An extended convection diffusion model for red blood cell-enhanced transport of thrombocytes and leukocytes

Transport phenomena of platelets and white blood cells (WBCs) are fundamental to the processes of vascular disease and thrombosis. Unfortunately, the dilute volume occupied by these cells is not amenable to fluid-continuum modeling, and yet the cell count is large enough that modeling each individual cell is impractical for most applications. The most feasible option is to treat them as dilute species governed by convection and diffusion; however, this is further complicated by the role of the red blood cell (RBC) phase on the transport of these cells. We therefore propose an extended convection-diffusion (ECD) model based on the diffusive balance of a fictitious field potential, Psi, that accounts for the gradients of both the dilute phase and the local hematocrit. The ECD model was applied to the flow of blood in a tube and between parallel plates in which a profile for the RBC concentration field was imposed and the resulting platelet concentration field predicted. Compared to prevailing enhanced-diffusion models that dispersed the platelet concentration field, the ECD model was able to simulate a near-wall platelet excess, as observed experimentally. The extension of the ECD model depends only on the ability to prescribe the hematocrit distribution, and therefore may be applied to a wide variety of geometries to investigate platelet-mediated vascular disease and device-related thrombosis.