Computational models for fluid exchange between microcirculation and tissue interstitium

The aim of this work is to develop a computational model able to capture the interplay between microcirculation and interstitial flow. Such phenomena are at the basis of the exchange of nutrients, wastes and pharma- cological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective targeting techniques to treat vascularized tumors with drugs. We develop a model applicable at the micro- scopic scale, where the capillaries and the interstitial volume can be described as independent structures capable to propagate flow. We facilitate the analy- sis of complex capillary bed configurations, by representing the capillaries as a one-dimensional network, ending up with a heterogeneous system characterized by channels embedded into a porous medium. We use the immersed boundary method to couple the one-dimensional with the three-dimensional flow through the network and the interstitial volume, respectively. The main idea consists in replacing the immersed network with an equivalent concentrated source term. After discussing the details for the implementation of a computational solver, we apply it to compare flow within healthy and tumor tissue samples.