Electro-poroelastohydrodynamics of the endothelial glycocalyx layer

Abstract

We consider pressure-driven flow of an ion-carrying viscous Newtonian fluid through a non-uniformly shaped channel coated with a charged deformable porous layer, as a model for blood flow through microvessels that are lined with an endothelial glycocalyx layer (EGL). The EGL is negatively charged and electrically interacts with ions dissolved in the blood plasma. The focus here is on the interplay between electrochemical effects, and the pressure-driven flow through the microvessel. To analyse these effects we use triphasic mixture theory (TMT) which describes the coupled dynamics of the fluid phase, the elastic EGL, ion transport within the fluid and electric fields within the microvessel. The resulting equations are solved numerically using a coupled boundary-finite element method (BEM-FEM) scheme. However, in the physiological regime considered here, ion concentrations and electric potentials vary rapidly over a thin transitional region (Debye layer) that straddles the lumen-EGL interface, which is difficult to resolve numerically. Accordingly we analyse this region asymptotically, to determine effective jump conditions across the interface for BEM-FEM computations within the bulk EGL/lumen. Our results demonstrate that ion-EGL electrical interactions can influence the near-wall flow, causing it to become reversed. This alters the stresses exerted upon the vessel wall, which has implications for the hypothesised role of the EGL as a transmitter of mechanical signals from the blood flow to the endothelial vessel surface.