Modelling the Endothelial Glycocalyx Layer
This thesis concerns the construction of a mathematical model for blood flow in microvessels coated with an endothelial glycocalyx layer (EGL). Special attention is focused on the effect of the wall layer on the system as a whole and the interaction between blood, EGL and the wall vessel. Interest in this problem is motivated by its implications for better understanding of the clinical function of the EGL which is extremely challenging to measure in-vivo. The early parts of this thesis investigate the motion of a rigid particle through a microtube which has a non-uniform wall shape, is filled with a viscous Newtonian fluid, and is lined with a thin poroelastic layer. This is relevant to the transport of small rigid cells (such as neutrophils) through microvessels that are lined with an EGL. We describe a new boundary-integral representation for Biphasic Mixture Theory, which allows us to efficiently solve elastohydrodynamicmobility problems using Boundary Element Methods. In this context, we examine the impact of geometry upon creation of viscous eddies, fluid flux into the EGL, as well as the role of the EGL in transmitting mechanical signals to the underlying endothelial cells. We then examine electrochemical properties of the EGL by introducing a charge effect into a mathematical model. The asymptotic solutions obtained enable us to investigate some of the important physical phenomena inherent in electroviscous ow in porous media. The results facilitate construction of a numerical technique that allows to simulate a two-dimensional ow through a wavy wall particle-free channel lined with ionised porous material. The data obtained, particularly shear stress exerted on the vessel wall, is of importance for understanding the physiological role of the EGL as a mechanotransducer.
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