On complexity and homogeneity measures in predicting biological aggressiveness of prostate cancer; Implication of the cellular automata model of tumor growth.

Abstract

We propose a novel approach for the quantitative evaluation of aggressiveness in prostate carcinomas. The spatial distribution of cancer cell nuclei was characterized by the global spatial fractal dimensions D0, D1, and D2. Two hundred eighteen prostate carcinomas were stratified into the classes of equivalence using results of ROC analysis. A simulation of the cellular automata mix defined a theoretical frame for a specific geometric representation of the cell nuclei distribution called a local structure correlation diagram (LSCD). The LSCD and dispersion Hd were computed for each carcinoma. Data mining generated some quantitative criteria describing tumor aggressiveness. Alterations in tumor architecture along progression were associated with some changes in both shape and the quantitative characteristics of the LSCD consistent with those in the automata mix model. Low-grade prostate carcinomas with low complexity and very low biological aggressiveness are defined by the condition D0 < 1.545 and Hd < 38. High-grade carcinomas with high complexity and very high biological aggressiveness are defined by the condition D0 > 1.764 and Hd < 38. The novel homogeneity measure Hd identifies carcinomas with very low aggressiveness within the class of complexity C1 or carcinomas with very high aggressiveness in the class C7.