Bušík Martin, Slavík Martin, Cimrák Ivan
University of Žilina, Univerzitná 8215/1, Žilina 01026, Slovakia.
Comput Math Methods Med. 2018 Sep 27;2018:7842857. doi: 10.1155/2018/7842857. eCollection 2018.
Modelling of cell flow for biomedical applications relies in many cases on the correct description of fluid-structure interaction between the cell membrane and the surrounding fluid. We analyse the coupling of the lattice-Boltzmann method for the fluid and the spring network model for the cells. We investigate the bare friction parameter of fluid-structure interaction that is mediated via dissipative coupling. Such coupling mimics the no-slip boundary condition at the interface between the fluid and object. It is an alternative method to the immersed boundary method. Here, the fluid-structure coupling is provided by forces penalising local differences between velocities of the object's boundaries and the surrounding fluid. The method includes a phenomenological friction coefficient that determines the strength of the coupling. This work aims at determination of proper values of such friction coefficient. We derive an explicit formula for computation of this coefficient depending on the mesh density assuming a reference friction is known. We validate this formula on spherical and ellipsoidal objects. We also provide sensitivity analysis of the formula on all parameters entering the model. We conclude that such formula may be used also for objects with irregular shapes provided that the triangular mesh covering the object's surface is in some sense uniform. Our findings are justified by two computational experiments where we simulate motion of a red blood cell in a capillary and in a shear flow. Both experiments confirm our results presented in this work.
生物医学应用中的细胞流动建模在很多情况下依赖于对细胞膜与周围流体之间流固相互作用的正确描述。我们分析了用于流体的格子玻尔兹曼方法和用于细胞的弹簧网络模型之间的耦合。我们研究了通过耗散耦合介导的流固相互作用的裸摩擦参数。这种耦合模拟了流体与物体界面处的无滑移边界条件。它是浸入边界方法的一种替代方法。在这里，流固耦合是通过惩罚物体边界速度与周围流体速度之间局部差异的力来实现的。该方法包括一个现象学摩擦系数，它决定了耦合的强度。这项工作旨在确定这种摩擦系数的合适值。我们推导了一个根据网格密度计算该系数的显式公式，假设已知参考摩擦。我们在球形和椭球形物体上验证了这个公式。我们还对进入模型的所有参数进行了公式的敏感性分析。我们得出结论，只要覆盖物体表面的三角形网格在某种意义上是均匀的，这样的公式也可用于形状不规则的物体。我们的发现通过两个计算实验得到了验证，在这两个实验中我们模拟了红细胞在毛细血管和剪切流中的运动。两个实验都证实了我们在这项工作中给出的结果。
