Finite element analysis of blood flow through biological tissue

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 xo. 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. The correspondence between the finite element results and the network results strongly depends on the quantification of the hierarchy, which should be closely related to the hierarchical fluid pressure. Two methods for hierarchical quantification have been used, one of which is based on the network fluid pressure and the other on the segment diameters. With the first method a good correlation between x0 and fluid pressure, and consequently a good correspondence between finite element and network results, are found. The second method yields a poor correlation between xo and fluid pressure. However, still satisfying correspondence between finite element and network results is found.