FRACTAL DIMENSIONS OF MYCOSIS FUNGOIDES

Abstract

Prior to an investigation of early diagnosis of mycosis fungoides (MF) using fractal geometry, we set out to see if MF lesions are fractal in nature. We analyzed three aspects of MF lesions: the dermoepidermal profile of photomicrographs of patch stage lesions and normal skin, the perimeter of patch and plaque stage lesions, and the size distribution of patch and plaque lesions on the skin surface. The perimeter of plaque lesions was measured on close-up photographs by the divider walk method using various step sizes. Based on the perimeter values, the fractal dimension was determined. The dermoepidermal profile of MF patch lesions was analyzed by the divider walk method for self-affine fractals. The size distribution of MF patch and plaque lesions was determined by counting the number of patch and plaque lesions with an area greater than or equal to a specific size A on scaled photographs of a 19.6 cm × 19.6 cm affected region. A plot of number of lesions with area greater than or equal to A vs. lesion area on log-log paper allows the detection of a power-law distribution, indicative of one type of self-similar fractals. The dermoepidermal profile of patch stage lesions and normal skin was found to be self-affine fractals. Global measurements of normal thin skin and of patch stage lesions were distinct. All observed patch and plaque lesion area distributions were a fractal set. The perimeter of non-confluent plaque lesions was not fractal. This work revealed fractal dimensions in two aspects of MF lesions. Further investigation of application of fractal geometry to the diagnosis and staging of MF is planned.