Networks and Heterogeneous Media (NHM)

Computational models for fluid exchange between microcirculation and tissue interstitium

Pages: 135 - 159, Volume 9, Issue 1, March 2014      doi:10.3934/nhm.2014.9.135

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Laura Cattaneo - MOX, Department of Mathematics "Francesco Brioschi", Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy (email)
Paolo Zunino - Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 3700 O'Hara Street, Pittsburgh, PA 15261, United States (email)

Abstract: 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 pharmacological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective therapies to treat vascularized tumors with drugs. We develop a model applicable at the microscopic scale, where the capillaries and the interstitial volume can be described as independent structures capable to propagate flow. We facilitate the analysis 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.

Keywords:  Perfusion, intestitial flow, tumors enhanced permeability and retention, immersed boundary method.
Mathematics Subject Classification:  Primary: 76Z05; Secondary: 65M60.

Received: May 2013;      Revised: August 2013;      Available Online: April 2014.