A Computational Model of Microcirculatory Network Structure and Transient Coronary Microcirculation

Detailed existing studies on microvessels are combined within a biophysically-based modeling framework to construct a mathematical and computational model of the coronary microcirculation. Morphometric data of porcine coronary arteries, veins and capillaries are used to build a network structure of a capillary bed. The Poiseuille flow steady state equations are solved on the capillary model and coupled to a transient, finite difference flow model applied to the arteriole/venule networks. The coupling of the two schemes is achieved using a non-linear root-finding algorithm which seeks to satisfy the flow and pressure conditions at the interfacing vessels simultaneously. Convergence is achieved rapidly in a small-scale network. Empirical models of phase separation and Fahraeus-Lindqvist effect are incorporated to account for the non-Newtonian properties of blood in microvessels. Apparent blood viscosity is modeled as a function of vessel diameter and hematocrit (volume fraction taken up by red blood cells) and their solution is iterated at each time step of the finite difference scheme. The resulting algorithm is able to assess the transient flow occurring in a spatially-heterogeneous network while maintaining its computational efficiency and the biophysical basis.