Fractal geometric analysis of colorectal polyps

Abstract

Colorectal polyps have a subjectively self-similar structure which suggests that these structures may have fractal elements and that the fractal dimension may be a useful morphometric discriminant. The fractal dimensions of images from haematoxylin and eosin-stained sections of 359 colorectal polyps (214 tubulovillous adenomas, 41 'pure' tubular adenomas, 29 'pure' villous adenomas, 68 metaplastic polyps, and 7 inflammatory polyps) were measured using a box-counting method implemented on a microcomputer-based image analysis system. Results were assessed using polychotomous logistic regression, confusion matrices, and kappa statistics. All examined polyps were shown to have a fractal structure in the range of scales examined. The fractal dimension was significantly different between different diagnostic categories (P < 0.0001) and was a useful discriminant between these categories (kappa statistic 0.60 for the confusion matrix with size as the other variable). The fractal dimension did not shown any significant correlation with the grade of epithelial dysplasia (P > 0.05). This study shows that colorectal polyps have a fractal structure over a defined range of magnification and Euclidean morphometric measurements will be invalid outside precisely defined conditions of resolution and magnification. The fractal dimension is a better way of quantitating the polyp shape and is a useful morphometric discriminant between diagnostic categories.