speed of sound increases with temperature, however, in fatty tissue

the sound propagation slows down at higher temperature [23].

The attenuation coefficient α consists of scattering, αs, and absorption compo-

nents, αa:

α = αs + αa, (2.4)

and dictates how deep ultrasound can penetrate into tissue. In biologic tissue the

absorption losses, which convert acoustic energy into heat, were found to dominate

the attenuation [23,24]. Absorption mechanisms in biological tissue are complex and

comprised of classical absorption due to viscosity and relaxation phenomenon. Both

depend on the frequency of the wave, f . Many texts indicate relaxation phenomenon

is the dominant mechanism in biological tissue. Relaxation time refers to the time

required for a particle to return to its neutral position. It is an inherent property of the

medium governed by its molecular structure. If the relaxation time is short compared

to the period of the wave, it’s effect is negligible. If the relaxation time is comparable

to the wave period, the particle may not have time to return to its neutral state before

the next compressional or rarefactional portion of the wave arrives. When this occurs,

the wave is moving in one direction whereas the molecules are moving in the other

direction. Thus, more energy is required to reverse the direction of particle motion.

Maximum absorption occurs when the relaxation motion of the particles in a medium


is completely out of synchronization with the wave motion. In heterogeneous medium

such as tissue, multiple relaxation processes with varied relaxation frequencies overlap.

Absorption in tissue is linearly proportional to ultrasound frequency below 15MHz.

The attenuation of tissue as a function of frequency can be approximated as

α = a(f)b, (2.5)

where a and b are constants depending on the medium. For water, b equals 2, for

most soft body tissue it is close to 1. For example, in brain tissue a = 60 and b =

1.2, and in liver, a is between 36 and 90 and b is 1.0 - 1.3 [25].

When ultrasound propagates in a medium, the momentary variations in pressure,

p at any point are defined as acoustic pressure [22]:

p(x, t) = p0 cos(ωt− kx)e−αx, (2.6)

where p0 is the pressure amplitude, equal to the product of density, speed of sound,

and amplitude of particle motion ρcu0. To propagate the pressure wave from the

transducer outwards, the medium closer to the transducer does continuous work on

the medium away from the source. The time-averaged rate at which work per unit

area is done across any plane through which sound is propagating, is called intensity,

I, which is calculated as p2/ρc, and can be written as:

I = I0e−2αx, (2.7)

where I0 equals 0.5p0u0. And the acoustic power, which is the total work done by the

ultrasound source transducer per unit time [22], is expressed as:

W0 = πa2I0. (2.8)

While there is much more to the theory of ultrasound waves, understanding of ultra-

sound pressure, intensity and acoustic power is sufficient for the understanding of the

work presented here.


2.1.2 Focusing and Steering of Ultrasound

Focusing of the ultrasound field can be achieved by using a lens, by making a self-

focusing transducer or by using a phased-array of many small transducers. An example

of a spherically curved transducer is shown in Figure 2.2a. The position of the focal

spot is dependent on the radius of curvature. Greater radius of curvature allows

focusing ultrasound deeper in the tissue, however, it also increases the focal region

length and decreases the intensity. An array of the small ultrasound transducers,

each driven individually by its own RF signals, can also produce a focused ultrasound

beam. To focus the beam the input signals of each transducer have to be delayed by

an appropriate amount. The time delays for each channel are calculated to ensure

in-phase arrival of the ultrasound wave from each element at the focal spot. This is

referred to as electronic focusing, and its schematic representation is shown in Figure

2.2b.

In order to focus the ultrasound beam in a different location, the position of

a single-element transducer has to be adjusted, which is commonly achieved using

motors to translate the transducer to a different position (Figure 2.2c). Dependence

on mechanical translation of the transducer limits how rapidly the focal spot can

be steered. Phased-array transducers allow more flexible and dynamic control of the

ultrasound focus. The ultrasound beam is steered electronically by computing the

appropriate RF-signal time delays (Figure 2.2d). The ability to control each channel

individually becomes vital when ultrasound experiences aberrations on its way to

the desired focus. To compensate for the aberration, the transducer RF time delays

can be adjusted accordingly, making it possible to focus through an inhomogeneous

medium. Compensation of phase aberrations is shown in Figure 2.3.

2.2 Effects of Ultrasound on Tissue

The absorption of ultrasonic energy leads to tissue heating, and this heating has

been used for many therapeutic applications. It has also been realized that the non-

thermal effects that occur as ultrasound travels through tissue can be beneficial [26].


Figure 2.2: Schematic representation of single-element spherically-curved transducerand planar phased-array transducer. (a) Focusing of the ultrasound is determined bythe radius of the curvature of the single-element transducer. (b) In the phased-arraytransducer, focusing is controlled by setting the time delays of the RF signal on eachchannel based on the difference in time it takes to travel from individual elements tothe focal position. Elements 1 and 4 are further from the desired focal location, andtherefore they should start emitting before the channels 2 and 3. (c) Steering of thesingle-element transducer is controlled by mechanical translation of the transducer,(d) and phased-array transducer is steered electronically by manipulating the timedelays of each channel’s RF input signal.


Figure 2.3: Schematic representation of ultrasound defocusing due to dephasing ofthe ultrasound when passing through a medium with a higher speed of sound (left).To compensate for the phase aberrations, RF signals for channels 2 and 3 are delayedby the time equivalent to the difference between the time it takes to travel distanced in a medium with speed of sound c0 and c.

This section will first describe the thermal effect of ultrasound on tissue and will then

introduce the non-thermal effects, such as cavitation and acoustic radiation force.

2.2.1 Thermal Effects

Tissue heating is the objective for most FUS applications. The thermal damage

threshold depends on exposure times and acoustic power. Small temperature increases

of a few degrees above body temperature can lead to increased blood supply to the

heated region. Rapid temperature increases to higher than approximately 56◦C, can

lead to instantaneous cell death and coagulative necrosis. In hyperthermia treatments,

which are often combined with chemo- or radiation therapy [26], tissue is held at tem-

peratures of 43 - 50◦C for up to an hour to prevent cells from dividing. To achieve

necrosis, longer exposures are required when lower ultrasound power is used. The

damage threshold varies across types of tissue, and it is linearly proportional to the


log of the exposure duration. A approximately 1◦C temperature increase halves the

necessary exposure duration for thermal damage. The tradeoff between temperature

and duration is characterized by a thermal dose equation which describes the thermal

exposure as the time in minutes at 43◦C that achieves an equivalent bioeffect [1, 27]:

t43 =

∫ tend

t=0

kT (t)−43◦Cdt, (2.9)

where tend is the duration of the ultrasound exposure. k = 2 for T ≥ 43◦C and k = 4

below 42◦C. At 43◦C, 240 minutes of exposure will cause necrosis in all types of tissue

[27]. All tissues will survive a few minutes of 43◦C exposure [1]. The cooling effects

from blood perfusion and thermal conduction may limit the reliability of thermal

treatment. In a region where heat is being produced at a constant rate, temperature

increases linearly with time only for a brief period of time after exposure begins. Then,

due to thermal conduction and perfusion, the heat begins flowing away from the heat

source and gets removed by blood flow. In FUS treatments, with short exposures

of a few seconds, the blood perfusion effects are small and the heat transference is

dominated by thermal conduction [28,29]. For longer exposures, perfusion dominates

the heat transfer. Due to the variability of conduction and perfusion parameters

across tissues and anatomical locations, the temperature elevation during ultrasound

treatment has to be monitored to ensure adequate control of the therapy.

2.2.2 Non-Thermal Effects

2.2.2.1 Cavitation

In addition to its heating effects, propagation of an ultrasound wave through tissue can

cause the formation of small gas bubbles which concentrate acoustic energy. Energy

can also be focused by the oscillation of small bubbles that are already present. Such

interaction between the ultrasound and the propagation medium is called cavitation,

and it can change the permeability of cell membranes or lead to the complete destruc-

tion of tissue. Cavitation occurs in tissues that have small gaseous nuclei. When this


tissue is sonicated, the bubbles expand and contract proportionally to acoustic pres-

sure. The amplitude of pulsation is highest when the ultrasound frequency is near the

resonance frequency of the bubbles. The resonance frequency depends on the bubble

size, properties of the gas, the tissue and the gas/tissue interface. Vibration of the gas

bubbles removes the energy from the propagating sound wave, partly by scattering

it, and partly by converting it to heat. Oscillating bubbles tend to absorb much more

acoustic power than the surrounding tissue. Stable cavitations cause microstreaming

of fluid around the bubble and produce highly localized shear stress. The stress can

lead to cell damage and increases in cell wall and blood vessel permeability [1].

Oscillation of bubbles at sufficiently high acoustical pressures becomes non-linear,

causing the bubbles to expand and collapse violently. This collapse is referred to as

inertial cavitation. The acoustic pressure of a collapsing bubble can be on the order

of several thousand atmospheres, resulting in a shock wave and a temperature rise of

several thousands degrees Kelvin. Collapsing of bubbles leads to disintegration of tis-

sue and creates a fluid-filled cavity [30]. The pressure threshold for inertial cavitation

depends on frequency and on the tissue. For example, in in vivo dog muscle studies,

the threshold pressure increased with frequency at approximately 5.3 MPa/MHz [31].

One of the promising applications of both stable and inertial cavitation relies

on their greater absorption of ultrasound energy in tissue. Combined with a FUS

treatment, cavitation phenomena can reduce the amount of energy necessary for the

treatment and increase the volume of focal coagulation. Cavitations are also believed

to be instrumental in enhancing local drug delivery. For example, drugs can be encap-

sulated within a bubble or incorporated into the shell of a bubble. Once the bubbles

are injected into the blood stream and accumulate at a particular target location,

ultrasound can induce their inertial cavitation and release the drug [32].

2.2.2.2 Acoustic Radiation Force

Acoustic radiation force is another physical mechanism by which ultrasound interacts

with tissue. Ultrasound exerts force on the medium within its field that consists

of an oscillatory component, having the same frequency as the sound wave with a

time average of zero, and a component that has non-zero time average. This offset


Figure 2.4: Illustration of acoustic radiation force exerted on a medium at the focalspot causing the longitudinal displacement and the transient shear wave propagatingin transverse direction.

component is called acoustic radiation force, and it arises from non-linearities in the

sound field [33]. Acoustic radiation force is often defined as a unidirectional force

that is applied to absorbing or reflecting targets in the propagation path of the wave,

caused by a momentum transfer from the acoustic wave to the medium [34]. Assuming

plane wave propagation, the acoustic radiation force applied to tissue is:

F =2αaI

c, (2.10)

where F is force per volume and I is the temporal average intensity of the acoustic

beam at a point in the tissue. In the case of a focused transducer, the radiation force

is usually negligible outside of the focal zone. In water-like elastic media, such as

biological tissues, the shear modulus is small compared to the bulk compressibility.

Thus, the action of the radiation force initiates a wave that propagates both in lon-

gitudinal (compressional) mode and in transverse (shear) mode as shown in Figure

2.4 [35, 36]. The displacement of tissue x(t) at the focus depends on the radiation

force at the focus and on its spatial distribution. The response of tissue to acoustic

force was studied in detail by several authors [37, 38]. Based on these results, it is

common to model tissue displacement as an overdamped response (Figure 2.5):


Figure 2.5: Tissue response to acoustic radiation force.

x(t) =

0 if t ≤ 0;Fk

(1− exp(− tτrise

)) if 0 ≤ t ≤ tUS;

x(tUS) exp(− tτdecay

) if t ≥ tUS.

(2.11)

The effects of tissue displacement under acoustic radiation force are being explored

in medical applications related to “remote palpation”, wherein viscoelastic proper-

ties of internal tissues are assessed remotely [37, 39]. The displacement generated by

focused ultrasound is the basis for emerging diagnostic techniques aimed to detect

changes in tissue mechanical properties, such as vibro-acoustography [40,41], acoustic

radiation force impulse imaging [42] and Supersonic imaging [43, 44]. [42]. In vibro-

acoustography, radiation force is used to create mechanical vibration of tissue at a

target location, which induces an acoustic signal that can be recorded from outside

the body. Acoustic radiation force impulse imaging uses a short ultrasound pulse to

“push” the tissue and then uses ultrasound imaging to monitor the propagation of the

transient shear wave created by the “push”. This technique was used by K. Nightin-

gale et al. [42] to induce acoustic streaming in a cyst fluid in order to differentiate

it from solid breast lesions in vivo. Supersonic imaging is based on the ultrasonic

generation of a shear source moving at supersonic speeds within the body. Similar to


the “sonic boom” created by a supersonic aircraft, the resulting shear waves construc-

tively interfere along a Mach cone, creating two intense plane waves. The propagation

of these planar shear waves through the medium is then imaged using ultrasound [43].

In the context of MRgFUS, the displacement of tissue due to acoustic radiation force

presents an excellent opportunity to visualize the position of the focal spot and the

quality of focusing without having to heat tissue. MRI methods used to image tissue

displacement are discussed in the next section.

2.3 Imaging of Ultrasound Effects on Tissue with

MRI

2.3.1 MR Thermometry

While use of both ultrasound and MR imaging have been explored for temperature

monitoring applications, MRI has become the modality of choice in currently available

FUS therapeutic systems. Taking advantage of numerous contrast mechanisms, MRI is

excellent for both anatomical and functional imaging and can provide a sophisticated

set of tools for guidance of FUS therapy.

The temperature sensitivity of MR parameters remains an important research

topic, and the use of measured parameters such as proton resonance frequency (PRF),

relaxation times, proton density, diffusion coefficients and magnetization transfer are

all actively being explored. However, PRF-based temperature mapping has found the

greatest acceptance for many temperature measurement applications, including the

guidance of FUS therapy. In breast FUS treatments, T1-based temperature imaging

has often been incorporated due to the insensitivity of fat’s resonance frequency to

temperature changes. A detailed overview of MR thermometry is presented in [45].

The purpose of this section is to explain the theory and the common pulse sequences

used for PRF- and T1-based thermometry.


2.3.1.1 PRF-based Temperature Mapping

According to nuclear magnetic resonance (NMR) phenomenon, magnetic nuclei pre-

cess in the presence of an external magnetic field, with Larmor resonance frequency

f proportional to the applied field strength B0 and gyromagnetic coefficient γ:

f = γB0. (2.12)

In water molecules the electrons create a microscopic magnetic field B0s, which shields

the hydrogen nuclei H1 from the external field B0, altering the resonance frequency

of water protons according to:

f = γ(B0 −B0s). (2.13)

When the water temperature rises, molecular Brownian motion increases, which

causes the hydrogen bonds to stretch, bend and break [46]. This increases the elec-

tron shielding of the H1 nucleus, effectively lowering the local magnetic field and

thus lowering the proton resonance frequency. This change of frequency is commonly

referred to as the PRF shift. The effect of the electron-screening is linear with tem-

perature over -15◦C to 100◦C, with proportionality constant α. In pure H2O, α has

been measured to be -1.03 ± 0.02 * 10−2 ppm/◦C [46]. The PRF shift with temper-

ature can be directly observed spectroscopically or can be inferred indirectly using

phase mapping methods. The latter approach is used in MRI PRF-shift thermometry.

Gradient-recalled echo (GRE) imaging sequences are used to obtain the temperature

maps by measuring the change of phase resulting from temperature-dependent PRF

shifts [47]. To measure the phase shift ∆φ due to temperature change ∆T, the phase

of tissue at an initial temperature T0 is often used as a reference or baseline. In a

simple reference-subtraction approach, the reference phase image is acquired before

the focused ultrasound is applied to heat tissue, and is then subtracted from phase

images obtained in the heated tissue. The resulting phase difference is proportional


to the PRF shift and the echo time (TE), and can be used to calculate ∆T as follows:

∆T =φ(T )− φ(T0)

2πγαB0TE, (2.14)

where φ(T ) is the phase in the heated tissue image, φ(T0) is the phase of a reference

Figure 2.6: Magnitude and phase images of a gel phantom obtained before and duringfocused ultrasound ablation. In the magnitude image, heating of the focal spot is seenas decreased signal intensity due to T1 increase with temperature. In the phase image,heating is seen as an elevated phase due to PRF shift. The temperature rise map,computed by subtraction of the two phase images, is overlaid on a magnitude image.

(baseline) image at a known initial temperature, and TE is the echo time. Example

phase images obtained before and during FUS ablation of a gel phantom are shown

in Figure 2.6. To ensure the accuracy of PRF shift thermometry, the principle factors

that need to be considered are the magnetic susceptibility, the external field drift and

the tissue composition. As magnetic susceptibility χ0 of tissue changes with temper-

ature, magnetic flux density changes as well which in turn affects the local magnetic

field. The change of susceptibility with temperature is tissue-dependent [48], and was


measured to be 0.0016 ppm/◦C in muscle tissue [49]. In practice, the temperature

sensitivity of the susceptibility has little effect on thermometry applications and is

typically not accounted for. The drift of the external field due to intensive gradient

utilization [50], however, can lead to substantial drift of the background phase and

may result in significant errors in PRF-based thermometry. Therefore, the phase drift

is always monitored by tracking the phase of tissue or of an external phantom that

remains at a constant temperature. Depending on the spatial distribution of the phase

drift, the phase drift correction is calculated either as an average or as a planar fit

to the phase values in the external region of interest (ROI). Owing to tissue-type

independence of the PRF temperature constant [51], tissue composition does not af-

fect the performance of PRF-shift thermometry in aqueous tissue. The absence of

hydrogen bonds in adipose tissue [46] makes PRF-based MR thermometry inaccurate

in tissue with high fat content and essentially impossible in pure fatty tissue. This

limitation of PRF thermometry makes temperature monitoring challenging during

MRgFUS treatments in the breast and requires alternative methods. Therefore, in

current FUS breast studies, the T1 temperature dependence of fat is often exploited

to improve image guidance.

2.3.1.2 T1-based Temperature Mapping

Bipolar interactions of macromolecules and water molecules lead to spin-lattice relax-

ation in biological tissue. Similar to the PRF shift method, the principle phenomenon

causing temperature sensitivity of the relaxation time is molecular Brownian motion.

The temperature dependence of these molecular interactions is reflected in changes of

the spin-lattice relaxation time T1, which increases with an increase in temperature

in both fat and water [52–54]. Detailed derivation of temperature dependence of the

relaxation times is presented by Bottomley et al. in Ref. [55]. In the general form, T1

can be expressed as a function of temperature as:

T1(T ) = T1(T0) +m(T − T0), (2.15)


where m is the rate of T1 change with temperature, which is determined empirically

for each tissue, and T0 is the initial temperature. The temperature dependence of

T1 was found to be tissue dependent and on the order of 1-2% /◦C across differ-

ent tissue types [56–59]. The quality of T1-based thermal mapping depends on the

accuracy of measuring T1. However, many accurate T1- mapping methods, such as

inversion recovery and saturation recovery, are very time-consuming and make T1-

based thermometry unsuitable for monitoring rapidly changing temperature during

FUS therapy [45]. Additionally, in biological tissue, heating leads to tissue coagula-

tion and protein denaturation, which in turn cause irreversible changes in T1. These

changes are not easily separable from temperature-dependent T1 changes and put

an upper limit on a temperature interval over which T1-based thermometry is feasi-

ble. Since T1 changes affect the signal intensity of the image, signal variation can be

monitored to detect temperature changes. The effect of a temperature rise on T1 can

be seen in the magnitude image in Figure 2.6, where the signal intensity decreased

in the focal spot during heating. A dual-echo GRE sequence has been proposed to

simultaneously acquire a T1-weighted magnitude image and a phase image, to im-

prove the temperature sensitivity of MR thermometry [60]. This method is sometimes

used in place of PRF-shift thermometry during breast FUS treatments [8], in order

to improve focal spot visualization. The temperature sensitivity of signal intensity

in fat tissue of a T1-weighted FSE pulse sequence was studied by Hynynen et al. in

Refs. [59]. The FSE signal intensity was found to decrease linearly with temperature

at a rate of -0.97±0.02%/◦C from normal body temperature to above the threshold

for thermal coagulation. It was shown that low temperature elevations, which do not

cause tissue damage, were visible on FSE magnitude difference images.

Since publication of these studies, quantitative T1-based thermometry in breast

tissue remains challenging due to the highly inhomogeneous nature of breast tissue

and due to the tissue-type dependence of the T1 temperature sensitivity. In 2009,

the topic of quantitative T1-weighted thermometry in fat was revisited by Kuroda et

al. [61, 62], who showed a reproducible linear relationship between temperature and

the T1 of methylene (CH2) and methyl (CH3) protons. It was found that the CH3

component of fat had higher temperature sensitivity than CH2. However, temperature


maps based on CH3 T1 had more noise due to a much lower proportion of CH3 than

of CH2 in fat.

2.3.2 MR Acoustic Radiation Force Imaging

The purpose of MR Acoustic Radiation Force Imaging (MR-ARFI) is to measure

the displacement of tissue induced by acoustic radiation force. Because of the nature

of the phenomenon that is being imaged, MR-ARFI is closely related to other MR

techniques aimed at imaging motion of the spins, such as flow and diffusion-weighted

imaging and MR elastography. Therefore, prior to introducing the existing MR-ARFI

methods, a brief overview of key MRI spatial encoding concepts and displacement-

encoding techniques is presented.

2.3.2.1 MRI Spatial Encoding

Similar to the inherent proton frequency shift caused by temperature changes, the

precession frequency of the protons can be controlled using the MRI scanner’s linear

gradient fields. This principle is used in MRI to achieve spatial localization of the

spins. For example, if a linear gradient Gx is applied in conjunction with the static

magnetic field of the MRI scanner, B0, the hydrogen nuclei at position x will precess

with frequency:

f = γ(B0 +Gxx). (2.16)

If the position of the proton of interest shifts, the precession frequency of the pro-

ton will also shift by γGx∆x. Similar to PRF-shift MRI thermometry, motion-based

proton frequency shifts can be detected as the phase shift:

φ = 2πγ

∫ δ

0

Gx(t)x(t)dt, (2.17)


Figure 2.7: Illustration of MR flow encoding scheme. (a) The x position of the station-ary and moving spins is shown for three time points that correspond to the time pointwhen encoding gradient turns on, when the positive polarity of the gradient changesto the negative polarity and when the gradient is turned off. (b) Bipolar encodinggradient and corresponding phase accrual by stationary and moving spins.


where δ is the duration of the encoding gradient Gx. The position of the proton

moving at constant velocity v0 is then described as

x(t) = x0 + v0(t)t, (2.18)

where x0 is the position of the proton before the encoding gradient Gx was applied.

Defining gradient moments m0 and m1 as

m0 =

∫ δ

0

Gxdt, (2.19)

m1 =

∫ δ

0

Gxtdt, (2.20)

the encoded phase can be expressed according to:

φ = 2πγ[m0x0 +m1v0]. (2.21)

In order to measure specific properties of a spin, such as position or velocity, the

gradient waveforms are manipulated to generate the desired gradient moments. A

common approach to flow encoding, or velocity encoding, is the use of bipolar gradi-

ents which are shown in Figure 2.7. The gradient consists of two lobes with equal area

and opposite polarity. The total area under the gradient waveform, and therefore the

zeroth gradient moment, is zero. Therefore, no net phase is accumulated by stationary

spins. The blood moving through a vessel at constant velocity, as shown in Figure 2.7,

will accumulate non-zero net phase in the image. In the case of incoherent motion,

like diffusion of water molecules due to Brownian random motion, phase accumulation

will be different for each spin in the voxel which will cause signal cancellation for some

spins and lead to overall signal attenuation. The degree of attenuation is proportional

to the dimensionless product of the diffusion coefficient D and the b-value, which is

a factor determined by the integral of the diffusion gradient waveform and can be

described as:

S = S0 exp(−bD). (2.22)


Figure 2.8: Illustration of MR Elastrography encoding scheme, showing a train ofbipolar encoding gradients and mechanical motion of the external actuator (dashedline). To measure the speed of the shear wave propagation, several MR images areacquired at several time offsets spanning from the start of mechanical motion to theonset of displacement encoding.

Pulse sequences with higher b-values are more sensitive to diffusion. MR Elastography

is another technique that measures the motion of the spins, however, its end goal is

to quantify the elastic properties of tissue. Elastography was first performed using

ultrasound imaging in 1991, by comparing the images obtained with and without

externally applied compression of tissue [63]. Soon afterward, in 1995, the first MR

elastography approach was proposed by a research group at the Mayo Clinic [64]. In

this approach, an external actuator vibrating at 300 Hz was used to set up harmonic

mechanical wave propagation in the tissue of interest. Then, a train of bipolar encod-

ing gradients, played at the frequency of the excited mechanical wave, was applied

to encode tissue displacement (Figure 2.8). Using external actuators to set up me-

chanical waves in tissue limits the use of this elastography approach to areas of the

body that externally generated shear waves can reach. Shear waves are increasingly

attenuated with depth. To overcome this limitation, longitudinal compression can be


used. Another solution to initiate shear waves deep inside the tissue is to put the

source of the shear waves inside the tissue, using focused ultrasound. R. Souchon et

al. proposed using elastography encoding techniques to image shear waves generated

by focused ultrasound, pulsed at a desired pulse rate at a desired location in the

body [35]. This technique used acoustic radiation force of the focused ultrasound to

set up the shear waves in the tissue and was named MR transient elastography. In

was not until a few months later that the term MR Acoustic Radiation Force Imaging

emerged from the work of N. McDannold et al. [65].

2.3.2.2 Early Work in MR-ARFI

Building upon work in MR elastography [64, 66] and ultrasound acoustic radiation

force impulse imaging [34], N. McDannold proposed a new approach to imaging acous-

tic radiation force induced tissue displacement [65], based on a diffusion-weighted

line-scan sequence (Figure 2.9a). This sequence was applied using the experimental

setup shown in Figure 2.9b. Ultrasound was applied from below the phantom and the

encoding gradients were applied in the direction of propagation of the sound beam.

In order to eliminate phase unrelated to acoustic force, two phase images were ob-

tained with opposite encoding gradient polarity, and the phase difference between

them was analyzed. The magnitude and the phase difference are shown in Figure

2.10. Due to the random bulk motion of the setup, each line in the line scan had an

additional phase offset, which shows up as stripes of variable intensity in the phase

image (Figure 2.10). An additional reconstruction step had to be performed to cor-

rect for this artifact. The region corresponding only to the phantom was segmented

out of the phase difference image. Then, a linear regression is performed line by line

in the readout direction using least-squares curve fitting. The resulting constant and

linear phase terms were removed from each line to obtain the corrected phase image

shown in Figure 2.10. Additional non-linear background phase terms still remained

after correction and required additional processing to be eliminated. J. Chen et al.

followed up with a modification to the unipolar technique [67]. It was proposed that a

set of two repeated bipolar gradients can replace the two unipolar encoding gradients,

as shown in Figure 2.11. This alteration helped to eliminate the nonlinear background


(a) (b)

Figure 2.9: (a) MR-ARFI pulse sequence diagram proposed by N. McDannold etal., showing emission of the ultrasound pulse synchronized with the second unipolardiffusion gradient. (b) Schematic of MR-ARFI experimental setup, showing the gelphantom placed on top of ultrasound transducer.

Figure 2.10: Magnitude and phase images obtained with the unipolar line-scan MR-ARFI sequence. Different-intensity stripes can be seen in the uncorrected phase image.After correction applied to the ROI in the phantom, the phase looks smooth in thecenter of the image and increased phase due to displacement in the focal spot is nowmore apparent.


Figure 2.11: The modification of displacement encoding configuration proposed by J.Chen et al. The unipolar gradients are replaced with repeated bipolar gradients, witheach lobe having area equal to half of the area of a single unipolar gradient.


phase, whose presence was attributed to eddy currents, and substantially reduce the

sensitivity in the constant and linear terms to bulk motion contributions [67]. Break-

ing the unipolar gradient into two gradients of half the duration also led to significant

reduction of the b-value and therefore reduced the overall signal loss due to diffusion

weighting of the pulse sequence. Approximating the trapezoid shape gradient as a

rectangle, the b-value of the unipolar gradient set shown in Figure 2.11 is

b = γ2G2xδ

2(δ + T180 −δ

3), (2.23)

where γ = 2πγ, T180 is the duration of the 180◦ RF pulse and necessary crushers and

δ is duration of a single unipolar gradient. For a repeated bipolar case the b-value is

b =1

6γ2G2

xδ3. (2.24)

SNR analysis of two types of encoding for a range of encoding durations, performed

for white matter tissue parameters, showed that for encoding durations longer than 5

ms, the bipolar encoding configuration had a significant advantage over the unipolar

one due to reduced diffusion sensitivity (Figure 2.12).

2.4 Generalized MRgFUS Protocol and Specific

Challenges

There are several types of MRgFUS applications that are currently being performed

clinically or in clinical trials, and there are currently two vendors providing MRgFUS

technology. There are some differences in treatment protocols between applications

and vendors. However, there are several key steps that are universal across all types of

MRgFUS treatments. Figure 2.13 shows a flow chart of the key steps of a generalized

MRgFUS treatment protocol, and several images to illustrate some of the steps. Step 0

is a part of the MRgFUS procedure that is only performed when there is a need for CT

images to plan the treatment. In the case of transcranial MRgFUS, pre-operative CT

images of a patient’s head are obtained in order to estimate skull parameters for phase


Figure 2.12: Comparison of displacement SNR for unipolar and repeated bipolar en-coding configurations. Unipolar encoding has higher diffusion weighting than bipolarencoding, which leads to reduced MR signal in the unipolar case. The results showthat for gradient durations greater than 5 ms, the repeated bipolar configuration leadsto a significant increase in displacement SNR compared to the unipolar case. For bothencoding configurations, an optimal gradient duration exists.

aberration correction. A calibration step is usually the first stage for any MRgFUS

procedure. It provides the system with the necessary information to determine the

transducers home position and orientation. The calibration image in Figure 2.13a

shows the contour of the hemispherical transducer template overlaid on the MR image

of the patient’s head inside the actual transducer. The template and the actual image

have to be aligned in this step. Similar to the CT imaging step, the registration step

of the procedure is performed in cases when other types of images are needed to

plan the treatment. In the case of a transcranial procedure, the pre-operative head

CT images, often obtained on a different day, get registered with MR images of the

actual patient setup. In practice, this step is reported to be time consuming, and

is often performed manually due to unsatisfactory performance of current automatic

registration techniques. The registration example in Figure 2.13b shows the MR image

with the CT image of the skull overlaid. The green circle demarcates the region


within which the transducer can focus. The accuracy of registration is essential for

the accurate calculation of the phase aberration corrections that are performed in step

3. During the planning stage, the region of treatment and the acoustic parameters of

the sonications are defined first. Then, if necessary, the phase correction values are

computed for each transducer element. If certain regions in the beam path have to

be spared from ultrasound energy, these so-called “no pass” regions are also marked

in the planning step.

The goal of the verification step is to ensure that the actual focal spot reaches

the planned target location. Verification is performed using sonications of sub-lethal

ultrasound energy. The temperature rise is monitored with PRF-shift thermometry

or T1-weighted imaging. As shown in the verification example in Figure 2.13a, the

heated spot and the desired location (which is marked with a circle) coincide. If, during

geometric verification, the actual and the planned locations of the focal spot differ

by more than 1 mm, adjustment of the electronic focusing has to be performed, and

the location of the new focus is verified. The last two steps are the treatment and the

assessment. During the treatment stage the planned region gets ablated spot by spot,

and the temperature rise at each spot location is monitored using MR thermometry.

After the desired thermal dose is achieved, the assessment imaging is performed. This

includes T2-weighted, contrast enhanced and diffusion-weighted imaging.

Two sections of this protocol are addressed in the thesis: verification and phase

aberration correction. As mentioned in the introduction, verification is based on imag-

ing of the sub-lethal-energy sonications. If verification shows that the actual focal spot

and the target are not aligned, the sonication is repeated, often more than once. When

the MRgFUS is used to treat a large tumor volume, for example 200-500 ml uterine

fibroid targets, low power sonications do not pose any risk to the tissue about to

be completely necrosed. However, in FUS functional neurosurgery, the targeted brain

structures are only few millimeters in size and the target temperature rise is only a few

degrees. Therefore, the sonications performed during verification stage can potentially

lead to the death of neurons outside of the target location and cause damage to the

patient’s brain function. Thus, reduction of the ultrasound energy delivered during

the verification stage is of great importance in clinical applications of MRgFUS.


(a) (b)

Figure 2.13: (a) Flow chart of the key steps of the MRgFUS protocol. Dashed line isused for the steps that are necessary only under certain conditions. (b) Examples ofsome images to illustrate the steps of transcranial MRgFUS procedure.


An important weakness of the current approach to verification and temperature

monitoring in general is its limited performance in fatty breast tissue. Due to these

limitations, the current approach relies on focusing the ultrasound beam on the center

of the tumor, where the fat content is low, and using PRF-shift thermometry to verify

the focus location inside the tumor. Once the transducer focusing is calibrated in

that location, the treatment in all planned locations is carried out whether or not the

position of each sonication can be verified and monitored [68]. This presents additional

motivation for the development of an alternative MRI tool that can accurately verify

focal spot positions in fatty breast tissue as well as other aqueous tissues.

Another challenge for transcranial MRgFUS is phase aberration caused by the

patient’s skull. Current approaches to correcting it use pre-operative CT imaging

of the head to estimate a particular patient’s skull properties. In addition to deliv-

ering ionizing radiation to patients who may be already in a fragile physical state,

this approach suffers from approximations in the algorithm and from CT-MRI mis-

registration errors. In this work, an alternative phase correction algorithm, free of

ionizing radiation, is proposed.

2.5 Summary

This chapter has introduced basic principles of ultrasound wave propagation and fo-

cusing, the key biological effects of the ultrasound, and MRI techniques that allow

visualization of tissue heating and displacement due to ultrasound. The general proto-

col of a MRgFUS treatment was presented and two areas for further development were

identified: visualization of the focal spot and correction for phase aberrations. The

subsequent two chapters address the topic of focal spot visualization by introducing

a novel MR-ARFI pulse sequence and optimizing it for in vivo brain imaging.

Chapter 3

2DFT MR-ARFI for Focal Spot

Localization

Early work in MR-ARFI was done with diffusion-weighted line-scan pulse sequences

[65,67] in order to avoid ghosting artifacts from view-to-view phase variations that are

common in diffusion-weighted imaging with 2D Fourier Transform (2DFT) readouts.

Line-scan imaging, however, does not benefit from the Fourier transform in the y

direction, resulting in SNR losses up to the square root of the number of phase

encodes in the y direction used for a similar image in 2DFT imaging. In previous

work, improvement in the SNR of line-scan MR-ARFI was achieved by replacing two

unipolar diffusion gradients with a pair of bipolar gradients. It was also shown that

depending on tissue relaxation time and diffusion, the duration of bipolar encoding

gradients can be optimized to achieve the maximum SNR. For example, for white

matter, simulation of displacement SNR showed that an encoding duration of 19 ms

(where each lobe of the bipolar gradient was 9.5 ms), corresponding to a b-value of 70

s/mm2, was optimal. We found that b-values much lower than 1000 s/mm2, typically

used in diffusion imaging, were sufficient to provide sensitivity to tissue displacement

due to radiation force. This was the basis for a new 2DFT-based MR-ARFI approach

that was developed and demonstrated, as is described in this chapter.

34

CHAPTER 3. 2DFT MR-ARFI FOR FOCAL SPOT LOCALIZATION 35

3.1 2DFT Spin-echo MR-ARFI Pulse Sequence

The 2DFT MR-ARFI spin-echo pulse sequence was developed by modifying a product

GE multi-echo multi-planar pulse sequence (filename memp.e). The sequence was

equipped with a pair of bipolar gradients as shown in Figure 3.1. As was proposed in

[67], the emission of the ultrasound was timed so that its start was synchronized with

the start time of the second lobe of the first bipolar gradient, and the sound ended at

the end of the first lobe of the second bipolar gradient (Figure 3.1). The pulse sequence

was tested on a 3T GE Signa MR scanner (GE Healthcare, Waukesha) with two types

of ultrasound transducers: a concave 208-channel focused transducer (ExAblate 2000)

and a planar 1024-channel phased-array transducer, both manufactured by InSightec

Ltd. (Tirat Carmel, Israel). The central frequencies were 1 MHz and 550 kHz for the

concave and planar transducers respectively. The concave transducer was immersed

in an oil tank positioned in a MRI scanner table and covered with a membrane. The

planar transducer was covered with a Mylar membrane that was filled with circulating

degassed water during procedures. The type of the transducer will be specified in each

study.

The strength of the displacement encoding gradient was set to maximum, 40

mT/m, in all of the MR-ARFI acquisitions shown in this thesis. A single-channel 4-

inch-diameter solenoid breast coil (InVivo/MRI Devices, Waukesha) designed for the

ExAblate system was used in all phantom and ex vivo tissue experiments reported

here. To obtain displacement images, two phase images were acquired with the pulse

sequence as described by McDannold et al. [65]: one with the encoding direction

parallel to the ultrasound beam direction φ+, and another one with encoding anti-

parallel. Then the subtraction of phase images was performed in order to double

the displacement due to acoustic radiation force and remove the background phase

due to inhomogeneities of the magnetic field [65]. The final phase difference due to

displacement was expressed as:

∆φd =1

2(φ+ − φ−), (3.1)


Figure 3.1: Pulse sequence diagram of the MR-ARFI spin-echo pulse sequence. Thegray box encloses the displacement encoding module of the pulse sequence showing thetiming of encoding gradients and the emission of the ultrasound pulse (red line). Thewaveform of tissue displacement, x, is shown. An optional readout gradient used toacquire a gradient-echo image simultaneously with the spin-echo image is shown witha dotted line and is fully introduced in the last part of this section. The dephaseris shown in dotted line because its polarity depends on whether the gradient-echoreadout is added or not.


Figure 3.2: Left: The photograph shows a freshly excised porcine whole brain and itsdimensions. Right: Schematic representation of the experimental setup showing theconcave transducer in the oil bath with a coupling gel pad above. The tissue sampleis placed on top of the gel pad and coupled using degassed water. The solenoid RFcoil is placed around the sample, and the acoustic absorber is positioned on top ofthe brain sample.

The phase difference ∆φd due to tissue displacement will be referred to as displace-

ment phase in this thesis.

3.1.1 2DFT MR-ARFI in Ex V ivo Brain Tissue

3.1.1.1 Methods

The pulse sequence was first demonstrated in ex vivo porcine brain tissue using the

concave transducer. The tissue sample and the experimental setup are shown in Figure

3.2. The whole porcine brain sample was placed on top of the coupling gel pad, and

an acoustic absorber was positioned on top of the brain to prevent reflection of the

ultrasound at tissue-air interface. The ultrasound beam was focused inside the brain

at a depth of 100 mm from the center of the transducer. The transducer emitted


pulses with acoustic power of 17.6 W and with duration of 19 ms, which equals an

encoding duration of 6.1 ms, plus the duration of the crushers and the slice-select

gradient of the 180◦ RF pulse, T180. Other imaging parameters were FOV of 18 × 18

cm2, TR of 1 s, TE of 40.4 ms and BW of 62.5 kHz. Images were acquired in coronal

(matrix size 128 × 128) and axial planes (matrix size 128 × 64).

The relationship between the measured displacement and acoustic radiation force

is expected to be linear, and the relationship between acoustic radiation force and

acoustic intensity, or acoustic power, is described as linear in Equation 2.10. Therefore,

the tissue displacement is expected to have linear dependence on acoustic power.

This was verified by obtaining displacement phase images for acoustic power levels

increasing from 4.4 W to 17.6 W. Average displacement in a 2 by 2 pixel region-

of-interest (ROI) at the focal spot was measured for each power level, and linear

regression was used to fit the data.

The displacement of tissue was then measured in multiple locations in the brain

sample. To steer the ultrasound beam to a new location, the concave transducer was

mechanically translated in the X and Y directions. Position of the transducer in Z

direction remained constant. Mean displacement in each location of the focal spot was

compared to the standard deviation of displacement phase in the background region

of the brain where tissue remained stationary. To get an estimate of the displacement

amplitude, instantaneous tissue response was assumed and the displacement phase

was converted to displacement according to the following equation:

∆x =∆φdγGencδ

, (3.2)

where Genc is the amplitude of the encoding gradient and δ is the duration of encoding.

3.1.1.2 Results

Magnitude and phase images of a porcine brain obtained with 2DFT spin-echo MR-

ARFI sequence are shown in Figure 3.3. For the given imaging parameters, the SNR of

gray matter was approximately 70, and the SNR of white matter - approximately 90.

On the coronal phase images, it can be seen that encoding along the direction of the


(a)

(b)

Figure 3.3: (a) Example of coronal 2DFT spin-echo MR-ARFI images, magnitude andphase, obtained in an ex vivo brain. FOV = 18 x 18 cm2. Encoding was performedin the slice-select direction. The focal spot of the ultrasound beam can be visualizedin the individual phase images and in the displacement phase image. (b) Exampleof axial MR-ARFI magnitude and phase images, where encoding was performed in-plane.


ultrasound beam results in a positive phase shift at the focal spot, and encoding in the

anti-parallel direction gives a negative phase shift. The spatial phase variation across

the brain sample in both phase images is eliminated by the subtraction of φ+ and

φ−. The resulting phase difference image has a spatially uniform phase distribution

across the whole brain sample with a standard deviation of 0.02 radians. The average

displacement phase in the focal spot is 0.38 radians, giving a displacement SNR of

19.

Figure 3.4: Top: Displacement images obtained with the transducer focused to thesame location, emitting at acoustic powers from 4.4 to 17.6 Watts. Bottom: averagedisplacement at the focal spot plotted as a function of acoustic power and linearregression fit to the data. The correlation coefficient R2 of the fit was 0.99. The slopeof the regression is 0.07 rad/W.


Figure 3.5: The focal spot was steered across nine unique locations in the brain samplewith constant power level. The displacement phase amplitude varied from 0.35 radto 0.44 rad, which corresponds to 2.6 µm and 3.4 µm, assuming instantaneous tissueresponse.

The effect of the increase in acoustic power on the displacement at the focal spot

is shown in Figure 3.4. The displacement increases linearly with power at the rate of

0.07 rad/W. For successful application of the adaptive focusing algorithms that will be

discussed later, it is important that the relationship between the tissue displacement

and acoustic power is linear. Steering the ultrasound beam to nine different locations


in the brain sample is demonstrated in Figure 3.5. The focal spot is equally well

visible in all nine locations with the displacement varying between 2.6 µm and 3.4

µm, resulting in displacement SNR between 17 and 22.

3.1.2 Focal Spot Visualization in Fatty Tissue

As previously described, during the planning stage of MRgFUS in the breast, a low

temperature test spot is created to verify the actual location of the focal spot in

relation to the planned position. Due to the unreliable performance of PRF-based

thermometry in fatty inhomogeneous tissue, two alternative approaches have been

proposed for focal spot localization during breast MRgFUS treatments. One method

relies on T1-weighted imaging of the test spots with a fast spin-echo (FSE) sequence

[59], and the second approach is to image displacement in the focal spot using MR-

guided acoustic radiation force imaging (MR-ARFI) [65, 69]. In this section, both

methods are tested in ex vivo cadaveric breast tissue to evaluate the potential of each

as a targeting tool during MRgFUS treatments in highly adipose breast tissue.

3.1.2.1 Methods

A set of MR-ARFI and T1-weighted FSE images were acquired in an ex vivo human

breast tissue sample without skin, with no known breast pathology. The breast was

placed into a cylindrical container with a mylar acoustic window at one end (Figure

3.6). The container was filled with degassed saline solution, and weighed down by

an acoustic absorber plate. A gel pad coupled the ultrasound energy between the

membrane and the breast.

Ultrasound beam was focused at six unique locations inside predominantly fat

tissue of the breast sample. For the six locations, first, FSE images were obtained

with the ultrasound off. Then, imaging was performed with ultrasound on using MR-

ARFI and FSE sequences. Both types of images were obtained in the X-Y plane with a

slice thickness of 3 mm, FOV of 22 × 11 cm2, matrix size of 256 × 64, BW of 15.6 kHz.

During the MR-ARFI acquisition, ultrasound was on for 19 ms each TR, where TR

was 1 s (1.9 % duty cycle). With the acoustic power of 28 W, the energy deposition for


Figure 3.6: Schematic of the ex vivo breast experimental setup, based on a fat-suppressed image. From the bottom: UF transducer in an oil bath inside the scannertable, acoustically transparent gel pad, container with degassed saline solution andbreast tissue, gel pad to weight down the sample with acoustic absorber plate on top.The RF coil is placed around the container.

one MR-ARFI acquisition was 38 J. FSE parameters were based on the Ref. [59]. To

produce a measurable small temperature rise, during the FSE acquisition, 20-second

sonications were performed at 100 % duty cycle with acoustic power of 23 W. This

resulted in an energy deposition of 460 J per sonication. MR-ARFI had an echo time

of 41 ms and FSE, using echo-train-length (ETL) of 8, had an echo time of 12 ms.

The previous work on FSE thermometry in fat determined that a TR of 400 ms was

optimal for focal spot visualization on a 1.5 T scanner. To estimate the optimal FSE

TR for a 3 T scanner, in this study, TR was varied from 200 ms to 700 ms. Different

TRs were tried at different focal spot locations.

The displacement phase images were computed as previously described. Using

the method from Ref. [59], FSE magnitude difference were found by subtraction of

the baseline magnitude image. To analyze SNR of displacement phase images and the

FSE magnitude difference images, a 4 × 4 pixel ROI was prescribed in each individual


Figure 3.7: MR-ARFI and FSE images obtained with the transducer focused at fourdifferent locations. Left: the top row shows phase images obtained with encodinggradients anti-parallel to the direction of ultrasound. The focal spot can be easilyvisualized on all four images. The bottom row shows the displacement phase imagesproduced by subtraction of the two phase images obtained with opposite encodingpolarity. Right: Magnitude images obtained during the 20 s continuous ultrasoundsonication. The focal spot can not be seen in either of the four magnitude images. Onthe magnitude difference images, however, the focal spot can be localized.

focal spot, and the mean value was calculated. Then the noise was calculated as the

standard deviation in a 20 × 20 pixel ROI placed away from the focal spots in both

displacement phase and magnitude difference images.

3.1.2.2 Results

Four examples of images obtained with both MR-ARFI and FSE are shown in Figure

3.7. A set of MR-ARFI phase images obtained with encoding gradients anti-parallel

to the direction of the beam are shown for the four locations of the focal spot. Cor-

responding displacement phase images are shown below. FSE magnitude images col-

lected at the end of the 20 s sonications are also shown together with the correspond-

ing magnitude difference images. Comparing MR-ARFI phase and FSE magnitude


Figure 3.8: Plot of the SNR measured at the focal spot of the FSE magnitude differ-ence images obtained at different TRs.

images before subtraction, it was observed that the focal spots were completely in-

distinguishable on the magnitude FSE images, however, all focal spot locations were

well depicted on the MR-ARFI phase images even before the subtraction. The SNR

of the FSE magnitude difference images of the focal spot varied across different TR’s

as show in Figure 3.8. A TR of 500 ms resulted in the maximum SNR of 11.5 mea-

sured at the focal spot of the FSE magnitude difference image. The average SNR of

displacement phase at the focal spot, measured with MR-ARFI, was found to be 43.

3.1.2.3 Discussion

This study showed that both T1-weighted imaging and MR-ARFI allow visualization

of the FUS focal spot. The FSE TR for optimal visualization of the focal spot was

found to be 500 ms at 3 Tesla magnetic field, which was slightly longer than the TR of

400 ms found in rabbit visceral fat at 1.5T [59]. Depositing ten times less ultrasound

energy than during FSE acquisition, the MR-ARFI approach provided much higher

SNR at the focal spot, located in predominantly fat tissue of the breast sample. In

addition, if phase wraps do not obscure the focal spot location, the individual MR-

ARFI phase images can be used for focal spot visualization without having to find the

phase difference. For the magnitude FSE images obtained during the 20 s sonications,


however, a higher temperature rise or image subtraction would be required to detect

the focal spot.

At body temperature, fatty tissue is expected to be less stiff, which would result

in even higher displacement than was measured in room-temperature breast tissue.

3.2 Imaging Temperature and Displacement

One of the motivations behind developing MR-ARFI methods for visualization of the

ultrasound focal spot is reducing the amount of energy deposited during the acqui-

sition compared to the energy necessary to produce a measurable temperature rise

with MR thermometry. During MR-ARFI acquisitions presented so far, the ultra-

sound pulse, used to displace the tissue, was on the order of 10 ms to 20 ms, with

duty cycle kept at 1-2 %. The acoustic power required to achieve measurable displace-

ment varies from one material to another. Therefore, in spite of having a 1 % duty

cycle, there may be a broad range of total energy deposition. This leads to a question

whether tissue may be heating even during low duty cycle MR-ARFI acquisitions.

In previous work, the temperature rise produced by the MR-ARFI ultrasound

pulses was estimated as a function of time. The temperature rise was measured using

MR thermometry during sonications applied with continuous wave exposures, scaled

based on the time-averaged acoustic power used for the MR-ARFI pulses [65]. For

example, if MR-ARFI image had 100 phase encodes, TR of 1 s, ultrasound pulse

duration of 10 ms and ultrasound power of 10 W, the total energy deposited during

such an acquisition would be 10 ms x 100 × 10 W = 10 J. To estimate the temper-

ature rise caused by a 10 J energy deposition, a continuous sonication can be tested

such that the product of its duration and power equal 10 J. One option is to emit a

continuous ultrasound pulse for 10 s with acoustic power of 1W. While this approach

gives an accurate estimate of the temperature rise after a single MR-ARFI acquisi-

tion, in practice, several acquisitions may be necessary to localize the focal spot, and

in adaptive focusing applications where displacement at the focal spot is measured

several hundred times in order to correct for phase aberrations, it is essential to moni-

tor temperature continuously, rather than make one discrete measurement. Therefore,


(a) (b)

Figure 3.9: (a) Photograph of the planar 1024-channel phased-array transducer usedin this study. The Mylar membrane, shown deflated in this picture, is filled up withcirculating degassed water during the procedure. The inlet and outlet for circulatingwater is shown. (b) Schematic of the experimental setup using the planar transducer.Porcine brain inside a gel holder is placed into a plastic container filled with de-gassed water and covered with an acoustic absorber. The container is put on top ofthe phased-array planar transducer covered with an inflated membrane filled withdegassed water. A solenoid RF coil is placed around the container.

in this section it is shown how a 2DFT spin-echo MR-ARFI pulse sequence can be

modified to provide simultaneous measurement of displacement and temperature rise

in tissue.

3.2.1 Methods

In order to monitor a temperature rise during an MR-ARFI acquisition, an additional

read-out was inserted between the 90◦ and 180◦ RF pulses, shown with a dotted line

in Figure 3.1. The echo time of this gradient-echo acquisition is adjustable. The pulse

sequence was tested in ex vivo porcine brain tissue using 550 kHz 1024-channel phase-

array transducer (Figure 3.9a) and the experimental setup, shown in Figure 3.9b.

The ultrasound beam was focused inside tissue 72 mm away from the face of the

transducer. The ultrasound acoustic power was varied from 37 W to 185 W in steps

of 18 W, and at each power level a temperature rise map and a displacement map were


acquired simultaneously. Temperature maps, based on the PRF shift, were calculated

from the phase of the gradient-recalled echo images by subtracting the reference

phase image obtained with ultrasound turned off, according to Equation 2.14. The

displacement phase maps were calculated as previously described in Equation 3.1.

The following imaging parameters were used: FOV = 16 × 16 cm2, matrix size = 128

× 128, BW = 15.63 kHz, TR = 1 s, gradient-echo TE = 10 ms and spin-echo TE =

47 ms. The duration of encoding gradient lobe was 5.9 ms, resulting in a b-value of

38 s/mm2. The duration of the ultrasound pulse was 18 ms.

3.2.2 Results

The results of simultaneous measurements of displacement and temperature rise using

the modified MR-ARFI pulse sequence are shown in Figure 3.10. Figure 3.10a shows

the cropped temperature and displacement maps for each level of acoustic power, and

Figure 3.10b-c show the plots of mean temperature rise and mean displacement cal-

culated in the ROI inside the focal spot. Both temperature and displacement increase

linearly with acoustic power.

3.3 Summary

In this chapter the 2DFT spin-echo MR-ARFI pulse sequence was demonstrated to

visualize the location of a focal spot in ex vivo brain tissue and in fatty cadaveric

breast tissue. It was shown that MR-ARFI displacement phase images have SNR of 20

and higher, and the MR-ARFI magnitude images of brain, for example, have SNR of

70-90. The high image quality is complimented by the drastic reduction in deposited

ultrasound energy necessary to visualize the focal spot. In case of the breast tissue

example, 10 times less energy was required to visualize the focal spot with MR-ARFI

than with the previously-proposed T1-weighted FSE. The MR-ARFI displacement

SNR was also nearly 4 times higher than the SNR in the T1-weighted FSE approach.

Finally, to assure not only high quality, but also a safe MR-ARFI acquisition, it was

demonstrated that a spin-echo MR-ARFI pulse sequence can be easily equipped with


Figure 3.10: (a) Cropped temperature rise and displacement phase maps obtainedusing the modified dual-echo MR-ARFI pulse sequence for a range of acoustic powerlevels. Mean displacement phase (b) and mean temperature rise (c) at the focal spotare plotted as a function of acoustic power. Linear fits to the data are also shown.

temperature monitoring capabilities. Therefore, the temperature rise can be measured

together with displacement. The price of incorporation of the additional readout is an

increase in the echo time of the original spin-echo by several milliseconds. The rates

of both the temperature and displacement dependence on acoustic power is expected

to be different in different tissue types, depending on the tissue absorption coefficient,

its viscoelastic properties, and the level of perfusion. The next chapter will go into

more detail about the parameters of the 2DFT spin-echo MR-ARFI pulse sequences

that can be optimized in order to provide the optimal quality of displacement phase


images in vivo.

Chapter 4

Adapting 2DFT MR-ARFI for In

V ivo Brain MRgFUS

In the previous chapter, a 2DFT spin-echo MR-ARFI pulse sequence was demon-

strated and tested in ex vivo tissue. Since all MR-ARFI sequences have motion-

encoding gradients similar to those in diffusion-weighted MRI, they are prone to sim-

ilar pitfalls, with the biggest one being sensitivity to motion [70]. In 2DFT diffusion-

weighted pulse sequences, organ motion may result in severe ghosting artifacts in the

phase-encode direction due to incoherent phase changes occurring at each TR [70].

Due to the scanner table vibrations, the ghosting artifacts were visible even in ex vivo

MR-ARFI images, shown in Chapter 3. Therefore, to successfully translate 2DFT

MR-ARFI guidance into human applications, it is necessary to ensure that the se-

quence provides satisfactory image quality not only ex vivo, but also in the presence

of patient motion.

In the first part of this chapter, the effect of brain motion on MR-ARFI displace-

ment images obtained with the 2DFT-based sequence was investigated. First, the

influence of the encoding gradient configuration on the level of image ghosting was

analyzed by comparing two bipolar encoding configurations: repeated bipolar [67] and

inverted bipolar designs [71, 72]. Both configurations were tested with and without

cardiac gating. Then, using the optimal encoding configuration, the effect of encoding

gradient duration on the SNR of displacement images was studied. The displacement

51

CHAPTER 4. ADAPTING 2DFT MR-ARFI FOR IN V IV O BRAIN MRGFUS52

Parameter In V ivo 1 In V ivo 2 Ex V ivo 1 Ex V ivo 2Encoding time [ms] 3 - 22 0 - 22 0 - 22 1Ultrasound pulse [ms] none none 0 - 26 9.5Echo time [ms] 22 - 60 14 - 60 14 - 60 95Repetition time [ms] 1000 1000 1000 800Field-of-view [cm2] 24x24 24x24 16x16 16x12Matrix size 256x128 256x128 128x128 256x128Bandwidth [kHz] 15.63 15.63 15.63 8.1

Table 4.1: MR imaging parameters used in different experiments. In vivo 1 are theparameters used for a comparison of two bipolar encoding configurations. In vivo 2and ex vivo 1 are the in vivo and ex vivo parameters used in the optimization of theencoding duration study. Ex vivo 2 parameters were used during the tissue responsemeasurement study.

signal was obtained by measuring the displacement in the focal spot in ex vivo brain

tissue, and the displacement phase noise was measured using in vivo brain images of

human subjects, without ultrasound.

The second part of this chapter focuses on the influence of the temporal tissue

response to acoustic force on the amount of encoded displacement phase. It was

previously reported that it took 17 ms for tissue displacement to reach maximum

in a phantom material [65]. Therefore the researchers applied the ultrasound pulse

milliseconds before the encoding gradient. In order to maximize encoded displacement

phase for a given encoding configuration, the tissue response has to be known. Here it

is demonstrated how this response can be measured with an MR-ARFI-based method.

It is then shown how for a particular tissue, the relative position of the encoding

gradients and the ultrasound pulse can be optimized in order to further maximize the

displacement phase.


4.1 Comparing Bipolar Encoding Configurations

in Spin-echo MR-ARFI

4.1.1 Methods

The repeated and inverted bipolar encoding configurations (Figure 4.1) have equiva-

lent sensitivity to the displacement of tissue due to the radiation force. However, when

it comes to brain bulk motion, the repeated bipolar configuration is expected to be

much less susceptible than inverted configuration, which has a non-zero first gradient

moment. To analyze the influence of the encoding scheme on the motion artifacts of

the in vivo brain MR-ARFI images, four normal volunteers were scanned using the

MR-ARFI sequence shown in Figure 3.1 with both types of encoding configurations.

No ultrasound was applied. Three different encoding durations, δ, were used: 3 ms,

12.2 ms and 22 ms. Images with and without cardiac gating were obtained. Every

scan was repeated twice.

The direction of encoding was chosen based on the expected direction of the

ultrasound beam in the real treatments, in the superior-interior direction. The echo

time varied from 22 ms to 60 ms, depending on the encoding gradient’s duration.

Other imaging parameters are listed in the first column of Table 4.1. The eight-

channel head RF coil was used.

The image quality was analyzed by comparing the average signal intensity, mea-

sured in the area outside of subjects head boundaries, to the left and to the right from

the head, in every image as shown in Figure 4.2. These measurements were aggre-

gated into four different groups. Groups 1 and 2 consisted of images obtained using

repeated and inverted bipolar encoding respectively. No cardiac gating was used in

these groups. Groups 3 and 4 consisted of images obtained with cardiac gating using

repeated and inverted bipolar encoding respectively. Each group contained images

obtained with three different encoding durations. First, the effect of encoding con-

figuration was studied by comparing group 1 to group 2 and group 3 to group 4.

The sample size of each group was 22. The effect of gating was studied by comparing

groups 1 and 3, and then groups 2 and 4. Statistical significance of the observations


Figure 4.1: Diagram of the two types of displacement encoding configurations showingthe timing of the displacement encoding gradients (thin black line) and the ultrasoundemission (thick red line). In repeated bipolar configuration, a single ultrasound pulseis applied during the second and the third lobes of the bipolar gradient pair. In theinverted bipolar configuration, the ultrasound emission is broken into two pulses, oneapplied during the second lobe, and one during the fourth lobe of the encoding bipolarpair.


Figure 4.2: (a) Example magnitude images obtained using the spin-echo MR-ARFIpulse sequence with repeated and inverted bipolar encoding configurations for not-gated and gated cases, using 22 ms encoding. Dashed line shows the regions outsideof brain, where the average signal was measured. Increased signal intensity in thebackground is more pronounced in the images acquired using the inverted bipolarconfiguration. The effect of gating on the level of ghosting is seen in the repeatedbipolar images. (b) Average background signal intensity is presented for ungatedand gated cases. The comparison between repeated and inverted bipolar encodingshowed significantly higher background signal for the inverted case both with andwithout gating (p = 0.01). The effect of gating on the reduction of motion artifactwas found statistically significant for the repeated bipolar configuration (p = 0.02),and statistically insignificant for the inverted bipolar configuration (p = 0.07).


(p <0.05) was evaluated using a matched paired t-test. Standard deviation of the

measurements in each group was computed and is shown with error bar in Figure

4.2b.

4.1.2 Results

The example magnitude images obtained using two encoding configurations without

and with cardiac gating are shown in Figure 4.2a. Image artifact, observed as elevated

background signal in the phase encode direction is more pronounced in the inverted

bipolar case for both ungated and gated cases. The effect of cardiac gating on the level

of ghosting is seen in repeated bipolar images. Average background signal intensity

is presented for the ungated and gated cases in Figure 4.2b. Comparison between

repeated and inverted bipolar encoding showed significantly higher background signal

for the inverted case both with and without gating (p = 0.01). The effect of gating on

the reduction of motion artifacts was found statistically significant for the repeated

bipolar configuration (p = 0.02), and statistically insignificant for the inverted bipolar

configuration (p = 0.07). However, in the inverted bipolar encoding case, the ghosting

artifact appears more coherent when gating is used. Based on these results repeated

bipolar configuration was selected for further optimization.

4.2 Optimization of Encoding Duration for MR-

ARFI in the Presence of Motion

4.2.1 Methods

Using the encoding configuration that resulted in lower motion artifacts in the previ-

ous section, the repeated bipolar configuration without gating, the expected displace-

ment SNR was studied as a function of encoding gradients duration. To compute

the expected displacement SNR in brain, displacement signal measurements were

performed in ex vivo brain, and displacement noise, or standard deviation of dis-

placement with no ultrasound applied, was measured in volunteers. Displacement


SNR was computed for the duration of the encoding gradients, δ, varied from 0 ms to

22 ms, where the longest gradients corresponded to diffusion weighting with b-value

of 225 s/mm2 and ultrasound pulse duration of 26 ms.

Ex vivo displacement phase was measured in a whole porcine brain tissue (n = 5).

The displacement phase images were calculated according to Equation 3.1. Displace-

ment signal was taken as the mean displacement phase calculated in a small ROI in

the focal spot of ex vivo images. The brain tissue was obtained from a pig approxi-

mately 24 hours before the experiments and was refrigerated. During the study, the

tissue was kept at room temperature.

The experimental setup (Figure 3.9b) consisted of the gel holder containing the

brain tissue sample which was placed into a plastic container filled with degassed water

and was covered with acoustic absorber. The plastic container was positioned on top of

the ultrasound transducer covered with an acoustically transparent Mylar membrane

filled with water. A solenoid breast RF coil was placed around the container. The

ultrasound beam was focused inside the brain at a depth of 54 mm from the center of

the transducer. The transducer emitted pulses with acoustic power of 23 W and with

duration equal to the encoding duration plus the duration of the crushers and the

slice-select gradient of the 180◦ RF pulse, T180. Other imaging parameters are listed

in the second column of Table 4.1.

The expected in vivo displacement noise was calculated using displacement im-

ages obtained in normal volunteers (n = 5), by measuring the standard deviation of

displacement phase in the ROI inside the brain. The MR-ARFI pulse sequence shown

in Figure 3.1 with parameters listed in the third column of Table 4.1.

4.2.2 Results

The effect of duration of the repeated bipolar encoding gradient on in vivo dis-

placement phase is shown in Figure 4.3. The images in Figure 4.3a show that with

increasing encoding duration the displacement at the focal spot increases, however,

the level of motion image artifacts due to patient motion increases as well. The mean

displacement at the focal spot, obtained in ex vivo tissue, and the standard deviation


(a)

(b)

Figure 4.3: (a) Magnitude and displacement phase images for ex vivo (top) and in vivo(bottom) brain obtained using a range of encoding gradient durations. The dotted lineshows the ROIs used to compute displacement signal and noise. (b) (Left) Plot of exvivo mean displacement phase (displacement signal), and in vivo displacement phasestandard deviation (displacement noise). The data is plotted as mean +/- standarddeviation calculated from the measurements in 5 subjects and samples. (Right). Plotof displacement phase SNR estimated by dividing displacement signal measured exvivo by displacement noise measured in vivo. In this plot, the fitting curve was foundby dividing the fitting curves shown in b. The optimal duration of encoding gradientis approximately 12 ms.


of displacement phase, calculated in brain images in the ROI shown in Figure 4.3a, are

plotted as a function of gradient duration in Figure 4.3b. The following polynomial

functions were fitted to the data:

∆φd = 2.1× 10−3t2 + 1.3× 10−2t− 2.3× 10−2 (4.1)

σ∆φd = 1.5× 10−5t3 − 9.2× 10−5t2 + 1.9× 10−4t+ 2× 10−2. (4.2)

The fits had correlation coefficient r equal to 0.99.

The SNR estimates of displacement phase, based on finding a ratio between dis-

placement phase measured ex vivo and standard deviation of displacement phase,

noise, measured in vivo, are plotted in Figure 4.3a. The results of the SNR estima-

tion show that the encoding gradient duration of approximately 12 ms maximizes the

expected in vivo displacement phase SNR.

4.3 Measuring Tissue Response with MR-ARFI.

Optimal Encoding Timing.

4.3.1 Methods

Due to the observed non-instantaneous response of tissue to acoustic radiation force,

tissue displacement does not reach maximum immediately after ultrasound turns on,

and it does not decrease to zero instantly at the end of the ultrasound pulse. Therefore,

in the bipolar encoding design, synchronous application of ultrasound and encoding

may not be the most optimal. Knowledge of tissue response can help compute the

offset of the ultrasound pulse in relation to encoding that can further optimize the

SNR of displacement images. In this section, it is shown how tissue temporal response

can be measured with MR-ARFI. Then the optimal offsets between the ultrasound

pulse and the encoding gradient is computed for the time constants of the tissue

response experimentally measured using MR-ARFI.

To measure tissue response with MR-ARFI, the displacement was sampled over

time with an encoding gradient of much shorter duration than ultrasound pulse as


Figure 4.4: Partial diagram of MR-ARFI pulse sequence, modified for the measure-ment of tissue time constants. The gradient waveforms of the encoding gradient onlyare shown here. Short unipolar gradients are used. The timing of three ultrasoundemissions is shown (red line). Tissue displacement corresponding to each ultrasoundpulse is shown in blue. Black arrow indicates the endpoints of the gradient-ultrasoundoffset time, which was varied in this study. The offset of 0 ms (top displacement wave-form) corresponds to the case, where the end of the encoding gradient and the startof the ultrasound pulse have the same time, which is circled in the diagram. Theduration of the ultrasound pulse is 9.5 ms and the duration of the encoding gradientis 1 ms.

schematically shown in Figure 4.4. The ultrasound pulse duration was set to 9.5 ms,

and the repeated bipolar encoding configuration was replaced with a unipolar one of

1 ms duration. The timing of the gradients was kept constant, but the start time of

the ultrasound emission was offset in such a way that the gradient sampled the dis-

placement of tissue before the ultrasound was turned on, during the ultrasound pulse,


and after it was turned off. Gradient-ultrasound offset time of 0 ms corresponded to

the case where the end of the encoding gradient and the start of the ultrasound pulse

had the same time. Offset time greater than 9.5 ms indicated that the gradient was

used to encode displacement after the ultrasound was turned off.

This approach was tested in ex vivo brain tissue using the experimental setup

described above (Figure 3.9b) with the transducer focused 67 mm away from its

center, and acoustic power of 100 W. The imaging parameters used in this experiment

are listed in the fourth column of Table 4.1. For the times when encoding gradient

overlapped with the ultrasound pulse, the full width at half maximum (FWHM) of

the displacement profile at the focal spot was measured. For all time points of the

measurements, the average displacement at the focal spot was measured.

Using experimentally obtained tissue response parameters, the tissue response

was modeled according to Equation 2.11. Encoding gradients were set to the opti-

mal repeated bipolar configuration and optimal duration of 12 ms. Then, the phase

was computed using Equation 2.21. The displacement phase was calculated for syn-

chronous application of ultrasound pulse and encoding gradient, which corresponded

to an offset time of 0 ms. The offset times then were varied from 10 ms to + 10 ms

in 200 µs steps, which shifted the timing of the ultrasound pulse compared to the

encoding gradient.

4.3.2 Results

Using the pulse sequence described in Figure 4.4, the displacement of tissue during

the ultrasound pulse emission and several milliseconds before and after was measured.

The displacement phase measurements are shown in Figure 4.5. In Figure 4.5a the

displacement profiles passing through the focal spot, obtained at different offset times,

are stacked together. This image demonstrates the displacement at the focal spot and

away from the focal spot over time. The FWHM of the displacement at the focal

point is plotted in Figure 4.5b. The mean displacement at the focal spot is plotted

as a function of offset time in Figure 4.5c. Continuous increase of tissue displacement

is observed during application of ultrasound pulse, from 0 ms to approximately 9.5


ms in the offset time. The longer ultrasound is on the wider becomes the focal spot

(Figure 4.5b) due to the propagation of the shear wave away from the focus. Linear

regression was used to fit the FWHM data. Figure 4.5b showed that FWHM of the

focal displacement increased linearly at the rate of 0.35 m/s.

To characterize the tissue response, exponential functions were fitted to displace-

ment phase data using two intervals: during the ultrasound pulse emission and after

ultrasound emission stopped (Figure 4.5c). The rise time constant and decay time

constant were found using these fits. For the ex vivo brain tissue sample studied

here, the rise time constant was found to be 5.97 ms and decay time constant was

5.94 ms.

The normalized displacement phase, calculated using 12 s long repeated bipolar

encoding gradient and tissue response with rise and decay time constants of 5.97

ms and 5.94 ms is shown in Figure 4.6. The displacement phase obtained when the

delay time was zero was used to normalize the phase measurements. The normalized

displacement phase is plotted as a function of ultrasound delay time. It was found

that when the emission of the ultrasound pulse starts several milliseconds before the

encoding gradient, the displacement phase was greater than 1. This result indicates

that for the tissue responding to radiation force with tissue constants of approximately

6 ms, starting the ultrasound emission approximately 3.2 ms before the corresponding

encoding gradient can increase the amount of encoded displacement phase by 44%

compared to the default timing shown in Figure 4.1.

4.4 Discussion

The studies described in this chapter demonstrate how several parameters can be

optimized in order to achieve the highest SNR of MR-ARFI displacement images

during in vivo applications in the head. In addition, a modifications of the MR-ARFI

pulse sequence was developed to allow measurement of tissue response.

Firstly, image artifacts due to patient brain motion were shown to be significantly

higher if an inverted bipolar encoding configuration was used with the spin-echo 2DFT


Figure 4.5: (a) (Left) Example of displacement phase image obtained using the pulsesequence shown in Figure 4.4. The dotted line indicates the position of the displace-ment profile at the focal spot that was measured at each gradient-ultrasound offsettime. (Right) The displacement profiles are plotted together to demonstrate the evo-lution of the tissue displacement in time. (b) FWHM of the displacement focal spot:displacement FWHM increases linearly with time with the rate 0.35 m/s. (c) Averagedisplacement at the focal spot as a function of the gradient-ultrasound offset time.Tissue response was characterized by finding fits to the displacement data during andafter the ultrasound pulse application. τrise was found to be 5.97 ms and τdecay was5.94 ms.

MR-ARFI sequence. Cardiac gating resulted in a significant reduction of motion arti-

facts only in half of the cases. In addition, the subjects scanned here had heart rates


Figure 4.6: Plot of the normalized displacement phase computed using Equation 1for tissue response parameters τrise of 5.97 ms, τdecay of 5.94 ms, and repeated bipolarencoding configuration of 12 ms. The results indicated that offsetting ultrasound by3.2 ms increases displacement phase by θ of 44% compared to default timing.

ranging from 40 to 70 beats per minute, which introduced TR and scan time varia-

tions. The increased TR would slow down the 2DFT pulse sequence, leading to longer

procedure times. For example, heart rate of 40 beats per minute would lengthen the

TR and the total scan time by 50% .The decreased TR would lead to higher ultra-

sound duty cycle, given the ultrasound pulse duration is kept constant in each scan.

With ultrasound pulse duration of 20 ms, heart rate of 70 beats per hour would lead

to slight increase of the duty cycle from 2% to 2.3%. Therefore, repeated bipolar

encoding without cardiac gating was found to be an optimal sequence configuration.

The optimal encoding duration was then determined to be 12 ms for the maximum

displacement phase SNR in brain. This is a shorter duration than 19 ms, which

was found optimal for displacement SNR based on instantaneous tissue response

assumption and minimizing of T2 and diffusion weighting [67]. The previous study

used line-scan imaging and did not have to account for SNR loss due to patient motion

artifacts. In the future, for more accurate SNR optimization, it would be beneficial

to assess how human brain tissue displaces in vivo. In situations, when acoustic

power can be further increased without compromising the safety of the procedure,


the duration of the ultrasound and encoding does not need to be increased. However,

when maximum allowed power is already being applied and the displacement SNR is

still not sufficient, the ultrasound duration and encoding can be adjusted taking into

account the optimization described here. The optimal timing of encoding may differ

across tissue types, as the the relationship between the encoded phase and the gradient

duration goes from linear to non-linear depending on the temporal tissue response.

In tissue with greater diffusion coefficient, the optimal duration of the gradient may

be found shorter than 12 ms discussed here. The maximum of the SNR curve is not

expected to shift with acoustic power, however.

Secondly, it was demonstrated that displacement SNR can be further increased

by finding an optimal delay of the ultrasound emission with respect to the encoding

gradients. To accurately model the effectiveness of encoding configuration in a par-

ticular tissue, it is important to know the exact tissue time constants: the rise and

decay times. Since the tissue response parameters are not known for most tissues [35],

a method to measure time response for tissue under investigation was developed here.

Bipolar encoding gradients were replaced with short, unipolar gradients and the time

between the ultrasound pulse and the gradient was varied in order to sample the

tissue displacement before, during, and after ultrasound application. For the ex vivo

porcine brain sample studied here, the rise and decay time constants were found to be

approximately 6 ms, which is of the same order of magnitude as values reported for ex

vivo liver and in vivo muscle in [34,73]. In this study 2DFT spin-echo MR-ARFI was

used to measure tissue response, however, this approach of tissue response sampling

can be used in other implementations of MR-ARFI, for example, GRE 2DFT MR-

ARFI [74]. Knowledge of the tissue response time constants can help optimize the

offset time between the ultrasound pulse and the bipolar encoding gradients. For the

12 ms duration of the repeated bipolar encoding gradients, it was shown that offset-

ting the ultrasound pulse in relation to the encoding by 3.2 ms increases the amount

of encoded displacement phase and therefore can improve the SNR of displacement

phase images. Depending on the temporal tissue response, the effect of the offset time

will change. Tissue with short relaxation times will reach maximal displacement and

return to its initial displacement state faster, and therefore, little encoded phase loss


will be encountered during the rise and decay of the displacement.

While a repeated bipolar encoding gradient duration of 12 ms, with ultrasound

pulse of approximately 19 ms, has been shown here to optimize the displacement phase

SNR, it also would result in a focal spot with FWHM of approximately 15 mm in ex

vivo brain tissue. In some MR-ARFI applications, optimization of the FWHM of a

focal spot may be an additional objective. For example, in adaptive focusing applica-

tions, the displacement measurements are used to infer the intensity of the ultrasound

beam. Therefore the displacement of tissue due to the shear wave propagation would

lead to erroneous intensity estimations in locations surrounding the beam focus or

foci [75]. To avoid errors due to shear wave displacement obscuring the actual inten-

sity estimation, the duration of the ultrasound pulse and the encoding gradient may

be reduced below 12 ms in 2DFT spin-echo MR-ARFI. And to compensate for the

consequent loss of displacement SNR, acoustic power may be increased.

In conclusion, to adapt existing spin-echo MR-ARFI pulse sequences for in vivo

applications in brain, the effect of motion artifacts on displacement phase should be

minimized by selecting the optimal encoding configuration and duration of the gra-

dient. To increase displacement phase SNR further, tissue response can be measured

and used to calculate the optimal timing of the ultrasound pulse emission and the

encoding gradient.

4.5 Summary

Manipulating various parameters of MR-ARFI acquisition, it was demonstrated in

this chapter that the 2DFT spin-echo MR-ARFI is overall a robust method across a

wide range of parameters. However, to maximize the efficiency of the method, several

approaches to optimization of the 2DFT spin-echo MR-ARFI pulse sequence pre-

sented in this chapter could be considered. While some of them are specific to the

2DFT sequence, others, such as optimization of ultrasound and encoding relative tim-

ing based on the tissue response time constants, can be applied in MR-ARFI sequences

with any types of readout. In the next chapter, the phase aberration correction topic

will be introduced in detail. Two methods to correct for the phase aberrations using


adaptive focusing and MR-ARFI will be demonstrated.

Chapter 5

Novel Adaptive Focusing

Algorithms

This chapter addresses the challenging issue of ultrasound propagation and focusing

through acoustically inhomogeneous tissue. Iterative and non-iterative methods are

introduced and tested in simulations and experiments.

When ultrasound propagates through layers of acoustically inhomogeneous tissue,

such as skull bone or ribs, the difference in acoustic properties across skull and between

skull and brain tissue produce amplitude and phase aberrations [76]. This affects the

position, shape and intensity of the ultrasound beam [77, 78]. While in the case of

ribs, it may be possible to find an acoustic window to transmit the sound between

the ribs only, there is no natural acoustic window in the human skull.

Invasive methods had to be used in the past to focus ultrasound in the brain in

animal models. In the early 1970s, sections of skull had to be removed in living rats

and cats to prevent aberrations [79]. Later, craniotomies were used in rabbits [80]. To

help overcome the detrimental effects of the skull on transcranial ultrasound treat-

ments, modern phased-array transducers are [81–83] designed with a large number of

elements, which can be individually phased to compensate for aberrations caused by

the skull.

There has been a range of approaches investigated for measuring the aberrations

caused by the skull. In some less invasive studies, skull aberrations were measured by

68

CHAPTER 5. NOVEL ADAPTIVE FOCUSING ALGORITHMS 69

Figure 5.1: Block diagram of the adaptive focusing process. A phased-array wavesource generates a monochromatic wavefront with desired time delays. The wavefrontpropagates through the aberrating medium. A detector defines a target position forthe optimization procedure and provides a feedback signal. A computer analyzes thesignal and reprograms the time delays and optionally the amplitudes of the individualsources until the waves are optimally focused on the target.

implanting a hydrophone into a brain. The sound waves emitted by the hydrophone

were recorded using the phased-array transducer around the skull, and the appropriate

time delays to correct for these aberrations were then applied to the elements of the

transducer [77]. Completely non-invasively, the skull aberrations can be estimated by

measuring skull acoustic properties with MRI [84,85] or CT [78,86–88]. Currently the

CT-based aberration correction approach is being used in transcranial MRgFUS due

to the limited ability of conventional MRI to measure bone density, which is used to

estimate the speed of sound in the skull.

Iterative and non-iterative approaches [71,75] to ultrasound focusing that do not

rely of the knowledge of acoustic properties of an aberrator have recently emerged.

These methods are based on the concept of adaptive focusing, the process during

which the emissions of individual elements of the phased-array are manipulated until

the intensity at the desired location is maximized. In these methods the intensity


at the focal point is measured indirectly using MR-ARFI. The adaptive focusing

approaches are introduced in more detail below.

5.1 Introduction to Adaptive Focusing

Adaptive focusing is a process in which the aberrations of the propagating waves

are estimated and then used to compute the time delays (or phase shifts) necessary

to compensate for the aberrations. In some cases, the necessary time delays can be

estimated directly by measuring the timing of the echoes from bright reflectors, such as

a kidney stones or air bubbles [89]. In other cases, measurements of field properties,

such as intensity or radiation force are used to find the optimal time delays. The

estimation is often performed in several iterations and is sometimes referred to as

autofocusing [90]. The general block diagram of the adaptive focusing process is shown

in Figure 5.1.

For the ultrasound wave case, the incident wavefront is generated using a phased-

array transducer. A computer sets the phase delays for each of the elements individu-

ally to a value between 0 and 2π. The phase delays are computed based on the output

of the detector that measures the intensity of the field. The field at the detector is

the result of interference of ultrasound waves from the different transducer elements

transmitted through the aberrating medium. The detector monitors the target area

where the intensity needs to be maximized and provides feedback for the adaptive

focusing algorithm. The adaptive focusing algorithm finds the unique configuration

of phase delays for which the contributions from each element of the transducer are

in phase at the target. The iterative methods use feedback information to update the

focusing of the transducer continuously, and non-iterative methods first perform a

set of measurements to collect sufficient feedback which is then used to set all of the

transducer elements to the optimal phase at once.


Figure 5.2: Illustration of continuous and partitioning focusing algorithms. Greenmark indicates the transducer channels whose time delays are being adjusted. Graycolor indicates the channels to which the optimal time delay was assigned. For thecontinuous algorithm, the channels are adjusted sequentially. Once the optimal phaseis found for a channel, the phase of the transducer is updated and the algorithmproceeds to the next channel. The partitioning algorithm randomly selects half ofthe transducer elements and adjusts their overall phase. Once the optimal phase isfound for a particular group, the transducer phase is updated and the next randomgroup is selected.

5.2 Adaptive Focusing using the Partitioning Al-

gorithm

New iterative adapting focusing algorithms have been recently introduced in op-

tics [91] and ultrasound [92]. In both works, a continuous sequential approach was

proposed (Figure 5.2), in which the phase delays of each transducer element were

manipulated one by one until the intensity of light or acoustic radiation force at the


focal spot were maximized. Vellekoop et al. [91] also considered a partitioning al-

gorithm (Figure 5.2). In the partitioning algorithm half of the transducer elements

are randomly selected and their phase is varied. Once the optimal phase is found for

a particular group, the transducer phase is updated and the next random group is

selected. The process continues until the convergence of the detector measurements.

Figure 5.3: Illustration of the relative posi-tions of the phased-array transducer andthe acrylic aberrating plates placed be-tween the transducer membrane and thetissue sample.

Comparing the two algorithms in op-

tical applications, Vellekoop et al. re-

ported that in the presence of noise, the

effect of phase manipulation of a single

source is more challenging to detect than

the effect of phase modulation of a larger

group of elements. Therefore, the parti-

tioning algorithm was recommended as

a way to improve focusing where there

is noise. For the first several iterations,

the rate of improvement of the field in-

tensity was greater for the partitioning

algorithm than for the continuous one.

However, it became harder and harder to

improve focusing at later iterations, since

each new adjustment was not orthogonal

to the previous one and affected the pre-

viously optimized elements.

In MRgFUS applications, MR-ARFI

can be used to indirectly measure ultra-

sound intensity. Since MR-ARFI images have finite SNR, it is important to use fo-

cusing methods that would be least susceptible to noise. In addition, acquisition of

each MR-ARFI image relies on emission of a short ultrasound, which if repeated over

a long period of time can lead to tissue heating both at the focal spot and other

undesired locations. Therefore, the partitioning algorithm that allows more rapid im-

provement of beam focusing and is less susceptible to noise during the initial steps


of the process is demonstrated in the next section of this chapter. Implementation

of the partitioning algorithm is presented and its performance is compared to the

continuous algorithm.

5.2.1 Methods

The partitioning algorithm was experimentally tested using the planar phased-array

transducer shown in Figure 3.9a as the wave source, a combination of numerical and

physical aberrations, and MR-ARFI as the detecting mechanism. The experimental

setup, shown in Figure 3.9b was used with addition of two 5 mm thick acrylic (speed

of sound 2800 m/s, approaching the bone speed of sound) plates between the surface

of the transducer membrane and a sample. The relative positions of the transducer

and the aberrating plate projected on the MR-ARFI displacement phase image are

schematically shown in Figure 5.3. The plates were of different size and were placed in

such a way that fraction of the ultrasound beam propagated through 10 mm acrylic.

Another fraction propagated through the 5 mm acrylic. The rest did not cross any

acrylic on its path to the focus.

Figure 5.4 shows the phase delays of the channels of the focused phased-array

transducer. Acrylic plates perturbed the focal shape, and the numerical aberrations

nearly destroyed the focus. To reduce the number of iterations in the algorithm, the

transducer elements were grouped into 16 groups, and the system was treated as 16-

element system. Following the steps of the partitioning algorithm, in each iteration, 8

elements selected at random were grouped together and their phases were adjusted.

The phase shift between 0 and 2π, ∆Φ, in π/4 increments, was added to the phase

of the group. Then the displacement image was obtained using 2DFT spin-echo MR-

ARFI.

The displacement phase images were calculated according to Equation 3.1. Imag-

ing and acoustic parameters used in the experiments were as follows: TE = 39 ms, TR

= 500 ms, FOV = 16 × 7, matrix = 128 × 58, BW = 15.63 kHz, encoding duration

12 ms, ultrasound pulse duration 19 ms, acoustic power = 47 W and focal depth =

72 mm. The displacement was measured as average signal in the 2 pixels by 2 pixels


Figure 5.4: Illustration of initial phase distribution across the elements of the focused1024-channel phased-array transducer. After the acrylic plates were added into thesetup, the focal spot remained visible on displacement phase image, however, it wasno longer circularly-shaped. Addition of the numerical aberrations further reducedintensity and affected the geometry of the focal spot.

ROI in the focal spot. The ∆Φ that maximized the displacement at the focal spot

during one iteration was added to the transducer elements under test in the follow-

ing iteration. Only five iterations were completed during the experiment due to the

limited duration of the available scan time.

To investigate how the partitioning algorithm would perform if there was time to

complete 3 × N iterations, considered sufficient in [91], the phased-array transducer

was simulated using Field II, ultrasound simulation program [93]. In this simulation,

all 1024 elements were considered as individual channels, so N was equal to 1024.

Phase aberrations selected randomly between 0 and 2π were added to the phased

delays of the focused transducer’s elements. Both the partitioning and continuous

algorithms were applied to correct for the phase aberrations. Similarly to the experi-

ment, ∆Φ between 0 and 2π was added to the elements under test and the intensity


Figure 5.5: (a) Displacement phase images obtained during iteration 4. As the phaseadded to the N/2 elements of the transducer changes, the displacement phase at thefocal spot varies sinusoidally. (b) Average displacement at the focal spot during oneiteration. The delta phase for which the displacement was maximum in this iterationwas assigned to the group of elements under test in the following iteration.

at the focal spot was computed using the field simulator. The number of iterations,

completed for each algorithm was 3 × N. Four cases were simulated: without noise,

with noise of standard deviation σ, 2 × σ and 3 × σ.

5.2.2 Results

Example displacement phase images obtained during one iteration are shown in Figure

5.5a. The average displacement at the focal spot is plotted as a function of the phase,


Figure 5.6: (a) Displacement profiles at the focal spot after each iteration was com-pleted. Black dashed line indicates the displacement level before the numerical aber-rations were added. Iterations 4 and 5 partially corrected for the aberrations createdby the acrylic plates. (b) Average displacement at the focal spot after each aberration.

∆Φ, which was added to the group under test. This plot is shown in Figure 5.5b.

As the sound waves of the group under test go in and out of phase with the waves

emitted by the rest of the transducer elements, the displacement at the focal spot

changes sinusoidally. In several cases, several foci are visible in the focal area. These

cases require special care when choosing ultrasound and encoding duration (Chapter

5), because the shear waves propagating away from each of the spot can add up and

alter the perception of the overall focal field intensity.

The displacement profiles crossing the focal spot are plotted in Figure 5.6. This

figure shows that after the third iteration the numerical aberrations were corrected

for, and iterations 4 and 5 helped improve the focusing through the acrylic plates.

Overall, five iterations of the partitioning algorithm resulted in three-fold increase of

the displacement at the focal spot.

Figure 5.7 shows the results of simulated adaptive focusing algorithms. As pre-

dicted by Vellekoop et al., the partitioning algorithm gives more rapid improvement

of the focal spot intensity for the first 100 iterations, compared to the continuous

approach. However, soon after that, the intensity improvement slows down and falls


(a) (b)

Figure 5.7: (a) Simulated intensity for 400 iterations of continuous and partitioningalgorithms. For the first 100 iterations partitioning algorithms increases intensity at ahigher rate than continuous algorithm, however, the rate decreases for higher iterationnumbers. (b) Simulated intensity for 3 × N iterations with no noise and with linearlyincreased three noise levels: σ, 2σ and 3σ.

Figure 5.8: Intensity during the 400 iterations of the partitioning and continuousalgorithms with and without noise.


behind the continuous algorithm results (Figure 5.7a). Figure 5.7b shows how both

algorithms perform for 3 × N iterations. When there is no noise added in simulations,

the continuous algorithm converges to maximum intensity equal to intensity of case.

The partitioning algorithm, however, never reaches the maximum and converges at

intensity level of approximately 15 % of maximum intensity. In the presence of noise,

however, the partitioning algorithm shows much less sensitivity to noise, and the rate

of intensity improvement is considerably less affected by it compared to the continu-

ous algorithm case (Figure 5.7b). A zoomed-in plot of the intensity as a function of

iteration with and without noise is shown in Figure 5.8.

5.2.3 Conclusion

In conclusion, adaptive focusing using the partitioning algorithm, previously intro-

duced for optical applications, was experimentally demonstrated in this section. It

was shown that a significant increase of ultrasound intensity can be achieved using

several iterations of the algorithm. It was not, however, experimentally determined

at what level of intensity the algorithm converges, compared to the unaberrated case.

Simulations allowed running the algorithm to completion and comparing it to the con-

tinuous algorithm. It was shown that the partitioning algorithm performs superiorly

to the continuous algorithm during approximately the first N/10 iterations both with

and without noise. This suggests the potential advantage of using the partitioning al-

gorithm compared to the continuous algorithm in situations of noisy measurements.

In the end on 3×N iterations, however, the partitioning algorithm fails to achieve

complete correction of the aberrations. Therefore, it may be valuable to use the par-

titioning algorithm as a first step in focusing procedure and then switch to other

methods. This would achieve rapid improvement in fewer steps which would improve

the SNR of all subsequent measurements and would increase the efficiency of other

approaches.


5.3 Adaptive Focusing Using Non-Iterative Algo-

rithms

In addition to iterative approaches, the adaptive focusing of ultrasound transduc-

ers have been demonstrated experimentally and in simulations using a non-iterative

Hadamard-encoded algorithm. In this method, the emissions of the transducer ele-

ments are encoded according to the columns of the Hadamard matrix and the intensity

corresponding to particular encoding is measured indirectly using MR-ARFI. After 4

× N measurements are completed, the information is used to solve a series of linear

equations for the amplitude and phase aberrations, experienced by each individual

element. Using that information, the phase delays of each element are adjusted and

the optimal focusing is achieved. This method has not yet been applied to focus the

clinical hemispherical ultrasound arrays.

In this section of Chapter 5, a new non-iterative algorithm, aimed at reducing

the number of measurements necessary to achieve desirable focusing, is described and

tested on the hemispherical array using simulations and experiments. This method

is based on the Hadamard-encoding approach, however, it uses Zernike encoding in-

stead. The approach was inspired by observing certain spatial patterns of the human

skull phase aberrations measured using CT-method introduced in Chapter 2. Before

introducing the new approach to non-iterative adaptive focusing, several key back-

ground concepts are discussed here.

The total pressure at the focal point of a phased-array transducer is a superposition

of the spherical waves emitted by each element. In the ideal case, when there are no

aberrations, it can be written as

pideal =∑N

i=0 ei, (5.1)

where ei is the emission signal of a single element consisting of amplitude and phase.

Skull aberrations perturb this relationship, so the total pressure becomes

p =∑N

i=0 gi · ei, (5.2)


where gi are the complex coefficients that relate the emissions of the elements with

the resulting field in the focal point [75], and thus represent the aberrations. The

amplitude of gi corresponds to attenuation while the complex angle of gi corresponds

to the time or phase aberrations. Correcting for these coefficients in the emmisions ei

will compensate for the aberrations. Phase aberrations are corrected by shifting the

phases of the elements’ emission signals, ei, by the opposite of the phase of gi.

In the demonstrated non-iterative approach, a Hadamard matrix H was used to

encode groups of transducer elements into virtual transducers. The resulting pressure

at the focus, p, is then given by

p =∑N

i=0 gi · hi, (5.3)

where hi are the elements of the column vectors hi of the Hadamard matrix encoding

the virtual transducers. For each encoding, the pressure, p, is indirectly estimated

using MR-ARFI measurements [75]. The complex aberrations, gi, are then found by

solving Equation 5.3. Using the notation from B. Larrat et al. [75], the equation can

be presented in matrix form:

pH = g ·H, (5.4)

where pH is a vector of focal pressures corresponding to the encoded emissions hi. In

this method, the Hadamard encoding is replaced with an encoding based on Zernike

polynomials (ZPs) [94].

ZPs are an infinite set of two-dimensional, rotationally-invariant [95] polynomials

that form a complete, orthogonal basis over the unit disk. Since their first introduction

in 1930’s by F. Zernike [94], these polynomials have been used in a wide range of

applications in computer vision and optics. ZPs have shown tremendous potential in

image recognition and continue remaining a topic of active research in this field [96].

ZPs are also commonly used in microscopy [97], astronomy [98, 99], ophthalmology

[100] to model and correct for the aberrations of light waves. While the potential of

ZPs has not yet been demonstrated in ultrasound applications, it appears to be an

intuitive transition from optics, and will be demonstrated here.


On a continuous unit circle, ZPs are described by the equations

Zmn (ρ, θ) =

√

2(n+ 1)ZRmn (ρ)cos(mθ) form > 0;√

2(n+ 1)ZRmn (ρ)sin(|m|θ) for m < 0;√

(n+ 1)ZRmn (ρ) for m = 0;

(5.5)

where n is the radial polynomial order and m is the azimuthal frequency. The radial

component of the Zernike polynomial, ZRmn , is defined as

ZRmn (ρ) =

∑(n−|m|)/2s=0

(−1)s(n−s)!s!(

n+|m|2−s)!(n−|m|

2−s)!

ρn−2s. (5.6)

Rotation invariance property makes ZPs a valuable and robust mathematical tool

in both image recognition and wave aberration modeling. If the original image or

aberration decomposed into Zernike basis contains Zernike polynomial of magnitude

Zmn, then in the rotated version of the original image the magnitude of this polynomial

will remain Zmn.

Example ZPs of the first five orders are shown in Figure 5.9. To simplify notation

in this section, polynomials are arranged into a sequence of increasing radial and

frequency modes and are given a mode number reflecting their order in the sequence.

For example, Z00 , Z−1

1 , Z11 , Z−2

2 , Z02 , Z2

2 become simplyZ1, Z2, Z3, Z4, Z5, Z6. The

dotted line in Figure 5.9 shows the order in which ZPs are sorted into a sequence of

Zk polynomials.

The next sections are structured as follows. The first section studies the skull

thickness and the corresponding phase aberration data from five patients. Similarities

and differences between different subjects are assessed qualitatively and quantitatively

by looking at the correlations between different data sets. In the second section,

a non-iterative adaptive focusing approach based on ZPs is introduced and tested

with five patient data sets using simulation of the clinical hemispherical phased-array

transducer. The effect that the Zernike-based phase aberration correction has on

beam intensity is then validated experimentally ex vivo using MR-ARFI. Finally, the

potential benefit of using phase corrections obtained in previous studies to provide


Figure 5.9: Zernike polynomials computed for the first five orders. Orders m andn are shown in parenthesis as (m,n). Dotted line shows the sequential order of thepolynomials used in this chapter, which are labeled as Z1, Z2 and so on.


Figure 5.10: (a) Positions of the elements of the hemispherical transducer (ExAblate4000, InSightec, Tirat Carmel, Israel). Experimental setup: (b) Hemispherical trans-ducer filled with degassed water and the tissue mimicking phantom placed in thenatural focus of the hemisphere. (c) Acoustic absorber is placed over the phantomand the RF coil is positioned around the absorber.

the initial guess for correction of a new data set is tested.

5.3.1 Analysis of Skull-Based Aberrations

5.3.1.1 Methods

The skull phase aberration data used in this section was obtained during five transcra-

nial MRgFUS treatments performed by Ernst Martin and Beat Werner (MR-Center,

University Children’s Hospital, Zurich, Switzerland). During these treatments, pa-

tients underwent a selective central lateral thalatomy performed using a clinical pro-

totype FUS system (ExAblate 4000, InSightec, Tirat Carmel, Israel) and a 3 Tesla

MRI scanner (GE, Milwaukee, USA) [13]. The FUS system consisted of a hemispheric

1024 elements phased-array transducer, shown schematically in Figure 5.10a, operat-

ing at a central frequency of 650 kHz. For every patient, preoperative CT images of

the head were acquired in order to calculate the phase aberration values by analyzing

bone density, bone thickness and beam refraction passing through the water-bone and

bone-brain interfaces for each element of the transducer [78]. The algorithm for mod-

eling the phase aberrations based on CT images was developed by InSightec Ltd. It is


used in the ongoing clinical trials of transcranial MRgFUS. The mean and the stan-

dard deviation of phase aberration values across all the elements were calculated for

each subject. Correlation coefficients were calculated between the aberration values

for every pair of data sets, using Matlab function computing correlation coefficients

based on covariance (corrcoef.m). The CT images were also used to obtain thickness

maps of the skulls, calculated as the distance between the inner and outer surfaces

of the skull. The inner and outer surfaces were segmented using a threshold of 476

Hounsfield units. Only the most superior slices of CT data set, approximately the top

half of the skull, were segmented, as that is the portion of the skull through which

most of the ultrasound energy is passing. After segmentation, the coordinates of the

inner and outer boundaries of the skull were processed using GeoMagic (Geomagic

Inc.) 3D software. The inner and outer surfaces were constructed from the boundary

coordinates, and the distance between the two surfaces was calculated based on the

nearest point approach.

5.3.1.2 Results

Skull thickness maps calculated by segmentation of the five patients’ head CT images

are shown in Figure 5.11a. These data were used as anatomic references for the

phase aberration data calculated for each element of the transducer (Figure 5.11b).

Qualitative comparison of the shapes and variations of thickness across the five skulls

shows a range of difference in the shape, size, and bone thickness. Despite these

differences, some thickness variation patterns can be recognized in all of the skulls.

For example, there is thickening in the posterior medial section of the skull in all

five subjects. The skull thickness variation patterns observed in Figure 5.11a can

be traced to the phase aberration values seen by each transducer element, shown

in Figures 5.11b. The average phase aberration, computed using unwrapped phase

aberration data, varied between 10.53 rad and 13.23 rad with standard deviation

between 1.38 rad and 2.3 rad.

The unwrapped phase aberration data are plotted as a function of transducer

element for each of the five subjects in Figure 5.12. Very similar patterns of phase

distribution across the transducer elements can be observed for the subjects 1, 2 and 3.


Figure 5.11: Patient skull data: a) skull thickness map displayed on the surface ofthe skull, calculated by segmenting head CT images of the patients (color scales aredifferent across five subjects); b) unwrapped phase aberration data calculated foreach element of the hemispherical transducer during the MRgFUS treatments basedon skull thickness, density and refraction through the skull using InSightec’s software.Small rectangular tiles schematically represent the elements of the transducer.


Figure 5.12: Unwrapped phase aberration data calculated for each element of thehemispherical transducer (also presented in Figure 5.11 ) plotted as a function oftransducer element number. Similar patterns of phase destribution across the trans-ducer elements can be observed for the subjects 1, 2 and 3.


Figure 5.13: Graphic presentation of the correlation coefficients between phase aber-ration data from five subjects, showing that subjects 1, 2 and 3 have phase aberrationpatterns more similar to each other than subjects 4 and 5.

The similarities between the subjects data are also demonstrated with the correlation

coefficients in in Figure 5.13. The correlation coefficients across pairs of subjects are

displayed graphically. Correlation coefficients for subjects 1, 2 and 3 are greater than

0.8. Subjects 4 and 5 have a correlation coefficient of 0.65. The correlation between

any two subjects across the two groups is less than 0.4. These results suggest that

the five data sets can be divided into two groups based on the level of correlation

between the data: subjects 1, 2 and 3 would form one group, and subjects 4 and 5

would form another.

5.3.2 Simulation of Non-iterative Adaptive Focusing Algo-

rithm Based on Zernike Polynomials

5.3.2.1 Methods

In this section, discrete Zernike polynomials were calculated using the Matlab Zernike

function (zernfun.m) (P. Fricker, MATLAB Central File Exchange, 2005) which im-

plements the analytical expressions in Equations 5.5 and 5.5. The polynomials were


sampled at the (x, y) locations of each element of the hemispherical transducer.

These locations are plotted in Figure 5.10a. Since orthogonality of continuous ZPs

is perturbed by discrete sampling [101, 102], the Gram-Schmidt process was used to

orthonormalize the discrete polynomials. Their mutual orthogonality was tested by

computing the Gram matrix before and after orthonormalization. To apply ZPs in

the adaptive focusing algorithm, which is explained in detail in [75], a full rank N by

N Zernike matrix, Z, was constructed using the orthonormalized discrete ZPs:

Z = [ZT1 Z

T2 Z

T3 ...Z

Ti ...Z

TN ], (5.7)

where ZTi is an orthonormalized discrete ZP of order i, written as a column vector.

Using notation introduced in [75] and Zernike encoding, the relationship described by

Eq. 5.4 can be re-written as

pZ = g · Z. (5.8)

In order to estimate g, the phase delays of each ZTi emission can be optimized relative

to a reference emission ZT1 . The values of pZ are inferred by measuring the intensity

of the field produced by the superposition of each ZTi with the reference emission.

The pressure, pZ1 , produced by the first virtual transducer emission, ZT1 , is referred

to in this section as reference pressure with an amplitude of 1 and zero phase. Using

a method described by B. Larrat et al. [75], four intensity measurements Iai , Ibi , Ici

and Idi are necessary for each ZTi emission combination in order to estimate phase

and amplitude of pZ . The four transmit superpositions sai , sbi , s

ci , s

di that are used to

obtain the four desired intensity measurements are

sai = (ZT1 + ZT

i ), (5.9)

sbi = (ZT1 − ZT

i ), (5.10)

sci =√

2(ZT1 + jZT

i ), (5.11)

sdi =√

2(ZT1 − jZT

i ). (5.12)


In Hadamard encoding, half of the elements will transmit at full power while

half of the elements will be turned off for each of the four superpositions. In Zernike

encoding, transmission amplitude for the elements can take on any value between

zero and full power. To take advantage of the full dynamic range of the transducer,

scaling coefficients cai , cbi , c

ci andcdi are applied to sai , s

bi , s

ci and sdi to set the maximum

amplitude of each transmission to 1, the maximum available power.

After making the four intensity measurements, pZ can be calculated using

Re(pZi ) =1

2ρc(

Iaica2i

− Ibicb2i

), (5.13)

Im(pZi ) =1

2ρc(

Idicd2i

− Icicc2i

). (5.14)

Equation 5.14 takes into account the density, ρ, and the speed of sound, c, of the

tissue of interest. The aberrations vector g can be calculated as

g = pZ · Z−1, (5.15)

where the phase and amplitude of g represent the phase and relative amplitude of the

aberrations.

The Zernike-encoding-based algorithm for estimation of aberrations was tested

using a hemispherical transducer model, simulated using the Rayleigh-Sommerfield

method [103]. The ultrasound field modeling algorithm was obtained from a collabo-

rator of the adaptive focusing project, Yoni Hertzberg. The transducer was simulated

in a monochromatic regime (710 kHz) and focused on the natural focus of the hemi-

sphere. The pressure field, calculated on a 5 by 5 mm grid with a spatial step of 0.1

mm, was converted to intensity by taking the square of pressure. At the desired fo-

cal spot location, the complex values of pZi were calculated for each Zernike-encoded

emission, ZTi . The influence of the number of ZPs used for aberration correction was

studied by implementing the algorithm with the number of ZPs increasing from 1

to N, where N is 960, the number of active elements in the transducer. For each set

of Zernike polynomials, Equation 5.14 was solved using an N by N Zernike matrix


Figure 5.14: (a) Two examples of normalized Zernike polynomials sampled at (x, y)coordinates of the hemispherical transducer displayed using different scales. (b) Grammatrix calculated for a set of normalized Zernike polynomials indicates compromisedorthogonality. (c) Zernike polynomials and (d) Gram matrix after orthonormalizationusing Gram-Schmidt process.

with pZi values set to zero for i greater than the number of Zernike-encoded emissions

used. Then, corrections were calculated using ZPs up to order i and were applied to

compensate for the patients’ aberration. Relative intensity was calculated as the ratio

of intensity after correction to intensity without aberrations.

5.3.2.2 Results

Example Zernike polynomials Z2 and Z12 calculated for (x,y) coordinates of the hemi-

spherical transducer are shown in Figure 5.14a, normalized such that the norm of each

polynomial was equal to 1. The Gram matrix, expected to be an identity matrix for

a set of orthonormal vectors, exhibited several non-zero entries (Figure 5.14b) below

and above the main diagonal, indicating compromised orthogonality of the set. This

was corrected using the Gram-Schmidt orthogonalization process, and the new Z2


Figure 5.15: (a) Bar graph of the normalized values of |pZi |2 calculated for each Zernike-encoded emission up to the 50th order. (b) Relative intensity at the focal spot mea-sured after aberration correction, calculated using increasing number of ZPs, wasapplied.

and Z12 polynomials and new Gram matrix are shown in Figure 5.14c, d.

The first fifty squared absolute values of pZi , normalized by the highest value for

each data set, are shown in Figure 5.15a. These results indicate the relative contri-

bution of each order of ZPs to the overall aberration correction. It can be seen that

for all of the five examples of aberration, the intensities resulting from the emissions

encoded with the lower orders of ZPs have the highest values, thus pointing at the

overall greater correction effectiveness of the low order ZPs. The greater effect of low

order Zernike correction on the intensity at the focal spot can be observed in Figure

5.15b. The relative intensity for each of the five examples achieves 90% of unaberrated

intensity using fewer than 170 orders of ZPs.


5.3.3 Experimental Validation of Non-iterative Adaptive Fo-

cusing Algorithm based on Zernike Encoding

5.3.3.1 Methods

The effect on focal point intensity from phase aberration correction values calculated

using the Zernike-based adaptive focusing algorithm was studied experimentally by

measuring displacement in the focal spot using MR-ARFI. Aberrations measured

from subject 1 were applied to the hemispherical transducer and then compensated

for using the phase correction values calculated in the simulations described in the

previous section. Displacement measurements were performed for phase corrections

using the following number of ZPs: 4, 10, 30, 50, 70, 90, 110, 130, 200, 500, 700 and

960, where 960 is N, the number of active elements in the transducer.

Measurements were performed using the hemispherical transducer operated at 710

kHz, placed vertically into a 1.5 Tesla MRI scanner (GE, Milwaukee, USA) and filled

with degassed water. A tissue-mimicking phantom based on 5% fat milk (Malabi Dairy

Dessert of Gad Dairies, Bat-Yam, Israel) was positioned in the plane of the natural

focus using a holder as shown in Figure 5.10b. An acoustic absorber was placed on top

of the phantom (Figure 5.10c). Tissue displacement was imaged using a 2D Fourier

Transform spin-echo MR-ARFI pulse sequence with repeated bipolar displacement

encoding gradients. Displacement encoding was applied along the dominant direction

of the ultrasound beam, as shown with an arrow in Figure 5.10b. The duration of each

encoding lobe was 6.1 ms, the duration of the ultrasound pulse was 19 ms. Imaging

was performed in the plane perpendicular to the dominant direction of the ultrasound

using a solenoid breast RF coil. The following imaging parameters were used: TE =

41 ms, TR = 500 ms, FOV = 30 × 20 cm, matrix size = 256 × 82, BW = 15.63 kHz

and slice thickness = 6 mm.

5.3.3.2 Results

The displacement phase images obtained after correcting for the aberration of sub-

ject 1 with an increasing number of ZPs are shown in Figure 5.16a. The average

displacement at the focal spot, normalized such that the maximum displacement of


Figure 5.16: (a) Experimentally obtained displacement phase maps measured at thefocal plane using MR-ARF after aberration corrections calculated for various ordersof ZPs were applied to correct aberrations of subject 1.(b) Normalized mean dis-placement measured at the focal spot over 2 by 2 pixels region of interest. Results aredisplayed as mean ± standard deviation of background displacement noise.

the unaberrated case is 1, is shown in Figure 5.16b. Similar to the intensity calculated

using simulations, the behavior of the displacement at the focal spot indicates that

the effect of the lower orders of ZPs on aberration correction is much greater than

that of the higher orders. Ninety percent of the unaberrated displacement is achieved

while correcting the aberrations of subject 1 with aberration corrections estimated

using fewer than 200 orders of ZPs.

5.3.4 Zernike-encoded Adaptive Focusing: Discussion

In this part of the chapter, Zernike polynomials, commonly used to describe aber-

rations of light in microscopy, astronomy and ophthalmology, have been applied to

correct for the aberrations of ultrasound waves. The experiments described here serve


as an initial exploration into the use of ZPs to accelerate and improve the ultrasound

phase aberrations correction process. Applying a Zernike-based correction algorithm

to compensate for the phase aberrations of five patients showed that a majority of

the correction was achieved by fitting aberrations with low order ZPs, using 170 or

fewer modes to achieve 90% of the unaberrated intensity. Taking into account the

fact that four measurements are required to estimate each pZi , in the context of using

displacement phase images to drive this focusing algorithm, 4 × 170=680 MR-ARFI

acquisitions may be sufficient to achieve sufficient focusing. This offers drastic time

savings compared to the 4 times 960=3840 measurements that would be necessary to

achieve complete correction, using previously proposed full sampling [75]. Restoration

of the beam intensity after application of Zernike-based corrections was demonstrated

in simulations using aberration data from multiple subjects, and it was also validated

experimentally for one subject’s aberration data.

Since the displacement phase images have finite signal-to-noise ratio (SNR), the

estimates of the pressure at the focal point pZi will be noisy. Increasing the beam

intensity at the focal spot prior to making measurements for an adaptive focusing al-

gorithm would improve the SNR and allow for better estimation of correction values.

It was found that phase aberrations amongst some subjects are much more correlated

than with other subjects, therefore suggesting that the similarity between the sub-

jects’ aberrations maybe exploited to generate initial aberration estimate for a new

patient based on the previous patients.

Further studies of initial phase correction estimates’ effectiveness would help to

establish if these methods are suitable for a clinical setting. First, a larger population

of skull measurements should be analyzed, to determine the trends of corrections

across a larger sampling of subjects. Several outcomes could arise from such a study

that would allow for a better initial estimate of aberration correction. Just as there

were two clear groups observed when analyzing correlation between the five subjects

studied here, it may be found that a small number of representative skulls can give

appropriate initial estimates for the large majority of subjects. Alternatively, it may

be found that certain low order Zernike-based corrections are largely consistent across

the population, which would allow for a common low-order correction to be used as an


initial estimate for each new subject. In future work, the effects of noise and blurring

(due to shear waves and other effects) in the displacement phase measurements on

the performance of adaptive focusing algorithms need to be assessed. Finally, the use

of spherical harmonics for characterizing aberrations and corrections should be also

explored. It may be the case that spherical harmonics offer even greater correction

efficiency, either in place of or in combination with Zernike polynomials.

In this chapter, the application of Zernike polynomials to phase aberration cor-

rection was shown to be beneficial for adaptive focusing applications of transcranial

ultrasound. Simulation and experimental results showed that skull-based phase aber-

rations can be well approximated by the number of ZPs representing only a fraction

(less than 20%) of the number of elements in the hemispherical ultrasound trans-

ducer, which would allow for more than a 5 × speedup in aberration correction as

compared to full sampling approaches proposed before. The concentration of relative

contribution to phase aberration correction at lower order ZPs and the improvement of

intensity at the focal spot after correction with initial estimate may make the Zernike-

based approach introduced here more robust to MR-ARFI measurement noise. These

improvements can potentially greatly increase the viability of MR-ARFI-based adap-

tive focusing for a clinical transcranial MRgFUS therapy.

5.4 Summary

This chapter briefly introduced the milestones in the development of transcranial

ultrasound focusing based on MR-ARFI. The background and theory behind itera-

tive and non-iterative adaptive focusing approaches have been discussed. With the

goal to develop an adaptive focusing algorithm that is robust to noise, able to con-

verge on the optimal solution, requires minimum number of MR-ARFI measurements

and minimum ultrasound energy, several approaches have been analyzed. The weak-

nesses and strengths of the partitioning iterative algorithm, previously used in optics,

were demonstrated experimentally and in simulations. The partitioning algorithm

appeared to be a promising effective first step in the adaptive focusing process, es-

pecially in the presence of noise. In addition, it was shown that using the phase


aberration information from previous subjects may help rapidly improve the focusing

of the transducer in just a few steps. Finally, non-iterative Zernike-encoded algorithm

was shown to approach its convergence using only a fraction of steps necessary to

achieve complete correction with other algorithms, including the Hadamard-encoded

algorithm. In the next chapter, the need for a more rapid MR-ARFI methods that can

shorten the duration of adaptive focusing process and reduce the amount of deposited

ultrasound energy will be addressed in detail.

Chapter 6

Echo Planar Readout for Rapid

MR-ARFI

MR-ARFI-based adaptive focusing algorithms [71, 75] are currently of great interest

in MRgFUS transcranial treatments, as they do not require a pre-surgical CT scan,

and can provide superior corrections. Unfortunately, current approaches require the

acquisition of as many as 4×N MR-ARFI images [75], where N is number of trans-

ducer elements. In the previous chapter, a method that can potentially reduce the

number of MR-ARFI measurements to 4× 200 was introduced. Nevertheless, acquisi-

tion of 800 images would be also quite time consuming, and would requires a patient

remain still in the magnet for an impractical length of time. In addition, acquisition

of several hundreds of MR-ARFI images would expose the patient to as many ultra-

sound emissions times the number of phase encoded in the image and can potentially

lead to undesired tissue heating. Therefore, there is a critical need to reduce the total

scan time, to decrease the number of ultrasound emissions and to monitor the thermal

effect of the sound on tissue in order for the adaptive focusing approach to be suitable

for clinical applications.

To address the need for a faster MR-ARFI method as a tool for adaptive focusing

in the brain, and to reduce heat deposition, a rapid MR-ARFI technique based on

single-shot EPI was developed. This chapter introduces the rapid MR-ARFI pulse

sequence and its evaluation.

97

CHAPTER 6. ECHO PLANAR READOUT FOR RAPID MR-ARFI 98

Figure 6.1: (a) Simplified pulse sequence diagram for a limited FOV single-shot flybackEPI MR-ARFI. The timing of the ultrasound pulse (FUS) is shown with the dottedline. (b) The experimental setup showing the transducer location, tissue sample, andcoil positions. The transducer is covered with a plastic membrane filled with degassedwater for acoustic coupling. A plastic cylinder (dashed line), containing the samplein a coupling gel block, is placed on top of the membrane. A Mylar membrane onthe lower side of the cylinder provides coupling with the transducer while containingthese materials. A second piece of gel block is located on top of the tissue.

6.1 Single-Shot EPI MR-ARFI

Repeated bipolar displacement encoding gradients, selected as the optimal gradients

for MR-ARFI, were combined with a limited FOV single-shot spin-echo EPI readout

to accelerate focal spot displacement imaging. Displacement maps were compared

with those obtained using 2D spin-echo MR-ARFI, discussed in the previous two

sections. In addition, a temperature measuring capability was introduced in order to

monitor any heating at the focal spot that could occur during repeated MR-ARFI

acquisitions. To evaluate the benefits and limitations of an EPI-based MR-ARFI

sequence, tests were performed in a phantom and in ex vivo porcine brain tissue.

A single-shot flyback EPI pulse sequence was developed with a limited FOV in the

phase-encode direction [104]. A rectangular slab was excited by applying orthogonal

slice select gradients for the 90◦ and 180◦ RF pulses, as shown in Figure 6.1a. Repeated

bipolar displacement encoding gradients were placed around the 180 RF pulse. The

amplitude of the gradients was set to 4 G/cm, and the duration of each lobe was 6.1


Parameter EPI 2DFT spin-echoEcho time [ms] 108 41Repetition time [ms] 1000 1000Field-of-view [cm2] 16x5 16x16Matrix size 128x30 256x128Bandwidth [kHz] 62.5 15.63

Table 6.1: MR imaging parameters used in EPI and 2DFT MR-ARFI acquisitions.

ms, which corresponds to a b-value of 42 s/mm2. Displacement phase images obtained

with EPI MR-ARFI were compared to those obtained with the 2D spin-echo MR-

ARFI sequence described in Chapter 3. Imaging was performed on a 3T MRI scanner

(Signa, GE Medical Systems, Waukesha, WI). Images were acquired in the X-Y plane

with imaging parameters listed in Table 6.1.

The MRI scanner was equipped with an MR-compatible 2D planar phased-array

ultrasound transducer (ExAblate 2000, InSightec Inc, Haifa, Israel), shown in Figure

3.9a. The array had 1024 rectangular elements and a total area of 80 × 80 mm2. It

was operated at the central frequency of 550 kHz in continuous wave mode. The MRI

pulse sequence triggered the FUS system to emit ultrasound for 19 ms synchronously

with the encoding gradients (Figure 6.1a), so that for the TR of 1 s, the duty cycle

was 2%. The ultrasound beam was focused at a depth of 76 mm from the center of

the transducer. The focal spot size at full width at half maximum intensity at the

focus was 2.8 mm in diameter and 18 mm in the beam direction based on a beam

field simulation (Field II [93]).

The displacement measurements were performed in either a tissue mimicking

phantom designed to match the ultrasound attenuation and speed of sound in tissue

or in ex vivo porcine brain. A custom made phantom (ATS Laboratories, Bridgeport,

CT) had the following properties: density = 1040 kg/m3, speed of sound = 1455 m/s,

absorption coefficient = 95 dB m−1 MHz−1, acoustic impedance = 1.54× 106 kg m−2

s−1, amplitude reflection coefficient = 1.7× 10−2, heat capacity = 3765 J kg−1 K−1,

thermal conductivity = 0.33 W m−1 K−1. This was provided courtesy of InSightec

Inc. The whole brain was obtained from a pig approximately 24 hours before the ex-

periment and was kept refrigerated. During the experiment, the degassed tissue was


kept at room temperature.

The experimental setup is shown in (Figure 6.1b). The phantom or the brain in

a gelatin-based block was placed into a plastic holder with a Mylar membrane on

the bottom. This cylinder was then positioned on top of the water filled membrane

over the FUS transducer. A solenoid RF coil was placed around the plastic holder.

To map the displacement, a pair of images were obtained with identical imaging

and sonication parameters, but with opposite polarity of the encoding gradients, as

described in Chapter 3. Both phase images were unwrapped and corrected for bulk

motion phase by subtracting constant and linear background phase corrections. From

these images a phase difference image was calculated and converted to displacement

assuming instantaneous tissue response using Equation 3.2.

6.1.1 Displacement vs. Intensity

6.1.1.1 Methods

In the first demonstration of EPI-based MR-ARFI, displacement maps were obtained

with the rapid EPI-based sequence in a phantom. The duty cycle was calculated as

the fraction of sonication time to imaging repetition time in percent. Displacement

images were obtained with applied acoustic power of 93 W, 117 W and 156 W using

a duty cycle of 2%. Taking into account the energy loss due to attenuation in the

phantom and in the brain tissue, corresponding acoustic intensities (spatial peak) at

the focus were estimated to be 370 W/cm2, 465 W/cm2 and 620 W/cm2.

6.1.1.2 Results

Figure 6.2 displays the results obtained with the limited FOV single-shot EPI MR-

ARFI sequence. Two MR-ARFI acquisitions using opposite encoding gradient polarity

were needed to obtain the displacement images. With TR set to 1 s, the scan time

necessary to obtain the displacement image is 2 s, which is approximately hundred

times shorter than would be necessary when using 2DFT spin-echo MR-ARFI with

128 phase encodes. Overall, the images exhibit some geometric distortion caused by

off-resonance effects, which are a common artifact of single-shot EPI, related to high


Figure 6.2: Magnitude and displacement images of a phantom, obtained with EPI-based MR-ARFI using 2% duty cycle of ultrasound. A representative magnitude imageobtained at 620 W/cm2, indicates no sign of the focal spot. Displacement images ofthe phantom obtained for three values of intensity show the focal spot location andthe dependence of the peak displacement on the acoustic intensity.

sampling bandwidth in phase-encode direction. The focal spot is not visible on the

magnitude image even for the highest intensity of 620 W/cm2. However, it is well

depicted in the displacement images. The peak displacement increases with increasing

intensity, as was also shown in Chapter 3.

6.1.2 Measuring Temperature with Modified EPI-based MR-

ARFI

6.1.2.1 Methods

The goal of the second experiment was to measure the temperature rise in a phantom

and in brain tissue that is produce by one single-shot EPI MR-ARFI acquisition and

also by a set of continuously repeated 3000 EPI MR-ARFI acquisitions. The latter was

only performed in a phantom. For this experiment, the readout of the single-shot EPI

was shifted from the spin echo by 8 ms to introduce temperature sensitivity, and the

displacement encoding gradients were set to zero to disable displacement sensitivity.


Figure 6.3: Cropped temperature maps obtained in the brain tissue sample and in thephantom using the EPI-based MR-ARFI sequence, with the readout shifted from thespin echo to introduce temperature sensitivity. Intensity levels are given in W/cm2.(a)-(c). No temperature rise was detected after a single sonication in the ex vivo braintissue and in the phantom. (d). A small temperature rise of 4 ◦C was measured after3000 sonications. (e). The temperature increased non-linearly with sonication time.

The temperature maps were calculated by subtracting a reference phase obtained from

the acquisitions with the ultrasound switched off, from the phase obtained with the

ultrasound switched on. The temperature rise was found using the PRF relationship,

introduced in Chapter 2.

6.1.2.2 Results

The results of the temperature measurements are shown in Figure 6.3. The temper-

ature maps were reconstructed for the phantom and the ex vivo brain tissue. For a

2% duty cycle, no temperature rise was detected after a single sonication either in

the brain tissue or in the phantom at all of the tested intensity levels. After 3000 son-

ications, a temperature rise of 3.9 ± 0.7◦C was measured in the phantom, as shown

in Figure 6.3d. The temperature increased approximately linearly for the first 500

sonications at 0.005◦C per second (or per sonication) and then rose at much slower

rate (Figure 6.3e).


6.1.3 Comparison of EPI and 2DFT Spin-echo MR-ARFI

6.1.3.1 Methods

The third experiment, performed in the brain tissue, was designed to demonstrate

that the reduced FOV EPI displacement images depict displacement similar to that

in the 2DFT spin-echo sequence. For the same two power levels as in the previous

experiment, the ultrasound transducer was defocused in 4 steps by addition of phase

aberrations to 512, 256, 128 and 0 elements out of 1024 elements of the transducer.

The phase aberration values were randomly selected between π and π. At each of

the four levels of phase aberration, three EPI-based and one 2DFT spin-echo based

displacement maps were obtained. EPI acquisition was repeated three times in order

to average the image over three measurements. In each, the displacement from a four

pixel region of interest in the focal spot was measured.

The standard deviation of the noise in the displacement maps was calculated

for both 2DFT spin-echo and EPI approaches. According to the method described

in [105], the standard deviation of noise in the phase image is inversely proportional

to the SNR of the corresponding magnitude image. Therefore, the SNR values were

calculated for a ROI that covers most of the brain image and the noise standard

deviations for the corresponding phase images were found. As the displacement image

is a subtraction of two phase images, obtained with positive and negative polarities

of the encoding gradient, the standard deviation of the displacement noise is a square

root of the sum of the phase noise variances.

6.1.3.2 Results

Magnitude and displacement images obtained in brain tissue with EPI-based MR-

ARFI and with 2DFT spin-echo based MR-ARFI are shown in Figure 6.4. Geometric

distortions are observed in EPI-based images, which also have approximately 3 times

lower magnitude SNR than the spin-echo MR-ARFI due to a longer echo time and

higher bandwidth. In spite of the SNR loss, the gain in scan time duration makes

the single-shot EPI approach 42 times more SNR efficient than the 2DFT spin-echo

method. For an EPI-based displacement map, the scan time is only 2 × TR, here 2


Figure 6.4: (a) Magnitude images and (b) displacement maps obtained in ex vivobrain tissue with EPI- based and 2DFT spin-echo MR-ARFI. Both displacementimages show the focal spot.

seconds, compared to the spin-echo-based sequence where the scan time is 2 × 128 ×TR, here 256 seconds. If the EPI-based MR-ARFI was used during adaptive focusing

procedure, the time savings we demonstrate here would accelerate it by 128 times.

Additional acceleration methods are required to bring the scan time down further

from 102 minutes (3 × N × 2 × TR) to a shorter scan. Further, the displacement

maps obtained with both methods depict equally well the displacement in the focal

spot, despite the much shorter scan time in the EPI-based sequence.

To demonstrate the suitability of the method for adaptive focusing of the trans-

ducer, Figure 6.5 shows how the phase aberrations applied to the transducer elements


Figure 6.5: a. Cropped displacement images obtained with varying number of defo-cused transducer elements for acoustic intensity of 123 W/cm2 and 246 W/cm2. b.Plot of the mean displacement in the focal spot as a function of the number of thetransducer elements affected by random phase aberrations. All data is displayed asmean standard deviation, where displacement noise is calculated from the magnitudeimages. Linear fits to the data are shown with solid or dashed lines. The correlationcoefficient of the fits r2 was 0.99 for both the EPI and 2DFT spin-echo pulse sequences.


affect the intensity of displacement in the focal spot. The results acquired with EPI

and with 2DFT spin-echo sequences for two different intensity levels are presented

in the plot. As the phase aberrations decrease, the displacement amplitude increases

linearly at the same rate for both EPI and 2DFT spin-echo. The standard deviation

of the displacement noise averaged over 12 EPI measurements was 0.25 µm, which is

three times higher than 0.08 µm measured from eight 2DFT spin-echo images.

6.1.4 Conclusion

In this chapter, a rapid MR-ARFI method has been developed and tested in a phan-

tom and in brain tissue. This method offers hundredfold time savings, and requires

much fewer ultrasound emissions than a 2DFT spin-echo approach. For the intensity

levels used here, there was no measurable temperature rise after a single-shot EPI-

based MR-ARFI acquisition. For the highest intensity of 620 W/cm2 there was less

than a 4◦C temperature rise after 3000 continuously repeated acquisitions. Much lower

intensity of 123 W/cm2, sufficient to produce the displacement in the brain tissue, is

not expected to cause any heating when the sonications are performed in a perfused

brain in vivo. However, it would be recommended to monitor the temperature as a

precautionary measure during adaptive focusing procedures.

In comparison to the 2DFT spin-echo MR-ARFI, the EPI-based MR-ARFI has

lower SNR and suffers from geometric distortion. However, the distortions are a con-

cern in localization, but less so in adaptive focusing. To improve the image quality of

the EPI-based displacement images, it would be beneficial to optimize the duration

of encoding gradients taking into account the diffusion, T2 and the temporal response

of the imaged tissue. In addition, the total scan time duration may be traded off for a

higher SNR by increasing the TR. This will also reduce the ultrasound duty cycle and

slow down any potential heat accumulation. With these improvements, the single-shot

EPI MR-ARFI would become a more accurate method for focal spot localization, as

well as a more sensitive feedback tool for adaptive focusing in the head. Ultimately,

it is envisioned that the two sequences would be used together: high resolution 2DFT

spin-echo for localization and EPI-based MR-ARFI for adaptive focusing.


Replacing the slab excitation approach with a two-dimensional excitation RF pulse

as described in [106] would allow for multi-slice imaging during MR-ARFI. However,

caution should be taken when doing interleaved multi-slice imaging, as the duty cycle

will increase by the number of slices, and the total ultrasound energy delivered to the

tissue over time will increase.

Previously it has been shown that in perfused tissue using MR-ARFI with low

power ultrasound pulses is not expected to produce tissue heating [65, 72]. The tem-

perature measurements were performed only after a single ultrasound application. In

this study, 3000 equivalent-to-MR-ARFI ultrasound sonications were repeated in a

phantom. After a thousand of sonications, a small temperature rise 4◦C was mea-

sured in a phantom, however, the phantom was not perfused and very high power

ultrasound pulses were used. Therefore, in perfused tissue, even after several thou-

sand sonications, the temperature rise is expected to be much less than 4◦C. This is

a valuable advantage of the single-shot MR-ARFI method as it makes it safe to be

repeated as many times as necessary to complete an adaptive focusing procedure.

6.2 Summary

In summary, this chapter demonstrated that single-shot EPI-based MR-ARFI method

can play a valuable role in MR-ARFI-based adaptive focusing during the phase aber-

ration correction stage of MRgFUS treatments by reducing the imaging time and the

sonication time, and at the same time providing satisfactory images of the focal spot,

its location and intensity.

Chapter 7

Summary

Originally proposed several decades ago, focused ultrasound therapy has gained a

momentum over the past several years with several applications getting FDA or CE

approval. MRI guidance has played an invaluable role in the successful development

of this non-invasive and non-ionizing therapy. With InSightec Ltd., who partners with

General Electric, and Philips, who launched their own MRgFUS line, the number of

clinical and prototype MRgFUS systems is rapidly growing across the world, generat-

ing promising therapeutic results and exciting research. With numerous applications

of MRgFUS evolving, many challenges still remain to be addressed. In this thesis,

several methods have been proposed to improve current approaches to focal spot vi-

sualization with MRI and to correct phase aberration correction from skull bone. In

this chapter the proposed MRI tools for MR-guided focused ultrasound surgery are

summarized and the directions for future work are outlined.

7.1 Focal Spot Visualization

Two aspects of focal spot localization were considered in this work: unnecessary ultra-

sound energy deposition and poor performance of the current visualization approach

in fatty tissue such as breast tissue. To address both issues, a 2DFT spin-echo MRI

technique based on imaging of tissue displacement, MR-ARFI, was developed and im-

plemented in Chapters 3 and 4 . The technique was successfully demonstrated in ex

108

CHAPTER 7. SUMMARY 109

vivo porcine brain tissue and in a tissue mimicking phantom. A comparison study was

also performed to contrast the performance of 2DFT MR-ARFI with the previously

proposed T1-weighted FSE in fatty breast tissue.

Compared to using a low temperature rise ultrasound sonications and visualizing

the heating at the focal spot with PRF-based or T1-based thermometry, the 2DFT

MR-ARFI method required approximately 10 times less ultrasound energy. The use

of the method was found particularly beneficial in breast tissue, where in fat it had

four times higher SNR than T1-weighted FSE.

In order to monitor the ultrasound energy deposition during tissue displacement

imaging, the 2DFT spin-echo MR-ARFI sequence was equipped with an optional

gradient-echo capability, which could be used to obtain temperature and displace-

ment images simultaneously. Monitoring the temperature of tissue during a MR-ARFI

acquisition was demonstrated in ex vivo brain tissue for a range of acoustic power

levels.

To adapt the 2DFT MR-ARFI method for in vivo applications in the head, sev-

eral steps to optimize displacement SNR were demonstrated. Firstly, the duration

of encoding gradients that maximized the displacement SNR while keeping motion

artifacts to minimum was experimentally determined. Secondly, the optimal relative

timing of the ultrasound pulse and encoding gradients was demonstrated for tissue of

a particular temporal tissue response. The temporal response of tissue to acoustic ra-

diation force was non-invasively measured using the modified 2DFT MR-ARFI pulse

sequence. The full width at half maximum of the focal displacement as a function of

the ultrasound pulse duration was also studied. Depending on the application, if the

focal spot size needs to be smaller than that produced using the optimal duration of

encoding and ultrasound, the duration of those pulses may be reduced.

In addition to the 2DFT spin-echo MR-ARFI, the reduced field-of-view single-shot

EPI MR-ARFI pulse sequence was also developed for rapid displacement imaging in

Chapter 6. The single-shot approach was shown to obtain a displacement image much

faster than the 2DFT approach, which would help reduce the time of the MR-ARFI-

driven adaptive focusing procedures.


7.2 Adaptive Focusing

Chapter 5 is devoted to MRI-guided methods for correction of phase aberrations

presented an iterative and a non-iterative adaptive focusing approaches, combined

with MR-ARFI. Several aspects of MR-ARFI-driven adaptive focusing are consid-

ered important to make a method clinically relevant. The method should eliminate

or minimize the effect of the aberration on the ultrasound focus. It should be robust

against noise, take little time, and deposit a minimum of ultrasound energy. Looking

to satisfy these design constraints, the partitioning algorithm, previously introduced

in optics, was first implemented. This method was found to provide a more rapid

initial improvement of the ultrasound intensity at the focal spot than the continu-

ous algorithm. It was also shown that compared to the continuous adaptive focusing

method, the partitioning method was more robust to noise. However, from the con-

vergence of the adaptive focusing process point of view, the partitioning algorithm

exhibited suboptimal performance, with the ultrasound intensity at the focal spot

converging to a fraction of the “ideal-case” intensity.

Another method developed in this work relies on using Zernike polynomials to

describe the phase aberrations from the skull. Similar to the partitioning algorithm,

the idea to implement Zernike polynomials in the aberration correction was also

inspired by the work previously done in optics. Since 1930’s, Zernike polynomials have

been applied to correct for aberrations of light as well as to aid image recognition.

Implementing Zernike polynomials to encode ultrasound emissions in the non-

iterative adaptive focusing algorithm showed that Zernike polynomials are an effective

basis for describing the phase aberrations experienced using hemispherical transducer

focusing through a human skull. It was found that for a 960-element transducer

transmitting through a human skull, approximately 170 modes of Zernike polynomial

may be nearly sufficient to bring the intensity at the focal spot to 90% of the intensity

of the “ideal-case.” Studying the cross-correlation between the phase aberrations data

of five patients showed that some subjects have much more similar phase aberrations

than others. Therefore, it may be of value to use the aberration data from previous

patients to generate an initial guess of the aberration of a new patient.


7.3 Future Work

There are several directions for future work on the topics described in this work. As the

number of studies using MR-ARFI increases, it may be soon that this approach will

transition into clinical use. For successful adoption of displacement imaging, existing

MR-ARFI pulse sequences and reconstruction techniques may be further improved

upon. To shorten the acquisition time of 2DFT MR-ARFI, image undersampling

combined with compressed sensing approaches as well as partial k-space acquisition

may be interesting to explore. Baseline and referenceless approaches can be also looked

into for the reconstruction of the displacement phase images as an alternative of

having to scan twice with opposite polarity encoding gradients.

Further technical development is necessary to use MR-ARFI with more complex

transducer geometries, such as the transcranial hemispherical phased-array. Given

the geometry of the hemispherical transducers, the components of the total acoustic

radiation force induced by the different sections of the hemisphere point in different

directions and can add destructively at the focal spot. Therefore, looking at the

superposition of the radiation force vectors at the focal spot along the Z direction,

may underestimate the intensity at the focal spot. To preserve the linear relationship

between the ultrasound intensity and the displacement of tissue measured with MR-

ARFI, an efficient method sensitive to the components of the radiation force pointing

at different directions is needed.

Adaptive focusing is still a fairly new topic in MRgFUS, and while it has shown

promise as an alternative approach to current CT-based aberration correction method,

there remains room for improvement. In the studies published so far, the researchers

typically use one MR-ARFI pulse sequence throughout the whole focusing algorithm,

and normally show the performance of a single algorithm. In the future work, it

maybe worthwhile to develop a hybrid adaptive focusing approach. This approach

would switch between focusing algorithms and MR-ARFI techniques in a fashion

that would ensure the greatest robustness to noise and minimize the scan time neces-

sary to accomplish the procedure. In the iterative methods, such as the partitioning

algorithm, it may be beneficial to apply adaptive sampling methods such as gradient


descent and golden section search. In non-iterative approach, it would be of interest

to compare Zernike encoding with spherical harmonics encoding. In the future, there

is a great potential for MRI to take up more roles in adaptive focusing. For example,

estimation of the skull bone thickness and shape using MRI appears to be a feasible

task. While at the moment MR images can not provide information on the density of

the cortical bone, skull segmentation based on MR may still provide a valuable initial

estimate of the skull phase aberration.

The ideas for the previously described future work were inspired by the projects in

this thesis. However, the field of MRgFUS is growing in several directions and there

is much exciting work to be done in fields such as ultrasound neurostimulation, drug

delivery, and blood brain barrier opening. Consequently, the interest and demand for

the MRI tools developed here are also growing, opening the door to further work with

fascinating opportunities and interesting challenges.

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