Multi-Scale Particle Simulation of Red Blood Cell in Microcirculation

Abstract

The complex rheology of red blood cell (RBC) in microcirculation has been a topic of interest for many decades. As RBC is highly deformable, shape change affects the microcirculation and such effect should be accounted accurately to understand the rheology of blood flow. A particle based model is developed to construct the red blood cell (RBC) based on the minimum energy principle. A bead-spring network is utilized to represent the cross-sectional plane of RBC membrane. The total energy of the RBC is associated with spring stretch/compression, bending and constraint of fixed area. Shape optimization of swollen RBC due to continuous deflation is performed. A bi-concave RBC shape is accurately achieved when the circular shape is deflated to 65%. Dissipative particle dynamics (DPD), a coarse-grained Mesoscopic particle simulation is used to simulate the flow. RBC in its equilibrium shape is placed inside a microchannel of height 10 μm to study the deformation of the cell under shear. Force exerted on RBC particles by plasma particles were determined and solved as the external force in the DPD equation to calculate the position and velocity of each particle. As the simulation started, the RBC experienced the shear and drag force by surrounding plasma and evolved to the characteristic parachute type shape as observed in experiments. Once the RBC reached the steady deformation, it continued with the same shape and stayed in the center of the channel. It is observed that the parachute shape and its motion along the centerline of the flow help reducing the drag and subsequently achieving the state of minimum energy. Formulation and results were validated against the experimental and computational results reported in the literature.