Honors College

Document Type

Honors Thesis


Biomedical Engineering


Andre Khalil

Committee Members

Paula Drewniany, Christopher Mares, Karissa Tilbury, Brian Toner

Graduation Year

August 2020

Publication Date

Summer 8-2020


Breast cancer is one of the most frequent cancers among women worldwide and holds the second place in cancer-related death. Mammography is the most commonly used screening technique, however, the dense nature of some breasts makes the analysis of mammograms challenging for radiologists. The 2D Wavelet Transform Modulus Maxima (WTMM) is one mathematical approach that is used to for the analysis of mammograms. In 2014, a team from the CompuMAINE Lab characterized differences between benign microcalcification clusters (MC) from malignant MC by calculating their fractal dimension, D, with the aid of the 2D WTMM method. In a different implementation of the 2D WTMM method, this same team did research in 2017 where they quantified tissue disruption in breast tissue microenvironment using the Hurst exponent, H. The goal of this study was to further explore the potential relationship between the fractality of MC clusters and tissue disruption in the microenvironment surrounding these clusters. Statistical relationships are explored between the fractal dimension, D, of MC clusters and the Hurst exponent, H measuring tissue disruption. A “2D fractal dimension vs. Hurst exponent plot” was graphed to show this relationship used to distinguish between benign and malignant cases. In the graph, a quadrilateral region extending horizontally from Hurst value of (0.2,0.8) centered at 0.5 and stretching vertically from fractal dimension value of (1.2,1.8) centered 1.5 was identified. Analysis of this region has showed that the 60% of the malignant cases and 21% benign cases are found inside the quadrilateral for CC view and 68% of the malignant cases and 12% of benign cases are found inside the region for MLO view. As a conclusion, based on the outcomes of this study one can hypothesize that with further analyses, loss of tissue homeostasis describing the state of the microenvironment of a breast tissue and the fractal nature of MC clusters have a quantifiable relationship to distinguish benign cases from malignant cases in mammogram analysis.