Shayne M Plourde1, Zach Marin1, Zachary R Smith2, Brian C Toner1, Kendra A Batchelder1, Andre Khalil3. 1. CompuMAINE Laboratory, Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA. 2. CompuMAINE Laboratory, Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA; Department of Physics and Astronomy, University of Maine, Orono, ME 04469, USA. 3. CompuMAINE Laboratory, Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA. Electronic address: andre.khalil@maine.edu.
Abstract
BACKGROUND: When screening for breast cancer, the radiological interpretation of mammograms is a difficult task, particularly when classifying precancerous growth such as microcalcifications (MCs). Biophysical modeling of benign vs. malignant growth of MCs in simulated mammographic backgrounds may improve characterization of these structures METHODS: A mathematical model based on crystal growth rules for calcium oxide (benign) and hydroxyapatite (malignant) was used in conjunction with simulated mammographic backgrounds, which were generated by fractional Brownian motion of varying roughness and quantified by the Hurst exponent to mimic tissue of varying density. Simulated MC clusters were compared by fractal dimension, average circularity of individual MCs, average number of MCs per cluster, and average cluster area. RESULTS: Benign and malignant clusters were distinguishable by average circularity, average number of MCs per cluster, and average cluster area with p<0.01 across all Hurst exponent values considered. Clusters were distinguishable by fractal dimension with p<0.05 in low Hurst exponent environments. As the Hurst exponent increased (tissue density increased) benign and malignant MCs became indistinguishable by fractal dimension. CONCLUSIONS: The fractal dimension of MCs changes with breast tissue density, which suggests tissue environment plays a role in regulating MC growth. Benign and malignant MCs are distinguishable in all types of tissue by shape, size, and area, which is consistent with findings in the literature. These results may help to better understand the effects of the tissue environment on tumor progression, and improve classification of MCs in mammograms via computer-aided diagnosis.
BACKGROUND: When screening for breast cancer, the radiological interpretation of mammograms is a difficult task, particularly when classifying precancerous growth such as microcalcifications (MCs). Biophysical modeling of benign vs. malignant growth of MCs in simulated mammographic backgrounds may improve characterization of these structures METHODS: A mathematical model based on crystal growth rules for calcium oxide (benign) and hydroxyapatite (malignant) was used in conjunction with simulated mammographic backgrounds, which were generated by fractional Brownian motion of varying roughness and quantified by the Hurst exponent to mimic tissue of varying density. Simulated MC clusters were compared by fractal dimension, average circularity of individual MCs, average number of MCs per cluster, and average cluster area. RESULTS: Benign and malignant clusters were distinguishable by average circularity, average number of MCs per cluster, and average cluster area with p<0.01 across all Hurst exponent values considered. Clusters were distinguishable by fractal dimension with p<0.05 in low Hurst exponent environments. As the Hurst exponent increased (tissue density increased) benign and malignant MCs became indistinguishable by fractal dimension. CONCLUSIONS: The fractal dimension of MCs changes with breast tissue density, which suggests tissue environment plays a role in regulating MC growth. Benign and malignant MCs are distinguishable in all types of tissue by shape, size, and area, which is consistent with findings in the literature. These results may help to better understand the effects of the tissue environment on tumor progression, and improve classification of MCs in mammograms via computer-aided diagnosis.