Fractal dimension analysis shows relations between varicose venous patterns and their response to treatment

Similarity fractal dimensions may predict clinical outcomes of Varithena treatment for superficial varicose veins of the great saphenous vein. Eight patients with symptomatic varicose veins received Varithena treatment. Six patients were Clinical-Etiology-Anatomy-Pathophysiology (CEAP) classification C4 (skin changes), one was C5 (healed ulcer), and one was C6 (active ulcer). Standardized 2D digital photographs taken pre- and post-treatment of 143 distinct vein segments (average 17.9 segments/patient) across all participants were analyzed. Clinical results and quantitative analysis were performed following sonography, radiofrequency ablation (RFA), and Varithena injection. Tributary ratios, Strahler ordering principles, and similarity fractal dimensions based on vein radius, length, area, and volumes were determined. Treatment improved symptoms and patient-assessed appearance. With increasing Strahler order, vein tributary decreased linearly while vein length and radius increased linearly. Bifurcation ratio/length ratio and bifurcation ratio/radii ratio demonstrated similar fractal dimensions of 1.42 and 1.45, respectively, indicating a fractal nature. Higher ratios and fractal dimensions correlated with increased likelihood for additional treatment (p < 0.01). This limited-sized study demonstrates varicose veins follow fractal ordering principles. Higher fractal dimensions and ratios predicted incomplete vein occlusion, suggesting fractal analysis could enhance mathematical modeling of venous disease, potentially helping identify cases requiring additional treatment in complex presentations.