红细胞在微小血管中的流动理论分析
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摘要
近几年,红细胞在微小血管中的流动分析问题,越来越受到人们的关注。微循环体系是人体血液循环系统中最基层的结构和功能单位,在整个血液循环中起重要作用,而微小血管作为微循环的主要组成部分,直接与组织细胞相接触,承载着主要的物质运输,但是迄今为止,有关此课题的研究还不多。由于该课题的可行性和重要性,作者对其进行了初步的综合理论分析。
首先,本文对微循环流体力学的研究与进展进行了概述,阐述了微观流体力学的目的和意义,并对微观血液流变学数值研究的国内外发展状况和发展趋势做了简单回顾和介绍。
其次,介绍了前向跟踪法(Front-tracking Method),又名界面追踪法的概念,解释了该方法的基本理论,并对其进行了总结与讨论,最后以举例的方式阐述了如何在红细胞研究中应用该方法。
然后,对晶格Boltzmann方法进行了简介,详细介绍了晶格Boltzmann万法常用的边界条件,并对该方法进行了改进,使其更加适用于本文的模型。
最后,给出了本文的模拟与仿真结果。在本文的模拟过程中,将前向跟踪法与晶格波尔兹曼法相结合来研究三维双凹碟形胶囊式红细胞的变形。将红细胞模拟为内含牛顿流体的双凹碟形弹性薄膜胶囊,薄膜内外的液体看做具有不同物理特性的流体,使用晶格波尔兹曼方法的多块策略改善细胞模型附近的网格,增加三维计算的准确度和效率。本文使用的细网格仅覆盖每个计算轴的40%,同时选用离散为连接4098个点的8192个三角元的细胞薄膜模型,不仅提高了网格分辨率,而且节省了计算时间；从理论上证明了在雷诺数不大于0.25的剪切流中,惯性作用对细胞变性的影响都很小；同时得到了无因次参数为0.05,细胞内外粘度比为0.2时三维健康红细胞的360°稳定坦克履行为。不仅成功模拟了惯性作用下典型的三维红细胞坦克履行为,而且使用的细网格仅占整个计算区域的6.4%,在保证计算准确度的同时提高了计算效率,为模拟三维红细胞变形提供了一种更加可行的途径。
In the recent years, the flow simulation problem of red blood cells in the tiny blood vessels has been given more and more attention. Microcirculation is human blood circulation system's most basic structure and functional unit, which plays an important role in the whole blood circulation. The tiny blood vessels as the main composition of the microcirculation contact with tissue cells directly, bearing the main material transportation, however, so far, the research about this topic is not much. Due to the feasibility and importance of this issue, the author conducts a preliminary comprehensive theoretical analysis.
First of all, this paper summarizes the research and progress on microcirculation fluid dynamics, expounds the purpose and significance of the microscopic fluid mechanics, and reviews and introduces simply the micro-hemorheology numerical research situation and the development trend both at home and abroad.
Secondly, introduces the concept of the Front-tracking method, explains its basic theory and theorem, summarizes and discusses the method, and then elaborates how to study blood cells research with this method by example.
Then, introduces the lattice Boltzmann method briefly, recommends in detail the boundary conditions that the lattice Boltzmann method commonly used, and improves the method so that it is more suitable for model mentioned in this paper.
Finally, the simulations are given in this paper with the simulation results. Lattice Boltzmann method combines with the front-tracking method to study the three dimensional deformation behavior of biconcave discoid capsule erythrocyte model. The RBC model chose as an elastic biconcave discoid thin membrane capsule containing Newton fluid, fluid which in and outside of the erythrocyte model can have different physical properties, multi-block strategy of Lattice Boltzmann Method is used to improve the grid around the erythrocyte model. In this method, thin grid covers only 40% of each calculation shaft, and a cell membrane model discreting 8192 triangle elements connecting 4098 points is chosen, which not only improves the grid resolution, but also saved calculation time; the inertia effect on red blood cells deformation in shear flow is theoretically proved to be small when Reynolds number was less than 0.25; and the 360°stable tank-treading motion of healthy red blood cells is simulated when non-dimensional parameter is 0.05, with the viscosity ratio between inside and outside the erythrocyte is 0.2. Not only successfully simulate typical three-dimensional erythrocyte tank-treading motion under inertial function, but also improve the calculation accuracy and efficiency by using fine meshes which accounted only 6.4% of the whole calculation area, and so provide a more feasible approach for simulating the three-dimensional erythrocyte deformation.
首先,本文对微循环流体力学的研究与进展进行了概述,阐述了微观流体力学的目的和意义,并对微观血液流变学数值研究的国内外发展状况和发展趋势做了简单回顾和介绍。
其次,介绍了前向跟踪法(Front-tracking Method),又名界面追踪法的概念,解释了该方法的基本理论,并对其进行了总结与讨论,最后以举例的方式阐述了如何在红细胞研究中应用该方法。
然后,对晶格Boltzmann方法进行了简介,详细介绍了晶格Boltzmann万法常用的边界条件,并对该方法进行了改进,使其更加适用于本文的模型。
最后,给出了本文的模拟与仿真结果。在本文的模拟过程中,将前向跟踪法与晶格波尔兹曼法相结合来研究三维双凹碟形胶囊式红细胞的变形。将红细胞模拟为内含牛顿流体的双凹碟形弹性薄膜胶囊,薄膜内外的液体看做具有不同物理特性的流体,使用晶格波尔兹曼方法的多块策略改善细胞模型附近的网格,增加三维计算的准确度和效率。本文使用的细网格仅覆盖每个计算轴的40%,同时选用离散为连接4098个点的8192个三角元的细胞薄膜模型,不仅提高了网格分辨率,而且节省了计算时间；从理论上证明了在雷诺数不大于0.25的剪切流中,惯性作用对细胞变性的影响都很小；同时得到了无因次参数为0.05,细胞内外粘度比为0.2时三维健康红细胞的360°稳定坦克履行为。不仅成功模拟了惯性作用下典型的三维红细胞坦克履行为,而且使用的细网格仅占整个计算区域的6.4%,在保证计算准确度的同时提高了计算效率,为模拟三维红细胞变形提供了一种更加可行的途径。
In the recent years, the flow simulation problem of red blood cells in the tiny blood vessels has been given more and more attention. Microcirculation is human blood circulation system's most basic structure and functional unit, which plays an important role in the whole blood circulation. The tiny blood vessels as the main composition of the microcirculation contact with tissue cells directly, bearing the main material transportation, however, so far, the research about this topic is not much. Due to the feasibility and importance of this issue, the author conducts a preliminary comprehensive theoretical analysis.
First of all, this paper summarizes the research and progress on microcirculation fluid dynamics, expounds the purpose and significance of the microscopic fluid mechanics, and reviews and introduces simply the micro-hemorheology numerical research situation and the development trend both at home and abroad.
Secondly, introduces the concept of the Front-tracking method, explains its basic theory and theorem, summarizes and discusses the method, and then elaborates how to study blood cells research with this method by example.
Then, introduces the lattice Boltzmann method briefly, recommends in detail the boundary conditions that the lattice Boltzmann method commonly used, and improves the method so that it is more suitable for model mentioned in this paper.
Finally, the simulations are given in this paper with the simulation results. Lattice Boltzmann method combines with the front-tracking method to study the three dimensional deformation behavior of biconcave discoid capsule erythrocyte model. The RBC model chose as an elastic biconcave discoid thin membrane capsule containing Newton fluid, fluid which in and outside of the erythrocyte model can have different physical properties, multi-block strategy of Lattice Boltzmann Method is used to improve the grid around the erythrocyte model. In this method, thin grid covers only 40% of each calculation shaft, and a cell membrane model discreting 8192 triangle elements connecting 4098 points is chosen, which not only improves the grid resolution, but also saved calculation time; the inertia effect on red blood cells deformation in shear flow is theoretically proved to be small when Reynolds number was less than 0.25; and the 360°stable tank-treading motion of healthy red blood cells is simulated when non-dimensional parameter is 0.05, with the viscosity ratio between inside and outside the erythrocyte is 0.2. Not only successfully simulate typical three-dimensional erythrocyte tank-treading motion under inertial function, but also improve the calculation accuracy and efficiency by using fine meshes which accounted only 6.4% of the whole calculation area, and so provide a more feasible approach for simulating the three-dimensional erythrocyte deformation.
引文
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[2]Back L. H., Liem T. K., Kwack E. Y. Flow measurements in a highly curved atherosclerotic comonary artery cast of man [J]. Biomech. Engr.,1992,114(2):232-240.
[3]冯元桢.生物力学[M].北京：科学出版社,1983.
[4]Sobin S, Fung Y. C. Elasticity of the Pulmonary Alveolar Microvascular Sheet in the Cat [J]. Journal of the American Heart Association,1972,30:440-450.
[5]Bugliarello G., Hsiao G. C. A Mathematical Model of the Flow in Axial Plasmatic Gaps of The Smaller Vessels. Biorheology,1970,7:5-36
[6]Lew H. S., Fung Y. C. The Motion of the Plasma Between the Red Cells in the Bolus Flow [J]. Biorhe
[7]Skalak R. Effect of Hematocrit and Rouleaux on Apparent Viscosity in Capillaries [J]. Biorheology,1972,9:67-82..
[8]Sobin S., Fung Y. C. Elasticity of the Pulmonary Alveolar Sheet [J]. Journal of the American Heart Association,1972,30:451-469.
[9]修瑞娟.世界微循环研究的回顾与展望[J].中国微循环,1999,3(1)：5-8.
[10]郭尚平.脏器渗流多孔介质的物理特征[J].力学学报,1982,13(1)：26-33.
[11]黄伟.心血管系统的生理流动虚拟现实[D].北京工业人学硕十学位论文,2003.
[12]检验地带网.血.液流变学原理及临床应用[EB/OL]. http://www.labdd.com/a/zhuanti/xue--liubianzhuanti/8029.html,2010--7-9/2011-04-01.
[13]张翼.浅谈《临床血液流变学》培养和提高学生综合素质的有效途径[J].数理医药学,2009,3：12-16
[14]Discher D. E., Mohandas N., Evans E. A. Molecular maps of red cell deformation:hidden elasticity and in situ connectivity [J]. Science,1994,266:1032-1035.
[15]Suresh S., Spatz J., Mills J. P., et al. Connections between single-cell biomechanics and human disease states:gastrointestinal cancer and malaria [J]. Acta Biomaterialial,2005, 15-30.
[16]Strey H., Peterson M., Sackmann E. Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition [J]. Biophysical Journal,1995,69(2):478-488.
[17]Lee J. C. Discher D. E. Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding [J]. Biophysical Journal,2001,81(6):3178-3192.
[18]Barthes-Biesel D. Motion of spherical microcapsule freely suspended in a linear shear flow. J Fluid Mech [J].1980,100:831-53.
[19]Yue P, Feng JJ, Bertelo CA, et al. An arbitrary Lagrangian-Eulerian method for simulating bubble growth in polymer foaming [J]. Comput Phys,2007,226:2229-49.
[20]Pozrikidis C. Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow [J]. Fluid Mech,1995,297:123-52.
[21]Ramanujan S, Pozrikidis C. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow:Large deformations and the effect of capsule viscosity [J]. Fluid Mech,1998,361:117-43.
[22]Lac E, Barthes-Biesel D, Pelekasis DA, et al. Spherical capsules in three-dimensional unbounded stokes flows:effect of the membrane constitutive law and onset of buckling [J]. Fluid Mech 2004,516:303-34.
[23]Lac E, Barthes-Biesel D. Deformation of a capsule in simple shear flow:effect of membrane prestress [J]. Phys Fluids,2005,17:072105.
[24]Peskin CS. The immersed boundary method [J]. Acta Numer,2002,11:479-517.
[25]Eggleton CD, Popel AS. Large deformation of red blood cell ghosts in s simple shear flow [J]. Phys Fluids,1998,10:1834-45.
[26]Keller SR, Skalak R. Motion of a tank-treading ellipsoid particle in a shear flow [J]. Fluid Mech,1982,120:27-47.
[27]Yu H, Luo LS, Girimaji SS. LES of turbulent square jet flow using an MRT lattice Boltzmann model [J]. Comput Fluids,2006,35:957-65.
[28]Feng ZG, Michaelides EE. Proteus:a direct forcing method in the simulations of particulate flows [J]. Comput Phys,2005,202:20-51.
[29]Peng Y, Luo LS. A comparative study of immersed-boundary and interpolated bounce-back methods in LBE [J]. Prog Comput Fluid Dyn,2008,8:156-67.
[30]Filippova O, Hanel D. Grid refinement for lattice-BGK models [J]. Comput Phys,1998, 147:219-28.
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