Multiscale methods for modeling tissue perfusion and angiogenesis:a work in progress

Speaker: Joao Silva Soares
Affiliation: Center for Mathematics and its Applications - ITL Lisboa
When: Tuesday 24th May 2011
Time: 12:15:00
Abstract: D̢۪Angelo, Zunino and Quarteroni have developed a multiscale methodology to handle numerically complex problems that arise naturally in microcirculation and perfusion of biological tissues through networks of vascular beds. The problem is composed by two scales: (i) at the macroscale, the tissue is treated as a homogenized porous media, usually saturated with plasma where relevant chemical species diffuse, advect and react; and (ii) the microscale is a finite and discrete network of small vessels (arterioles and capillaries), from which plasma permeates, and are naturally considered as a network of one dimensional models of fluid flow in circular tubes. Starling̢۪s filtration law, a widely established description of the permeation of plasma from the arteriole into the tissue, couples both scales in a nonlinear fashion, i.e. the amount of fluid delivered from the vessel into the tissue (or vice versa) generally depends locally on the dependent variables of both scales.