3D Particle Simulations of Deformation of Red Blood Cells in Micro-Capillary Vessel

Abstract

With the increase in arteriosclerosis, thrombosis, etc., in order to find out the cause, research of the flow characteristic of blood attracts attention. As for the analysis of the flow phenomenon of the RBC (Red Blood Cell or Erythrocyte), the numerical simulation (Wada et al., 2000, Tanaka et al., 2004) as well as experiment observation (Gaehtgens et al., 1980) is becoming a strong tool. Particle methods, such as SPH method (Monaghan J., 1992) and the MPS method (Koshizuka, 1997), treats both solid and liquid as particles, and can be applied to complicated flow analysis. When applying a particle method to the flow analysis of RBC, RBC is divided into the elastic film and internal liquid, and its deformation was analyzed in detail (Tanaka et al., 2004, Tsubota et al., 2006). The RBC which is actually flowing in our body occupies 40-60% by volume ratio of blood (hematocrit), and is numerous. The objective of our research is clarifying the flow characteristic of the blood flow containing many RBCs. We reported preliminarily simulation of 2D blood flow (Nagayama et al., 2004), where many RBCs were simply treated as a lump of an elastic particle, the flow was analyzed qualitatively. Moreover, three dimensional RBC was modelled with double structure, and the RBC shape in flow was more realistic (Nagayama et al., 2005). The relation of the blood vessel diameter and the bloodflow with many RBCs was studied by 2D model (Nagayama, 2006) and by 3D model (Nagayama et al., 2008a). The model was also applied to 3D blood flow in capillary bend tube (Nagayama et al., 2008b). The objective is to understand the fundamental flow phenomenon in a blood vessel. In this paper, 3 dimensional blood flows with RBCs in capillary tube were simulated. In Section 2, simulation model was described. And the shape of single red blood cell in static fluid was shown. In Section 3, blood flows with RBCs in capillary straight tube were simulated. And the relations of the blood vessel diameter and the hematocrit were investigated. Furthermore, transient phenomena of interacting red blood cells and their shape were investigated. In Section 4, the model is applied to the capillary vessel flow at finger tip edge. The capillary vessel is modelled as two cases. One case is bent tube and another is bent and twisted tube, and RBC deformation were investigated.