Mammogram synthesis using a three-dimensional simulation. III. Modeling and evaluation of the breast ductal network

A method is proposed for realistic simulation of the breast ductal network as part of a computer three-dimensional (3-D) breast phantom. The ductal network is simulated using tree models. Synthetic trees are generated based upon a description of ductal branching by ramification matrices (R matrices), whose elements represent the probabilities of branching at various levels of a tree. We simulated the ductal network of the breast, consisting of multiple lobes, by random binary trees (RBT). Each lobe extends from the ampulla and consists of branching ductal segments of decreasing size, and the associated terminal ductal-lobular units. The lobes follow curved paths that project from the nipple toward the chest wall. We have evaluated the RBT model by comparing manually-traced ductal networks from 25 projections of ductal lobes in clinical galactograms and manually-traced networks from 23 projections of synthetic RBTs. A root-mean-square (rms) fractional error of 41%, between the R-matrix elements corresponding to clinical and synthetic images, was computed. This difference was influenced by projection and segmentation artifacts and by the limited number of available images. In addition, we analyzed 23 synthetic trees generated using R matrices computed from clinical images. A comparison of these synthetic and clinical images yielded a rms fractional error of 11%, suggesting the possibility that a more appropriate model of the ductal branching morphology may be developed. Rejection of the RBT model also suggests the existence of a relationship between ductal branching morphology and the state of mammary developmentand pathology.