digital breast tomosynthesis: basic understanding of...

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James T. Dobbins III, Ph.D., FAAPM

Director, Medical Physics Graduate Program

Ravin Advanced Imaging Laboratories Departments of Radiology, Biomedical Engineering, and Physics

and Medical Physics Graduate Program Duke University Medical Center

AAPM 2012 Annual Meeting

Digital breast tomosynthesis: basic understanding of physics principles

© James T. Dobbins III, PhD. All rights reserved.

Acknowledgments and financial disclosure

James Dobbins: Grant support from NIH (ROI CA80490) and GE Healthcare. Patent jointly held by GE and Duke; JTD is co-inventor. Has spoken at GE sponsored events. Unpaid participant at GE Medical Advisory Board mtgs. Duke University: Grant support from Siemens.

FDA statement: discussion will include off-label uses and applications and devices not yet approved


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Tomosynthesis: section imaging from multi-projection image reconstruction

(limited angle tomography)

Tao Wu et al, Med Phys 30(3), 2003 © James T. Dobbins III, PhD. All rights reserved.

Breast tomosynthesis with FFDM detector Niklason et al

1997 Image from: Niklason LT et al: Radiology 205:399-406, 1997.

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Advantages of tomosynthesis

•  Improves conspicuity by removing overlying structures

•  Permits section imaging with high resolution in reconstruction plane

•  Easily performed on the high volume of mammography patients

•  Potentially lower cost than breast CT


Breast Tomosynthesis Human subject examples

•  Subject 48 normal screen

Courtesy of and copyright by Joseph Lo, PhD

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skin, surface blood vessels, subq fat pockets


intramammary lymph nodes


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lymph nodes


pectoralis


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•  Subject 158 - mammo miss of cancer Courtesy of and copyright by Joseph Lo, PhD


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Geometry of tomosynthesis image acquisition


Geometries of motion

Parallel path Partial isocentric

Isocentric

Chest tomosynthesis

Breast tomosynthesis

CBCT, RadOnc tomosynthesis


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Parameters: • up to 49 projection images

• up to ~ ±250 angle range

• compression paddle to keep objects still

Breast tomosynthesis clinical implementation


Tomosynthesis image formation


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Tomosynthesis algorithms

•  Shift-and-add •  ART (algebraic reconstruction techniques) •  Tuned aperture computed tomography (TACT) •  Iterative methods (MLEM) •  Matrix inversion tomosynthesis (MITS) •  Filtered backprojection (FBP)


Shift-and-add reconstruction (simple backprojection)

Acquisition geometry Shift-and-add image formation


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Conventional tomo section After deblurring

The importance of deblurring


Matrix Inversion Tomosynthesis (MITS)


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Direct solution using linear algebra and the known acquisition geometry

• Much faster computationally than iterative deblurring

• Better performance at narrow tube angles than filtered backprojection

• However…. susceptible to noise at the lowest spatial frequencies ( < ~ 0.1 cycles/mm)


Removing the blur with MITS

Removing the blur with MITS

•  Matrix form (freq space)

•  Rewritten

•  Solving for true structures

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Filtered backprojection


Filtered backprojection methodology

Spatial frequency

FT

Acquire projection images; take Fourier transform Multiply by ramp filter

Reconstruct by shift-and-add Multiply by roll-off filter


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Projection/Slice Theorem

Courtesy of and copyright by James Mainprize, PhD

Simple Backprojection

Reconstructed Fourier Back Projection Original Fourier

− Very blurry. +Noise tolerant


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Filtered Backprojection Principles of FBP for cone-beam imaging

Intuitive Interpretation •  Backprojection causes blur •  Correct the blur with an “inverse filter”

MTF(k) Inverse filter=1/MTF(k)

Ramp Filter Reconstruction Filter


Filtered Backprojection



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Filtered Backprojection •  Ramp filter

provides exact reconstruction when: – Noise free – Sufficient samples

(no missing data)


Tomosynthesis (Limited View / Limited Angle)



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Iterative reconstruction strategies


Iterative Reconstruction Algorithm

-  Breast volume is sampled using a three-dimensional matrix of elements (voxels)

-  Typical voxel size: 0.1 mm × 0.1 mm × 1 mm -  The value of a voxel is the linear x-ray attenuation coefficient µ of that element

YX

Z

Courtesy of and copyright by Tao Wu, PhD

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Maximum Likelihood Expectation Maximization (ML-EM)

µ(n)

Δµ(n+1)

Initial 3D Model

Calculated Projections:

Y (n)

µ(end)

Forward projection

Update

Optimized Likelihood Function

Measured Projections:

Y

µ(0)


ML-EM Reconstruction: Likelihood Function

Likelihood Function

• L=P(Y|µ): probability of getting the measured projections Y, given a 3D model µ

• µ(n) is updated iteratively so that L(n+1) > L(n)

• The reconstruction solution is the 3D attenuation distribution model that maximizes L


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Optimization of acquisition parameters


Key design criteria for tomosynthesis

•  Must have effective blur removal for out-of-plane structures

•  Must handle between-plane structures “reasonably”

•  Rapid recon time highly desirable •  Ability to use narrow tube angles

desirable


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Goals:

• Produce well-defined slice images

• Reduce out-of-plane blur artifacts

• Minimize image noise

Three parameters:

• Number of projection images, holding total dose constant

• Angle of tube movement

• Number of reconstructed planes


Optimization of acquisition parameters

MITS

Conv Tomo

11 proj images 61 proj images

Tomosynthesis impulse response function 20-degrees of tube movement

Courtesy of and copyright by Devon J. Godfrey, PhD

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21 PROJECTIONS

16o total angle

61 PROJECTIONS

16o total angle

Note: Total exposure is not equivalent in this example, so disregard SNR variation


0 0.2 0.4 0.6 0.8 1 1.20

100

200

300

400

500

cycles/mm

ENN

PS (m

m2 m

R)

N = 21N = 31N = 41N = 51N = 61N = 71

(a)

0 0.2 0.4 0.6 0.8 1 1.20

100

200

300

400

500

cycles/mm

ENN

PS (m

m2 m

R)

N = 21N = 31N = 41N = 51N = 61N = 71

(b)

NPS measurements of MITS reconstructions

Anterior plane Central plane

20-degree tube motion, 19 planes, 16.7 mm plane spacing

Exposure x Normalized NPS


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Acquisition parameters

Num proj images

Total tube angle

Plane spacing

Algorithm

Breast

11-49

15-50o

1 mm

FBP, MLEM, MITS, SART


Dose optimization

•  Current dose levels: 1-2 X single-view FFDM (2-4 mGy)

•  Dose appropriate for mass or calcs or both?

•  Need to optimize x-ray spectra; kVp, filtration

•  Potential role of noise reduction algorithms to reduce dose

•  Additional dose optimization needed as radiologists gain clinical experience and better define tasks


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Translational issues remaining

•  Likely use: screening, diagnostic, or both? •  Recall and biopsy rate: clinical trial •  Improvement in PPV? •  Diagnostic decision making and pt outcomes: larger

trials needed •  How many views: MLO, CC or both •  Should a standard FFDM also be taken? •  Tomo performance for calcs •  Impact of tomo on dx workups (sufficient specificity to

send directly to biopsy from tomo?) •  Comparison of breast CT and breast tomo

Breast tomo applications:


1.  Better visibility of chest wall 2.  Reduced compression required 3.  Better spatial resolution 4.  Reduced dose 5.  Better visibility of masses in dense

breasts

The main advantage of DBT over conventional mammography is:

Answer: 5 – Better visibility of masses in dense breasts Ref: C. M. Hakim et al, “Digital breast tomosynthesis in the diagnostic environment: a subjective side-by-side review.” Am J. Roentg 195:W172-W176, 2010.


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Answer: 1 – Reduced resolution in depth direction

Ref: J. M. Boone et al, “Dedicated breast CT: radiation dose and image quality evaluation.” Radiology 221:657-667, 2001.

The main limitation of DBT when compared to breast CT is:

1.  Reduced resolution in depth direction 2.  Reduced resolution in x-y plane 3.  Increased dose 4.  Higher cost 5.  Reduced visualization of chest wall


Answer: 2 – A ramp filter

Ref: J. Dobbins and D. Godfrey, “Digital x-ray tomosynthesis: current state of the art and clinical potential.” PMB 48:R65-R106, 2003.

Deblurring in filtered back projection is provided by:

1.  An apodization filter 2.  A ramp filter 3.  A resampling function 4.  An inversion matrix 5.  An iterative process


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Dobbins JT III, Godfrey DJ: Digital x-ray tomosynthesis: current state of the art and clinical potential. Physics in Medicine and Biology, 48:R65-R106, October 2003.

Dobbins JT III: Tomosynthesis imaging: at a translational crossroads. Medical Physics 36:1956-1967, 2009.

Review articles:

PDF: stacks.iop.org/PMB/48/R65


digital breast tomosynthesis: basic understanding of...

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