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Why the Presence of Point-Wise ("Punctate") Calcifications or Linear Configurations of Calcifications Makes Breast Cancer More Probable: A Geometric Explanation

When a specialist analyzes a mammogram for signs of possible breast cancer, he or she pays special attention to point-wise and linear-shaped calcifications and point-wise and linear configurations of calcification – since empirically, such calcifications and combinations of calcifications are indeed most frequently associated with cancer. In this paper, we provide a geometric explanation for this empirical phenomenon. 1 Signs of Breast Cancer Early diagnostics of breast cancer is important. Breast cancer is curable if detected early. One of the most frequently used methods of detecting breast cancer is regular mammography. When a mammogram shows calcifications, a specialist determines whether these calcifications are indicative of the cancer. If yes, additional tests are performed (such as biopsy) that enable the doctors to diagnose cancer and start the treatment. How specialists diagnose breast cancer. Calcifications are classified as suspicious based on the size of the classification and on the geometric shape of their configuration; see, e.g., [3, 4]. Specifically, in terms of size: • small, point-wise (“punctuate”) calcifications are highly suspicious, while • larger-size calcifications are considered benign. In terms of configurations: • calcification that group together in a small area (point) or that form a straight line are suspicious, while