A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries
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A coupled SPH-DEM approach to model the interactions between multiple red blood cells in motion in capillaries Hasitha-Nayanajith Polwaththe-Gallage . Suvash C. Saha . Emilie Sauret . Robert Flower . Yuantong Gu
Received: 30 July 2015 / Accepted: 11 November 2015 Springer Science+Business Media Dordrecht 2015
Abstract Red blood cells (RBCs) are the most common type of blood cells in the blood and 99 % of the blood cells are RBCs. During the circulation of blood in the cardiovascular network, RBCs squeeze through the tiny blood vessels (capillaries). They exhibit various types of motions and deformed shapes, when flowing through these capillaries with diameters varying between 5 and 10 lm. RBCs occupy about 45 % of the whole blood volume and the interaction between the RBCs directly influences on the motion and the deformation of the RBCs. However, most of the previous numerical studies have explored the motion and deformation of a single RBC when the interaction between RBCs has been neglected. In this study, motion and deformation of two 2D (two-dimensional) RBCs in capillaries are comprehensively explored using a coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM) model. In order to clearly model the interactions between RBCs, only two RBCs are considered in this study even
though blood with RBCs is continuously flowing through the blood vessels. A spring network based on the DEM is employed to model the viscoelastic membrane of the RBC while the inside and outside fluid of RBC is modelled by SPH. The effect of the initial distance between two RBCs, membrane bending stiffness (Kb) of one RBC and undeformed diameter of one RBC on the motion and deformation of both RBCs in a uniform capillary is studied. Finally, the deformation behavior of two RBCs in a stenosed capillary is also examined. Simulation results reveal that the interaction between RBCs has significant influence on their motion and deformation. Keywords Multiple Red blood cells Smoothed particle hydrodynamics Computational biomechanics Blood flow Meshfree method Hydrodynamics interactions
1 Introduction H.-N. Polwaththe-Gallage S. C. Saha E. Sauret Y. Gu (&) School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD 4001, Australia e-mail: [email protected] R. Flower Research Program Leader, Research and Development, Australian Red Cross Blood Service, Kelvin Grove, QLD 4059, Australia
Blood is a suspension of different blood cells in plasma and the majority of the blood cells are RBCs. The diameter of average healthy matured RBC varies between 6 and 8 lm (Dupire et al. 2012) at rest. The volumetric ratio of the RBCs to the total blood volume is called hematocrit and its value for a healthy person varies from 40 to 50 % (Shvartsman and Fine 2003). The hematocrit value of the blood affects the motion and deformation of the RBCs as the interaction
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between RBCs makes a significant impact on the flow field. Fa˚hræus and L
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