The Effects of the Endothelial Surface Layer on Red Blood Cell Dynamics in Microvessel Bifurcations

Carlson Triebold, Purdue University

Abstract

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 one vessel flows into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. However, these studies 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 surface layer (ESL) that is 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 RBC model. The model is also used to investigate RBC deformation and 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 resistance of the ESL to compression is modeled using an osmotic pressure difference. The study includes isolated cells that pass through the bifurcation one at a time with no cell-cell interactions and two cells that pass through the bifurcation at the same time and interact with each other. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. For isolated cell simulations, decreasing hydraulic resistivity and/or decreasing osmotic pressure difference produced four behaviors: 1) RBC distribution nonuniformity increased; 2) RBC deformation decreased; 3) RBCs slowed down slightly; and 4) RBCs penetrated more deeply into the ESL. The presence of an altered flow profile and the ESL’s resistance to penetration were primary factors responsible for these behaviors. In certain scenarios, ESL penetration was deep enough to present a possibility of cell adhesion, as can occur in pathological situations. For paired cell simulations, more significant and complex changes were observed. Three types of effects that alter partitioning as hydraulic resistivity is changed are identified. Decreasing hydraulic resistivity in the ESL produced lower RBC deformation. Including cell-cell interactions tended to increase deformation sharply compared to isolated cell scenarios. ESL penetration generally decreased for lower hydraulic resistivities except in scenarios with significant cell-cell interactions. This was primarily due to changes in flow profiles induced by the altered hydraulic resistivity levels.

Degree

Ph.D.

Advisors

Barber, Purdue University.

Subject Area

Hydraulic engineering|Materials science|Mechanics

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