磁场、多孔性和各向异性动脉壁有多处狭窄段时对血液流动的影响

Kh·S·梅克赫默; M·H·哈劳恩; M·A·艾可特

doi:10.3879/j.issn.1000-0887.2011.08.009

磁场、多孔性和各向异性动脉壁有多处狭窄段时对血液流动的影响

doi: 10.3879/j.issn.1000-0887.2011.08.009

阿兹哈尔大学理学院数学系,开罗 11884,埃及;
艾因〖KG-*4〗·〖KG-*4〗夏姆斯大学教育学院数学系,开罗 11566,埃及;

详细信息

中图分类号: R318.01; R543.5; O361.3
计量
- 文章访问数: 1496
- HTML全文浏览量: 179
- PDF下载量: 716
- 被引次数: 0
出版历程
- 收稿日期: 2010-09-16
- 修回日期: 2011-04-10
- 刊出日期: 2011-08-15

Effects of Magnetic Field,Porosity and Wall Properties for Anisotropically Elastic Multi-Stenosis Arteries on the Characteristics of Blood Flow

Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt;
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt;
Department of Mathematics, Faculty of Science, Suez Canal University, Suez 41522, Egypt

摘要

摘要: 建立一个血液流动的数学模型：多孔介质在磁场作用下，血液流过一段有多处狭窄段的弹性动脉；用一个各向异性的弹性圆柱形管道模拟动脉，用粘性不可压缩的导电流体表示血液，动脉有轻微的局部性狭窄，形成一段内腔局部变窄的动脉，并完成该模型的数学分析．详细阐述了血管壁参数对血液流动的影响，参数包括纵向和圆周向的粘弹性应力分量Tt和Tθ、血管壁的各向异性度γ、血管及其周边结缔组织的总质量M、完全栓管中粘性约束的贡献C和弹性约束的贡献K，并用图形表示壁面剪切应力的分布、径向和轴向的速度等．还研究了狭窄形状参数m、渗透率常数κ、Hartmann数Ha和血管狭窄区的最大高度δ，对血液流动特征的影响．研究表明，流动受到周边结缔组织（动脉壁运动）的影响式微，血管壁的各向异性度，是确定动脉材料的一个重要指标．进一步发现壁剪切力分布，随着Tt和γ的增加而增加，随着Tθ，M，C和K的增加而减少．壁面剪切应力分布的传播，以及壁面处阻力阻抗的传播，栓管与自由管相比要低得多；狭窄段咽喉处的剪切应力分布特性，完全栓管和自由管正相反．靠近中心线的俘获区大小，随着渗透率κ的增加而增大；随着Hartmann数Ha的增加而减小．最后，狭窄段非对称时，逐渐形成俘获区；狭窄段对称时，不出现俘获区，各向同性自由管（无初始应力）中俘获区的大小，比完全栓管中的小得多．
- 狭窄 /
- 各向异性 /
- 自由管 /
- 栓管 /
- 俘获区
Abstract: A mathematical model for blood flow through an elastic artery with multi-stenosis under effect of a magnetic field in a porous medium was presented.The arterial segment under consideration was simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood.The analysis was carried out for an artery with mild local narro wing in its lumen forming a stenosis.The effects of arterial wall parameters that represent the viscoelastic stresses components acting along the longitudinal and circumferential directions T_t and T_θ respectively,the degree of anisotropy of the vessel wall γ, the total mass of the vessel and the surrounding tissues M and the contributions of the viscous and elastic constraints to the total tethering C and K respectively on the resistance impedance, the wall shear stress distribution,the radial and axial velocities had been well illustrated.Also the effects of the stenosis shape m,the constant of permeability κ,the Hartmann number Ha and the maximum height of the stenosis size δ on the fluid flow characteristics were investigated.The obtained results show that the flow was appreciably influenced by the surrounding connective tissues of the motion of the arterial wall and the degree of aniso tropy of the vessel wall play an important role to determine the material of the artery.Further the wall shear stress distribution increases with increasing Tt and γ while it decreases with increasing T_θ,M,C and K.The transmission of the wall shear stress distribution and the resistance impedance at the wall surface through a tethered tube were substantially lower than those through the free tube while the shearing stress distribution at the stenosis throathad inverse character through to tally tethered and free tubes.The trapping bolus increases in size to ward the line center of the tube as the constant of permeability κ increases and it decreases by increasing Hartmann number Ha.Finally the trapping bolus appears gradually in the case of non-symmetric stenosis while it seems to disappear in the case of symmetric stenosis and the size of trapped bo lus for the stream lines in the free isotro pictube(means the tube which initially unstressed) was smaller than those in the tethered tube.
- stenosis /
- degree of anisotropy /
- free tube /
- tethered tube /
- trapping bolus

HTML全文

参考文献(28)

[1]	Chakravarty S, Ghosh Chowdhury A. Response of blood flow through an artery under stenotic conditions[J]. Rheol Acta, 1988, 27(4): 418-427. doi: 10.1007/BF01332163
[2]	Mekheimer Kh S, Haroun Mohammed H, El Kot M A. Induced magnetic field influences on blood flow through an anisotropically tapered elastic arteries with overlapping stenosis in an annulus[J]. Can J Phys, 2011, 89(2): 201-212. doi: 10.1139/P10-103
[3]	Craig I J D, Watson P G. Magnetic reconnection solutions based on a generalized Ohm’s law[J]. Solar Physics, 2003, 214(1): 131-150. doi: 10.1023/A:1024075416016
[4]	Stud V K, Sephon G S, Mishra R K. Pumping action on blood flow by a magnetic field[J]. Bulletin Math Biology, 1977, 39(3): 385-390.
[5]	Agrawal H L, Anwaruddin B. Peristaltic flow of blood in a branch[J]. Ranchi Univ Math J, 1984, 15: 111-121.
[6]	Abd Elnaby M A, Haroun M H. A new model for study the effect of wall properties on peristaltic transport of a viscous fluid[J]. Communications in Nonlinear Sci and Num Simulation, 2008, 13(4): 752-762. doi: 10.1016/j.cnsns.2006.07.007
[7]	Haroun M H. On non-linear magnetohydrodynamic flow due to peristaltic transport of an old rayed 3-constant fluid[J]. Z Naturforsch A, 2006, 61: 263-274.
[8]	Haroun M H. Non-linear peristaltic flow of a fourth grage fluid in an inclined asymmetric channel[J]. Computational Material Sci, 2007, 39(2): 324-333. doi: 10.1016/j.commatsci.2006.06.012
[9]	Mekheimer Kh S, El Kot M A. The micropolar fluid model for blood flow through stenotic arteries[J]. Int J Pure and Appl Math, 2007, 4(36): 393-405.
[10]	梅克赫默 Kh S, El 科特 M A. 磁场和Hall电流对狭窄动脉中血液流动的影响[J]. 应用数学和力学, 2008, 29(8): 991-1002.(Mekheimer Kh S, El Kot M A. Influence of magnetic field and Hall currents on blood flow through stenotic artery[J]. Applied Mathematics and Mechanics(English Edition), 2008, 29(8): 1093-1104.)
[11]	Mekheimer Kh S, El Kot M A. The micropolar fluid model for blood flow through a tapered arteries with a stenosis[J]. Acta Mech Sin, 2008, 24(6): 637- 644. doi: 10.1007/s10409-008-0185-7
[12]	Mekheimer Kh S, El Kot M A. Suspension model for blood flow through arterial catheterization[J]. Chem Eng Comm, 2010, 197(9):1-20.
[13]	Biswas D, Chakraborty U S. Pulsatile blood flow through a catheterized artery with an axially nonsymmetrical stenosis[J]. Applied Mathematical Sciences, 2010, 4(58): 2865-2880.
[14]	Srivastavaa V P, Rastogi Rati, Vishnoi Rochana. A two-layered suspension blood flow through an overlapping stenosis[J]. Computers and Mathematics With Applications, 2010, 60(3): 432-441. doi: 10.1016/j.camwa.2010.04.038
[15]	Sankar D S, Lee Usik. Two-fluid Casson model for pulsatile blood flow through stenosed arteries: a theoretical model[J]. Commun Nonlinear Sci Numer Simulat, 2010, 15(8): 2086-2097. doi: 10.1016/j.cnsns.2009.08.021
[16]	Srivastava V P, Mishra Shailesh, Rastogi Rati. Non-Newtonian arterial blood flow through an overlapping stenosis[J]. A A M International Journal, 2010, 5(1): 225-238.
[17]	Siddiqui S U, Verma N K, Mishra S, Gupta R S. Mathematical modeling of pulsatile flow of Casson’s fluid in arterial stenosis[J]. Applied Mathematics and Computation, 2009, 210(1): 1-10. doi: 10.1016/j.amc.2007.05.070
[18]	Layek G C, Mukhopadhyay S, Gorla Rama Subba Reddy. Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction[J]. International Journal of Engineering Science, 2009,47(5/6): 649-659. doi: 10.1016/j.ijengsci.2009.01.011
[19]	Pincombe B, Mazumdar J, Hamilton-Craig I. Effects of multiple stenoses and post-stenotic dilatation on non-Newtonian blood flow in small arteries[J]. Medical & Biological Engineering & Computing, 1999, 37(5): 595-599.
[20]	Tashtoush B, Magableh. Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries[J]. Heat Mass Transfer, 2008,44(3): 297-304.
[21]	Li M X, Beech-Brandta J J, Johnb L R, Hoskinsc P R, Eassona W J. Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses[J]. Journal of Biomechanics, 2007, 40(16): 3715-3724. doi: 10.1016/j.jbiomech.2007.06.023
[22]	Mishra B K, Verma N. Magnetic effect on blood flow in a multiple stenosed artery[J]. Appl Math Comp, 2007, 1: 1-7.
[23]	Chakravarty S, Datta A, Mandal P K. Analysis of nonlinear blood flow in a stenosed flexible artery[J]. Int J Engng Sci, 1995, 33(12): 1821-1837. doi: 10.1016/0020-7225(95)00022-P
[24]	Chakravarty S. Pulsatile blood flow through arterioles[J]. Rheol Acta, 1987, 26(2): 200-207. doi: 10.1007/BF01331978
[25]	Atabek H B, Lew H S. Wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube[J]. Biophysical Journal, 1966, 6(4): 481-503. doi: 10.1016/S0006-3495(66)86671-7
[26]	Atabek H B. Wave propagation through a viscus fluid contained in a tethered, initially stressed, othotropic elastic tube[J]. Biophysical Journal, 1968,8(5): 626-649. doi: 10.1016/S0006-3495(68)86512-9
[27]	Kalita P, Schaefer R. Mechanical models of artery walls[J]. Arch Comput Methods Eng, 2008, 15(1): 1-36. doi: 10.1007/s11831-007-9015-5
[28]	Chakravarty S, Sarifuddin, Mandal P K. Unsteady flow of a two-layer blood stream past a tapered flexible artery under stenotic conditions[J]. Comp Methods in Appl Math, 2004, 4(4): 391-409.