Mathematical Analysis for the Flow of Sickle Red Blood Cells in Microvessels for Bio Medical Application

Sickle cell disease (SCD) is an inherited monogenic disease which is characterized by distorted red blood cells (RBCs) that cause vaso-occlusion and vasculopathy. In the pathogenesis of SCD, polymerized hemoglobin turn RBCs into fragile, less deformable cells, and are subsequently more susceptible to endothelial adhesion after deoxygenation. Presently, electrophoresis and genotyping are used as routine tests for diagnosis of SCD. These techniques are expensive and require specialized laboratories. Lab-on-a-chip technology is a low-cost microfluidics-based diagnostic tool which holds significant promise for rapid screening of RBC deformability. To explore the sickle RBC mechanics for screening purposes, we present a mathematical model for the flow of single RBC with altered rheological properties and slip effect on capillary wall in microcirculation. We consider single-file flow of cells through the axis symmetrical cylindrical duct, applying lubrication theory as plasma trapped between successive red blood cells. The rheological parameters used from published literature for normal RBC and corresponding variation has been taken for the purpose of this simulation to present the condition of the disease. An analytical solution has been found for realistic boundary conditions and results are simulated using MATLAB. We found that the height of plasma film in the capillary increases with increase in cell deformability and compliance which affects the forward flow velocity in the capillary. Rigid RBCs with increased adhesion between cell and capillary wall shows reduction in velocity and occurrence of vaso-occlusion events in extreme conditions. These rheological properties of the cells coupled with microfluidics mechanics can mimic the physiological condition and provides unique insights with novel possibilities for the design of microfluidics base diagnostic kit towards effective therapeutic intervention of SCD.