Fractal Analysis of Mammographic Parenchymal Patterns in Breast Cancer Risk Assessment1

Rationale and Objectives

To evaluate fractal-based computerized image analyses of mammographic parenchymal patterns in the task of differentiating between women at high risk and women at low risk for developing breast cancer.

Materials and Methods

The fractal-based texture analyses are based on a box-counting method and a Minkowski dimension, and were performed within the parenchymal regions of normal mammograms. Four approaches were evaluated: 1) a conventional box-counting method, 2) a modified box-counting technique using linear discriminant analysis (LDA), 3) a global Minkowski dimension, and 4) a modified Minkowski technique using LDA. These fractal based texture features were extracted from regions of interest to assess the mammographic parenchymal patterns of the images. Receiver operating characteristic analysis was used to evaluate the performance of these features in the task of differentiating between the two groups of women.

Results

Receiver operating characteristic analysis yielded an A_z value of 0.74 based on the conventional box-counting technique and an A_z value of 0.84 based on the global Minkowski dimension in the task of distinguishing between the two groups. By using LDA to assess the characteristics of mammograms, A_z values of 0.90 and 0.93 were obtained in differentiating the two groups, for the modified box-counting and Minkowski techniques, respectively. Statistically significant improvement was achieved (P < .05) with the new techniques compared to the conventional fractal analysis methods. A simulation study, which used the slope and intercept extracted from the least square fit of the experimental data with the LDA approaches, yielded A_z values similar to those obtained with the conventional approaches in the task of differentiating between the two groups.

Conclusions

The proposed LDA approach improved significantly the separation between the two groups based on experimental data. Because this approach was used as a linear classifier rather than as a regression function, it combined the fractal analysis with the knowledge of the high- and low-risk patterns, and thus better characterized the multifractal nature of the parenchymal patterns. We believe that the proposed analyses based on the LDA technique to characterize mammographic parenchymal patterns may potentially yield radiographic markers for assessing breast cancer risk.

Key Words: Fractal analysis, image analysis, risk assessment, texture analysis, mammographic parenchymal patterns