Effect of dispersion of vessel diameters and lengths in stochastic networks. I. Modeling of microcirculatory flow

A microvascular network model is proposed with random arrangement and random dimensions of vessels. In addition to stochasticity of the topological characteristics of the model networks, as previously introduced by Fenton and Zweifach (1981, Ann. Biomed. Eng., 9, 303-321), the vessel diameters and lengths are treated as random variables following certain probability distributions for each vascular order. Flow and pressure distributions are calculated for each network configuration assuming a linear relationship between the blood flow rate and pressure drop for each vascular segment. The mean, coefficient of variation, skewness, kurtosis, and histograms of the hemodynamic variables are computed using an ensemble of random networks. The results indicate that dispersion of vessel diameters and lengths may significantly affect the distributions of microvascular variables such as capillary flow and pressure, and the flow distribution at bifurcations. It is shown that the dispersion of vessel diameters causes a decrease of total flow whereas the dispersion of lengths causes its increase.