Near-wall microfludics in the microcirculation

Abstract

The microcirculation is the network of arterioles, capillaries and venules that deliver blood to the body's tissues. Lining the walls of these microvessels is a hydrated negatively-charged membrane-bound macromolecular layer known as the Endothelial Glycocalyx Layer (EGL). The EGL can extend half a micron or more into the blood stream. It plays an important role in the microcirculation as it modi es the velocity pro le of blood ow. It is also believed to play a role in regulating the permeability of the vessel, as well as being involved in mechanical signalling and in ammatory cell tra cking (Weinbaum et al., 2007). It is also hypothesised that in plays an important function in disease states such as ischemia-reperfusion injury, diabetes and atherosclerosis (Reitsma et al., 2007). Current models of microvessels with the presence of the EGL typically assume a uniform vessel cross-section and EGL thickness. This is not realistic due to the presence of endothelial cells that protrude into the microvessel. Furthermore, experimental results indicate that the EGL may not be heterogeneous throughout the microcirculation. In order to model a more realistic microvessel, a model was produced that can simulate a microvessel with an arbitrary shape for the endothelium and EGL. We also consider a modi cation of this model which allows for an EGL that can deform elastically. The model was solved numerically using the Boundary Element Method (BEM), implemented using bespoke code that allowed the problem to be solved using an arbitrary surface mesh of the endothelium and EGL. Simulations were performed using this bespoke numerical scheme using a sine-sine surface as a model for the undulating shape of the endothelium. Two possible con gurations for the EGL were tested, one where the EGL is uniformly thick and one where the EGL is concentrated in the cell-cell junctions. Results from these simulations showed that the shear stress pro le on the endothelium is altered by the distribution of the EGL. This can have important implications for processes such as mechanical signalling. We therefore conclude that it is worth continuing work to simulate the ow through physiologically realistic geometries using, using confocal microscope data from a venule which has already been obtained, and from which BEM meshes have already been created.