A computational model of red blood cells using an isogeometric formulation with T-splines and a lattice Boltzmann method

IF 3.4 2区 工程技术 Q1 ENGINEERING, MECHANICAL Journal of Fluids and Structures Pub Date : 2024-02-07 DOI:10.1016/j.jfluidstructs.2024.104081
Yusuke Asai , Shunichi Ishida , Hironori Takeda , Gakuto Nakaie , Takuya Terahara , Yasutoshi Taniguchi , Kenji Takizawa , Yohsuke Imai
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Abstract

The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high-order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with T-splines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid–structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be Gs=4.0×106 N/m, and the bending modulus is estimated to be EB=4.5×1019 J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.

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使用 T-样条线等距计算法和晶格玻尔兹曼法的红血细胞计算模型
红细胞(RBC)膜通常由 Skalak 应变能和 Helfrich 弯曲能函数建模,为此需要膜表面的高阶表示。我们使用 T-样条线等距离散法建立了一个红细胞数值模型。采用变分公式计算膜上的外部载荷,直接离散化二阶参数导数。对于流体与结构的相互作用,通过沉浸边界法将等距分析与晶格玻尔兹曼法结合起来。RBC 的参考构型为扁球体,体积缩小为 0.95,自发曲率为零。通过数值测试,估计表面剪切弹性模量为 Gs=4.0×10-6 N/m,弯曲模量为 EB=4.5×10-19 J。我们证明,对于生理粘度比,RBC 在剪切流中的典型运动是滚动和复杂摆动,但在非常高的剪切速率下会出现简单摆动或槽踏。我们还表明,计算得出的 RBC 通道流表观粘度与经验方程相当吻合。我们最后证明,大通道(RBC 直径的两倍)RBC 的最大膜应变可能大于小通道(RBC 直径的四分之三)。这是由于 RBC 在通道流中的滑动形状和降落伞形状的应变分布不同造成的。
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来源期刊
Journal of Fluids and Structures
Journal of Fluids and Structures 工程技术-工程:机械
CiteScore
6.90
自引率
8.30%
发文量
173
审稿时长
65 days
期刊介绍: The Journal of Fluids and Structures serves as a focal point and a forum for the exchange of ideas, for the many kinds of specialists and practitioners concerned with fluid–structure interactions and the dynamics of systems related thereto, in any field. One of its aims is to foster the cross–fertilization of ideas, methods and techniques in the various disciplines involved. The journal publishes papers that present original and significant contributions on all aspects of the mechanical interactions between fluids and solids, regardless of scale.
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