Mathematical model to determine the effect of a sub-glycocalyx space

We consider the drainage of blood plasma across the capillary wall, focusing on the flow through the endothelial glycocalyx layer that coats the luminal surface of vascular endothelial cells. We investigate how the presence of a sub-glycocalyx space between the porous glycocalyx and the impermeable endothelial cells affects the flow, using the Darcy and Stokes equations to model the flow in the glycocalyx and sub-glycocalyx space, respectively. Using an asymptotic analysis, we exploit the disparity of length scales to reduce the problem complexity to reveal the existence of several asymptotic regions in space. We provide a detailed characterization of the flow through the glycocalyx layer in terms of the microscale system parameters, and we derive analytic macroscale results, such as for the flux through and hydraulic conductivity of the glycocalyx layer. We show that the presence of a sub-glycocalyx space results in a higher flux of blood plasma through the glycocalyx layer, and we use our theoretical predictions to suggest experiments that could be carried out to shed light on the extent of the layer.