Tumorgrading beim Prostatakarzinom hat eine signifikante Intra- und Interobservervariabilität von ca. 40–80 %. Kombinierte geometrische und statistische Methoden könnten ein objektives Grading bieten.

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 R,nyi 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.

In order to analyze sympathetic nerve discharges as an entity, not as the decomposed parts, a non-linear mathematical analyzing technique including chaos and fractal theory was utilized in healthy normal subjects. Muscle sympathetic nerve activity (MSNA) was recorded using the microneurography technique during supine position and tilt up position. MSNA was integrated by the integrator and analyzed in the computer system using the non-linear mathematical analyzing technique. Time series data of the sympathetic nerve discharges were quantified in R-R interval time series data and analyzed with the Lorenz plot. Fractal dimension analysis of the MSNA was performed by the changing coarse graining level (box-counting method). Both during supine position and tilt up, MSNA showed the characteristics of fractals. After the tilt up of the bed, MSNA tone was increased and the fractal dimensions of both R-R interval and MSNA were increased. Our results suggest that MSNA tone contributed to the increases of the fractal dimension.