A Mathematical Model for Understanding Fluid Flow Through Engineered Tissues Containing Microvessels

Abstract

Knowledge is limited about fluid flow in tissues containing engineered microvessels, which can be substantially different in topology than native capillary networks. A need exists for a computational model that allows for flow through tissues dense in nonpercolating and possibly nonperfusable microvessels to be efficiently evaluated. A finite difference (FD) model based on Poiseuille flow through a distribution of straight tubes acting as point sources and sinks, and Darcy flow through the interstitium, was developed to describe fluid flow through a tissue containing engineered microvessels. Accuracy of the FD model was assessed by comparison to a finite element (FE) model for the case of a single tube. Because the case of interest is a tissue with microvessels aligned with the flow, accuracy was also assessed in depth for a corresponding 2D FD model. The potential utility of the 2D FD model was then explored by correlating metrics of flow through the model tissue to microvessel morphometric properties. The results indicate that the model can predict the density of perfused microvessels based on parameters that can be easily measured.