The effects of the endothelial surface layer on red blood cell partitioning, deformation, and penetration of that layer*

Blood is 40-45% red blood cells by volume. This large fraction significantly affects blood flow leading to several nonlinear phenomenon including the heterogeneous distribution of red blood cells (RBCs) and the oxygen they carry. Those distributions significantly depend on how RBCs are divided or partitioned at diverging vessel bifurcations where blood flows from one vessel into two downstream vessels. Blood flow is also affected by a layer that coats vessel walls that includes a poroelastic medium known as the endothelial surface layer (ESL). Despite the importance of both RBC partitioning and the ESL, very few studies have considered both. Here we use a two-dimensional mathematical model of RBCs, the surrounding flow, and a poroelastic ESL to consider how properties of the ESL may affect RBC dynamics at diverging bifurcations. The RBCs are modeled as interconnected damped springs (viscoelastic elements) and the flow using the Stokes (viscous) flow equations. The ESL's resistance to flow (hydraulic resistivity) is modeled using a Brinkman approximation and its resistance to structural compression is modeled using a superimposed external pressure that corresponds to an osmotic pressure difference that is usually seen at ESL-flow interface. Results using lone cells passing through the bifurcation suggest that decreasing the hydraulic resistivity and compression resistance increased partitioning nonuniformity slightly (leads to more heterogeneous RBC distribution), decreased RBC deformation, decreased relative RBC velocity, and increased RBC penetration into the ESL. Additional preliminary results using pairs of cells passing through the bifurcation suggest that interaction increases partitioning nonuniformity, RBC deformation, and RBC penetration into the ESL. Increased RBC deformation has been correlated with release of vasodilators like ATP and nitric oxide while increased penetration has been correlated with more clotting.