Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile

In order to address the problem of blood flow over the endothelium in small arteries, the near-endothelial region is here studied in more detail. The method used is a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids, named unstructured Lattice Boltzmann equation (ULBE). It is a new scheme based on the idea of placing the unknown fields at the nodes of the mesh and evolving them based on the fluxes crossing the surfaces of the corresponding control volumes. The study shows a significant variation and a high sensitivity of wall shear stress to the height of the endothelium corrugation and the presence of erythrocytes. The latter were modelled as deformable, viscous particles within a fluid continuum.