Fractal dimension can distinguish models and pharmacologic changes in liver fibrosis in rats

Abstract

Fractal analysis measures the complexity of geometric structures. The aim of this study was to evaluate the feasibility and accuracy of fractal analysis in liver fibrosis. A total of 77 rats were included: 10 sham, 46 with fibrosis secondary to bile duct ligation (BDL), and 21 with fibrosis due to CCl₄ intoxication. Measurements included the fractal dimension of Kolmogorov (D_k), histologic lesions, the area of fibrosis by image analysis, liver hydroxyproline content, messenger RNA fibronectin, serum hyaluronate level, and portal pressure. Fibrotic rats were given placebo, octreotide, or O²-vinyl 1-(pyrrolidin-1-yl)diazen-1-ium-1,2-diolate (V-PYRRO/NO). Intraobserver agreement of D_k was excellent with the intraclass (ic) correlation coefficient r _ic = 0.91 (P < .0001) as well as the interobserver agreement with r _ic = 0.88 (P < .001). D_k was correlated with other measurements or markers of fibrosis: the area of fibrosis (r = 0.75; P < .0001), hydroxyproline content (r = 0.51; P < .001), serum hyaluronate level (r = 0.52; P < .001), and portal pressure (r = 0.52; P < .01). D_k was significantly different between the 2 models of fibrosis (P < .0001), unlike the area of fibrosis, and this relationship was independent of other histologic lesions. The significant decrease in fibrosis observed with octreotide or V-PYRRO/NO was similarly reflected by D_k or the area of fibrosis. The diagnostic accuracy for the fibrosis model was 97% with the 5 main measurements or markers of fibrosis studied, with D_k isolated at the first step by stepwise analysis. In conclusion, fractal analysis is suitable for analyzing liver fibrosis and has excellent reproducibility. This is the only quantitative morphometric method that can discriminate among the models of fibrosis and is sensitive enough to detect pharmacologically induced changes in liver fibrosis.