受支架支撑的血管管壁变形及应力分析

摘要：为了计算动脉粥样硬化和局部斑块形成的堵塞对血管壁工作状态的影响,本文根据血液流动的连续性方程、运动方程及管壁运动方程,在给定了血压波形函数的基础上,求得了狭窄血管管壁的径向位移及环向应力。分析了不同狭窄程度对血管壁变形及应力的影响;给出了不同狭窄情况下及局部斑块硬化程度不同时,血管植入支架所需的作用力。从而计算出了植入支架后血管壁的径向位移及应力状态。本文的研究结果可供临床上对狭窄血管植入支架后的变形与受力分析,和支架的正确安放参考,可避免发生堵塞严重或血管过渡硬化时,由于安放支架不当而使发生血管破裂的医疗事故。     

Numerical calculation of two-dimensional flow in the channel with a partially compliant wall

The present paper is concerned with the flow in a two-dimensional channel whose wall is partially compliant. The flow field is calculated by the finite-difference method. Results are as follows: (1) When the upstream condition is given by steady flow (Reynolds number Re = 50), a compliant part of the wall oscillates with a frequency nearly equal to the characteristic frequency of the elastic wall. Absolute values of the pressure drop across the compliant part become small compared with those of the plane Poiseuille flow with wholly rigid walls. This ensures under physiological conditions that the blood can be transported more easily toward distal parts due to the compliance of vessel walls. (2) When the upstream condition is given by a pulsatile flow (Womersley number α = 8), interaction arises between characteristic frequency of the wall and basic frequency of the main stream near the compliant wall. As the basic frequency of pulsatile flow decreases, absolute values of mean pressure, which drop across the compliant wall, also become small compared with those of pulsatile flow between wholly rigid walls.     

A study on the stability of blood vessels

The paper deals with an analytical study on the stability of blood vessel walls. The theory of small deformation superposed on a known state of finite deformation, together with the anisotropic visco-elastic constitutive relations of Vaishnav and Patel [1] for vascular tissues, are employed for the purpose. By using the material functions of Young et al. [2], the latent instabilities of canine middle descending thoracic aortic wall are predicted in terms of the circumferential and axial extension ratios.Paper presented by J. C. Misra at the Fourth International Congress of Biorheology, Jikei University School of Medicine, Tokyo (Japan), July 27–August 1, 1981.     

Wave propagation in a fluid flowing through a curved thin-walled elastic tube

The pulsatile flow in a curved elastic pipe of circular cross section is investigated. The unsteady flow of a viscous fluid and the wall motion equations are written in a toroidal coordinate system, superimposed and linearized over a steady state solution. Being the main application relative to the vascular system, the radius of the pipe is assumed small compared with the radius of curvature. This allows an asymptotic analysis over the curvature parameter. The model results an extension of the Womersley's model for the straight elastic tube. A numerical solution is found for the first order approximation and computational results are finally presented, demonstrating the role of curvature in the wave propagation and in the development of a secondary flow.     

旋转爆震燃烧室轴向和周向长度对其出口流场压力和温度的影响

为了研究旋转爆震燃烧室与涡轮的匹配特性,利用二维欧拉方程数值研究了基于当量H₂/Air燃烧的旋转爆震燃烧室出口流场特性,对比分析了不同燃烧室轴向长度和周向长度出口总压脉动、总压畸变以及出口温度分布规律。结果表明:旋转爆震燃烧室在稳定工作状态下,其出口总压的脉动值会呈现周期性振荡;燃烧室尺度对发动机出口流场的不均匀性有很大影响,随着燃烧室轴向长度的增大或周向尺寸的减小,其出口总压脉动均值、畸变指数和出口温度分布系数均会减小,其出口流场均匀性提高。此外,爆震波高度随着周向尺寸的增大而增大;轴向尺寸对爆震波高度几乎不产生影响。     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

脉动流条件下动脉狭窄血管内脂质浓度极化现象的计算机数值模拟

在脉动流条件下,用计算机数值模拟的方法对低密度脂蛋白(LDL)在动脉狭窄血管段内的质量传输进行了研究。计算结果表明．无论是在定常流还是在脉动流条件下．LDL都将聚积于血管狭窄处峰口附近的流动分离点,LDL壁面浓度在此处最高。在脉动流条件下,LDL在血流受扰动区的聚积高于定常流的值;而且．流动分离点处LDL壁面浓度峰值覆盖的区域也宽于定常流。本文所揭示出的LDL在血管狭窄处的质量传输现象可能在动脉粥样硬化的局部性和动脉狭窄的形成中起着很重要的作用。     

Generation of Adverse Pressure Gradient in the Circumferential Flashback of a Premixed Flame

Circumferential upstream propagation of a premixed flame in a region confined between two concentric tubes is considered. The cold flow in this configuration features rotational motion and the flame is modelled as an interface separating the burned and unburned gases. Through an analytical solution of the integral form of the governing equations, it is shown that the static pressure increases across the flame. Hence, the circumferential propagation of the flame is associated with the generation of an adverse pressure gradient. The theoretical prediction of the pressure increase is, further, supported by the experimental observations and discussed in the context of the theory of flame back pressure. The results extend the recent findings on the generation of adverse pressure gradient during the axial propagation of swirling flames, to the circumferential direction. It is argued that the demonstrated pressure gain across the flame can significantly facilitate flame flashback.     

脉动血压对在体轴向极限强约束血管壁应力分布的影响

本文详细分析正弦脉动压力载荷对动脉管壁应力分布的影响。结果表明,对某确定时刻,包含在运动方程中的惯性项对血管壁应力的影响很小,可忽略不计;在体轴向极限强约束下,血管壁周向应力随时间的变化曲线与压力曲线同相位和同周期,而且振幅不随频率的快慢而改变。一个心动周期内,血管内、外壁处周向应力随时间变化的平均值只与脉动压力载荷的平均值有关,而振幅主要与脉压有关,在内壁处随平均压的改变有一定变化,但在外壁处受平均压的影响很小。     

局部狭窄血管中血液振荡流的速度和切应力

本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型，给出了血液的轴向流速，径向流速和切应力的包含压力梯度项的解析表达式，并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算，详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明，与均匀管情况相比，在狭窄段内，血液振荡流轴向流速无论平均值还是脉动幅值均明显增大，且径向流速不再为零。但径向流速仍远小于轴向流速。同时，切应力也不再仅由轴向流速梯度提供，径向流速梯度也将产生切应力，但是在计算管壁切向上的切应力时，径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力（平均值和脉动值）将随着狭窄高度的增大而增大，在狭窄最大高度处达到最大，因而沿流动方向产生了较大的切应力梯度。     

The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision.     

The blood flow and the motion of vessel wall

The correlation problem between the blood flow and the motion of vessel wall in the mammalian circulatory system is discussed in this paper. Supposing the blood flow is under the stable oscillatory condition, a set of formulas for velocity distribution, pressure distribution, displacement of vessel wall and constraining stress are obtained. Kuchar’s formulas are extended from steady flow to unsteady oscillatory flow by means of the formulas obtained in this paper. The problem of elasticity effect of vessel wall is also discussed.     

Asymmetrical oscillation of a bubble confined inside a micro pseudoelastic blood vessel and the corresponding vessel wall stresses

Asymmetrical oscillation of a micro-bubble confined inside a deformable pseudoelastic vessel with comparable initial radius with the bubble is studied in detail. Unlike the symmetric oscillation in an unconstrained environment, the oscillating bubble under the constraint of a pseudoelastic vessel gradually becomes as an ellipsoid from a sphere (this is called asymmetrical effect), and leads to substantially larger stresses within the vessel wall. Influence of inertial effect, circumferential stiffness and pre-existing blood pressure on bubble’s asymmetrical oscillation are taken into account in the paper. Computational results show that a vessel wall with larger circumferential stiffness corresponds to larger stress amplitude with higher frequency within the wall, where the stress amplitude and the pertinent frequency are the two most dominating parameters in determining the failure event under cyclic loading, as well known in the community of materials science. Similar results have been obtained for the case of decreasing in thickness of vessel walls, and for the case of increasing pre-existing pressure in the liquid filling the vessel. These conclusions support the notion that the asymmetric effect is one of the primary mechanisms for the clinical injuries of those with thinner vessel walls, such as capillary and small blood vessels, and for the higher risk of elder and hypertension patients in the shock-wave lithotripsy and other medical procedures involving shock waves, such as ultrasound-assisted encapsulated drug delivery.     

THE COUPLE MOTION BETWEEN VESSEL WALL AN DBLOOD IN THE ENTRANCE REGION OF A TAPERED VESSEL

ＴＨＥＣＯＵＰＬＥＭＯＴＩＯＮＢＥＴＷＥＥＮＶＥＳＳＥＬＷＡＬＬＡＮＤＢＬＯＯＤＩＮＴＨＥＥＮＴＲＡＮＣＥＲＥＧＩＯＮＯＦＡＴＡＰＥＲＥＤＶＥＳＳＥＬＣｅｎＲｅｎ－ｊｉｎｇ（岑人经）ＱｉｎＣｈａｎ（秦婵）ＴａｎＺｈｅ－ｄｏｎｇ（谭哲东）（ＳｏｕｔｈＣ...     

Numerical modelling of rotating tangential layers (jets) in shells under strong uniform magnetic field

A numerical study of tangential layers in steady‐state magnetohydrodynamic rotating flows is presented using CFD to solve the inductionless governing equations. The analysis considers two basic flow configurations. In the first, a fluid is enclosed in a cylinder with electrically perfect conducting walls and the flow is driven by a small rotating, conducting disk. In the second, a flow is considered in a spherical shell with an inner rotating sphere. The fluid in both cases is subjected to an external axial uniform magnetic field. The results show that these flows exhibit two different types of flow cores separated from each other by a tangential layer parallel to the axis of rotation. The inner core follows a solid‐body rotation while the outer is quasistagnant. A counter‐rotating jet is developed in the tangential layer between the cores. The characteristics of the tangential layer and the properties of the meridional motion are determined for a wide range of Hartmann numbers. Distributions of angular velocity of circumferential flow and electric potential are obtained and the results are compared with those of analytic methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid

Steady-state motion of a bubble in the shape of an ellipsoid of revolution has been studied [1, 2]. Steady-state motion and small oscillations of an ellipsoid of revolution around the equilibrium state were studied with the help of Lagrangian equations [3]. In this paper, possible equilibrium shapes of a bubble in the form of a triaxial ellipsoid are studied. The dependence of the pressure difference at the stagnation point and within the gas bubble on deformation is determined for steady-state motion. The stability of the equilibrium shape with respect to small perturbations of the axes of the ellipsoid is investigated through analysis of potential energy in the neighborhood of the extremum.     

Mechanical buckling of a functionally graded cylindrical shell with axial and circumferential stiffeners using the third-order shear deformation theory

This paper deals with an analytical approach of the buckling behavior of a functionally graded circular cylindrical shell under axial pressure with external axial and circumferential stiffeners. The shell properties are assumed to vary continuously through the thickness direction. Fundamental relations and equilibrium and stability equations are derived using the third-order shear deformation theory. The resulting equations are employed to obtain the closed-form solution for the critical buckling loads. A simply supported boundary condition is considered for both edges of the shell. The comparison of the results of this study with those in the literature validates the present analysis. The effects of material composition (volume fraction exponent), of the number of stiffeners and of shell geometry parameters on the characteristics of the critical buckling load are described. The analytical results are compared and validated using the finite-element method. The results show that the inhomogeneity parameter, the geometry of the shell and the number of stiffeners considerably affect the critical buckling loads.     

Effect of elastic wall motion on oscillatory flow of micropolar fluid in an annular tube

Summary Oscillatory flow of a micropolar fluid in an annular tube is investigated. The outer wall of the tube is taken to be elastic and the variation in the diameter of the elastic wall due to pulsatile nature of pressure gradient is assumed to be small. The wall motion is governed by a tube law. The nonlinear equations governing the fluid flow and the tube law are solved using perturbation analysis. The steady-streaming phenomenon due to the interaction of convected inertia with viscous effects is studied. The analysis, is carried out for zero mean flow rate. It presents the effects of the elastic nature of the wall combined with micropolar fluid parameters on the mean pressure gradient and wall shear stress for different catheter sizes and frequency parameters. It is found that the effect of micropolarity is of considerable importance for small steady-streaming Reynolds number. Also, it is observed that the relationship between mean pressure gradient and the flow rate depends on the amplitude of the diameter variation, flow rate waveforms and the phase difference between them.