Investigation into the diversity in the fractal dimensions of arterioles and venules in a microvascular network – A quantitative analysis

Abstract

Fractal dimension is a robust fractal parameter for estimating the morphology of vascular networks. It reflects the property of vascular networks that may vary and thus, differentiate between individual networks and/or identify physiological and pathological conditions. As such, fractal dimension differs also between arteriolar and venular compartments, yet the underlying reason is so far unclear. In order to understand the mechanisms behind these differences, we quantitatively analyzed the impacts of vessel attributes on the fractal dimension. Fractal dimension and vessel attributes given by vessel density (VD), vessel length density (VL), and diameter index (DI=VD/VL) were analyzed in three microvascular networks of the rat mesentery, which were reconstructed from experimental data. The results show that differences in diameter between arterioles and venules are primarily responsible for arterio-venous differences in fractal dimension. Moreover, multiple linear regression analysis demonstrates that the sensitivity of the variation of fractal dimension to vessel length and diameter varies with the type of the vessels. While the change of vessel length contributes 57.8 ± 3.4% to the variation of arteriolar dimension, vessel diameter contributes 63.9 ± 4.8% to the variation of venular dimension. The present study provides an explanation for the different fractal dimension and dimension variation in arteriolar and venular compartments. It highlights the importance of estimating the fractal dimensions of arterioles and venules separately, which will enhance the ability of feature extraction by fractal analysis in physiological and clinical application.