Modelling the glycocalyx–endothelium–erythrocyte interaction in the microcirculation: a computational study

A novel, coarse-grained, single-framework ‘Eulerian’ model for blood flow in the microvascular circulation is presented and used to estimate the variations in flow properties that accrue from all of the following: (i) wall position variation, associated with the endothelial cells' (ECs) shape, (ii) glycocalyx layer (GL) effects and (iii) the particulate nature of blood. We stress that our new model is fully coupled and uses only a single Eulerian computational framework to recover complex effects, dispensing altogether with the need for, e.g. re-meshing and advected sets of Lagrangian points. Physically, blood is modelled as a two-component, incompressible fluid – the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets of increased viscosity. Interfacial membrane effects are present to mimic key blood properties and to avoid droplets' coalescence. The model is encapsulated within a multi-component lattice Boltzmann method that uses a sub-lattice ‘wavy wall’ closure to represent the ECs. Between this boundary and the flow domain, the model incorporates a coarse-grained representation of the endothelial GL, which is known to cover microvessel walls. The endothelial glycocalyx is modelled as a medium of variable and adaptive porosity, with approaching droplets being subject to a repulsive elastic force. Numerical simulations are presented to show the combined and simultaneous influence on fundamental flow properties of the EC wall undulation, the glycocalyx compression and repulsion and the particulate nature of blood. Several characteristic hemodynamical features of microvessel flow are successfully reproduced, including the deformability of particulates and the Fahraeus–Lindqvist effect. Moreover, the importance of modelling the GL is manifest in the magnitude of and the temporal variations in the flow rate and wall shear stresses.