Finite element analysis of blood flow through biological tissue

摘要

Quantitative analysis of blood perfusion has been performed with a hierarchical mixture model of blood perfused biological tissue, for low Reynolds steady state Poiseuillian flow through two-dimensional, computer generated, rigid, arterial vascular trees. The mixture model describes blood flow through the vasculature by spatial and hierarchical flow components, both related to the blood pressure gradient via an extended Darcy equation. The Darcy-permeability tensor is derived from the geometry of the vascular tree, the fluid viscosity, and the vascular hierarchy which is quantified by a dimensionless parameter x_0. Finite element results of fluid pressure and flow on certain levels of the hierarchy are compared to correspondingly volume averaged pressures and flows calculated by hydraulic network analysis.