Principles of Breast
Tomosynthesis Acquisition
and Reconstruction
Andrew Maidment, PhD, FAAPM
Associate Professor of Radiology
Chief, Physics Section
Department of Radiology
University of Pennsylvania
Linear Tomography
Disclaimer
Andrew Maidment is a consultant
to Real-Time Tomography LLC,
and receives research support
from Hologic Inc. and Barco Inc.
Simple Tomosynthesis
Acquisition geometry
Backprojection image formation
1
Hologic Selenia Dimensions *
• 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
Current Systems
* Investigational Device -Limited by United States Law to Investigational Use
T. Mertelmeier 05/2006
Invasive Ductal Carcinoma
8
Digital Breast Tomosynthesis
 Modified mammo unit
for large angle range
(± 25o)
 Fast a-Se detector
24 x 30 cm2
 High DQE at low
exposures
 Several readout &
acquisition modes
 1… 2 fps
 Up to 49 projections
 CC and MLO
Work in progress
Images courtesy of Dr. Jelle Teertstra
NKI-AVL, The Netherlands
2
T. Mertelmeier 05/2006
slice close to the surface of the breast
slice at z = 21 mm above patient table
9
Human subject
Age 68
MLO position
6 cm compressed
28 kVp, W/Rh
133 mAs
49 projections
39 s scan
1 mm slices
Photon Counting
Tomosynthesis
scar (benign biopsy 1980)
invasive ductal CA with
lobular component
Image data Duke University, Dr. Jay Baker
Work in progress
Doc. No/Page 10(xx)
2007-xx-xx/Signature
Proc SPIE 5745, 529-540 (2005)
Geometry
•
One sweep  3D data
•
Multi-slit photon counting:
no electronic noise, no
ghosting, no scattered
radiation
Doc.No/Page
No/Page 11(xx)
Doc.
11(xx)
2007-xx-xx/Signature
2007-xx-xx/Signature
3
Case 1:
Potential to reduce false-negative diagnoses
GE DS DBT Prototype
Detector:
- a-Si (CsI)
- 23×19.2 cm2 area
- 100 m pixel size
Tomosynthesis Slice (Z = 24mm)
LMLO
Acquisition:
- 15 projections
- 40o arc (38o actual)
- 15s acquisition
- Mo/Mo, Mo/Rh and Rh/Rh
Invasive Carcinoma
Courtesy of Tao Wu, Ph.D.
Tomosynthesis Mammography Reconstruction
Using a Maximum Likelihood Method
Case 2:
Potential to reduce false-positive diagnoses
Courtesy of Tao Wu, Ph.D.
LMLO
4
Case 2:
Potential to reduce false-positive diagnoses
Courtesy of Tao Wu, Ph.D.
Z = 0 mm
Z = 10 mm
Z = 15 mm
Z = 20 mm
Image Theory
Z = 25 mm
Z = 30mm
Z = 35 mm
Z = 40 mm
SPIE MI 2006 6142-15
Linear Tomography
Feb 12,.2006
20
Tomosynthesis Reconstruction
Sampling geometry
±
Fourier slice theorem
 sampling is incomplete (in Fourier space)
 approximative inversion only
 artifacts
5
fz
45 V, 22°
23 V, 11°
12 V, 5.5°
6 V, 2.5°
fx
Tissue Imaging
1
0.08
SDNR (normalized)
0.07
Contrast
0.06
0.05
0.04
0.03
0.02
0.8
0.6
0.4
0.2
0.01
0
0
50
100
150
200
0
0
Angular Extent ()
50
100
150
200
Angular Extent ()
Angular Spacing, ∆θ=2°
6
Angular Range
• Increasing the angular range has the
effect of:
fz
fx
– 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
45 V, 22°
23 V, 22°
12 V, 22°
6 V, 22°
7
48
12
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
Difference
Breast CT
Breast Tomosynthesis
B.3 - 3D spatial frequency domain
CT
Modern Multi-slice VCT
scanners have nearly
isotropic response with
maximum spatial
frequencies of .8 to 1.0
cycles/mm
Courtesy J. Boone
32
z
y
x
Courtesy M Flynn
8
B.3 - 3D spatial frequency domain
TS vs CT
Unsampled frequencies along
33
fz
Simple Backprojection
Filtered Backprojection
fy
the y axis make TS and CT
complimentary.
fx
Courtesy M Flynn
Tomosynthesis
296
Geometric Accuracy
• 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
Mammogram
6.4 mm
25.6 mm
44.8 mm
Breast CT
9
Methods: Simulated Acquisition of
Phantom DBT Images
Methods: Simulated Acquisition of
Phantom DBT Images
• Phantom images are simulated assuming mono-energetic x-ray
beam without scatter, and an ideal detector.
DBT Projection
Phantom Section
X-ray Projection
Reconstructed Image
DBT Reconstructed Image
Methods: Supersampling
Results: Marker Position Error
0.25
4
4
3.5
3
2.5
2
1.5
1
6.1
6.2
6.3
6.4
6.5
x (mm) from Chest Wall
6.6
3
x 10
4
(xC-xT)
(yC-yT)
(zC-zT)
Ep
0.20
Error (mm)
Supersampled reconstructed Image Intensity
x 10
Supersampled reconstructed Image Intensity
• We reconstructed a series of 10 images with sub-pixel shifts within
the plane of reconstruction and combined them to form a
supersampled image.
0.15
0.10
0.05
2.5
0.00
0
10
20
30
40
50
2
Reconstructed Plane Depth z(mm)
1.5
6.52
6.53
6.54
6.55
6.56
x (mm) from Chest Wall
6.7
6.8
6.57
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.
10
Super-Resolution
FWHM Relative Error (%)
Results: Marker Size Error
This presentation studies super-resolution (SR), where multiple low
resolution (LR) images are combined to achieve sub-pixel resolution.
200%
6.4 mm
25.6 mm
44.8
150%
100%
50%
0%
0
0.2
0.4
0.6
0.8
1
1.2
Distance from the Plane of Focus (mm)
Relative marker size error was averaged over all markers at
the same depth in the phantom.
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.
Courtesy Sung Park
Results for Central Projection
Results for Central Projection
2.1 lp/mm
0.6
0.4
Signal
0.2
0
–0.2
–0.4
–0.6
–0.8
–1.0
–0.6
0.4
–0.2
0
0.2
Position (mm)
Sinusoidal Input (Normalized)
–0.4
0.6
1.0
2.00
0.8
0.6
1.75
0.4
1.50
0.2
Input Freq.
5.0 lp/mm
1.25
1.00
0
–0.2
0.75
–0.4
0.50
–0.6
0.25
–0.8
0
2.25
Fourier Transform Modulus (mm)
Fourier Transform Modulus (mm)
0.8
2.25
Signal
1.0
0
2
4
6
8
10
12
Spatial Frequency (lp/mm)
14
–1.0
–0.6
Alias Freq.
3.6 lp/mm
2.00
1.75
1.50
Input Freq.
5.0 lp/mm
1.25
1.00
0.75
0.50
0.25
–0.4
–0.2
0
0.2
0.4
0.6
Position (mm)
Sinusoidal Input (Normalized)
Central Projection (Parallel X-Ray Beam)
0
0
2
4
6
8
10
12
14
Spatial Frequency (lp/mm)
Central Projection (Parallel X-Ray Beam)
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).
11
Filtered Backprojection (FBP)
2.0
A) Central Projection
4.5
1.6
1.2
0.8
0.4
0
–0.4
–0.8
–1.2
B) Reconstruction
Input Freq.
5.00 lp/mm
4.0
Fourier Transform Modulus
Attenuation Coefficient μ (mm-1)
Bar Pattern Phantom
3.5
3.0
2.5
2.0
1.5
1.0
0.5
–1.6
–2.0
–0.6
–0.4
–0.2
0.2
0
Position (mm)
Sinusoidal Input
FBP (RA Filter)
FBP (RA and SA Filters)
0.4
0.6
0
0
2
4
6
8
10
12
Spatial Frequency (lp/mm)
FBP (RA Filter)
FBP (RA and SA Filters)
14
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.
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.
Anisotropy due to Oblique Incidence
Clinical Application
fz
F1
F2
F3
f
Detector Center
Reconstruction with 140 μm voxels
+ Interpolation at 35 μm.
Reconstruction with 35 μm voxels
+ No Further Interpolation.
Conventional Image
Super-Resolution Image
R
D
Detector Edge
12
Fourier Slice Thereom
Anisotropy of GE System
This presentation extends our prior research on super-resolution to an
obliquely pitched reconstruction plane.
• Source-to-COR: 48 cm
• COR-to-Detector: 20 cm
• Central Projection: α = 0°
Fourier Domain
Spatial Domain
Incident
X-Ray Beam
Final
Projection
νz
Null
Space
• θ varies between 0° at
midpoint of chest wall and
18.1° opposite chest wall.
ψ
Object
Intermediate
Projection
νx
ψ
z
x
Detector
First
Projection
Unexpectedly, we demonstrate that super-resolution is possible in areas of
Fourier space not sampled by any individual projection.
Methods
Bar Pattern Phantom
Pitch 30°
Pitch 60°
Super-resolution up to
5.0 lp/mm
Resolution up to
3.0 lp/mm
The Selenia Dimensions system (Hologic Inc., Bedford, MA) having 15
projections is simulated, assuming no sources of noise or blurring.
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.
(2
cos
ε
′)
ν 0x
z
z′
x′
Pitch 30º
x
Two reconstruction methods are considered: simple backprojection (SBP)
and filtered backprojection (FBP).
13
Clinical Application
Magnification
of Recon. with
140 μm voxels
at 0° pitch
Clinical Application
Recon. with
35 μm voxels
at 0° pitch
Recon. at
0° Pitch
Recon. at
30° Pitch
Recon. at
0° Pitch
Recon. with
35 μm voxels
at 30° pitch
Clinical Application
Recon. at
0° Pitch
Recon. at
30° Pitch
Recon. with
35 μm voxels
at 0° pitch
As the angular range of the tomosynthesis
projection (source) images is reduced, the
0%
Recon. with
35 μm voxels
at 0° pitch
0%
0%
0%
0%
Translation of
Recon. Plane
at 30° pitch
1. The z-resolution is improved
2. The in-focus plane thickness is
decreased
3. The blurring of out of plane objects in
decreased
4. The in-plane resolution is decreased
5. The noise in the image is increased
10
14
Answer
As the angular range of the tomosynthesis
projection (source) images is reduced, the
3. The blurring of out of plane objects in
decreased
As the number of projection (source) images
used in the reconstruction is increased,
0%
0%
0%
0%
0%
References: A D A Maidment, et al, Evaluation of a photon-counting breast
tomosynthesis imaging system, Proc. SPIE 5745 (2005).
1. The conspicuity of artifacts increases
2. The acquisition time decreases
3. The impact of detector noise is
decreased through noise averaging
4. The blurring of out-of-plane structures
is improved
5. In-plane resolution is increased
10
Answer
As the number of projection (source) images
used in the reconstruction is increased,
4. The blurring of out-of-plane structures is
improved
With regard to tomosynthesis spatial resolution
0%
0%
0%
0%
0%
References: A D A Maidment, et al, Evaluation of a photon-counting breast
tomosynthesis system, Proc. SPIE 6142 (2006).
1. It is inferior to CT spatial resolution inplane
2. In-plane spatial resolution is limited by
the detector pixel size
3. It is isotropic
4. Z-resolution is limited by the number
of projections
5. It is determined primarily by the x-ray
converter spatial resolution
10
15
Answer
With regard to tomosynthesis spatial
resolution
5. It is determined primarily by the x-ray
converter spatial resolution
Image Reconstruction
References: R J Acciavatti and A D A Maidment, Investigating the potential for
super-resolution in digital breast tomosynthesis, Proc SPIE 7961 (2011).
Proposed Reconstruction Methods
•
•
•
•
•
•
•
•
Tomo LSF
Simple Backprojection (“Shift & Add”)
Filtered Backprojection
ART
Maximum-Likelihood Expectation
Maximization
Total Variational Methods
Matrix Inversion (MITS)
Ordered Subset methods
and many more
16
Comparison of reconstruction alg.
T. Mertelmeier 05/2006
65
ramp
Invasive Ductal Carcinoma
ramp

spectral
ramp

spectral

slice thickness
ramp

spectral

slice thickness
(optimized)
Images courtesy of Dr. Jelle Teertstra
NKI-AVL, The Netherlands
DBT Reconstruction
— Artifact Reduction
Convex Hull Processing
Reconstruction images without artifact reduction
Courtesy S. Ng, RealTime Tomography, LLC
Z = 12mm
Z = 16mm
Z = 27mm
17
DBT Reconstruction
— Artifact Reduction
Results of artifact reduction (Maximum Contribution Deduction)
Z = 12mm
Z = 16mm
MITS
FBP
Multi-Planar
BPF
Courtesy S. Ng, RealTime Tomography, LLC
Z = 27mm
FBP with
H&G
MITS-FBP
blend
Iterative DBT Reconstruction Algorithms
(0)
Initial 3-D Model
(n)
Update
Forward projection
Calculated Projections: P (n)
Measured Projections: P
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.
Slides courtesy of Ying Chen, Joseph Lo, Jay Baker, Jim Dobbins
(n+1)
Optimized Likelihood Function
(end)
Likelihood function L=P(Y|): The probability of getting the measured
projections Y, given a 3-D model  of the breast volume.
18
Simultaneous Algebraic Recon Technique
(SART)
Iterative Maximum-Likelihood (ML)
6 iter
MGH case
9 iter
11 iter
Chan HP, et. al.
Tomosynthesis image reconstruction
methods include all of the following except
0%
0%
0%
0%
0%
1 iter
2 iter (0.1)
MGH case
2 iter (0.5)
Chan HP, et. al.
Answer
1. 3D multiscale gradient filtered
reconstruction
2. Filtered back-projection
3. Back-projection filtering
4. Maximum likelihood expectation
maximization
5. Total variational methods
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)
10
19
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
Functional Imaging
Invasive Ductal Carcinoma
Temporal Subtraction
ICRU-44 Breast Tissue
Iodine
0.27 mm Cu
1000
Post-contrast
Subtraction
1000000
900000
800000
700000
100
600000
500000
10
400000
300000
1
Photon Fluence
[# photons/mm2]
Mass attenuation[cm 2/g]
10000
Pre-contrast
200000
100000
0.1
0
0
5
10
15
20
25
30
Energy [keV]
35
40
45
50
Spiculated mass with rim enhancement.
20
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)
DE-DBT: Patient 2
Low Energy
High Energy
High Energy
Low Energy
• Age: 55
• Weight:
• Project 3 / Left breast
• Diagnosis: Invasive ductal carcinoma, poorly
SI DE ( x, y )  ln(SI H ( x, y ))  wt  ln(SI L ( x, y ))
differentiated – in situ and Invasive ductal
carcinoma
• Sign: mass in axillary tail region
21
Energy Subtraction
DE
• Advantages:
– Motion artifacts are rare
• Disadvantages:
Temp 1
– 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
Temp2
Multimodality Imaging
Courtesy Paul Carson, U Michigan
Combined Tomo/US System
22
Courtesy Paul Carson, U Michigan
Dual Modality Tomographic Scanner (UVa)
Tomo with
marked US
During x‐ray image acquisition the gamma camera is positioned out of the beam near the tube and close to the gantry arm PLC UoM / GE GR 6/5/06
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.
Current Protocol
UVa Charlottesville, VA
Positive Lymph Node
• 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
Single 1 mm thick slice
Infiltrating Ductal Carcinoma
Data courtesy of Mark Williams, Ph.D.
UVa Charlottesville, VA
X‐Ray Slice
Fused Slice
23
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
24