Deformation-Dependent Effective Vascular Permeability of a Biological Tissue Containing Parallel Microvessels

Abstract

This study describes a micromechanics model for estimating the effective vascular permeability for a biological tissue containing parallel microvessels subjected to finite deformations. The representative volume element in the proposed model consists of a hollow cylinder with the inner radius being the microvessel radius and the outer radius determined using the volume fraction of the microvessels in the tissue. The effective vascular permeability is determined using the Poiseuille equation for the microvascular flow, Darcy's law for the homogenized porous tissue, and finite deformation of the tissue matrix modeled as a nonlinear elastic material. The numerical results show that the effective vascular permeability decreases with an increase in the applied pressure on the tissue. The effective permeability can be significantly larger than the reference permeability when the applied pressure is much smaller than the microvascular pressure. On the other hand, the effective permeability becomes less than 30% of the reference permeability when the applied pressure is greater than two times the microvascular pressure. Finally, the effective vascular permeability increases monotonically with an increasing ratio of the deformed volume to the reference volume of the tissue.