Simulation of red blood cell motion in microvessels and bifurcations

The constitution and salient mechanical properties of mammalian red blood cells are well established. In principle, this information provides us with a basis for understanding and predicting blood flow, both in bulk and in narrow passages occurring in the microcirculation. However, the particular mechanical properties of the red blood cell membrane, the asymmetry of three-dimensional cell shapes in flow, and the strong cell-to-cell interactions occurring under typical physiological concentrations present us with substantial difficulties in analyzing and simulating red blood cell motion and deformation in flow. Progress can be made by making simplifying geometric assumptions to reduce the dimensionality of the mathematical problem. When blood flows through capillaries, the red blood cells often move in single files with approximately axisymmetric shapes. Computational approaches for axisymmetric configurations have led to predictions of flow resistance in narrow tubes in quantitative agreement with experimental data. A two-dimensional model was recently developed where a red blood cell is represented by a twodimensional assembly of viscoelastic elements. The model has been used to describe several aspects of red blood cell motion in microvessels discussed in this chapter, including transverse cell migration, cell-to-cell interactions, and partition of cells in diverging bifurcations.