Mathematical Modeling of Plasma and Cellular Transport in Pulsatile Arterial Blood Flow

Abstract: Blood is a biologically-complex two-phase fluid consisting of suspended cellular (blood) components and plasma. Blood's properties of transport affect the function of the heart while pumping under pulsatile flow conditions. A general and total analytical model for plasma transport and blood-cell transport through a cylindrical artery experiencing pulsatile pressure drops is developed. Equations used for developing the model are the incompressible Navier-Stokes equations with viscosity depending on hematocrit (the volume fraction of red blood cells), a convective- diffusive-migrative equation describing cellular transport, and an advective-diffusive equation describing plasma solute transport. Analytical solutions for the parameters are determined by separating variables and solving them using the axisymmetric fully developed pulsatile flow analytical solution of Womersley. In addition to giving the spatial distributions of velocity, hematocrit, plasma concentration, cellular concentration, wall shear stress, and volumetric flow rate the solutions provide information concerning changes that occur due to varying hematocrit levels. Numerical simulation results indicate that higher hematocrit values result in increased effective viscosity of blood. Increased blood viscosity causes decreased velocities in the direction of flow, decreases the maximum flow rates occurring during the pulse cycle, and increases frictional resistance to flow. Additionally, numerical simulation results demonstrate the existence of a "cell-rich core" along the centerline of vessels and a "plasma-depleted zone" near vessel walls. These zones develop because shear-induced migration of red blood cells towards the centerline. Plasma concentration decreases continuously downstream from the inlet due to a combination of advection, diffusion, and wall transport.

Keywords: Pulsatile blood flow, Plasma transport, Cellular transport, Hematocrit, Mathematical modeling, Non- Newtonian blood