(162i) A Non-Stiff Cytoskeleton-Based Continuum Computational Modeling for the Dynamics of Erythrocytes in Strong Viscous Flows

The motion of erythrocytes through vascular vessels has long been recognized as a fundamental problem in physiology and biomechanics; unfortunately, studies on the flow dynamics of erythrocytes still constitute a challenging problem in any type of research owing to the micron-size of the cell and its complex multi-layered membrane. In the area of our interest (i.e. computational investigations), several continuum and molecular-based models have been developed in the recent decades to study erythrocytes. In the continuum models, treating the erythrocyte membrane as a two-dimensional elastic solid with large area-dilatation modulus results in a very stiff computational problem especially for three-dimensional investigations. On the other hand, cytoskeleton-based molecular algorithms were able to model efficiently the global area-incompressibility of the skeleton, but their applicability to flow problems is usually restricted owing to large computational cost.

In this talk, we show that, by combining the current experience on erythrocyte computational algorithms via both continuum and molecular modelings, we develop a cytoskeleton-based continuum algorithm, based on the Skalak etal constitutive law, which accounts for the global area-incompressibility of the skeleton via a non-stiff, and thus efficient, procedure. In addition, we investigate the erythrocyte dynamics in shear flows for moderate and strong capillary numbers and small to moderate viscosity ratios. These conditions correspond to a wide range of surrounding medium viscosities and shear flow rates, and match those used in ektacytometry systems and the tank-treading frequencies in vivo.

Our computational results for the cell deformability and tank-treading frequency are in excellent agreement with experimental findings from ektacytometry and capture very accurately the shear modulus of the erythrocyte membrane. To the best of our knowledge, since the development of Skalak etal constitutive law nearly 35 years ago, our work is the first one to develop a non-stiff continuum-based algorithm for the accurate determination of erythrocyte dynamics.