principles of breast tomosynthesis acquisition …...1 principles of breast tomosynthesis...

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Principles of BreastTomosynthesis Acquisition

and Reconstruction

Andrew Maidment, PhD, FAAPMAssociate Professor of Radiology

Chief, Physics SectionDepartment of Radiology

University of Pennsylvania

Disclaimer

Andrew Maidment is a consultant to Real-Time Tomography LLC, and receives research support

from Hologic Inc. and Barco Inc.

Linear Tomography Simple Tomosynthesis

Acquisition geometry Backprojection image formation

2

Current Systems

Hologic Selenia Dimensions *

* Investigational Device -Limited by United States Law to Investigational Use

• 2D and 3D Imaging under same compression

• W Tube with Rh, Ag and Al Filtration

• 15 degree tomosynthesis sweep, 15 images, <5 second Tomosynthesis acquisition

• 200 mA generator, 0.1/0.3 mm focal spot

• 70 cm source-to-detector distance

• Retractable High Transmission Cellular grid

• 24 x 29 cm Selenium Direct Detector

Invasive Ductal Carcinoma

Images courtesy of Dr. Jelle Teertstra NKI-AVL, The Netherlands

8T. Mertelmeier 05/2006

Digital Breast Tomosynthesis

Work in progress

Modified mammo unitfor large angle range (± 25o)

Fast a-Se detector 24 x 30 cm2

High DQE at lowexposures

Several readout & acquisition modes

1… 2 fps

Up to 49 projections

CC and MLO

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Human subject

Age 68 MLO position6 cm compressed

28 kVp, W/Rh 133 mAs49 projections 39 s scan1 mm slices

scar (benign biopsy 1980)invasive ductal CA with lobular component

Image data Duke University, Dr. Jay Baker

Proc SPIE 5745, 529-540 (2005)

slice at z = 21 mm above patient tableslice close to the surface of the breast

Doc. No/Page 10(xx)2007-xx-xx/Signature

Photon Counting Tomosynthesis

Work in progress

Doc. No/Page 11(xx)2007-xx-xx/Signature

Doc. No/Page 11(xx)

2007-xx-xx/Signature

Geometry

• One sweep 3D data

• Multi-slit photon counting: no electronic noise, no ghosting, no scattered radiation

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GE DS DBT Prototype

Detector:- a-Si (CsI) - 23×19.2 cm2 area- 100 m pixel size

Acquisition: - 15 projections- 40o arc (38o actual) - 15s acquisition- Mo/Mo, Mo/Rh and Rh/Rh

Case 1: Potential to reduce false-negative diagnoses

Invasive Carcinoma

LMLO Tomosynthesis Slice (Z = 24mm)

Courtesy of Tao Wu, Ph.D.

Tomosynthesis Mammography Reconstruction Using a Maximum Likelihood Method

Case 2: Potential to reduce false-positive diagnoses

LMLO

Cou

rtesy

of T

ao W

u, P

h.D

.

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Case 2: Potential to reduce false-positive diagnoses

Z = 0 mm Z = 10 mm Z = 15 mm Z = 20 mm

Z = 25 mm Z = 30mm Z = 35 mm Z = 40 mm

Cou

rtesy

of T

ao W

u, P

h.D

.

Image Theory

Linear Tomography20SPIE MI 2006 6142-15 Feb 12,.2006

Tomosynthesis ReconstructionSampling geometry

sampling is incomplete (in Fourier space) approximative inversion only artifacts

±

Fourier slice theorem

6

fz

fx

45 V, 22° 23 V, 11°

12 V, 5.5° 6 V, 2.5°

Tissue Imaging

0 50 100 150 2000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Angular Extent ()

Con

trast

0 50 100 150 2000

0.2

0.4

0.6

0.8

1

Angular Extent ()

SDN

R (n

orm

aliz

ed)

Angular Spacing, ∆θ=2°

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Angular Range

• Increasing the angular range has the effect of:– Increasing the z-resolution– Decreasing the in-focus plane thickness– Increasing the blurring of out of plane objects– Increasing the rate of blurring of out of plane

objects• There is a point of diminishing returns that

varies with the pixel size

fz

fx

45 V, 22° 23 V, 22°

12 V, 22° 6 V, 22°

8

48 12

Difference

Number of Projections

• Increasing the number of projections reduces the conspicuity of artifacts

• The number of projections depends upon:– the angular range, – the pixel size, – the contrast of attenuating objects– the detector physics– anatomical constraints

Breast CT Breast Tomosynthesis

Courtesy J. Boone

32B.3 - 3D spatial frequency domain

CTModern Multi-slice VCT scanners have nearly isotropic response with maximum spatial frequencies of .8 to 1.0 cycles/mm

z

x

y

Courtesy M Flynn

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33B.3 - 3D spatial frequency domain

TS vs CTUnsampled frequencies along the y axis make TS and CT complimentary.

fz

fx

fy

Courtesy M Flynn

Simple Backprojection Filtered Backprojection

296

Mammogram

Tomosynthesis

Breast CT

• Anthropomorphic phantom:• 450 ml volume• 5cm compressed thickness• 200 micron isotropic resolution• 40% overall glandularity

• Fiducial markers • 1-voxel (200 micron) large• μ = 30 × μ(dense tissue)• 3 different distances from the

breast support • 6.4 mm, 25.6 mm, 44.8 mm

• 4 markers in a 20 mm square

Geometric Accuracy

6.4 mm 25.6 mm 44.8 mm

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• Phantom images are simulated assuming mono-energetic x-ray beam without scatter, and an ideal detector.

Phantom Section DBT Reconstructed ImageX-ray Projection

Methods: Simulated Acquisition of Phantom DBT Images

Methods: Simulated Acquisition of Phantom DBT Images

Reconstructed ImageDBT Projection

Methods: Supersampling

• We reconstructed a series of 10 images with sub-pixel shifts within the plane of reconstruction and combined them to form a supersampled image.

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.81

1.5

2

2.5

3

3.5

4x 10

4

x (mm) from Chest Wall

Supe

rsam

pled

reco

nstru

cted

Imag

e In

tens

ity

6.52 6.53 6.54 6.55 6.56 6.571.5

2

2.5

3x 10

4

x (mm) from Chest Wall

Supe

rsam

pled

reco

nstru

cted

Imag

e In

tens

ity

Results: Marker Position Error

0.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 50

Reconstructed Plane Depth z(mm)

Erro

r (m

m)

(xC-xT)(yC-yT)(zC-zT)Ep

EP were averaged over all markers at the same depth in the phantom. (Error bars = one SD.)

Shown separately are the errors along each coordinate.

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Results: Marker Size Error

Relative marker size error was averaged over all markers at the same depth in the phantom.

0%

50%

100%

150%

200%

0 0.2 0.4 0.6 0.8 1 1.2

Distance from the Plane of Focus (mm)

FWH

M R

elat

ive

Erro

r (%

)6.4 mm 25.6 mm 44.8

Super-Resolution

This presentation studies super-resolution (SR), where multiple low resolution (LR) images are combined to achieve sub-pixel resolution.

Courtesy Sung Park

Although SR has been described in modalities such as satellite imaging and computerized tomography, its potential in digital breast tomosynthesis (DBT) has not yet been identified.

Results for Central Projection

–0.6–1.0

–0.8

Position (mm)

Sign

al

–0.4 –0.2 0 0.2 0.4 0.6

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

1.0

Sinusoidal Input (Normalized)

00

0.25

Spatial Frequency (lp/mm)

Four

ierT

rans

form

Mod

ulus

(mm

)

2 4 6 8 10 12

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

14

Input Freq.5.0 lp/mm

Results for Central Projection

Parallel Beam Geometry:The input frequency (5.0 lp/mm) is imaged as if it were 2.1 lp/mm. These two frequencies are equidistant from the alias frequency (3.6 lp/mm).

–0.6–1.0

–0.8

Position (mm)Si

gnal

–0.4 –0.2 0 0.2 0.4 0.6

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

0.8

1.0

Sinusoidal Input (Normalized)Central Projection (Parallel X-Ray Beam)

00

0.25


Four

ierT

rans

form

Mod

ulus

(mm

)

2 4 6 8 10 12

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

Central Projection (Parallel X-Ray Beam)

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2.1 lp/mm

Alias Freq.3.6 lp/mm

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Filtered Backprojection (FBP)

Although reconstruction with the RA filter alone has the benefit of higher modulation, it generates high frequency spectral leakage and flattening artifacts in the spatial domain. The SA filter removes some of these artifacts.

–0.6–2.0

–1.6

Position (mm)

Atte

nuat

ion

Coef

ficie

ntμ

(mm

-1)

–0.4 –0.2 0 0.2 0.4 0.6

–1.2

–0.8

–0.4

0

0.4

0.8

1.2

1.6

2.0

Sinusoidal InputFBP (RA Filter)FBP (RA and SA Filters)

00

0.5


Four

ierT

rans

form

Mod

ulus

2 4 6 8 10 12

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

FBP (RA Filter)FBP (RA and SA Filters)

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Bar Pattern Phantom

A) Central Projection B) Reconstruction

The reconstruction can clearly distinguish frequencies higher than the detector alias frequency 0.5a-1 (3.6 lp/mm). Instead, the resolution is limited by the resolution of the x-ray converter. This ability is not present in acquiring the central projection alone.

Clinical Application

Reconstruction with 140 μm voxels+ Interpolation at 35 μm.

Reconstruction with 35 μm voxels+ No Further Interpolation.

Conventional Image Super-Resolution Image

Anisotropy due to Oblique Incidencefz

fF1

F2

F3

DR

Detector Center

Detector Edge

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Anisotropy of GE System

• Source-to-COR: 48 cm• COR-to-Detector: 20 cm• Central Projection: α = 0°

• θ varies between 0° at midpoint of chest wall and 18.1° opposite chest wall.

Fourier Slice Thereom

Unexpectedly, we demonstrate that super-resolution is possible in areas of Fourier space not sampled by any individual projection.

This presentation extends our prior research on super-resolution to an obliquely pitched reconstruction plane.

νx

νz

ψ

FinalProjection

FirstProjection

IntermediateProjection

Detector

IncidentX-Ray Beam

Object

ψ

x

z

Spatial Domain Fourier Domain

NullSpace

The pitch (30°) is well outside the angular sampling of the scanner: -7.5° to 7.5°. Reconstruction is performed along the oblique pitch of the input.

Methods

The Selenia Dimensions system (Hologic Inc., Bedford, MA) having 15 projections is simulated, assuming no sources of noise or blurring.

Two reconstruction methods are considered: simple backprojection (SBP) and filtered backprojection (FBP).

ε

cos(2ν 0x′)

x

z

Pitch 30ºx′z′

Bar Pattern Phantom

Pitch 30° Pitch 60°

Super-resolution up to5.0 lp/mm

Resolution up to3.0 lp/mm

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Magnification of Recon. with 140 μm voxels

at 0° pitch

Recon. with 35 μm voxels at 0° pitch

Recon. at0° Pitch




Recon. at30° Pitch

Recon. at0° Pitch



Translation of Recon. Plane at 30° pitch

Recon. at30° Pitch

Recon. at0° Pitch

As the angular range of the tomosynthesis projection (source) images is reduced, the

0%

0%

0%

0%

0%

10

1. The z-resolution is improved2. The in-focus plane thickness is

decreased3. The blurring of out of plane objects in

decreased4. The in-plane resolution is decreased5. The noise in the image is increased

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Answer

As the angular range of the tomosynthesis projection (source) images is reduced, the

3. The blurring of out of plane objects in decreased

References: A D A Maidment, et al, Evaluation of a photon-counting breast tomosynthesis imaging system, Proc. SPIE 5745 (2005).

As the number of projection (source) images used in the reconstruction is increased,

0%

0%

0%

0%

0%

10

1. The conspicuity of artifacts increases2. The acquisition time decreases3. The impact of detector noise is

decreased through noise averaging4. The blurring of out-of-plane structures

is improved5. In-plane resolution is increased

Answer

As the number of projection (source) images used in the reconstruction is increased,

4. The blurring of out-of-plane structures is improved

References: A D A Maidment, et al, Evaluation of a photon-counting breast tomosynthesis system, Proc. SPIE 6142 (2006).

With regard to tomosynthesis spatial resolution

0%

0%

0%

0%

0%

10

1. It is inferior to CT spatial resolution in-plane

2. In-plane spatial resolution is limited by the detector pixel size

3. It is isotropic4. Z-resolution is limited by the number

of projections5. It is determined primarily by the x-ray

converter spatial resolution

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Answer

With regard to tomosynthesis spatial resolution

5. It is determined primarily by the x-ray converter spatial resolution

References: R J Acciavatti and A D A Maidment, Investigating the potential for super-resolution in digital breast tomosynthesis, Proc SPIE 7961 (2011).

Image Reconstruction

Proposed Reconstruction Methods• Simple Backprojection (“Shift & Add”)• Filtered Backprojection• ART• Maximum-Likelihood Expectation

Maximization• Total Variational Methods • Matrix Inversion (MITS)• Ordered Subset methods• and many more

Tomo LSF

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ramp

ramp

spectral

ramp

spectral

slice thickness

ramp

spectral

slice thickness(optimized)

Comparison of reconstruction alg.


Images courtesy of Dr. Jelle Teertstra NKI-AVL, The Netherlands

Convex Hull Processing

Courtesy S. Ng, RealTime Tomography, LLC

DBT Reconstruction — Artifact Reduction

Z = 16mm Z = 27mmZ = 12mm

Reconstruction images without artifact reduction

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DBT Reconstruction — Artifact Reduction

Z = 16mm Z = 27mmZ = 12mm

Results of artifact reduction (Maximum Contribution Deduction)

Multi-PlanarBPF

Courtesy S. Ng, RealTime Tomography, LLC

MITS FBP FBP with H&G

MITS-FBP blend

Slides courtesy of Ying Chen, Joseph Lo, Jay Baker, Jim Dobbins

MITS good for high freq (calcs and margins),FBP good for low freq (parenchyma),FBP w/ filter reduces high freq noise but causes blur,MITS-FBP blend combines high & low freqs well.

Iterative DBT Reconstruction Algorithms

(n)

(n+1)

Initial 3-D Model

Calculated Projections: P (n)

(end)

Forward projection

Update

Optimized Likelihood Function

Measured Projections: P

(0)

Likelihood function L=P(Y|): The probability of getting the measured projections Y, given a 3-D model of the breast volume.

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6 iter 9 iter 11 iter

Iterative Maximum-Likelihood (ML)

Chan HP, et. al.MGH case

1 iter 2 iter (0.5)2 iter (0.1)

Simultaneous Algebraic Recon Technique (SART)

Chan HP, et. al.MGH case

Tomosynthesis image reconstruction methods include all of the following except

0%

0%

0%

0%

0%

10

1. 3D multiscale gradient filtered reconstruction

2. Filtered back-projection3. Back-projection filtering4. Maximum likelihood expectation

maximization5. Total variational methods

Answer

Tomosynthesis image reconstruction methods include all of the following except

1. 3D multiscale gradient filtered reconstruction

References: J T Dobbins and D J Godfrey, Digital x-ray tomosynthesis: current state of the art and clinical potential, Phys. Med. Biol. 48 (2003)

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Functional Imaging

Vascular Contrast Enhancement Methods

• The development of an independent vasculature is an essential step in the development of a cancer

• A contrast agent should be able to demonstrate these vessels and the lesion itself

Temporal Subtraction

0.1

1

10

100

1000

10000

0 5 10 15 20 25 30 35 40 45 50

Energy [keV]

Mas

s at

tenu

atio

n[cm

2 /g]

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

Phot

on F

luen

ce [#

pho

tons

/mm

2 ]

ICRU-44 Breast TissueIodine0.27 mm Cu

Post-contrastPre-contrast

Spiculated mass with rim enhancement.

Subtraction


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Temporal Subtraction

• Advantages:– Superior separation of pre- and post-contrast

images– High kVp pre- and post- contrast images– Reduced total dose

• Disadvantages:– Motion Artifacts

Dual-Energy Imaging

• At diagnostic energies, there are two main x-ray interactions– Photoelectric effect– Compton effect

• The relative contribution of the two effects depends upon the energy and the atomic number of the material

• Therefore, the attenuation coefficients of different materials have different trends as a function of energy

Dual-Energy CE-DBT (DECE-DBT)

Low Energy

High Energy Low Energy

High Energy

)),(ln()),(ln(),( yxSIwyxSIyxSI LtHDE

DE-DBT: Patient 2

• Age: 55

• Weight:• Project 3 / Left breast

• Diagnosis: Invasive ductal carcinoma, poorly

differentiated – in situ and Invasive ductal carcinoma

• Sign: mass in axillary tail region

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DE

Temp 1 Temp2

Energy Subtraction

• Advantages:– Motion artifacts are rare

• Disadvantages:– System modifications are necessary to allow

rapid change of filter material and kVp– Detector must be suited to rapid readout– Poorer separation of tissue and contrast

agent– Beam hardening artifacts

Multimodality Imaging

Combined Tomo/US System

Cou

rtesy

Pau

l Car

son,

U M

ichi

gan

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PLC UoM / GE GR 6/5/06

Tomo with marked US

Cou

rtesy

Pau

l Car

son,

U M

ichi

gan

Dual Modality Tomographic Scanner (UVa)

During x‐ray image acquisition the gamma camera is positioned out of the beam near the tube and close to the gantry arm

During gamma ray image acquisition the gamma camera positioned as close as possible to the chest wall edge of the compression paddle

Data courtesy of Mark Williams, Ph.D. UVa Charlottesville, VA

Current Protocol

• To date, researchers at U Va have imaged 18 subjects having a total of 23 biopsied lesions

• 25 mCi Tc‐99m Sestamibi• 2 mGy absorbed dose to breast• 8 mSv effective whole body dose

Data courtesy of Mark Williams, Ph.D. UVa Charlottesville, VA

Positive Lymph Node

Infiltrating Ductal

Carcinoma

X‐Ray Slice Fused Slice

Single 1 mm thick slice

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Advantages of tomosynthesis

• Improves conspicuity by removing overlying structures

• Permits section imaging with high resolution in coronal view and limited MPR

• Easily performed on the high volume of radiography patients

• Lower radiation dose compared with CT • Lower cost compared with CT

principles of breast tomosynthesis acquisition …...1 principles of breast tomosynthesis...

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