  The geometry of the blood vessel wall plays a regulatory role on the motion
of red blood cells (RBCs). The overall topography of the vessel wall depends on
many features, among which the endothelial lining of the endothelial surface
layer (ESL) is an important one. The endothelial lining of vessel walls
presents a large surface area for exchanging materials between blood and
tissues. The ESL plays a critical role in regulating vascular permeability,
hindering leukocyte adhesion as well as inhibiting coagulation during
inflammation. Changes in the ESL structure are believed to cause vascular
hyperpermeability and entrap immune cells during sepsis, which could
significantly alter the vessel wall geometry and disturb interactions between
RBCs and the vessel wall, including the wall-induced migration of RBCs and the
thickening of a cell-free layer. To investigate the influence of the vessel
wall geometry particularly changed by the ESL under various pathological
conditions, such as sepsis, on the motion of RBCs, we developed two models to
represent the ESL using the immersed boundary method in two dimensions. In
particular, we used simulations to study how the lift force and drag force on a
RBC near the vessel wall vary with different wall thickness, spatial variation,
and permeability associated with changes in the vessel wall geometry. We find
that the spatial variation of the wall has a significant effect on the
wall-induced migration of the RBC for a high permeability, and that the
wall-induced migration is significantly inhibited as the vessel diameter is
increased.
