International Journal of C 2009 Institute for Scientific Numerical Analysis and Modeling Computing and Information Dynamical Simulation of Red Blood Cell Rheology in Microvessels Tsorng-whay Pan and Tong Wang

This paper is dedicated to Professor Roland Glowinski for his 70th birthday Abstract. A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in microvessels. The biconcave RBC shape in static plasma and tank-treading behavior of single cell in shear flows have been successfully captured in this model. The behavior of the RBC in a Poiseuille flow and the lateral migration of the cells in a shear flow have been investigated. It is found that the RBCs exhibit parachute shape in a Poiseuille flow with the curvature closely related to the deformability of the cell membrane and the hematocrit (Hct) of the blood. With this spring model, RBCs can recover their initial shapes associated with the minimal elastic energy when the flow stops. The simulation results also show that the RBCs migrate to the center of the domain in the radial direction in a shear flow, which clearly indicates the Fahraeus-Lindqvist effect in microvessels. The rate of migration toward the center depends on the shape of the RBC; the bioconcave shape enhences this migration.

[1]  Robin Fåhræus,et al.  THE VISCOSITY OF THE BLOOD IN NARROW CAPILLARY TUBES , 1931 .

[2]  Ghassan S. Kassab,et al.  Computer Modeling of Red Blood Cell Rheology in the Microcirculation: A Brief Overview , 2005, Annals of Biomedical Engineering.

[3]  Charles S. Peskin,et al.  Modeling prosthetic heart valves for numerical analysis of blood flow in the heart , 1980 .

[4]  Lanping Amy Sung,et al.  3-D Nanomechanics of an Erythrocyte Junctional Complex in Equibiaxial and Anisotropic Deformations , 2005, Annals of Biomedical Engineering.

[5]  R. Skalak,et al.  Deformation of Red Blood Cells in Capillaries , 1969, Science.

[6]  Prosenjit Bagchi,et al.  Mesoscale simulation of blood flow in small vessels. , 2007, Biophysical journal.

[7]  R. Skalak,et al.  Motion of a tank-treading ellipsoidal particle in a shear flow , 1982, Journal of Fluid Mechanics.

[8]  C. Pozrikidis.  Axisymmetric motion of a file of red blood cells through capillaries , 2005 .

[9]  Aleksander S Popel,et al.  Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. , 2005, Journal of biomechanical engineering.

[10]  Witold Dzwinel,et al.  A discrete-particle model of blood dynamics in capillary vessels. , 2003, Journal of colloid and interface science.

[11]  Zhu Zeng,et al.  The measurement of shear modulus and membrane surface viscosity of RBC membrane with Ektacytometry: a new technique. , 2007, Mathematical biosciences.

[12]  S Chien,et al.  An elastic network model based on the structure of the red blood cell membrane skeleton. , 1996, Biophysical journal.

[13]  A. Popel,et al.  Large deformation of red blood cell ghosts in a simple shear flow. , 1998, Physics of fluids.

[14]  R. Glowinski.  Finite element methods for incompressible viscous flow , 2003 .

[15]  Thomas M Fischer,et al.  Shape memory of human red blood cells. , 2004, Biophysical journal.

[16]  R. Tran-Son-Tay,et al.  Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion. , 1984, Biophysical journal.

[17]  R. Glowinski,et al.  Fluidization of 1204 spheres: simulation and experiment , 2002, Journal of Fluid Mechanics.

[18]  A. Pries,et al.  Two-Dimensional Simulation of Red Blood Cell Deformation and Lateral Migration in Microvessels , 2007, Annals of Biomedical Engineering.

[19]  Shigeo Wada,et al.  Simulation Study on Effects of Hematocrit on Blood Flow Properties Using Particle Method , 2006 .

[20]  Yaling Liu,et al.  Rheology of red blood cell aggregation by computer simulation , 2006, J. Comput. Phys..

[21]  J. Fournier,et al.  A Gaussian model for the membrane of red blood cells with cytoskeletal defects , 2006, cond-mat/0603373.

[22]  Roland Glowinski,et al.  A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow , 1997 .

[23]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[24]  H Schmid-Schönbein,et al.  The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. , 1978, Science.

[25]  C. Peskin.  The immersed boundary method , 2002, Acta Numerica.

[26]  M. Dupin,et al.  Modeling the flow of dense suspensions of deformable particles in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  T. Biben,et al.  Steady to unsteady dynamics of a vesicle in a flow. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  C. Pozrikidis,et al.  Modeling and Simulation of Capsules and Biological Cells , 2003 .

[29]  J. Marsden,et al.  Product formulas and numerical algorithms , 1978 .

[30]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[31]  David Farrell,et al.  Immersed finite element method and its applications to biological systems. , 2006, Computer methods in applied mechanics and engineering.