Basic principles and applications of fractal geometry in pathology: a review

The basic principles and prospects of fractal geometry in pathology are promising. All articles found with a PubMed search with the keywords fractal dimension (FD) and related to pathology were reviewed. All fractal objects have FDs, commonly calculated with box counting. Fractal geometry has been applied to measure the irregularities of nuclear and glandular margins to distinguish malignant lesions from benign ones, to measure the infiltrative margin of a malignant tumor, to assess tumor angiogenesis and to measure the distribution of collagen in tissue. Fractal geometry has also been applied to assess the irregular distribution of chromatin in malignant cells. Biologic model formation is possible with fractal geometry. In the future, fractal geometry may help with the diagnosis, understanding of pathogenesis and management of lesions. It may also provide new insights into disease processes.