Computational Model of Human Capillary Hydrodynamics

Abstract

The present work lays out an accurate, three-dimensional computational fluid dynamics (CFD) model of a human blood capillary. This model is composed of red blood cells and blood plasma inside a cylindrical section of a capillary. The plasma flow is resolved using an incompressible Navier-Stokes solver. At the level of capillaries, red blood cells must be individually handled to correctly resolve the hydrodynamics in the system. They cannot be lumped in with the plasma and considered as a non-Newtonian suspension because of the relative scale of the capillaries and the blood cells. Red blood cells act as highly deformable, fluid filled vesicles which readily deform from their typical biconcave shape when passing through narrow capillaries. In the present model, the deformed shape of red blood cells is predicted using a combination of analytical models and experimental data on cell deformation. The cell volume, cell surface area, and plasma layer thickness are found to be the key parameters which define red blood cell deformation in capillaries. The red blood cells are imposed in the flow using the immersed boundary method (IBM). To save computational resources while still yielding an accurate model, the deformed shape of each red blood cell is calculated once prior to running the simulation and then held constant throughout the run. In order to validate the model, two parameters — apparent relative viscosity and hematocrit ratio — were examined. The present model shows good comparison to experimental values for both these parameters.