Numerical Simulation of the Flow-Induced Deformation of Red Blood Cells

A theoretical model is presented for describing the flow-induced deformation of red blood cells. The cells are modeled as deformable liquid capsules enclosed by a membrane that is nearly incompressible and exhibits elastic response to shearing and bending deformation. In the mathematical formulation, the hydrodynamics is coupled with the membrane mechanics by means of surface equilibrium equations expressed in global Cartesian coordinates. Numerical simulations are carried out to investigate the deformation of a cell in simple shear flow, in the physiological range of physical properties and flow conditions. The results show that the cell performs flipping motion accompanied by periodic deformation in which the cross section of the membrane in the plane that is perpendicular to the vorticity of the shear flow alternates between the nearly biconcave resting shape and a reverse S shape. The period of the overall rotation is in good agreement with the experimental observations of Goldsmith and Marlow for red blood cells suspended in plasma. Parametric investigations reveal that, in the range of shear rates considered, membrane compressibility has a secondary influence on the cell deformation and on the effective viscosity of a dilute suspension. The numerical results illustrate in quantitative terms the distribution of the membrane tensions developing due to the flow-induced deformation, and show that the membrane is subjected to stretching and compression in the course of the rotation. © 2003 Biomedical Engineering Society.