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Investigation of the effect of tube motion in breast tomosynthesis: Continuous
or step and shoot?
Article in Proceedings of SPIE - The International Society for Optical Engineering · March 2011
DOI: 10.1117/12.877348
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Investigation of the effect of tube motion in breast tomosynthesis:
continuous or step and shoot?
Eman Shaheen*a, Nicholas Marshalla, Hilde Bosmansa
a
Univeristy Hospitals Leuven, Herestraat 49, 3000 Leuven, Belgium
ABSTRACT
Digital breast tomosynthesis (DBT) is a 3D modality that may have the potential to complement or replace 2D
mammography. One major design aspect of DBT systems is the choice of tube motion: continuous tube motion during xray exposure or the step and shoot method where the tube is held fixed while x-rays are released. Systems with
continuous tube motion experience focal spot motion blurring but a reduced patient motion blurring due to potentially
faster total acquisition times when compared to the step and shoot approach. In order to examine the influence of focus
motion on lesion detectability, a simulation environment was developed where lesions such as microcalcifications and
masses are inserted into different thicknesses of theoretical materials. A version of the power law noise method was
employed to approximate realistic anatomical breast volumes. The simulated projection images were reconstructed and
appropriate metrics (peak contrast, contrast and signal-difference-to-noise ratio) of the lesions in the two different modes
were compared. Results suggest an increase of the peak contrasts in the microcalcification data sets by 8 – 9 % for the
step-and-shoot method when compared to the continuous mode (p <0.05). While the contrast and signal-difference-tonoise-ratio calculated for the same two modes almost overlapped for the mass datasets showing a difference of only 12%.
Keywords: breast tomosynthesis, tube motion selection, simulation, MTF, contrast
1. INTRODUCTION
There is currently significant interest in whether digital breast tomosynthesis (DBT) systems1 can improve the detection
of lesions compared to modalities such as 2D mammography and breast CT. This new modality is a form of limited
angle tomography that produces section images from a series of projection images acquired as the x-ray tube moves over
a prescribed path2. The total angular range of the tube movement currently ranges from 11° to 50° for DBT. The
projection images are then reconstructed into planes parallel to the detector.
Much attention is given to the optimization of detector performance, acquisition geometry, x-ray exposure parameters
and reconstruction algorithms3-5. One major factor worth investigating, and the topic of this work, is the choice of tube
motion. Most available DBT systems operate with a continuous tube motion where short x-rays are pulsed during
continuous motion of the gantry; inevitably this leads to some blurring due to focal spot motion during each exposure.
An alternative approach is the step and shoot method where the gantry comes to a complete stop at each angular location
before generating the x-rays. Provided that the tube stops completely (no mechanical jitter or reverberation), there will be
no focus motion blurring, although there may be increased patient motion blurring if the overall scan time is longer than
a continuous motion operated over the same angular range with the same number of exposures. The focal spot blur due
to continuous tube motion has been compared to pixel binning using the modulation transfer function (MTF)3,6, pixel
binning was found to dominate the MTF rather than the focal spot blur.
In this paper, we have investigated the effect of tube motion on the detectability of objects in an anatomical background
with the attempt to answer the question whether continuous tube motion significantly reduces the detectability of lesions
compared to the step and shoot method under ideal conditions of no patient motion and no mechanical instabilities.
*eman.shaheen@uzleuven.be , phone: +32 16 34 90 68
Medical Imaging 2011: Physics of Medical Imaging, edited by Norbert J. Pelc, Ehsan Samei, Robert M. Nishikawa,
Proc. of SPIE Vol. 7961, 79611E · © 2011 SPIE · CCC code: 1605-7422/11/$18 · doi: 10.1117/12.877348
Proc. of SPIE Vol. 7961 79611E-1
A simulation framework was built that includes anatomical backgrounds, realistic x-ray spectra, scatter, detector
response and noise. We report on the simulation framework and the results of the comparison between the two modes.
2. MATERIALS AND METHODS
In this study, 36 computer simulated breasts were generated including 3 different breast thicknesses 3, 5, 7 cm
representing small, medium and large breasts respectively. Each breast volume included either a soft tissue mass or a
microcalcification. The microcalcifications were inserted in the central portion of the simulated breast volume in terms
of x, y but in different z positions (corresponding to different depths in the simulated breast); insertion positions in the z
direction was in steps of 0.5 cm. The masses were inserted also in the center of the simulated breast but at a fixed z
position which was 1 cm from the bottom of the breast. The projections were generated to simulate the characteristics
and limitations of a real system with the mean glandular dose limited to the typical dose for a specific breast thickness:
1.2, 1.6 and 2.2 mGy for the 3, 5 and 7cm breast thicknesses respectively7. This work was repeated for the case of
continuous motion and step and shoot modes.
2.1
Simulation framework
2.1.1 Breast volume simulation
The characterization of anatomical background has been an area of considerable interest in 2D medical imaging
applications, such as mammography and chest radiography8,9. Burgess et al10 described breast structure in an image
segment by a power-law relationship: / , where
is the clutter magnitude (a constant), f is the spatial frequency and
β is the correlation of variations (a constant). Heine et al11 have measured the value of β to be in the range 2.8–3.0 in
digital mammograms. The power-law depiction of anatomical noise has been extended to 3D imaging by Metheany et
al12. In our simulation, β for the 3D breast volume to be simulated was chosen to be 1.5 following Sechopoulos et al5.
A cube representing the central portion of a compressed breast of a specific size was simulated by filtering white
Gaussian noise with zero mean unity standard deviation, generated and filtered in the spatial frequency domain by the
equation (1/ ). The inverse Fast Fourier Transform (FFT) of this cube was calculated and normalized to obtain a
volume in the spatial domain representing a mixture of adipose and glandular tissues. The values in the cube varied from
0-100 representing the percentage glandular fraction.
2.1.2 Simulation of projection images
The Siemens DBT system that was adopted in the simulation procedure has a nominal angular range of 50°, with 25
projection images. The a-Se detector pixel size was 0.085mm, the source to detector distance was 65cm and the center of
rotation was located at 4.7cm above the detector. The anode/filter combination used was W/Rh.
The volume containing the filtered noise was ray traced just once, per projection image, using the Siddon algorithm13
following the method proposed by Sechopoulos14 that accounts for beam hardening and polychromatic spectrum. Linear
fits were performed to relate the glandular fractions of the volume (voxel values) to the linear attenuation coefficients at
each energy level, from 10 to 30 keV in 0.5 keV steps, using the data for elemental attenuation coefficients from NIST15
and for the elemental composition of the glandular and adipose tissue from Hammerstein et al16.
In order to obtain simulated projections at a given dose level, the ray traced results were converted to air kerma images
arriving at the detector entrance using the appropriate number of x-rays incident on the breast. The total glandular dose
was set according to the typical dose for a given breast thickness and this value was used to set the total mAs for the
breast (based on technical factors for the system), divided by 25 to obtain the mAs per projection. A tungsten target
spectrum was generated for a given tube potential using the work of Boone et al17 to estimate the number of photons in
the spectrum for a given kV. This was then corrected using the inverse square law to a point at the breast entrance and
then filtered by the compression plate (assumed to be 2mm PMMA). Ray tracing can then estimate the number of
photons at the detector level and its energy weighted sum represented the air kerma image.
Proc. of SPIE Vol. 7961 79611E-2
To convert this air kerma image to a pixel value (PV) image, the relationship between PV and air kerma had to be
determined. This relationship was found empirically using the Siemens clinical tomosynthesis system by measuring the
air kerma incident on the detector with a calibrated dosimeter and recording the mean pixel value in the resulting image
over a 1 x 1 cm region close to the central ray. The variance of this region was also recorded to be used later in the noise
addition step.
In order to study the contrast properties for two different DBT modes, two types of lesions were inserted: a sphere with a
diameter of 250 µm of Calcium oxalate (CaC2O4) representing a microcalcification and a set of spheres of the material
suggested by Johns and Yaffe17 for invasive ductal carcinoma representing masses of different sizes (0.5, 1, 2, 4, 8mm).
These lesions were separately simulated using the methodology developed previously18 up until the step of obtaining an
ideal template for every projection image. These templates were multiplied with the projection image representing the
background. The result is a set of hybrid projection images.
2.1.3 Image modification and reconstruction
The hybrid projection images are considered to represent the ideal situation of an ideal detector with no noise and no
scattered radiation. Therefore, the images were modified to include scatter, noise and detector resolution. The work of
Boone20 was used to calculate the scatter to primary ratio (SPR). The scatter offset was estimated to be the mean pixel
value of the simulated region (60 x 60mm) multiplied by SPR. This offset value was added to the primary signal.
The FFT of the image, containing the primary and scatter signals, was then multiplied by an MTF measured using the
edge method. For the case of continuous tube motion, the measured MTF of the central projection image (angle = 0°), for
left-right (tube travel direction) and front-back direction, was used and the left-right MTF curve was modulated for the
oblique entry for non-zero projection angle using the formula given by Que and Rowlands21. For the step and shoot case,
assuming that the gantry reaches to a complete stop before the x-ray exposure, the measured MTF of the same system for
the front-back direction was used for the two directions with the assumption that the left-right and front-back curves are
isotropic. The MTF curve for the tube travel case was then corrected for oblique entry as mentioned before. Note that the
obliquity correction, applied on the left-right curve, for the specific angle used will only be approximately correct over
the small region at the center of the image. The MTF curves used for the simulation of the 0° angle are shown in figure 1.
1.0
left-right (tube travel)
continuous mode
0.9
0.8
front-back continuous
mode
0.7
front-back step and
shoot mode
MTF (u)
0.6
left-right (tube travel)
step and shoot mode
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
spatial frequency (mm-1)
Figure 1 MTF used for the simulation of continuous and step and shoot mode
Proc. of SPIE Vol. 7961 79611E-3
The noise waas modified as
a explained by
b Saunders and Samei22. A random white
w
noise im
mage was mu
ultiplied in thee
frequency dom
main by the square root of the noise pow
wer spectrum (NPS)
(
of the system
s
normaalized to unity,, resulting in a
colored noisee image. The relationship
r
between signall level and variance presentt in the imagee was then useed to scale thee
colored noisee image on a pixel-by-pixel
p
basis and thee resulting noise was added to the noiseleess image. To determine thee
relationship between
b
signaal and noise levels, the varriance found for
f different exposure
e
levels in the air kerma
k
to pixeel
value converssion test was fitted
f
against the
t mean signnal.
In order to reeconstruct thee volume, a sooftware proviided by Siemeens (TomoEnngine) based oon a modified
d filtered backk
projection (FB
BP) algorithm
m23 was used with
w a reconstrructed voxel size
s of 0.085 mm
m x 0.085 m
mm x 1 mm.
Some examplles of the simuulations are shhown in figurees 2 and 3.
Figure 2 A microcalcificati
m
on in the reconstructed in focuus plane, modelled by a small sphere
s
of 250µm
m diameter and consisting of
calcium oxallate, inserted intto a 5cm breastt in continuous mode (left) andd step and shoott mode (right)
Figure 3 A 2mm
2
mass inserted into a 3cm
m breast. Centrall projection imaage after all sim
mulation steps (lleft). Reconstru
ucted in focus
plane (right)
2.2
Image analysis
As mentionedd earlier, 3 brreast thicknessses were inveestigated with
h two types off inserts repreesenting micro
ocalcificationss
and masses. For the miccrocalcificationn datasets, a total of 66 microcalcificcations were simulated with
w
7, 11, 155
microcalcifications for the 3, 5, 7cm breeast datasets inn two modes (continuous,
(
s and shoott). As for the mass datasetss,
step
a total of 30 masses
m
were inserted
i
into thhe 3 breast thhicknesses dataasets with eacch set containiing 5 different sized massess
(0.5, 1, 2, 4, 8mm)
8
in the tw
wo modes. Foor the microcaalcification dattaset of the 7ccm breast, twoo additional co
onditions weree
simulated. Firrst, an ideal MTF
M such thatt MTF(u,v) = 1 for all frequ
uencies, and seecond, what w
was considered
d a worse casee
MTF. For thee worst case scenario,
s
the left-right (tubbe travel) MTF used for the continuous motion modee was used forr
both the frontt-back and lefft-right MTF curves.
c
The contrast (C,
( eq.1) and the signal diff
fference to noiise ratio (SdNR
R, eq.2) of thee masses weree used as metriics to measuree
the quality. The
T peak contrrast (PC, eq.3) was used to evaluate the microcalcifica
m
ation datasets because the estimation
e
of a
meaningful mean
m
value waas difficult duue to the smalll size of the microcalcifica
m
ations: contrasst measuremen
nts from meann
values in smaall circular RO
OIs resulted in
i unreliable measurements
m
s for C and SddNR. The meaasurements were
w
applied inn
the in-focus planes
p
of the reconstructedd volume of thhe breast for both
b
sets: the step and shooot mode and the
t continuouss
mode. Calcuulated C, PC
C and SdNR were compaared and anaalyzed with an extra paiired t-test ap
pplied on thee
microcalcification datasets (population = 33).
Proc. of SPIE Vol. 7961 79611E-4
(1)
(2)
0.5
(3)
where, µbkg is the mean of the pixel values in the background ROI (6 x 6 mm), µsignal is the mean of the pixel values in the
signal ROI (microcalcification or mass) and σ2bkg is the variance of the pixel values in the background ROI and σ2signal is
the variance of the pixel values in the signal ROI, max(signal) is the maximum pixel value in the signal ROI
(microcalcification).
3. RESULTS
Three different breast thicknesses were examined in this study, simulated under the same conditions except for the
choice of tube motion, which defined the MTF used. Due to the fact that the MTF in the tube motion direction of the
continuous mode is decreased by 18.6% and 26.9% at the 50% and 10% points of the MTF, respectively compared to the
step and shoot, a decrease in the image quality for the continuous method is expected.
3.1 Microcalcification datasets evaluation
The microcalcification datasets for the three breast thicknesses (3, 5, 7cm) in the two modes were evaluated in terms of
their peak contrast (PC) and compared as shown in figure 4.
y=x
3
2.5
3cm dataset
y = 1.091x
R² = 0.997
2.5
PC for step and shoot mode
y = 1.086x
R² = 0.990
3.5
PC for step and shoot mode
PC for step and shoot mode
1
3
4
y=x
2
1.5
1
5cm dataset
0.5
0
2
2
2.5
3
3.5
PC for continuous mode
4
0.9
y = 1.082x
R² = 0.982
0.8
y=x
0.7
0.6
0.5
7cm dataset
0.4
0.3
0
0.5
1
1.5
2
2.5
PC for continuous mode
3
0.3
0.4
0.5 0.6 0.7 0.8 0.9
PC for continuous mode
1
Figure 4 The PC of the microcalcification datasets for the continuous versus the step and shoot modes for 3, 5, 7cm (left to right)
As shown in the figure, the peak contrasts obtained with the step and shoot mode are higher than with the continuous
mode by approximately 8.6%, 9.1%, 8.2% for the 3, 5, 7cm datasets respectively. The t-test showed a significant
difference (p= 3.0650e-009, n=33).
3.2 Mass datasets evaluation
The mass datasets for the 3 breast thicknesses (3, 5, 7cm) in the two modes were evaluated in terms of their contrast (C)
and SdNR measurements. Both modes were analyzed and compared as shown in figures 5, 6.
Proc. of SPIE Vol. 7961 79611E-5
25
15
y=x
10
5
3cm dataset
0
25
y = 1.026x
R² = 1.000
20
y=x
15
10
5
5cm dataset
5
10
15
20
SdNR for continuous mode
25
20
y = 1.014x
R² = 1.000
15
y=x
10
5
7cm dataset
0
0
0
SdNR for step and shoot mode
y = 1.004x
R² = 1.000
20
SdNR for step and shoot mode
SdNR for step and shoot mode
25
0
5
10
15
20
SdNR for continuous mode
25
0
5
10
15
20
SdNR for continuous mode
25
Figure 5 SdNR for the mass datasets of the continuous mode versus the step and shoot mode for 3, 5 and 7cm (left to right)
respectively
1
Cont 3cm
Contrast value
0.8
Step Shoot 3cm
0.6
Cont 5cm
0.4
Step Shoot 5cm
Cont 7cm
0.2
Step Shoot 7cm
0
0
2
4
Mass size (mm)
6
8
Figure 6 Contrast of the mass datasets for the continuous and the step and shoot modes for the 3 breast thicknesses plotted against the
mass sizes
The SdNR measurements showed no difference between the two modes and the superiority of the step and shoot mode
over the continuous mode was at most 2%, for in the case of the 5cm breast dataset. As for the contrast, the increase was
at most 1% which can be seen in figure 6 where the two modes for each dataset were overlapping. Since the masses were
always inserted at the same position, at 1cm from the detector surface, it is clearly seen from figure 6 that the contrast
changes as expected for each set depending on the overlaying thickness of the breasts.
3.3 Investigation of the effect of different MTFs
Further investigation was made in an attempt to explore the influence of the MTF changes on the parameters used to
quantify image quality. Since the difference in measurements occurred mainly in the microcalcification datasets, we
adopted the largest dataset which is the 7cm and examined two further acquisition cases; the ideal situation which
(MTF(u,v)=1) and the worst case MTF (choosing the tube travel curve and assuming it is isotropic). The three modes
were compared in terms of PC against the ideal mode as shown in figure 7.
The maximum drop in contrast was approximately 24% and this was found for the worst case MTF, as might be
expected. This was followed by the continuous mode with a drop of approximately 22% while the best results were
found for the theoretical step and shoot mode, with a contrast loss of 16% compared to the ideal situation.
Proc. of SPIE Vol. 7961 79611E-6
PC
1
y=x
0.9
Step and Shoot
0.8
Continous mode
0.7
Worst MTF
0.6
0.5
y = 0.84x
Linear (Step and Shoot)
y = 0.78x
Linear (Continous mode)
y = 0.76x
Linear (Worst MTF)
0.4
0.4
0.5
0.6
0.7
0.8
PC for Ideal mode
0.9
1
Figure 7 Investigating the effect of applying different MTFs on the PC of the microcalcification datasets
4. DISCUSSION
Selection of the tube motion mode in a DBT system is an important system design parameter that can potentially
influence lesion detectability. The choice between a step and shoot mode versus continuous mode can be based upon
MTF, however the choice should go beyond this and examine the effect on parameters closer to the clinical practice. Use
of continuous mode results in a reduction of the MTF in the tube travel direction compared to step and shoot mode, but
the question arises whether this drop affects lesion detectability. Ideally, a system that could be operated in both the step
and shoot and the continuous modes would allow a direct comparison in a clinical environment on real patient cases.
Such a system was not available and hence a simulation approach was adopted in which MTF was changed to reflect
differences in tube motion.
The effect of blurring due to continuous motion was expected to have larger effects on small objects (such as
microcalcifications) than on large objects such as masses because microcalcifications contain a greater proportion of
high spatial frequencies. The reduction in MTF in going from continuous to step and shoot mode is greater at higher
spatial frequencies. For example, the reduction in MTF at 2 mm-1 is approximately 10% while the reduction at 6 mm-1 is
approximately 50%. This is reflected in the fact that peak contrast results for the microcalcifications are lower for the
continuous mode acquisitions (approximately 8%). For the masses, little difference was observed (approximately 2%).
Figure 7 shows that the drop in peak contrast from an ideal MTF (MTF(u,v) = 1) towards the theoretical MTF condition
of the step and shoot is larger than between the MTF conditions of the step and shoot and the continuous mode. These
results provide further evidence that the inclusion of system MTF, incorporating scatter or motion blurring effects for
example, can give valuable insight when modeling the influence of system resolution characteristics in a detection
study24.
We note that this study was applied to an a-Se detector with an intrinsically high pre-sampling MTF curve (the MTF
used for step and shoot mode), operated in the two different modes. Results from this work may not be directly
applicable when comparing two different detectors that have absolute differences in pre-sampling detector MTF. A DBT
system with a lower pre-sampling detector MTF may not be able to operate in continuous tube motion DBT mode
without significant reduction in lesion detectability.
Separate reading studies with human observers were not run to see whether the changes in contrast had also an effect on
detection or characterization of lesions, although might expect this to be the case. An obvious limitation of our study is
the use of the 2D MTF to characterize the step and shoot mode at the one side and the continuous mode at the other side
with ignoring other parameters such as system reverberation. These hypotheses approximate the real situation, ignoring
the patient motion effect due to longer acquisition time for step and shoot when compared to the acquisition time of a
continuous tube motion. The blurring caused by patient motion during the acquisition of the projection images is not
included in this study and could be investigated in future work.
Proc. of SPIE Vol. 7961 79611E-7
The metrics applied in this study (contrast, peak contrast and SdNR) are rather simple and are mainly used for image
quality assessment in projection images with a homogeneous background. A stronger estimate of the influence of
changing parameters such as MTF on lesion detectability may be found through the application of model observers to the
images9,25.
5. CONCLUSION
The present work investigated the influence of the tube motion on the detectability of simulated lesions in a simulation
environment. The results confirmed that the reduction in MTF in the tube travel direction due to tube motion had a
greater effect on microcalcifications compared to masses for all breast thicknesses included in the study. Step and shoot
mode provided higher peak contrast by approximately 8% compared to continuous tube motion for the microcalcification
datasets. A similar study for masses showed only a 2% difference in the contrast and SdNR measurements.
ACKNOWLEDGMENTS
This work was funded by the OPTIMAM project which is supported by CR-UK & EPSRC Cancer Imaging Programme,
in association with the MRC and Department of Health (England). We are grateful to Dr. Thomas Mertelmeier for
giving valuable input and for providing the reconstruction software “TomoEngine”.
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