On the Stratification of Adenocarcinomas into the Classes of Fractal Dimension Equivalence

Grading is a parameter that co-determines a risk of tumor progression. Grading is evaluated in a subjective manner during the histological examination of tumor structure. A lack of both a golden pattern for adenocarcinoma and standardization results in a high inaccuracy of the risk prediction in the statistical models. Using some histological features of adenocarcinomas, an approach based on the circular fractal geometrical model of adenocarcinomas and three global fractal dimensions of the Renyi family as the complexity measures of the spatial distribution of cancer cell nuclei was recently proposed. This study aims to validate the approach in prostate or colon adenocarcinomas. The ROC analysis demonstrated that two out of three complexity measures studied, i.e. the capacity dimension D0 and the information dimension D1 had statistically significant power to discriminate between the grades, i.e., structural classes of adenocarcinomas. The cut-off D0 values were calculated for those classes. On that basis, prostate carcinomas were restratified into seven classes of equivalence in such a manner that both sensitivity and specificity was equal 1.0. The novel cut-off D0 values for each complexity class from C1 to C7 were 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, and 1.7640, respectively. Colon carcinomas were re-stratified into three complexity classes with the cut-off D0 values 1 <; C1.6600, 1.6600 <; C2 <; 1.7670, and C3 > 1.7670. All values are in the ranges predicted by the circular fractal model. The novel classes overlap in 53% with the structural Gleason classes of prostate carcinomas, and in 25% with the subjective colon carcinoma grades. Those results validate the fractal geometrical model of adenocarcinomas. In addition, a reduction of a number of the subjective grades in prostate carcinomas could simplify grading, reduce inter- and intraobserver variability, and provide clinically useful stratification of cancer patients just into two categorie- . According to the D0-cut-off values, active surveillance would be the choice for prostate carcinomas of the class C1 and C2. Aggressive treatment should be offered for carcinomas in the class C3-C7.