Fractal properties and critical exponents in tumor
Abstract
In general, tumors exhibit irregular borders with geometrical properties which are expected to depend upon their degree of malignancy. To appropriately evaluate these irregularities, it is necessary to apply segmentation procedures on the image that clearly define the active region of the tumor and its border. In the present work, nosologic maps were obtained combining T2-weighted magnetic resonance images with in vivo magnetic resonance spectroscopy information on brain tumors. The image was segmented according to the nosologic map and tumor contours were determined. Several fractal properties were determined on the contour: the capacity or fractal dimension, the correlation dimension for a temporal series constructed from the original contour, and also a critical exponent coming from the contour roughness. The results obtained showed a good correlation between the roughness critical exponent and the degree of malignancy of the tumor.
