Comparing Interface Conditions for a 3D–0D Multiscale Interface Coupling With Applications in Tissue Perfusion

Abstract

Many pathologies are related to hemodynamic changes occurring at the microvascular level, where small vessels pierce the tissue, perfusing it with blood. Since there is a large number of vessels of small caliber, it is impractical to model the fluid flow through each one of them separately, as it is done in the case of large arteries using, for example, the Navier–Stokes equations. As an alternative, tissue perfusion is modeled here via three-dimensional (3D) partial differential equations (PDEs) for fluid flow through deformable porous media, where blood vessels are modeled as pores within a deformable solid representing the tissue. Since it is known that the local perfusion is related to the systemic features of surrounding blood circulation, we couple the PDE system with a zero-dimensional (0D) lumped circuit model, obtained by the analogy between fluid flows in hydraulic networks and current flowing in electrical circuits. An important feature in this multiscale 3D–0D coupling is the specification of interface conditions between the 3D and the 0D parts of the system. In this article, we focus on two types of interface conditions driven by physical considerations, and compare the behavior of the solutions for the two different scenarios.