In this review, we provide an overview of the simulation techniques employed for modelling the flow of red blood cells (RBCs) in blood plasma. The scope of this review omits the fluid modelling aspect while focusing on other key components in the RBC-plasma model such as (1) describing the RBC deformation with shell-based and spring-based RBC models, (2) constitutive models for RBC aggregation based on bridging theory and depletion theory and (3) additional strategies required for completing the RBC-plasma flow model. These include topics such as modelling fluid-structure interaction with the immersed boundary method and boundary integral method, and updating the variations in multiphase fluid property through the employment of index field methods. Lastly, we summarily discuss the current state and aims of RBC modelling and suggest some research directions for the further development of this field of modelling.
In this study, we investigated the rheology of a doublet that is an aggregate of two red blood cells (RBCs). According to previous studies, most aggregates in blood flow consist of RBC doublet-pairs and thus the understanding of doublet dynamics has scientific importance in describing its hemodynamics. The RBC aggregation tendency can be significantly affected by the cell’s deformability which can vary in both physiological and pathological conditions. Hence, we conducted two-dimensional simulation of doublet dynamics in a simple shear flow condition with different deformability between RBCs. To study the dissociation process of the doublet, we employed the aggregation model described by the Morse type potential function, which is based on the depletion theory. In addition, we developed a new method of updating fluid property to consider viscosity difference between RBC cytoplasm and plasma. Our results showed that deformability difference between the two RBCs could significantly reduce their aggregating tendency in a shear condition of 50 s−1, resulting in disaggregation. Since even in physiological conditions, the cell deformability may be significantly different, consideration of the difference in deformability amongst RBCs in blood flow would be needed for the hemodynamic studies based on numerical approach.
This study aimed to develop a numerical model capable of predicting changes in the cell-free layer (CFL) width in narrow tubes with consideration of red blood cell aggregation effects. The model development integrates to empirical relations for relative viscosity (ratio of apparent viscosity to medium viscosity) and core viscosity measured on independent blood samples to create a continuum model that includes these two regions. The constitutive relations were derived from in vitro experiments performed with three different glass-capillary tubes (inner diameter = 30, 50 and 100 μm) over a wide range of pseudoshear rates (5-300 s−1). The aggregation tendency of the blood samples was also varied by adding Dextran 500 kDa. Our model predicted that the CFL width was strongly modulated by the relative viscosity function. Aggregation increased the width of CFL, and this effect became more pronounced at low shear rates. The CFL widths predicted in the present study at high shear conditions were in agreement with those reported in previous studies. However, unlike previous multi-particle models, our model did not require a high computing cost, and it was capable of reproducing results for a thicker CFL width at low shear conditions, depending on aggregating tendency of the blood.
This article reviews numerical simulations of red blood cells (RBCs) mainly using the lattice Boltzmann method (LBM), focusing on the 2-dimensional deformation and aggregation of the cells in simple shear flow. We outline the incorporation of the immersed boundary method into the LBM, in which the membrane forces are obtained from the membrane model. The RBCs are simulated as a single biconcave capsule and as a doublet of biconcave capsules. The transition from swinging to tumbling motions of the RBCs, as induced by reducing the shear rate or increasing the membrane bending stiffness, is discussed. Also discussed is the aggregation tendency of the doublet of RBCs, for which homogenous deformability maintained RBC aggregation, whereas an increased deformability difference resulted in RBC dissociation.
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