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An Immersed Boundary Method for Computational Simulation of Red Blood Cell in Poiseuille Flow

机译:泊松流中红细胞计算模拟的浸入边界方法

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Blood is a multiphase fluid that is primarily made of red blood cells (RBCs), white blood cells, and platelets suspended in plasma. Under normal, healthy conditions, a freely suspended RBC is a biconcave discoid with 8 μm diameter and 2 μm thickness. RBCs constitute; 40-45% of the total blood volume. Being highly deformable particles, RBCs can easily squeeze through the smallest capillaries having internal diameter less than their characteristic size. The particulate nature of the blood and the deformability of the RBCs determine the overall rheological behavior of the blood [1]. The lattice Boltzmann method (LBM) in combination with IBM has been used for simulating the motion and deformation of elastic bodies immersed in fluid flow including red blood cells (RBCs). Zhang et al. [2, 3] studied the dynamic behavior of RBC in shear flow and channel flow and investigated several hemodynamic and rheological properties, using a combination of LBM and IBM. Cheng et al. [4] have proposed a proper model to simulate the fast boundary movements and a high pressure gradient occurred in the fluid-solid interaction. In their research mitral valve jet flow considering the interaction of leaflets and fluid has been simulated. Alizadeh et al. [5, 6] investigated numerically the motion and deformation of a RBC in a viscous shear flow utilizing a combined LBM-IBM. Several recent numerical studies have focused on the behavior of deformable RBCs in microvascular flows [7-13]. RBC motions are well described by existing numerical techniques. Li et al. [14] applied the lattice Boltzmann method (LBM) to simulate two-dimensional rigid particle suspensions through a stenosed microvessel. Hyakutake et al. [15] conducted a two-dimensional simulation of the stenosed microvascular flow with rigid RBCs assuming primary pulmonary hypertension due to the stenosis of lung arteriole. Xu et al. [16] performed a two-dimensional simulation of RBC aggregation flow through a stenosed microvessel. There are few studies that focus on the time variation of RBC shape and the flow resistance in stenosed microvessels that have diameter less than 10 μm [10]. Pozrikidis [17] have used boundary integral method to study motion and deformation of RBCs in the shear flow and the flow in the channel. Zhao et al. [18] have studied the time variations of RBCs deformation and flow resistance in the stenosed microvessels having a diameter less than 10μm, using boundary integral method. Eggleton and Popel [19] combined immersed boundary method (IBM) with finite element method to simulate three-dimensional deformation of a RBC in a shear flow. Bagchi [1] has simulated a suspension containing multiple cells in the range of vessel size 20-30 μm and discharge hematocrit 10-60%, using IBM. Sun and Munn [20, 21] have studied RBC deformation in a 20-40nm channel using lattice Boltzmann method (LBM). They modeled the RBCs as two-dimensional solid particles. Li et al. [22] have used LBM for two-dimensional simulating of rigid particle suspensions in a stenosed microvessel. IBM is one of the methods that have been used successfully in recent decades to simulate the dynamics of flexible bodies in the fluid flow. This method was introduced for the first time in 1972 by Peskin [23] to study the flow around heart valves and developed as an efficient method to solve problems involving fluid-solid interactions. It is a combinadon of both the mathematical formulation and numerical scheme [24-26]. In this research, moving and deformation of Red Blood Cell(RJBC) in microchannel with stenosis curve is investigated by Lattice Boltzmann method and immersed boundary. The results of this paper were compared to the available results and good agreements were observed.
机译:血液是一种多相流体,主要由悬浮在血浆中的红细胞(RBC),白细胞和血小板组成。在正常,健康的状况下,自由悬浮的RBC是直径8μm,厚度2μm的双凹盘状。红细胞组成;总血量的40-45%。作为高度易变形的颗粒,RBC可以轻松通过内径小于其特征尺寸的最小毛细管。血液的颗粒性质和RBC的可变形性决定了血液的整体流变行为[1]。格子Boltzmann方法(LBM)与IBM结合已用于模拟浸没在包括红细胞(RBC)的流体流中的弹性体的运动和变形。张等。 [2,3]结合LBM和IBM,研究了RBC在剪切流和通道流中的动力学行为,并研究了几种血液动力学和流变特性。程等。 [4]提出了一个合适的模型来模拟快速边界运动和流固耦合中发生的高压梯度。在他们的研究中,已经模拟了考虑小叶和流体相互作用的二尖瓣射流。 Alizadeh等。 [5,6]利用结合的LBM-IBM数值研究了RBC在粘性剪切流中的运动和变形。最近的一些数值研究集中在微血管流中可变形红细胞的行为[7-13]。现有的数值技术很好地描述了RBC运动。 Li等。 [14]应用格子玻尔兹曼方法(LBM)通过狭窄的微血管模拟二维刚性颗粒悬浮液。 Hyakutake等。 [15]进行了具有刚性RBC的狭窄微血管流动的二维模拟,假设是由于肺小动脉狭窄导致原发性肺动脉高压。徐等。 [16]通过狭窄的微血管对RBC聚集流进行了二维模拟。很少有研究关注直径小于10μm的狭窄微血管中RBC形状的时间变化和流动阻力[10]。 Pozrikidis [17]已经使用边界积分法来研究红细胞在剪切流和通道中的运动和变形。赵等。 [18]使用边界积分法研究了直径小于10μm的狭窄微血管中RBC变形和流动阻力的时间变化。 Eggleton和Popel [19]将浸入边界方法(IBM)与有限元方法结合起来,模拟了剪切流中RBC的三维变形。 Bagchi [1]使用IBM模拟了一个包含多个细胞的悬浮液,该细胞的大小在20-30μm的血管范围内,血细胞比容为10-60%。 Sun和Munn [20,21]使用格子Boltzmann方法(LBM)研究了20-40nm通道中的RBC变形。他们将RBCs建模为二维固体颗粒。 Li等。 [22]已经使用LBM对狭窄的微血管中的刚性颗粒悬浮液进行二维模拟。 IBM是近几十年来成功用于模拟流体中柔性体动力学的方法之一。这种方法由Peskin [23]于1972年首次引入,以研究心脏瓣膜周围的流动,并发展成为解决涉及流固相互作用的问题的有效方法。它是数学公式和数值方案的组合[24-26]。本研究利用格子Boltzmann方法和浸没边界研究了具有狭窄曲线的微通道中红细胞(RJBC)的运动和变形。将本文的结果与可用结果进行比较,并观察到良好的一致性。

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