An Anthropomorphic Breast Model for Breast Imaging Simulation and Optimization

Rationale and Objectives

Optimization studies for x-ray−based breast imaging systems using computer simulation can greatly benefit from a phantom capable of modeling varying anatomical variability across different patients. This study aimed to develop a three-dimensional phantom model with realistic and randomizable anatomical features.

Materials and Methods

A voxelized breast model was developed consisting of an outer layer of skin and subcutaneous fat, a mixture of glandular and adipose, stochastically generated ductal trees, masses, and microcalcifications. Randomized realization of the breast morphology provided a range of patient models. Compression models were included to represent the breast under various compression levels along different orientations. A Monte Carlo (MC) simulation code was adapted to simulate x-ray based imaging systems for the breast phantom. Simulated projections of the phantom at different angles were generated and reconstructed with iterative methods, simulating mammography, breast tomosynthesis, and computed tomography (CT) systems. Phantom dose maps were further generated for dosimetric evaluation.

Results

Region of interest comparisons of simulated and real mammograms showed strong similarities in terms of appearance and features. Noise-power spectra of simulated mammographic images demonstrated that the phantom provided target properties for anatomical backgrounds. Reconstructed tomosynthesis and CT images and dose maps provided corresponding data from a single breast enabling optimization studies. Dosimetry result provided insight into the dose distribution difference between modalities and compression levels.

Conclusion

The anthropomorphic breast phantom, combined with the MC simulation platform, generated a realistic model for a breast imaging system. The developed platform is expected to provide a versatile and powerful framework for optimizing volumetric breast imaging systems.

Breast imaging performance is highly affected by the spatial heterogeneity of the breast structure . Furthermore, breast density varies substantially across patients of different ages . As a result, optimizing breast imaging systems across a variety of cases requires the capability of modeling the heterogeneity and variability across patients. In recent years, a number of anthropomorphic breast models have been developed for breast-related research, including physical and computerized phantoms . Physical phantoms were employed for empirical performance measurements , whereas computerized phantoms were voxelized and embedded into computerized simulations . Computerized phantoms have shown advantages in optimization research because of their low cost, ability to imitate subtle tissue structures, and ability to represent varying physical properties. These phantoms are generally characterized into two categories: those based on data from computed tomography (CT) or magnetic resonance imaging (MRI) scans , and those defined by analytical descriptions of human anatomy . Phantoms based on CT or MRI data are highly realistic, because they are built from patient data; however, they are inherently limited by the employed scanning technique (eg, finite resolution, noise pattern, artifact). Furthermore, these phantoms are not representative of the whole population, because each phantom is built from one specific patient. In contrast, phantoms based on mathematical methods are not restricted by the imaging technique. While being not as realistic, they offer a larger flexibility of parameter, enabling breast models representative of large segments of the population. Furthermore, recent studies to improve on the realism of these phantoms have included advanced mathematical concepts such as fractal structure and self-similar structure implemented to model realistic breast structures .

Based on prior research, this work focuses on developing a mathematical breast phantom with compression models, which includes skin, adipose tissue, glandular tissue, ducts, microcalcifications, and masses . The phantom presented here improves on prior work in several ways with more realistic skin boundary definition, more accurate anatomical background structure, improved ductal connections and distribution, increased number of growing features in the stochastic mass definition, added microcalcifications, and the development of a deformation algorithm that compresses the breast along various orientations into various thicknesses objects. This project further includes dedicated Monte Carlo (MC) projection simulation and iterative image reconstruction software for simulating and optimizing breast imaging modalities.

Materials and methods

Breast Phantom Construction

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Skin

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Background Texture

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P(f)=1fβ, P

(

)

where f denotes spatial frequency and the β factor denotes the Hausdorff dimension of a fractal structure . Previous research suggested that mammograms possess a mean β value of 2.83 with a standard deviation of 0.35 , and that the β value in a two-dimensional mammographic projection corresponds to the β value in the three-dimensional (3D) volume . Thus, the 3D texture in this work employed a β values randomly selected between 2.13 and 3.53 (ie, β =2.83 ± 2*0.35).

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H(u,v,w)=⎧⎩⎨⎪⎪01(u2+v2+w2√)β2u=v=w=0otherwise, H

(

)

{

(

)

where (u,v,w)∈[(−U,−V,−W),(U,V,W)], (

)

∈

[

(

−

)

(

)

]

, and U, V, and W correspond to the Nyquist frequencies in the orthogonal direction (ie, 12Δx,12Δy,12Δz, 1

, with Δx,Δy,Δz Δ

z characterizing the voxel size in three dimensions). The filtered volume representing the designed inverse power law distribution was converted to spatial domain by inverse Fourier transform, and thresholded by assigning each voxel to either a glandular or an adipose tissue value to produce the desired glandular tissue density. This thresholded matrix, however, had glandular and adipose tissue scattered and discontinued within the volume. To better imitate the pattern of background tissues, an additional smoothing process was performed to expand both the glandular and adipose region to be continuous.

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Ductal Network

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Table 1

Parameters Used in the Ductal System Simulation for a Reasonable Visual Pattern

Parameter Symbol Value Radius of level 0r 0 1 mm Length of level 0l 0 5 mm Probability of a smaller progeny_p_ 1 32% Probability of bifurcation_p_ 2 28% Probability of no new progeny_p_ 3 40% Scaling factor between radii_a_ 0.8 Factor between radius and length_b_ 8 Lower limitation of segment length_q_ 1 % 40% Upper limitation of segment length_q_ 2 % 100% Polar angle of the new branch ± (37.5° ± 10°) Azimuthal angle of the new branch_φ_ ± (15° ± 5°)

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Microcalcification

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Breast Masses

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Compression Models

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(rR)6+(zT/2)2=1,wherer2=x2+y2,y>0. (

)

(

)

where

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x’=1α√x,y’=1α√y,z’=αz. x

′

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(xR’)2+(yR’)2+(zR’)2=1,y>0. (

′

)

(

′

)

(

′

)

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(x’R)2+(y’R)2+(|z’|T/2)2.75=1,y’>0. (

′

)

(

′

)

(

′

)

2.75

′

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(xR’)2=(x’R)2,(yR’)2=(y’R)2,(zR’)2=(|z’|T/2)2.75. (

′

)

(

′

)

(

′

)

(

′

)

(

′

)

(

′

)

2.75

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Phantom and System Validation

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Dosimetric Evaluation

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D=dϵdm=dϵρdV, D

where dϵ d

ϵ denotes the local deposited energy, dm denotes the mass of the voxel, ρ ρ denotes the density of the material in the voxel, and dV denoted the volume of the voxel. A 3D dose map representing the dose distribution in the breast phantom was generated after calculating the deposited dose in each voxel.

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Results

Mammographic Simulations

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β value Validation

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Volumetric Imaging

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Dosimetry

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Discussion

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An Anthropomorphic Breast Model for Breast Imaging Simulation and Optimization

Rationale and Objectives

Materials and Methods

Results

Conclusion

Materials and methods

Breast Phantom Construction

Skin

Background Texture

Ductal Network

Microcalcification

Breast Masses

Compression Models

Phantom and System Validation

Dosimetric Evaluation

Results

Mammographic Simulations

β value Validation

Volumetric Imaging

Dosimetry

Discussion

References

Further Reading

A Dedicated General Competencies Curriculum for Radiology Residents

A Quantitative Description of the Percentage of Breast Density Measurement Using Full-field Digital Mammography

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