Applied Math Colloquium | Lorena Bociu, Multiscale Interface Coupling of PDEs and ODEs for Tissue Perfusion

MC 5501 

Speaker

Lorena Bociu, Department of Mathematics, North Carolina State University

Title

Multiscale Interface Coupling of PDEs and ODEs for Tissue Perfusion

Abstract

In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the whole blood circulation. We propose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of poroelastic equations is coupled with a systemic 0D lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the rest of the circulatory system. We discuss well-posedness analysis for this multiscale model, as well as solution methods focused on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions.