Shape Analysis of Simulated Breast Anatomical Structures

Recent advances in high-resolution 3D breast imaging, namely, digital breast tomosynthesis and dedicated breast CT, have enabled detailed analysis of the shape and distribution of anatomical structures in the breast. Such analysis is critically important, since the projections of breast anatomical structures make up the parenchymal pattern in clinical images which can mask the existing abnormalities or introduce false alarms; the parenchymal pattern is also correlated with the risk of cancer. As a first step towards the shape analysis of anatomical structures in the breast, we have analyzed an anthropomorphic software breast phantom. The phantom generation is based upon the recursive splitting of the phantom volume using octrees, which produces irregularly shaped tissue compartments, qualitatively mimicking the breast anatomy. The shape analysis was performed by fitting ellipsoids to the simulated tissue compartments. The ellipsoidal semi-axes were calculated by matching the moments of inertia of each individual compartment and of an ellipsoid. The distribution of Dice coefficients, measuring volumetric overlap between the compartment and the corresponding ellipsoid, as well as the distribution of aspect ratios, measuring relative orientations of the ellipsoids, were used to characterize various classes of phantoms with qualitatively distinctive appearance. A comparison between input parameters for phantom generation and the properties of fitted ellipsoids indicated the high level of user control in the design of software breast phantoms. The proposed shape analysis could be extended to clinical breast images, and used to inform the selection of simulation parameters for improved realism. Keywords: Breast anatomy simulation, software breast phantoms, shape analysis, ellipsoidal fitting, Dice coefficient 1. INTRODUCTION One hundred and seventy years ago, Sir Astley Cooper published the first qualitative analysis of the distribution and shape of adipose tissue compartments in the breast. These compartments are formed by fibrous tissue septa, eponymously named Cooper’’s ligaments, which provide structural stability to the breast. Projections of Cooper’’s ligaments make up part of the parenchymal pattern in clinical breast images, which can influence cancer detection by masking the existing abnormalities or introducing false alarms. The parenchymal pattern is characterized using texture analysis of clinical images, and has been correlated with the risk of breast cancer. A direct quantification of the underlying breast anatomical structures was not possible until the recent advent of high resolution 3D clinical imaging modalities, namely, digital breast tomosynthesis and dedicated breast computed tomography. We have proposed a new method for shape analysis of breast anatomy by fitting ellipsoids to adipose tissue compartments. The ellipsoidal semi-axes were calculated by matching the moments of inertia of each individual compartment and of an ellipsoid. In this paper, the method is demonstrated on the analysis of simulated tissue compartments of an anthropomorphic software breast phantom. The software phantom of the breast was recently developed at the University of Pennsylvania for use in pre-clinical validation of breast imaging systems. A competitive * Joint first authorship. !"#$%&'()*&+$,+(-./-0(1234$%4(56(!"#$%&'()*&+$,+7("#$8"#(93(:5;9";8(<=(1"'%7(>59";8(!=(:$42$?&@&7(A;B%"(>=(C2$8$,+7 1;5%=(56(D1)E(F5'=(GH/H7(GH/HI<(J(K(-./-(D1)E(J(LLL(%5#"0(/M.NOPI--Q/-QR/G(J(#5$0(/.=///PQ/-=S/--PN 1;5%=(56(D1)E(F5'=(GH/H((GH/HI<O/ Downloaded From: http://proceedings.spiedigitallibrary.org/ on 09/24/2013 Terms of Use: http://spiedl.org/terms interaction of simulated compartments results in their irregular shape, qualitatively mimicking real breast anatomy. The properties of the fitted ellipsoids are used for characterization of various classes of anthropomorphic software phantoms with qualitatively distinctive appearance. Based upon these properties, we assessed the relationship between the input parameters of the simulation and the final appearance of the breast phantoms. In the long term, the proposed method could be extended to include shape analysis of real breast tissue (from clinical breast images or histological specimen). Such analyses would allow an informed selection of simulation parameters, aimed at improving the realism of anatomy simulation. 2. METHODS 2.1. Software breast phantoms The X-ray Physics Lab at the Univ. of Pennsylvania has over 15 years of experience in developing breast anthropomorphic software phantoms. The anthropomorphic software breast phantom used in this study is based upon recursive partitioning of the simulated breast volume using octrees. The octree-based simulation allows for fast generation of phantoms with very small voxel size. Control of the phantom is provided through selection of input parameters which specify the simulated breast size, glandularity, thickness of the skin and Cooper’’s ligaments, and the number, distribution, and size and shape of adipose compartments. The proposed shape analysis is used here to investigate the relationship between the properties of simulated tissue compartments and the corresponding input parameters, thus reflecting the level of user control over the phantom appearance. In this study, we have specifically focused on the effect of 2 parameters related to the relative size (rS) and the relative orientation, (i.e., aspect ratios, rO) of simulated tissue compartments. The simulated compartments are specified by shape functions fi(x), i=1,…..., K, consistent with the quadratic decision boundaries described by a maximum a posteriori (MAP) classifier: 1 1 det log 2 1 log 2 1 i i i i T i i q f s x s x x , (1) where K is the number of compartments, x is the 3D coordinate within the phantom volume, si (sxi, syi, szi) are compartment seed vectors, 1 i are positive definite matrices, and qi , (0 qi 1) are parameters corresponding to distribution priors in MAP. We define the relative size and orientation of a simulated compartment using the matrix 1 i , with eigenvalues 1/kai , 1/kbi, 1/kci and eigenvectors i nˆˆ , i uˆˆ , i vˆˆ :