Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany.
Biomech Model Mechanobiol. 2019 Apr;18(2):347-359. doi: 10.1007/s10237-018-1085-9. Epub 2018 Oct 30.
In this paper, a novel 3D numerical method has been developed to simulate red blood cells (RBCs) based on the interaction between a shell-like solid structure and a fluid. RBC is assumed to be a thin shell encapsulating an internal fluid (cytoplasm) which is submerged in an external fluid (blood plasma). The approach is entirely based on the smoothed particle hydrodynamics (SPH) method for both fluid and the shell structure. Both cytoplasm and plasma are taken to be incompressible Newtonian fluid. As the kinematic assumptions for the shell, Reissner-Mindlin theory has been introduced into the formulation. Adopting a total Lagrangian (TL) formulation for the shell in the realm of small strains and finite deflection, the presented computational tool is capable of handling large displacements and rotations. As an application, the deformation of a single RBC while passing a stenosed capillary has been modeled. If the rheological behavior of the RBC changes, for example, due to some infection, it is reflected in its deformability when it passes through the microvessels. It can severely affect its proper function which is providing the oxygen and nutrient to the living cells. Hence, such numerical tools are useful in understanding and predicting the mechanical behavior of RBCs. Furthermore, the numerical simulation of stretching an RBC in the optical tweezers system is presented and the results are verified. To the best of authors' knowledge, a computational tool purely based on the SPH method in the framework of shell-fluid interaction for RBCs simulation is not available in the literature.
本文提出了一种新的三维数值方法,用于模拟基于壳状固体结构与流体相互作用的红细胞(RBC)。假设 RBC 是一个薄壳,内部充满了内部流体(细胞质),而外部则是另一种流体(血浆)。该方法完全基于光滑粒子流体动力学(SPH)方法,既适用于流体,也适用于壳状结构。细胞质和血浆都被视为不可压缩的牛顿流体。由于壳的运动学假设,引入了 Reissner-Mindlin 理论。采用小应变和有限挠度的壳的总拉格朗日(TL)公式,提出的计算工具能够处理大位移和大旋转。作为一个应用实例,对单个 RBC 通过狭窄毛细血管时的变形进行了建模。如果 RBC 的流变行为发生变化,例如由于某些感染,那么它在通过微血管时的变形就会反映出这种变化。这可能会严重影响其为活细胞提供氧气和营养物质的正常功能。因此,这种数值工具对于理解和预测 RBC 的力学行为是很有用的。此外,还介绍了在光镊系统中拉伸 RBC 的数值模拟,并验证了结果。据作者所知,目前文献中尚无针对 RBC 模拟的壳-流相互作用的纯粹基于 SPH 方法的计算工具。