Realistic Simulation of Breast Tissue Microstructure

in Software Anthropomorphic Phantoms

Predrag R. Bakic,1 David D. Pokrajac,2

Raffaele De Caro,3 and Andrew D.A. Maidment1
1
Dept. of Radiology, University of Pennsylvania, Philadelphia, PA, USA
2
Computer and Information Sciences Dept., Delaware State University, Dover, DE, USA
3
Dept. of Human Anatomy and Physiology, University of Padova, Italy
Predrag.Bakic@uphs.upenn.edu

Abstract. Software anthropomorphic breast phantoms have been used in virtual

clinical trials for preclinical validation of breast imaging systems. Virtual trial
quality depends largely on the realism of the simulated breast anatomy. Our
phantom design has been focused on the simulation of large-scale and meso-
scale anatomical structures, including the breast outline, skin, and matrix of
Cooper’s ligaments and tissue compartments. Realism of such a design has
been confirmed in comparative studies of phantom and clinical power spectra
and parenchymal texture. We present a novel method for simulating the hierar-
chical organization of breast tissue subcompartments, seen in detailed histologi-
cal images. The subcompartmentalization introduces microstructure in breast
phantoms, resulting in improved realism of phantom images. The qualitative
validation of phantoms with simulated microstructure is discussed in this paper;
the quantitative validation in ongoing.

Keywords: Software breast phantoms, virtual clinical trials, small-scale tissue

simulation, stereology, testing realism.

1 Introduction

Virtual clinical trials (VCTs) have received considerable attention recently; a VCT is
an efficient way to perform optimization and preclinical validation of novel breast
imaging systems (1, 2). VCTs are based upon sophisticated computer simulations of
breast anatomy, image acquisition, image processing and display. The synthetic im-
ages generated by VCT can be assessed by model or human observers.
The quality of a VCT depends upon a number of factors including phantom
realism; the phantom realism needs to be commensurate with the diagnostic task in
question. The University of Pennsylvania (UPenn) breast anatomy model is based
upon the simulation of large-scale and meso-scale anatomical structures; a variety of
features are modelled, including the overall breast outline, the skin, the matrix of
Cooper’s ligaments and tissue compartments, and the assignment of adipose and fi-
broglandular tissue to these compartments.(3) The validity of this design has been
confirmed for a number of tasks, and the visual realism of the anatomy model is

H. Fujita, T. Hara, and C. Muramatsu (Eds.): IWDM 2014, LNCS 8539, pp. 348–355, 2014.
© Springer International Publishing Switzerland 2014
 Realistic Simulation of Breast Tissue Microstructure 349

supported by a number of comparative studies of phantom and clinical power spec-

tra (4, 5) and parenchymal texture (6-8).
That said, we are constantly striving to improve the breast anatomy model further.
In this paper, we present a novel method for simulating the hierarchical organization
of breast tissue subcompartments, seen in detailed histological images. The introduc-
tion of a hierarchy of subcompartments into our breast anatomy model results in more
realistic phantom images.

2 Methods

2.1 Histological Analysis

Our existing method for simulating breast tissue structures was motivated by the ob-
served appearance of tissue compartments in existing histology and computed tomo-
graphy breast images. In this paper we present a new analysis of histology slices
from two breasts specimens; one obtained after breast reduction and another after
mastopexy. The patients were aged 33 and 50, respectively. No abnormalities were
detected in the two analysed breast specimens. The histologic analysis was per-
formed at the University of Padova, Italy. Ten histology slices were analysed, at
least one slice from each breast quadrant.

(a) (b)
Fig. 1. An example of a breast histology image used in the size and shape analysis of adipose
tissue compartments: (a) histology section with the Azan-Mallory staining; two analysed com-
partments are highlighted; (b) a binarized version of the same histology section

Fig. 1(a) shows a detailed microscopic image of the breast obtained using Azan-
Mallory staining. The Azan-Mallory staining technique combines the original Mallory
350 P.R. Bakic et al.

connective tissue stain with azocarmine (9); as a result, collagen is stained blue, nuclei
and cytoplasm are red, and elastic fibres are pink or unstained. The section in Fig. 1(a)
is oriented so that the areolar region is superior. In this example, the adipose tissue
compartments are clearly encapsulated by the blue stained Cooper’s ligaments. Two
individual compartments have been highlighted to illustrate this observation.
Digital images of the stained histologic slices were binarized by thresholding. A
binarized image of the matching tissue section is shown in Fig. 1(b). The binarized
sections were used to estimate the size and shape of the tissue compartments. Two
parameters, mean volume and axial ratio, were calculated using the stereological un-
folding method by Saltykov, which assumes an ellipsoidal compartment shape (10).
From this, compartment size and shape distributions were calculated.
Examination of Fig. 1 suggests that the thickness of the Cooper’s ligaments de-
pends upon the volume of the associated compartments. Thus, we have also esti-
mated the volumetric fraction of the connective tissue and the average thickness of the
Cooper’s ligaments.
Finally, as seen in Fig. 1(a), the individual adipose compartments appear to be di-
vided into smaller compartments by interlobular fibrous septa. Due to their small
thickness, these interlobular fibrous septa may not be clearly visible in clinical breast
images; however, they certainly contribute to the small-scale tissue variations seen in
clinical images. The combination of the thicker Cooper’s ligaments and the thinner
interlobular fibrous septa indicate a hierarchical organization of tissue compartments.
This observation has motivated the modification of our breast anatomy model.

2.2 Computer Simulation

In order to increase the realism of our breast anatomy model, we have included a
simulation of subcompartments with septa of reduced thickness. We begin by simu-
lating a baseline phantom, P, containing large compartments and correspondingly
thick ligaments. We then simulate a second subcompartment phantom, S, having the
same size and outline as the baseline phantom, containing smaller compartments and
thinner ligaments; the internal structure of the second phantom will form the structure
of the subcompartments. The final phantom is obtained by superimposing the sub-
compartment phantom on the baseline phantom. Algorithmically, a voxel vp(x,y,z) of
P at spatial coordinate x,y,z is replaced by the corresponding voxel vs(x,y,z) of S if and
only if vs(x,y,z) is part of a ligament in S, and vp(x,y,z) belongs to a compartment in P.
We tested this method with a set of preliminary models in which each compart-
ment in P was divided on average into thirty subcompartments. In this test, we simu-
lated baseline phantoms with 333 compartments and subcompartment phantoms with
10,000 compartments. The simulated thickness of the interlobular fibrous septa was
selected to be 200μm in the subcompartment phantoms, 3 times smaller than the
600μm thickness of the primary Cooper’s ligaments in the baseline phantoms.
The simulated microstructure was assessed subjectively based upon synthetic
mammographic projections of phantoms with or without subcompartments. The
synthetic images were generated using the breast anatomy and imaging simulation
 Realistic Simulation of Breast Tissue Microstructure 351

pipeline, developed at the University of Pennsylvania for the purpose of conducting

VCTs of breast imaging systems (1). The pipeline includes modules for the simula-
tion of normal breast anatomy, insertion of lesions, breast positioning and deforma-
tion, clinical image acquisition, image reconstruction and post-processing, image
display, and image interpretation by model observers. External modules may be
included in the pipeline as plugins.
The software breast phantoms with and without subcompartments were subject to
simulated mammographic compression using a finite element deformation method
(11). Mammographic imaging was then simulated using a ray tracing projection
method, assuming a poly-energetic x-ray beam without scatter, and an ideal detector
model. The quantum noise was simulated by adding a random Poisson process.
The simulated image acquisition geometry corresponds to the Hologic Selenia Di-
mensions full-field digital mammography system (Hologic Inc., Bedford, MA). The
resulting synthetic raw projections are post-processed using a commercial software
package (Adara, Real Time Tomography, Villanova, PA).

3 Results and Discussion

3.1 Histological Analysis

Table 1 gives the values of average compartment volume, axial ratios and ligament
thickness, as estimated from histology slides, in three different regions of the breast:
subcutaneous (“Sub-Q”), posterior, and periglandular. These values have been aver-
aged over 30 analysed adipose compartments. Adipose tissue compartments have a
larger volume in the subcutaneous (0.84 ml) and posterior (0.94 ml) regions, as com-
pared to the periglandular region (0.26 ml). Visually, these estimates of compart-
ment volume agree with the observed appearance of breast tissue structures in these
regions of clinical images.
The orientation of the breast tissue compartments had relatively little dependence
upon region; the axial ratio varied from 2.02 in the subcutaneous region to 2.91 in the
posterior region. This range of axial ratios corresponds to an angular difference of
just 7 degrees. The variation in angular ratios is considerably larger in the posterior
region (0.30; i.e., 10% of the average angular ratio), as compared to the subcutaneous
region (0.14; 6%) and periglandular region (0.12; 6%). This suggests that some un-
derlying structure may exist in these areas, which constrains the shape and orientation
of the compartments.
Table 2 shows the volume fraction and thickness of the connective tissue, esti-
mated from the binarized images of the stained Cooper’s ligaments. The tabulated
values have been averaged over 10 analysed tissue slices. The estimated average
volume fraction was 12.3%, while the average thickness of Cooper’s ligaments was
289 μm. The estimated ligament thickness fits well within the range of thicknesses
used in our previous computer simulation of Cooper’s ligaments: 200-600 μm. The
volume fraction showed 11% variation relative to the mean value, while the ligament
thickness showed 5% variation relative to the mean value.
352 P.R. Bakic et al.

Table 1. Average values of compartment volumes and axial ratios in various breast regions,
estimated from breast histological sections

Region Volume (cm3) Axial ratio

Sub-Q 0.84 ± 0.04 2.02 ± 0.14
Posterior 0.94 ± 0.07 2.91 ± 0.30
Periglandular 0.26 ± 0.01 2.04 ± 0.12

Table 2. Average values of the connective tissue volume fraction and thickness, estimated from
Cooper’s ligaments in breast histological sections

Volume fraction (%) Thickness (μm)

Cooper’s ligaments 12.3 ± 1.4 289.2 ± 13.0

3.2 Computer Simulation

Fig. 2 shows preliminary results of the simulation of subcompartments in a breast
phantom. Fig. 2(a) show a cross-section of a baseline phantom simulated with

(a) (b) (c) (d)

Fig. 2. Simulation of breast tissue microstructure by subcompartmentalization. Shown are
sections of a software phantom (a) with and (b) without subcompartments, with corresponding
synthetic mammographic projections (c) with and (d) without subcompartments.
 Realistic Simulation of Breast Tissue Microstructure 353

subcompartments, while Fig. 2(b) shows the same phantom without subcompart-
ments. Figs. 2(c-d) show the corresponding synthetic mammographic projections of
these phantoms. In both cases, the phantoms have a total volume of 450 cm3, with
100 μm voxels. Subjectively, the projection image of the subcompartmentalized
phantom shows a higher level of realism. The simulated parenchymal pattern is en-
riched by the addition of small-scale structures. In addition, the simulated Cooper’s
ligaments appear less prominent and less geometric, as compared to the projection of
the phantom without subcompartments.
A quantitative analysis was performed by comparison of the Laplacian Fractional
Entropy (LFE) in clinical and synthetic images. The LFE measure describes the
relative content of non-Gaussian statistics in breast images (12). The LFE analysis of
the phantoms confirmed that the addition of subcompartments yields a considerable
improvement in the LFE measure; the phantom with subcompartments is much closer
to clinical images (8). The results of the LFE analysis are shown in Fig. 3. At low
spatial frequencies, the phantom without subcompartments exceeds the LFE estimated
in clinical mammograms. The peak LFE value of 92% occurs at 0.35 cyc/mm. At
spatial frequencies above this peak, the LFE drops to zero at 1.0 cyc/mm. Subcom-
partmentalization reduces the LFE values, thus matching closely those estimated in
mammograms. Based upon our current simulation method, subcompartmentalization
increases the simulation time proportional to the square root of the number of com-
partments. This may be potentially prohibitive for real-time VCT simulations. As a
viable alternative, we could pre-compute a number of subcompartment phantoms to
be combined randomly with baseline phantoms created in real time.

Fig. 3. Laplacian Fractional Entropy (LFE) as a function of spatial frequency, estimated from
phantoms generated with and without subcompartments. The phantom LFE values are shown
in comparison with those estimated from clinical mammograms and simulated Gaussian noise.
Error bars show ±1 standard deviation. (Reproduced with permission from Ref. #8.)
354 P.R. Bakic et al.

Our future work will include a more detailed analysis of phantoms containing sub-
compartments, and a more complete exploration of the various simulation parameters
for each of the tissue regions analysed in this work (subcutaneous, deep, and
periglandular). In this way, we hope to add spatial dependence to our anatomy simu-
lation method, further improving realism.

4 Conclusions

We have simulated the microstructure of breast tissue by adding subcompartments to

our current design of anthropomorphic breast phantoms. This modification was mo-
tivated by the hierarchical organization of Cooper’s ligaments and interlobular fibrous
septa, as shown by Azan-Mallory stained breast histologic slices.
Subjectively, synthetic images of phantoms with subcompartmentalization show an
improved level of realism; the simulated parenchymal pattern has been enriched,
while the simulated Cooper’s ligaments appear less geometric. The observed im-
provement in the appearance of phantom images is in agreement with a preliminary
quantitative validation based upon Laplacian Fractional Entropy analysis.

Acknowledgements. This work was supported in part by the US National Institutes

of Health (R01 grant #CA154444), the US Department of Defense Breast Cancer
Research Program (HBCU Partnership Training Award #BC083639), the US National
Science Foundation (CREST grant #HRD-0630388 and III grant # 0916690), and the
US Department of Defense/Department of Army (45395-MA-ISP, #54412-CI-ISP,
W911NF-11-2-0046), and the Delaware IDeA Network of Biomedical Research Ex-
cellence award. The content is solely the responsibility of the authors and does not
necessarily represent the official views of the NIH, NSF and DoD. The authors are
thankful to Drs. Veronica Macchi, Andrea Porzionato, and Cesare Tiengo from the
University of Padova for preparing histological breast slides and performing the
stereological analysis, and to Ms. Susan Ng from Real-Time Tomography (Villanova,
PA) for processing simulated projection images. ADAM is a scientific advisor to
Real-Time Tomography.

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