Numerical simulation of flow behaviors of cells in microvessels using dissipative particle dynamics

Abstract

Individual cell behavior in microcirculation reflects physiology and some pathologies of the microcirculatory system. To investigate the mechanical behaviors of red blood cells (RBCs) and circulating tumor cells (CTCs) in different flow conditions, Dissipative Particle Dynamics method coupled with different cell models was employed. The cell membrane was treated as a three-dimensional spring-based network model, combined with bending resistance, surface area and volume constraint. Also, the intercellular interaction energy for the RBC aggregation was modeled by the Morse potential. In addition, an adhesive dynamics model was introduced to capture the tumor cell adhesion. Firstly, a stretching test was carried out on the coarse-grained spring-based network RBC model and the stretching deformation was in excellent agreement with the optical tweezer experimental data. Based on this model, the effects of cell deformability, external driven force as well as the size of the stenosis on the motion and deformation of a single RBC flowing in the stenosed microvessel were investigated. The results indicated that the RBC enters into the stenosed region at a lower velocity with an increased deformation index. It has been also observed that the RBC can pass through the stenosis with a minimum diameter of 3m and exhibits asymmetrical behavior when it advances in the stenosed region. Next, the motion of two RBCs in a stenosed microvessel was simulated and the effects of intercellular interaction strength, RBC deformability as well as the initial cell orientation on the behaviors of the RBC deformation and aggregation as well as the flow resistance were investigated. The findings showed that the flow resistance increases dramatically before the RBCs reach the center of the stenosis but it decreases rapidly as they leave away from the stenosis. Especially, for the stiffer pair of RBCs with the initial inclination angle of 90°, the maximum value of the flow resistance is larger due to the weak deformation. Also, the stronger aggregation may lead to more flow resistance. In addition, for the two RBCs moving parallel to the main flow with little deformation, when the upstream position is nearer the vessel wall, the flow resistance is larger owing to the migration to the vessel center at the stenosis. The flow resistance produced by the flow of the aggregate with larger deformation is larger compared with the case of the aggregate flowing with zero inclination angle. Then, blood flow in microvessel was modeled as a suspension of multiple deformable RBCs. The cell distribution in the cross section revealed that RBCs migrate away from the wall to the tube center, resulting in a cell-free layer near the wall and blunt velocity profile. Also, the well-known Fahraeus and Fahraeus-Lindqvist effects were reproduced. Elevated aggregation strength and deformability can enhance the cell-free layer thickness and hence cause a reduced relative apparent viscosity and an increased discharge hematocrit. Following the analysis on the blood flow, the effects of flowing RBCs on the adhesion of CTC in microvessels were examined. It can be found that in the microvessel with a diameter of 5/3 of the CTC size, the CTC has a larger number of receptor-ligand bonds formed on the cell surface with the hematocrit due to a growing wall-directed force. But in a larger microvessel, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. CTC was found to move more slowly than the blood stream in smaller microvessels, which inhibits the CTC firm adhesion. The presence of CTC adhesion considerably increases blood flow resistance. In addition, the large deformation induced by a high flow rate and the occurrence of aggregation facilitates the CTC adhesion. Finally, a single cell passing through a narrow slit was simulated to investigate the effect of the cell deformability on the cell transmigration through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area only by 9.3% can enable the cell to pass the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell transit across the narrow slit.