Study on hemodynamics in patient-specific thoracic aortic aneurysm

The objective of this study is to investigate the hemodynamics in patient-specific thoracic aortic aneurysm and discuss the reason for formation of aortic plaque. A 3-Dimensional pulsatile blood flow in thoracic aorta with a fusiform aneurysm and 3 main branched vessels was studied numerically with the average Reynolds number of 1399 and the Womersley number of 19.2. Based on the clinical 2-Dimensional CT slice data, the patient-specific geometry model was constructed using medical image process software. Unsteady, incompressible, 3-Dimensional Navier-Stokes equations were employed to solve the flow field. The temporal distributions of hemodynamic variables during the cardiac cycle such as streamlines, wall shear stresses in the arteries and aneurysm were analyzed. Growth and rupture mechanisms of thoracic aortic aneurysm in the patient can be analyzed based on patient-specific model and hemodynamics simulation.     

血流动力学数值模拟与动脉粥样硬化研究进展

血流动力学因素被认为与动脉粥样硬化等病理改变密切相关。目前血流动力学数值模拟的对象,主要集中于分支动脉、弯曲动脉以及因血管内膜增生而导致的局部狭窄动脉,这些都是动脉粥样硬化多发的病灶部位。精确的血流动力学数值模拟,必须依赖于解剖精确的血管几何模型和生理真实的血流与管壁有限变形的非线性瞬态流－固耦合。只有在“虚拟血液流动”的基础上,综合考虑血管内的壁面剪应力、粒子滞留时间和氧气的跨血管壁传输等多种因素,血流动力学的数值模拟才能真正有助于人们理解动脉粥样硬化的血流动力学机理,才有可能应用于有关动脉疾病的外科手术规划中。      

一种新的脑动静脉畸形血液动力学模型

建立了一个新的非定常脑AVM血液动力学模型．模型克服了以往的定常AVM模型无法反映血流实际脉动，以及模型结构和血管性质描述上的缺陷，并依据临床实测数据提出了一种更为符合生理和病理实际的描述AVM供血动脉扩张现象的方法．模型模拟了AVM造成的脑血管压力、流量波形和脑血管输入阻抗的变化，并对脑AVM病人脑血管系统的输入阻抗进行了分析．为研究具有复杂结构的脑AVM血液动力摹的特征，提供了一个有效的工具。     

A Model of Arterial Adaptation to Alterations in Blood Flow

Mechanisms of arterial adaptation to changes in blood flow rates were tested by comparing the predictions of a proposed theoretical model with available experimental data. The artery was modeled as an elastic membrane made of a nonlinear, incompressible, elastic material. Stimulation of the vascular smooth muscle was modeled through the generation of an active component of circumferential stress. The muscular tone was modulated by flow-induced shear stress sensed by the arterial endothelium, and is responsible for the vasomotor adjustment of the deformed arterial diameter in response to changes in blood flow. This study addresses the hypothesis that the synthetic and proliferative activity of smooth muscle cells, leading to a change in arterial dimensions, is shear stress dependent and is associated with changes in the contractile state of the smooth muscle cells and changes in the circumferential wall stress. Remodeling to a step change in flow was formulated as an initial-value problem for a system of first order autonomous differential equations for the evolution of muscular tone and evolution of arterial geometry. The governing equations were solved numerically for model parameters identified from experimental data available in the literature. The model predictions for the time variation of the geometrical dimensions and their asymptotic values were found to be in qualitative agreement with available experimental data. Experiments for validating the introduced hypotheses and further generalizations of the model were discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A computer model of pulse wave and input impedance in human arteries

To predict the propagation of pressure and flow pulses in arterial system and the variation of vascular input impedance, a branched and tapered tube model is studied through one-dimensional transient flow analysis. Coupling the continuity and momentum equations yields a group of quasilinear hyperbolic partial differential equations which can be solved numerically by using the method of characteristics. Several boundary conditions of the arterial system are also simplified suitably. The propagation of the pulses of the arterial system and the vascular input impedance is calculated on computer by using the dimensions and the physiological data of the arterial system. The results point out that the pressure and flow pulses of the arterial system and the vascular input impedance produced by this theoretical model is consistent quite well with the experimental results published.     

Determination of the Parameters of Hydraulic Models of the Vascular Bed by the Input Impedance Method

On the basis of hydraulic models of the vascular bed, the possibility of quantitatively estimating the resistances, inertia coefficients and compliances of model elements, as well as the changes in these parameters, from the hydraulic input impedance is evaluated. It is shown that the input impedance method makes it possible to find stable estimates for the hydraulic model parameters using the least squares method. No significant differences between the parameters of hydraulic models of the vascular bed calculated by the input impedance method and measured independently were found. The possibility of using the input impedance method to estimate the arterial response of an organ is discussed.     

A multiscale model for analyzing the synergy of CS and WSS on the endothelium in straight arteries

A multiscale model was proposed to calculate the circumferential stress (CS) and wall shear stress (WSS) and analyze the effects of global and local factors on the CS, WSS and their synergy on the arterial endothelium in large straight arteries. A parameter pair [Zs,SPA] (defined as the ratio of CS amplitude to WSS amplitude and the phase angle between CS and WSS for different harmonic components, respectively) was proposed to characterize the synergy of CS and WSS. The results demonstrated that the CS or WSS in the large straight arteries is determined by the global factors, i.e. the preloads and the afterloads, and the local factors, i.e. the local mechanical properties and the zero-stress states of arterial walls, whereas the Zs and SPA are primarily determined by the local factors and the afterloads. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and the stress phase difference SPA might be appropriate indices to reflect the influences of the states of whole downstream arterial beds on the local blood flow-dependent phenomena such as angiogenesis, vascular remodeling and atherosgenesis. The project supported by the National Natural Science Foundation of China (10132020 and 10472027). The English text was polished by Yunming Chen.     

Effects of atrial fibrillation on the arterial fluid dynamics: a modelling perspective

Atrial fibrillation (AF) is the most common form of arrhythmia with accelerated and irregular heart rate (HR), leading to both heart failure and stroke and being responsible for an increase in cardiovascular morbidity and mortality. In spite of its importance, the direct effects of AF on the arterial hemodynamic patterns are not completely known to date. Based on a multiscale modelling approach, the proposed work investigates the effects of AF on the local arterial fluid dynamics. AF and normal sinus rhythm (NSR) conditions are simulated extracting 2000 \({\mathrm {RR}}\) heartbeats and comparing the most relevant cardiac and vascular parameters at the same HR (75 bpm). Present outcomes evidence that the arterial system is not able to completely absorb the AF-induced variability, which can be even amplified towards the peripheral circulation. AF is also able to locally alter the wave dynamics, by modifying the interplay between forward and backward signals. The sole heart rhythm variation (i.e., from NSR to AF) promotes an alteration of the regular dynamics at the arterial level which, in terms of pressure and peripheral perfusion, suggests a modification of the physiological phenomena ruled by periodicity (e.g., regular organ perfusion) and a possible vascular dysfunction due to the prolonged exposure to irregular and extreme values. The present study represents a first modeling approach to characterize the variability of arterial hemodynamics in presence of AF, which surely deserves further clinical investigation.     

Characteristic mechanical impedance of rheometers with axial symmetry. A theoretical and numerical analysis

The strain wave field generated in a linear viscoelastic medium confined between two infinitely large parallel planar surfaces, one fixed and the other oscillating sinusoidally in its own plane, has been well accounted for (Schrag, 1977). Here, we describe the strain wave field generated between a cylinder and a coaxial surrounding tube, both infinitely long. The tube or the cylinder remains stationary while the complementary component undergoes sinusoidal angular displacements around the common symmetry axis. This geometry is frequently used in dynamic rheometers. Both exact analytic expressions for the characteristic mechanical impedance and series expansions valid close to gap loading or surface loading conditions are provided. The exact analysis is valid for arbitrary gap width, cylinder radius, and linear viscoelastic properties of the medium within the rheometer gap. We also show how standard, modern desktop computers can be used to rapidly obtain accurate numerical values of the characteristic mechanical impedance of rheometers with axial symmetry using the exact analytic expressions.     

不同心排出量下主动脉瓣血流动力学的PIV实验研究

主动脉瓣发生病变时导致心排出量(cardiac output, CO)减少,而心排出量减少与主动脉瓣血流动力学耦合作用, 引发瓣膜继发性疾病.本文基于医学影像数据三维重构带有冠状动脉的主动脉根部,制备高度光滑和透明的主动脉根部实验模型, 构建体外脉动循环模拟系统,利用粒子图像测速技术(particle image velocimetry,PIV)研究冠状动脉存在时心排出量对主动脉瓣速度分布、黏性剪应力(viscous shear stress, VSS)和雷诺剪应力(Reynolds shear stress, RSS)等血流动力学的影响.研究结果表明: 冠状动脉的存在改变了主动脉窦中的涡旋运动和涡度,冠状动脉存在时流体经由冠状动脉流出, 主动脉窦中的涡旋运动逐渐消失,涡度较早开始减小. 峰值期, 中心对称流动两侧区域存在正、负高黏性剪切区域,存在冠状动脉一侧的升主动脉下游存在高雷诺剪应力区域.心排出量显著影响主动脉瓣的速度分布、VSS和RSS等血液流动和受力状况.随着心排出量增大, 冠状动脉存在时峰值期的最大速度、VSS和RSS增大, 即$CO=2.1$, 2.8, 3.5和4.2 l/min时, 最大速度分别为0.98, 1.13, 1.21和1.37 m/s, 最大VSS分别为0.87, 0.95, 0.96和1.02 N/m$^{2}$, 最大RSS分别为103.76, 116.25, 138.68和146.55 N/m$^{2}$. 心排出量较低时,主动脉瓣较低的跨瓣流动速度和黏性剪应力易导致血栓形成,研究结果可为主动脉瓣置换术提供理论参考.      

Numerical simulation of the process of autoregulation of the arterial blood flow

For describing the autoregulation of the blood flow in an artery under constant transmural pressure a mathematical model that takes into account the multilayer structure of the arterial wall, the diffusion and kinetic processes in the wall, and the nonlinear viscoelastic properties of the wall material is proposed. The limiting case of a thin-walled artery is studied analytically. The arterial-wall viscosity range on which the equilibrium state of the system is stable is estimated. Accurate stationary distributions of the nitric oxide, calcium and myosin concentrations in the arterial wall are found. Numerical simulation of the autoregulation process demonstrated the possibility of arterial adaptation to radius perturbations, the existence of slow oscillations, and system transition to a new equilibrium state with change in blood flow level. The results are in good agreement with the experimental data.     

T-Y tube model of human ascending aortic input impedance

Arterialimpedancehasitsparticularsignificancebecauseitdescribesthephysicalandgeometricalcharactersofthewholearterialsystem.Moreover.itisagoodmeasureoftheleftventricleafterload.Numerousexperimentalandtheoreticalresearchesha\'ebeendoneinthisarea.Itisshownth…     

Scattering of a whispering gallery mode by a cylindrically curved impedance strip

The analysis of edge-diffracted waves generated by the edge of a curved impedance sheet is of great importance for both theoretical and practical applications. This problem is considered here for a cylindrically curved strip illuminated by a whispering gallery mode, and is solved by reducing it to a matrix Hilbert equation. All the results are stated according to the terminology of the GTD. The expressions for several transfer (diffraction) coefficient are obtained in explicit forms. Though these expressions were derived for this particular geometry, they can be useful in the analysis of more complicated structures. When the impedance of the curved strip becomes zero, then all the expressions are reduced to known expressions related to the perfectly conducting sheet.     

Multi-scale modeling of hemodynamics in the cardiovascular system

The human cardiovascular system is a closedloop and complex vascular network with multi-scaled heterogeneous hemodynamic phenomena. Here, we give a selective review of recent progress in macro-hemodynamic modeling, with a focus on geometrical multi-scale modeling of the vascular network, micro-hemodynamic modeling of microcirculation, as well as blood cellular, subcellular,endothelial biomechanics, and their interaction with arterial vessel mechanics. We describe in detail the methodology of hemodynamic modeling and its potential applications in cardiovascular research and clinical practice. In addition,we present major topics for future study: recent progress of patient-specifi hemodynamic modeling in clinical applications, micro-hemodynamic modeling in capillaries and blood cells, and the importance and potential of the multi-scale hemodynamic modeling.     

血管输入阻抗的拟合方法与初值选取

研究了模拟动脉系统的集中参数模型的数据拟合问题,分析了用修正的Noordeergraaf五单元模型计算血管输入阻抗的有关问题,对参数拟合问题中被广泛运用的Newton迭代法与正交试验法作了评述,就其中至关重要的初值选取问题建议了一些简单实用的方法,讨论了参数选取的范围与参考值,并将数值计算结果与实测结果作了比较,所建议方法的有效性得到了证实。     

Leonardo's vision of flow visualization

Leonardo's studies of cardiovascular systems, in more than 50 surviving pages from two phases of his research (around 1508-1509 and 1513), are a clear demonstration of his observational genius and progressive deduction of cardiac mechanics and the vascular system. He carried out a detailed hemodynamic study of the aortic valve motion and the role of the Sinus of Valsalva in the closure dynamics of the aortic valve, and he accurately correlated the formation of vortices with the separation of a retarded (shear) layer from the lips of the leaflets. In-vivo verification of vortex formation in the Sinus of Valsalva during the systolic phase awaited the application of modern phase-averaged magnetic resonance imaging techniques. Did Leonardo actually build the glass model he twice mentioned, thus performing the first scientific flow visualization of impulsive vortex formation or other fluid mechanical phenomena? Evidence in support of this possibility can be found in both the unusually schematic style he employed for this suite of drawings and the recent flow imaging results obtained in our laboratory through laser-based imaging techniques.     

A structural multi-mechanism constitutive equation for cerebral arterial tissue

A structural multi-mechanism constitutive equation is developed to describe the nonlinear, anisotropic, inelastic mechanical behavior of cerebral arterial tissue. Elastin and collagen fibers are treated as separate components (mechanisms) of the artery. Elastin is responsible for load bearing at low strain levels while the collagen mechanism is recruited for load bearing at higher strain levels. This work builds on an earlier model in which both the elastin and collagen mechanisms are represented by isotropic response functions [Wulandana, R., Robertson, A.M., 2005. An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechan. 4 (4), 235–248]. Here, the anisotropic material response of the wall is introduced through the collagen mechanism which is composed of helically distributed families of fibers. The orientation of these families is described using either a finite number of fiber orientations or a fiber distribution function. The fiber orientation or dispersion function can be prescribed directly from arterial histology data, or, taking a phenomenological approach, based on data fitting from bi-axial measurements. The activation of the collagen mechanism is specified using a new fiber strain based activation criterion. The multi-mechanism constitutive equation is applied to the simple case of cylindrical inflation and material constants are determined based on available inelastic experimental data for cerebral arteries. While the proposed model captures all features of this inelastic data, there is a pressing need for further experiments to refine the model.     

Entropy generation of radial rotation convective channels

The exchange of heat between two fluids is established by radial rotating pipe or a channel. The hotter fluid flows through the pipe, while the cold fluid is ambient air. Total length of pipe is made up of multiple sections of different shape and position in relation to the common axis of rotation. In such heat exchanger the hydraulic and thermal irreversibility of the hotter and colder fluid occur. Therefore, the total entropy generated within the radial rotating pipe consists of the total entropy of hotter and colder fluid, taking into account all the hydraulic and thermal irreversibility of both fluids. Finding a mathematical model of the total generated entropy is based on coupled mathematical expressions that combine hydraulic and thermal effects of both fluids with the complex geometry of the radial rotating pipe. Mathematical model follows the each section of the pipe and establishes the function between the sections, so the total generated entropy is different from section to section of the pipe. In one section of the pipe thermal irreversibility may dominate over the hydraulic irreversibility, while in another section of the pipe the situation may be reverse. In this paper, continuous analytic functions that connect sections of pipe in geometric meaning are associated with functions that describe the thermo-hydraulic effects of hotter and colder fluid. In this way, the total generated entropy of the radial rotating pipe is a continuous analytic function of any complex geometry of the rotating pipe. The above method of establishing a relationship between the continuous function of entropy with the complex geometry of the rotating pipe enables indirect monitoring of unnecessary hydraulic and thermal losses of both fluids. Therefore, continuous analytic functions of generated entropy enable analysis of hydraulic and thermal irreversibility of individual sections of pipe, as well as the possibility of improving the thermal–hydraulic performance of the rotating pipe consisting of n sections. Analytical modeling enabled establishing of a mathematical model of the total generated entropy in a radial rotating pipe, while the generated entropy of models with radial rotating pipe were determined by experimental testing, with comparisons of the achieved results.     

Frictionless contact of an elastic punch subject to the normal load and bending moment

A two-dimensional contact problem of a trapezium shaped punch pressed into a frictionless, elastically similar half-plane and subject sequentially to the normal load and bending moment is considered. The model of a tilted flat punch is used to evaluate the pressure distribution and the contact deformation within the contact zone. Comparisons of the results generated by the analytical technique to those computed by the finite element method demonstrate the high level of accuracy attained by both methods. The presented numerical results illustrate the effects of the normal load, bending moment, and internal angles of the punch geometry on the contact stresses.