Objective grading of prostate carcinoma based on fractal dimensions: Gleason 3 + 4= 7a ≠ Gleason 4 + 3 =7b

Abstract

Significant intra- and interobserver variability ranging between 40 and 80% is observed in tumor grading of prostate carcinoma. By combining geometric and statistical methods, an objective system of grading can be designed. The distributions of cell nuclei in two-dimensional patterns of prostate cancer classified subjectively as Gleason score 3+3, 3+4, 4+3, 4+4, 4+5, 5+4, and 5+5 were analyzed with algorithms measuring the global fractal dimensions of the Rényi family and with the algorithm for the local connected fractal dimension (LCFD). The dimensions for global fractal capacity, information, and correlation (standard deviation) were 1.470 (045), 1.528 (046), and 1.582 (099) for homogenous Gleason grade 3 (n = 16), 1.642 (034), 1.678 (041), and 1.673 (084) for homogenous Gleason grade 4 (n=18), and 1.797 (042), 1.791 (026), and 1.854 (031) for homogenous Gleason grade 5 (n=12), respectively. The LCFD algorithm can be used to distinguish both qualitatively and quantitatively between mixed and heterogeneous patterns, such as Gleason score 3+4=7a (intermediate risk cancer) and Gleason score 4+3=7b (high-risk cancer). Sensitivity of the method is 89.3%, and specificity 84.3%. The method of fractal geometry enables both an objective and quantitative grading of prostate cancer.