Bio-Mechanical and Bio-Rheological Aspects of Sickle Red Cells in Microcirculation: A Mathematical Modelling Approach

Abstract

Sickle cell disease (SCD) is an inherited monogenic disease characterized by distorted red blood cells that causes vaso-occlusion and vasculopathy. Presently, electrophoresis of haemoglobin and genotyping are used as routine tests for diagnosis of the SCD. These techniques require specialized laboratories and are expensive. The low-cost microfluidics-based diagnostic tool holds a great attention for screening of red blood cell (RBC) deformability. In the present study, lubrication theory has been applied in order to develop a biomechanical model of microcirculation with altered rheological properties of sickle blood in the capillary, which is smaller in size compared to the cell diameter, to explain the multifactorial nature and pathogenesis of vaso-occlusion in SCD. The governing equations have been solved analytically for realistic boundary conditions and simulated using MATLAB. We found that the axial velocity of the cell decreases with a decrease in deformability and compliance. The height of the lubricating film predicts deformation of the cell with respect to local pressure in the microcirculation. Leak back and drag force depend non-linearly on the deformed cell radius with varying viscosity of the plasma and Reynolds number. The modelling predictions of this study is in coherence with experimental results. The analyzed parameters provide unique insights with novel possibilities to design a microfluidics-based effective therapeutic intervention for SCD.

Keywords

• sickle cell disease
• cell deformability
• lubrication theory
• blood flow modelling
• numerical simulation
• microfluidics