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The practical utility of computational biology is far-reaching, and it involves various aspects concerned with understanding biological phenomena in general, and gaining insights in the areas of health, biotechnology, and the environment, among others. In recent years, several research projects have been directed toward the health sector, with many of them studying mathematical and computational methods for computer-aided detection or diagnosis (CAD) of various diseases. At present, an effective screening technique for breast cancer is mammography, which helps to identify significant variations in the glandular tissue and appearance of tumoral lesions in the breast. Several CAD systems have been developed to support radiologists in the area of mammography; such systems can identify anomalous regions and masses with unusual morphological structure and abnormal density patterns.
When assessing an opacity in a mammogram, the following characteristics are taken into consideration: shape, definition or sharpness of the edges, roughness of the contour, variations in density or texture, and size. The regularity of the contour of a mass is the first parameter assessed: benign masses are often smooth, rounded, well-circumscribed, and surrounded by a halo of fairly low-density fat, whereas opacities with irregular contours and ill-defined edges are more likely to be malignant tumors. A malignant tumor is often characterized by the presence of spicules (a stellate lesion typical of infiltrating ductal carcinoma, for example) and by a poorly defined irregular contour, one that could be considered to be a fractal pattern. The term carcinoma, from the Greek word for "crab," was coined by Hippocrates; it indicates the infiltrative characteristics of a tumor as well as its ability to attack neighboring structures. Regardless, there are cases of malignant tumors with regular contours and benign masses with fractal-like contours; such cases are challenging for a physician to diagnose and make it difficult to build a classification model, leading to false negatives and false positives. These observations have led to the idea of applying the concept of fractal dimension (FD) to analyze the contours of breast lesions. As will be demonstrated in this chapter, fractal analysis can characterize the degree of complexity of a contour or shape, and can provide parameters to discriminate between benign masses and malignant tumors.
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