Evaluation of Breast Ductal Networks Using Ramification Matrices

We evaluated the use of ramification (R-) matrices in analysis and modeling of breast ducts. The elements of an R-matrix are the branching probabilities at different tree levels. The analysis was performed on 10 normal and 13 benign galactograms. The ductal trees were manually segmented from the galactograms and corresponding R-matrices were inferred. Effects of segmentation were tested by successively removing each of the terminal branches and computing the corresponding matrices on the clinical galactograms and a large number of synthetically generated ductal trees. We also examined a classification scheme to distinguish between normal and benign galactograms based upon the matrix coefficients. The classification using the r3,3 coefficient performed correctly for 90% of normal and 62% of benign cases (p=0.027).