Flow in elastic networks subject to pulsatile forcing

Abstract

The hemodynamics of a vascular vessel network can be affected by the presence of obstructions. We present a theoretical analysis of the effect that obstructions have on a vessel network under pulsatile inlet pressure, and analyze the importance of the level in which obstructions occur. The elasticity of the vessels is implemented following a recently developed model. Flow and pressure along the network are calculated for a network of equal vessels and for a network that follows Murray's law for radii. The effect of obstructions is evaluated in terms of an effective response, which relates the pressure difference, between the inlet and the outlet of the network, with the blood flow. Our calculations reveal that results obtained for a rigid network and those obtained by taking into account the elasticity of the vessel walls, are qualitatively different. The response of the network when a certain degree of obstruction is present is highly dependent on the level at which the obstructions occur