Abnormal physiological states in the erythrocytes or in the ambient plasma affect the ability of red blood cells (RBCs) to deform and thus to pass through the networks of microvessels. This lowers the amount of oxygen delivered to the body's tissues with mild or severe health consequences. The goal of this proposal is to investigate the effects on the dynamics of erythrocytes'deformation and motion of two classes of situation in which a physiological deviation from homeostasis, such as a disease state, involves a change in the rheology of the microcirculation. In particular we will study the effects of (i) paraproteinemia which increases the plasma viscosity, and (ii) changes in the properties of the erythrocyte's membrane which occur due to malaria. To elucidate the realistic motion of RBCs for both types of abnormalities in capillaries and post- capillaries, we propose to address the following aims: 1. Non-axisymmetric motion of a le of abnormal RBCs in a cylindrical microvessel. 2. Non-axisymmetric motion of a le of abnormal RBCs in a nonuniform microvessel. For both types of abnormalities and for all proposed geometries, our computational investigation will elucidate the deformation and motion of RBCs and the associated resistance in blood ow. Our work will also help elucidate the erythrocytes'aging and lifetime since the large deformations and the associated large interfacial stresses may damage the cell's membrane and accelerate the aging process. Of particular interest is the variation of the volume fraction of RBCs (or hematocrit) and the changes in the blood apparent viscosity (i.e. the well-known Fahraeus effect) which occurs in these vessels due to the strong hydrodynamic interactions of the cells with the vessel walls. To achieve these goals, we will utilize our novel three-dimensional Spectral Boundary Element algorithm for membrane dynamics in Stokes flow. This high-accuracy computational algorithm constitutes an efficient method to accurately determine even the most complicated interfacial shapes of erythrocytes and thus it is particularly suited for the proposed studies. This study helps advance our understanding on the effects of malaria and paraproteinemia in the vascular microcirculation. The results of this proposal can improve the control of these diseases and thus enhance public health.
