RESUMO
Red blood cells (RBCs) carry oxygen and make up 40-45% of blood by volume in large vessels down to 10% or less in smaller capillaries. Because of their finite size and large volume fraction, they are heterogeneously distributed throughout the body. This is partially because RBCs are distributed or partitioned nonuniformly at diverging vessel bifurcations where blood flows from one vessel into two. Despite its increased recognition as an important player in the microvasculature, few studies have explored how the endothelial surface layer (ESL; a vessel wall coating) may affect partitioning and RBC dynamics at diverging vessel bifurcations. Here, we use a mathematical and computational model to consider how altering ESL properties, as can occur in pathological scenarios, change RBC partitioning, deformation, and penetration of the ESL. The two-dimensional finite element model considers pairs of cells, represented by interconnected viscoelastic elements, passing through an ESL-lined diverging vessel bifurcation. The properties of the ESL include the hydraulic resistivity and an osmotic pressure difference modeling how easily fluid flows through the ESL and how easily the ESL is structurally compressed, respectively. We find that cell-cell interaction leads to more uniform partitioning and greatly enhances the effects of ESL properties, especially for deformation and penetration. This includes the trend that increased hydraulic resistivity leads to more uniform partitioning, increased deformation, and decreased penetration. It also includes the trend that decreased osmotic pressure increases penetration.
RESUMO
Red blood cells (RBCs) make up 40-45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5-1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL's resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell-cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL's resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.