Gravitational effects on global hemodynamics in different postures: A closed-loop multiscale mathematical analysis

We present a novel methodology and strategy to predict pressures and flow rates in the global cardio-vascular network in different postures varying from supine to upright. A closed-loop, multiscale mathematical model of the entire cardiovascular system (CVS) is developed through an integration of one-dimensional (1D) modeling of the large systemic arteries and veins, and zero-dimensional (0D) lumped-parameter modeling of the heart, the cardiac-pulmonary circulation, the cardiac and venous valves, as well as the microcirculation. A versatile junction model is proposed and incorporated into the 1D model to cope with splitting and/or merging flows across a multibranched junc-tion, which is validated to be capable of estimating both subcritical and supercritical flows while ensuring the mass conservation and total pressure continuity. To model grav-itational effects on global hemodynamics during postural change, a robust venous valve model is further established for the 1D venous flows and distributed throughout the entire venous network with consideration of its anatomically real-istic numbers and locations. The present integrated model is proven to enable reasonable prediction of pressure and flow rate waveforms associated with cardiopulmonary circu-lation, systemic circulation in arteries and veins, as well as microcirculation within normal physiological ranges, partic-ularly in mean venous pressures, which well match the in vivo measurements. Applications of the cardiovascular model at different postures demonstrate that gravity exerts remarkable influence on arterial and venous pressures, venous returns and cardiac outputs whereas venous pressures below the heart level show a specific correlation between central venous and hydrostatic pressures in right atrium and veins.     

Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries

Flow and pressure waves, originating due to the contraction of the heart, propagate along the deformable vessels and reflect due to tapering, branching, and other discontinuities. The size and complexity of the cardiovascular system necessitate a “multiscale” approach, with “upstream” regions of interest (large arteries) coupled to reduced-order models of “downstream” vessels. Previous efforts to couple upstream and downstream domains have included specifying resistance and impedance outflow boundary conditions for the nonlinear one-dimensional wave propagation equations and iterative coupling between three-dimensional and one-dimensional numerical methods. We have developed a new approach to solve the one-dimensional nonlinear equations of blood flow in elastic vessels utilizing a space-time finite element method with GLS-stabilization for the upstream domain, and a boundary term to couple to the downstream domain. The outflow boundary conditions are derived following an approach analogous to the Dirichlet-to-Neumann (DtN) method. In the downstream domain, we solve simplified zero/one-dimensional equations to derive relationships between pressure and flow accommodating periodic and transient phenomena with a consistent formulation for different boundary condition types. In this paper, we also present a new boundary condition that accommodates transient phenomena based on a Green’s function solution of the linear, damped wave equation in the downstream domain.     

弯曲动脉的血流动力学数值分析

利用计算流体力学的理论和方法对弯曲动脉中的血流动力学进行数值分析，是研究心血管疾病流体动力学机理的一种行之有效的方法。本文将升主动脉、主动脉弓和降主动脉联系起来作为弯曲动脉几何模型，给出了血液流动的边界条件以及计算条件。根据生理脉动流条件，对狗的弯曲动脉几何模型内发展中的血液流动进行了有限元数值模拟，并利用可视化方法对血液流动的轴向速度、二次流、壁面切应力等计算结果进行了分析。研究结果表明，在弯管内侧壁处，同时存在主流方向和二次流方向的回流，此处容易形成涡流。弯管内侧壁比外侧壁的壁面切应力具有更强的脉动性。     

Axially sheared and pre-stressed hollow cylinder within the context of the theory of interacting continua

Investigating the effects of altered transmural pressure is of great importance. Indeed, many data obtained from experiments on isolated dog carotid arteries and jugular veins serve to provide a foundation describing the collapse of both arteries and veins for both positive and negative transmural pressures. It has been also reported that transmural pressure induces matrix-degrading activity in porcine arteries ex vivo. An illustrative example dealing with the application of a transmural pressure and the resulting transmural filtration of fluid through a pre-strained hollow conduit subjected to combined finite deformations is investigated here. Some results that can provide additional useful insight can help in improving the method for performing prosthesis conduit material for use with living tissue, understanding problems which involves the diffusion of ideal fluid-saturated wall for various mechanical parameters such as the pre-stress/strain and applied or induced axial shear are discussed.     

Noise Field in the Human Chest Due to Turbulent Flow in a Larger Blood Vessel

An acoustic model of a larger human blood vessel is developed. This model takes into account the main features of the acoustic generation and propagation of noise in the human chest from the source (turbulent pressure fluctuations in blood flow) to a receiver resting on the skin, and allows the consideration of a simple stenotic narrowing in the vessel. The low Mach number turbulent wall pressure models of Corcos, Chase, Ffowcs Williams, and Smol'yakov and Tkachenko are used to describe random sources in the vessel. The relationships obtained permit one to analyse the dependence of the resultant acoustic field in the thorax on the parameters of the blood flow and the vessel, and show the possibility of finding characteristic signs of the presence of a stenosis by comparison of noise fields from intact and diseased arteries. This revised version was published online in July 2006 with corrections to the Cover Date.     

含有启动压力梯度的渗流问题及其无网格解法

针对两种典型的涉及启动压力梯度的渗流问题,给出了无量纲化的渗流控制方程、初始条件和边界条件,并使用无网格方法进行数值模拟。计算结果使用Gringarten—Bourdet图版进行井底压力分析,给出了一种计算动边界位置的方法,并详细讨论了动边界变化情况。     

Propagation of guided waves in pressure vessel

Pressure vessels usually operate under extremes of high/low temperatures and high pressures. Defect, such as crack and corrosion, can result in leakage or rupture failures, even catastrophic incidents. Guided wave-based structural health monitoring (SHM) technology is one of the most prominent options in non-destructive evaluation and testing (NDE/NDT) techniques. Propagation of guided waves in a typical pressure vessel is systematically investigated in this study for the application of guided wave-based SHM. Shape of the pressure vessel is a cylinder with two end caps. Because of geometric similarity, theory of guided wave propagation in the cylinderical structure is analyzed to study dispersive features of guided waves in the pressure vessel. Dispersion curves of three different types of guided wave modes, viz. the longitudinal, torsional and flexural modes, are calculated using theoretical method. Based on the analyses and experimental wave signals, central frequency and wave parameters of incident wave are optimized. Effect of contained liquid on propagation of guided waves, especially the L(0, 2) mode, in the pressure vessel is further investigated to minimize energy leakage of the wave to the contained liquid. The analytical method, finite element analysis (FEA) and experiments are applied to study propagation characteristics of guided waves in the pressure vessel, so as to demonstrate the feasibility of guided wave-based non-destructive evaluation and testing (NDE/NDT) for such kind of complex structures.     

低温和低压环境下炸药爆炸冲击波的传播特性

针对高海拔或高空的低温、低压环境对炸药爆炸冲击波传播的影响,利用量纲分析理论和AUTODYN有限元软件,研究了低温、低压及海拔高度对炸药爆炸冲击波参量（峰值超压、比冲量和波阵面运动轨迹）的影响规律,建立了相应的计算公式,并通过数值模拟和实验数据进行了对比验证。结果表明,该计算公式可以有效预测低温和低压环境下炸药爆炸冲击波参量。环境压力降低,爆炸冲击波峰值超压和爆炸远场（比例距离Z>0.2 m/kg1/3）比冲量减小,冲击波传播速度增大。环境温度降低,冲击波比冲量增大,传播速度降低,峰值超压影响不大。海拔高度在0～9 000 m范围内,每升高1 000 m冲击波峰值超压和爆炸远场比冲量分别平均降低约3.9%和3.2%。海拔升高,爆炸近场冲击波传播速度升高,爆炸远场冲击波传播速度则降低。高海拔环境下低压对冲击波峰值超压和比冲量的影响大于低温,爆炸近场冲击波传播速度取决于低压的影响,爆炸远场冲击波传播速度取决于低温的影响。     

Propagation of perturbations in the three-dimensional boundary layer on a delta wing in the viscid-inviscid interaction regime

The propagation of perturbations in the three-dimensional boundary layer on a planar delta wing in a hypersonic gas stream is investigated in the strong viscid-inviscid interaction regime. A characteristic associated with the induced pressure is found and an integral relation determining the velocity of its propagation is obtained. The directional diagrams of the propagation velocity of the characteristic surface in the boundary layer are determined for a series of constitutive parameters. This makes it possible to calculate the perturbation propagation velocities in the boundary layer when the velocity profiles in the longitudinal and transverse directions are known.     

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, A_g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when A_g increases.     

谱载荷下疲劳裂纹扩展随机规律的实验研究

简要介绍了谱载荷下疲劳裂纹扩展试验的理论基础、方法和过程。讨论了各种数据处理方法对参数估计的影响,研究了疲劳裂纹扩展的随机规律。由试验得到的疲劳裂纹扩展试验数据估计了裂纹扩展方程的参数,计算出结构可靠度曲线,通过对试验结果的分析难证了以下结论：以时间为参量的裂纹扩展随机过程模型和以裂纹长度为参量的模型在一定条件下是统一的;数据处理方法的选择与可靠性分析的结果有密切的联系;裂纹扩展寿命受裂纹扩展队机     

A time-periodic approach for fluid-structure interaction in distensible vessels

The analysis of periodic unsteady incompressible flow inside compliant vessels is of considerable interest for the simulation of blood flow in arteries. Weakly coupled fluid-structure interaction (FSI) models seem to be most suitable for this purpose. For weakly coupled solution methods, however, often convergence may not be achieved for compliant vessels with an axial length scale that is large compared to the characteristic radius. In this study, a time-periodic method for weakly coupled FSI models is presented. Approximate solutions of subsequent time-periods are obtained using the solution of the previous time-period as an initial solution. For the first period, not only suitable boundary conditions are derived from a 1-D wave propagation model, but also the initial axial pressure distribution. The time-periodic method was successfully applied to straight, curved and bifurcating geometries. The new approach proves to have a far better computational stability than weakly coupled methods based on timestep-wise coupling, especially in vessels with a length that is an order of magnitude larger than the radius.     

方形管内楔形障碍物对火焰结构与传播的影响

通过实验与数值模拟方法对CH4/空气预混火焰在有楔形障碍物的卧式燃烧方管内的传播进行了研究。采用多镜头Cranz Schardin高速摄像机和压力传感器等实验设备获得了高清晰度的障碍物诱导火焰失稳的分幅时序照片以及障碍物背风表面压力变化曲线。数值模拟则基于RANS方法与EDU-Arrhenius燃烧模型,计算结果与实验结果基本相符,反映了火焰在管内传播与变形的详细过程。通过综合分析实验与计算结果,得到了由楔形障碍物导致的火焰加速与变形的内在机理,揭示了火焰传播过程中由层流燃烧向湍流燃烧转捩的本质。     

多相燃料空气炸药爆炸压力场研究

采用高速运动分析系统对固态燃料FAE（Fuel Air Explosive）分散、爆轰过程进行光学测量,用压电传感器等组成的压力测试系统对FAE爆炸压力场进行测量,对固态燃料FAE燃料分散、爆轰波及冲击波进行了研究。分析了气-固-液多相爆轰的特征和压力波形的特点,研究了其冲击波峰值超压及比冲量随传播距离变化的规律。在云雾区内,多相爆轰波压力波形具有多峰结构,爆炸波峰值超压及冲量为一恒定值;爆轰区外,爆轰波转变成爆炸冲击波,峰值压力和比冲量迅速衰减,得到了峰值超压、比冲量随传播距离的变化规律。     

Spherical blast waves in multicomponent media

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].     

沉底水雷爆炸威力的数值计算

采用冲击波物理中的阻抗匹配镜像线方法处理物质交界面,利用无网格光滑粒子流体动力学法(smoothed particle hydrodynamics,SPH)方法模拟沉底装药的水下爆炸过程,得到了不同方向不同爆距处的峰值压力反射系数,分析了爆炸流场参量分布和变化规律,研究了不同水底砂层厚度和不同装药量对爆炸冲击波传播和流...     

Solitary waves in initially stressed thin elastic tubes

In the present work, we study the propagation of non-linear waves in an initially stressed thin elastic tube filled with an inviscid fluid. Considering the physiological conditions of the arteries, in the analysis, the tube is assumed to be subjected to a uniform inner pressure P₀ and an axial stretch ratio λ_z. It is assumed that due to blood flow, a finite dynamical displacement field is superimposed on this static field and, then, the non-linear governing equations of the elastic tube are obtained. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the longwave approximation is investigated. It is shown that the governing equations reduce to the Korteweg-deVries equation which admits a solitary wave solution. It is observed that the present model equations give two solitary wave solutions. The results are also discussed for some elastic materials existing in the literature.     

Analytical Solution for Isothermal Flow in a Shock Tube Containing Rigid Granular Material

Analytical solution of shock wave propagation in pure gas in a shock tube is usually addressed in gas dynamics. However, such a solution for granular media is complex due to the inclusion of parameters relating to particles configuration within the medium, which affect the balance equations. In this article, an analytical solution for isothermal shock wave propagation in an isotropic homogenous rigid granular material is presented, and a closed-form solution is obtained for the case of weak shock waves. Fluid mass and momentum equations are first written in wave and (mathematical) non-conservation forms. Afterwards by redefining the sound speed of the gas flowing inside the pores, an analytical solution is obtained using the classical method of characteristics, followed by Taylor’s series expansion based on the assumption of weak flow which finally led to explicit functions for velocity, density and pressure. The solution enables plotting gas velocity, density and pressure variations in the porous medium, which is of high interest in the design of granular shock isolators.     

基于主成分分析的结构不确定性建模与传播研究

基于主成分分析提出一种新的结构不确定性建模方法。首先,对结构不确定性参数的样本数据进行主成分分析,获取正交化的特征向量;其次,以特征向量方向为新坐标系,将样本数据向其投影;最后,计算新坐标系下样本的边界值,并建立相应的非概率区间模型,从而实现结构参数不确定性建模。基于主成分分析建立的不确定性模型相对紧凑,且在建模的同时能将相关参数转换为互不相关参数,使得不确定性传播问题可以便捷高效求解。两个算例及与传统区间模型和平行六面体模型的不确定性传播比较,验证了本文方法的正确性和有效性。     

Some properties of pulse wave reflection in arteries

The propagation of pressure and velocity waves in liquid-filled elastic tubes has often been the subject of careful analysis [1, 2] as a model of the behavior of pulse waves in arteries. Practical requirements often make it necessary to return to these theories in order to clarify various details. Below, we examine one such problem generated by the proposal to use the amplitude characteristics of the pulse wave as a medical diagnostic index [3, 4] rather than the pulse wave propagation characteristics, as is usually the case.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 134–139, May–June, 1993.The authors are grateful to them for supplying experimental data and useful discussions.