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。     

Impact of juxta-anastomotic stent implantation on the haemodynamics within a single representative patient AVF

An arteriovenous fistula (AVF), a vascular structure surgically created to enable haemodialysis, is commonly affected by stenosis in the juxta-anastomotic region. A new treatment involving the implantation of a flexible stent has shown good potential for retaining healthy AVFs. Since vascular disease in the AVF is known to be related to the haemodynamic environment within the vasculature, this study aims to understand the impact of the stent implantation on the flow dynamics within a single patient-specific AVF. A virtual stented geometry of the AVF was obtained with micro-CT images of a benchtop AVF model implanted with a Supera stent. Reynolds averaged Navier–Stokes simulations were conducted with physiological boundary conditions (Reynolds numbers varying from 345 to 730) applied on the AVF model with and without the presence of the stent. Velocity contour slices within the vein showed the concentration of high velocity in the stent encapsulated region. Moreover, the ratios of flow rate across the stent-lumen cross-sections over the flow rate across the vessel-lumen cross-sections suggested that the flow was being funnelled through the stent encapsulated regions of a malapposed section, despite the porous structure of the stent. A larger low velocity recirculation region translated to a larger vessel wall area of high Oscillatory Shear Index (OSI) and low Time-Averaged Wall Shear Stress (TAWSS) in the AVF model with the stent absent, compared to the stented model. This suggested that the adverse haemodynamic behaviour was being funnelled away from the vessel wall, possibly leading to a protective environment in the malapposed region of the vein.     

Modeling the response of nonlinear viscoelastic biodegradable polymeric stents

We analyze the response of nonlinear viscoelastic biodegradable polymers when subject to mechanical loading coupled with the diffusion of a fluid (water) through the polymers and the degradation that occurs over a period of time. We consider the quasi-linear viscoelastic (QLV) model introduced by Fung (1981) that has been found to be reasonably good in modeling tissues undergoing moderate deformations for modeling the nonlinear viscoelastic response of the biodegradable polymer that is being studied, i.e., poly-lactic acid (PLLA). We modify the QLV model to incorporate changes in the material parameters that are a consequence of the degradation that the polymers undergo. We assume that the rate of degradation increases with an increase in the magnitude of strains and concentration of water. We also assume that the degradation softens the polymers and that the rate of stress relaxation (or the rate of creep) of the polymer increases with degradation. Our primary intention is to examine the effect of viscoelasticity on the degradation in virtue of the time-dependent response of such bodies, and also due to the effect of the diffusion of water that leads to degradation. The problem leads to three different time histories associated with the strong coupling between the mechanical loading, diffusion of a fluid (water), and the degradation. As the biodegradable stent is placed inside a nonlinear viscoelastic arterial wall, we further examine the effect of the coupling between the response of the polymeric stent and arterial wall on the degradation of the biodegradable polymeric stent.     

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。      

OPTIMIZATION DESIGN OF DEGRADABLE POLYMER VASCULAR STENT STRUCTURE

聚合物血管支架由于材料刚度较低导致其径向支撑能力相对于金属血管支架较弱,通常采用增大支架筋宽和厚度的方式来提高其径向支撑能力,但这不仅会降低支架的柔顺性能,减小血管管腔获得面积,还会增大表面覆盖率,从而增大支架内再狭窄的风险.为了设计出具有较小筋宽和厚度的聚合物血管支架,提高其径向支撑能力,本文采用一种将Kriging代理模型和有限元方法相结合的优化方法来优化支架的结构.采用Kriging代理模型建立设计目标和设计变量之间近似的函数关系,采用优化拉丁超立方抽样方法选取初始样本点,采用EI函数平衡局部和全局搜索,以便获得全局最优解.选取ART18Z聚合物支架作为算例,首先将支架的筋宽和厚度各减小0.02 mm,然后采用优化方法优化ART18Z支架的几何结构参数.数值结果表明,优化后ART18Z支架的综合服役性能得到改善,文中提出的优化方法能有效地应用于聚合物血管支架的优化设计.     

Constitutive modeling of biodegradable polymers: Hydrolytic degradation and time-dependent behavior

A large range of biodegradable polymers has been used to produce implantable medical devices. Apart from biological compatibility, these devices shall be also functional compatible and perform adequate mechanical temporary support during the healing process. However, the mechanical behavior of biodegradable materials during its degradation, which is an important aspect of the design of these biodegradable devices, is still an unexplored subject. Based on the literature, the mechanical behavior of biodegradable polymers is strain rate dependent and exhibits hysteresis upon cyclic loading. On the other hand, ductility, toughness and strength of the material decay during hydrolytic degradation. In this work, it is considered a three-dimensional time-dependent model adapted from the one developed by Bergström and Boyce to simulate the performance of biodegradable structures undergoing large deformations incorporating the hydrolysis degradation. Since this model assumes that the mechanical behavior is divided into a time independent network and a non-linear time-dependent network, it enables to simulate the monotonic tests of a biodegradable structure loaded under different strain rates. The hysteresis effects during unloading–reloading cycles at different strain levels can be predicted by the model. A parametric study of the material model parameters evolution during the hydrolytic degradation was conducted to identify which parameters are more sensible to this degradation process. The investigated model could predict very well the experimental results of a blend of polylactic acid and polycaprolactone (PLA–PCL) in the full range of strains until rupture during hydrolytic degradation. From these results and analyses, a method is proposed to simulate the three-dimensional mechanical behavior during hydrolytic degradation.     

Effects of renal artery stenosis on realistic model of abdominal aorta and renal arteries incorporating fluid-structure interaction and pulsatile non-Newtonian blood flow

The effects of the renal artery stenosis(RAS) on the blood flow and vesselwalls are investigated.The pulsatile blood flow through an anatomically realistic model ofthe abdominal aorta and renal arteries reconstructed from CT-scan images is simulated,which incorporates the fluid-structure interaction(FSI).In addition to the investigationof the RAS effects on the wall shear stress and the displacement of the vessel wall,it isdetermined that the RAS leads to decrease in the renal mass flow.This may cause theactivation of the renin-angiotension system and results in severe hypertension.     

Model study of noise field in the human chest due to turbulent flow in a larger blood vessel

An acoustic generation of noise by a larger human blood vessel and noise transmission in the thorax is modelled and studied. In making this, the random statistical nature of the noise sources, the basic vessel properties and the main features of the human chest structure are taken into account. Also the effects of changes in the basic vessel parameters are considered as a first approach to study acoustic effects of a vascular stenosis. The analysis of the resultant acoustic field reveals its similarity to the acoustic fields recorded in the appropriate experiments. The variations in the basic vessel parameters are found to cause the corresponding changes in the sound level and the production of new frequency components in the acoustic power spectrum. The acoustic power from a slightly thickened vessel is shown to be approximately proportional to the fourth power of the flow Reynolds number in the originally normal vessel and the eighth power of the ratio of the vessel diameters.     

Coupled modeling of tumour angiogenesis,tumour growth,and blood perfusion

This paper proposes a more realistic mathematical simulation method to investigate the dynamic process of tumour angio-genesis by fully coupling the vessel growth, tumour growth and associated blood perfusion. The tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction. The haemodynamic calculation is carried out on the new vasculature, and an estimation of vessel collapse is made according to the wall shear stress criterion. The results are consistent with physiological observations, and further confirm the application of the coupled model feedback mechanism. The model is available to examine the interactions between angiogenesis and tumour growth, to study the change in the dynamic process of chemical environment and the vessel remodeling.     

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.     

One-dimensional numerical model for degradation and combustion of polymethyl methacrylate

A transient one-dimensional model is applied to study degradation and combustion of a poly methyl methacrylate (PMMA) sample. Ignition of PMMA is a complex interaction among different mechanisms, including solid fuel degradation, heat transfer, in-depth absorption of radiation, surface regression, gas-phase advective heat/mass transfer, and combustion. The present task has the significant feature of coupling the solid and gas phases. Besides the mathematical model has been solved numerically by using a fast iterative method and has yielded realistic results.     

Application of the lattice Boltzmann method to flow in aneurysm with ring‐shaped stent obstacles

To resolve the characteristics of a highly complex flow, a lattice Boltzmann method with an extrapolation boundary technique was used in aneurysms with and without transverse objects on the upper wall, and results were compared with the non‐stented aneurysm. The extrapolation boundary concept allows the use of Cartesian grids even when the boundaries do not conform to Cartesian coordinates. To ease the code development and facilitate the incorporation of new physics, a new scientific programming strategy based on object‐oriented concepts was developed. The reduced flow, smaller vorticity magnitude and wall shear stress, and smaller du/dy near the dome of the aneurysm were observed when the proposed stent obstacles were used. The height of the stent obstacles was more effective to reduce the vorticity near the dome of the aneurysm than the width of the stent. The rectangular stent with 20% height‐of‐vessel radius was observed to be optimal and decreased the magnitude of the vorticity by 21% near the dome of the aneurysm. Copyright © 2008 John Wiley & Sons, Ltd.     

Blood flow and microgravity

The absence of gravity during space flight can alter cardio-vascular functions partially due to reduced physical activity. This affects the overall hemodynamics, and in particular the level of shear stresses to which blood vessels are submitted. Long-term exposure to space environment is thus susceptible to induce vascular remodeling through a mechanotransduction cascade that couples vessel shape and function with the mechanical cues exerted by the circulating cells on the vessel walls. Central to such processes, the glycocalyx – i.e. the micron-thick layer of biomacromolecules that lines the lumen of blood vessels and is directly exposed to blood flow – is a major actor in the regulation of biochemical and mechanical interactions. We discuss in this article several experiments performed under microgravity, such as the determination of lift force and collective motion in blood flow, and some preliminary results obtained in artificial microfluidic circuits functionalized with endothelium that offer interesting perspectives for the study of the interactions between blood and endothelium in healthy condition as well as by mimicking the degradation of glycocalyx caused by long space missions. A direct comparison between experiments and simulations is discussed.     

A prediction of in vivo mechanical stresses in blood vessels using thermal expansion method and its application to hypertension and vascular stenosis

Mechanical stimuli play critical roles in cardiovascular diseases, in which in vivo stresses in blood vessels present a great challenge to predict. Based on the structural–thermal coupled finite element method, we propose a thermal expansion method to estimate stresses in multi-layer blood vessels under healthy and pathological conditions. The proposed method provides a relatively simple and convenient means to predict reliable in vivo mechanical stresses with accurate residual stress. The method is first verified with the opening-up process and the pressure-radius responses for single and multi-layer vessel models. It is then applied to study the stress variation in a human carotid artery at different hypertension stages and in a plaque of vascular stenosis. Our results show that specific or optimal residual stresses exist for different blood pressures, which helps form a homogeneous stress distribution across vessel walls. High elastic shear stress is identified on the shoulder of the plaque, which contributes to the tearing effect in plaque rupture. The present study indicates that the proposed numerical method is a capable and efficient in vivo stress evaluation of patient-specific blood vessels for clinical purposes.     

Mathematical modeling and parametric investigation of blood flow through a stenosis artery

In this study, a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel. The stenosis disease is caused because of the abnormal narrowing of flow in the body. This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel. Mathematical modeling helps us analyze such issues. A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method. The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid. A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem. Moreover, the flow characteristics such as the impedance, the wall shear stress in the stenotic region, the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed. The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel, which has a direct impact on the wall shear stress. It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.

     

弯曲狭窄管内血液流的分析

与血管狭窄有关的异常血液动力学特征在血管疾病的发生和发展过程中起着重要的作用,由于血管狭窄和弯曲的综合影响,将会出现一系列有趣的流体力学现象,本文研究具有对称狭窄的弯曲小动脉内定常血液流动,在一定的假设条件下,直接从支配血液流动的Navier-Stokes方程求出问题的摄动解,由此求得弯曲狭窄管內血液流动的轴向速度、二次流速度及压力梯度等分析表达式,并进一步求得轴向和周向血管壁切应力。本文的结果是先前有关狭窄直管和弯曲均匀管流动研究的拓广。     

Patient-specific finite element analysis of popliteal stenting

Nitinol self-expanding stents are used for the endovascular management of peripheral artery diseases of the popliteal artery, which is located behind the knee joint. Unfortunately, the complex kinematics of the artery during the leg flexion leads to severe loading conditions, favouring the mechanical failure of the stent, calling for a specific biomechanical analysis. For this reason, in the present study we reconstruct by medical image analysis the patient-specific popliteal kinematics during leg flexion, which is subsequently exploited to compute the mechanical response of a stent model, virtually implanted in the artery by structural finite element analysis (FEA). The medical image analysis indicates a non-uniform configuration change of the artery during the leg flexion, leading to an increase of the vessel curvature above the knee. The computed mechanical response of the stent reflects the non-uniform configuration change of the artery as after the flexion the average stress is higher in the part of the stent located above the knee. Although the proposed analysis is limited to a case-study, it shows the capability of patient-specific FEA simulations to compute the mechanical response of a stent model subjected to the complex and severe loading conditions of the popliteal artery during leg flexion.     

光纤陀螺加速退化试验的可行性

以可靠性试验技术为基础,对加速退化试验方法在光纤陀螺产品中实施的可行性进行了探索研究。对光纤陀螺所用器件在长期使用条件下性能变化及其对陀螺整机性能的影响进行了分析,阐述了光纤陀螺性能退化存在的可能性,并通过光纤陀螺长期使用实验数据进行验证,得出了光纤陀螺具有性能退化特性的结论。采用可靠性摸底试验方法对光纤陀螺性能退化在温度环境应力下的可加速性进行了探索,通过温度加速应力下光纤陀螺实际工作性能数据分析得出其性能退化具有加速性,对光纤陀螺实施加速退化试验可行。     

Effects of magnetic field,porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented. The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood. An artery with mild local narrowing in its lumen forming a stenosis is analyzed. The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions T _t and T _θ , respectively. The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated. Also, the effects of the stenosis shape m, the constant of permeability X, the Hartmann number H _α and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated. The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery. Further, the wall shear stress distribution increases with increasing T _t and γ while decreases with increasing T _θ , M, C, and K. Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes. The trapping bolus increases in size toward the line center of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased. Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis. The size of trapped bolus for the stream lines in a free isotropic tube (i.e., a tube initially unstressed) is smaller than those in a tethered tube.     

Nonlinear viscoelastic-degradation model for polymeric based materials

This study presents a phenomenological constitutive model for describing response of solid-like viscoelastic polymers undergoing degradation. The model is expressed in terms of recoverable and irrecoverable time-dependent parts. We use a time-integral function with a nonlinear integrand for the recoverable part and another time-integral function is used for the irrecoverable part, which is associated with the degradation evolution in the materials. Here, the degradation is attributed to the secondary and tertiary creep stages. An ‘internal clock’ concept in viscoelastic materials is used to incorporate the accelerated failure in the materials at high stress levels. We ignore the effect of heat generation due to the dissipation of energy and possible healing in predicting the long-term and failure response of the polymeric materials. Experimental data on polymer composites reported by Drozdov (2011) were used to characterize the material parameters and validate the constitutive model. The model is shown capable of predicting response of the polymer composites under various loading histories: creep, relaxation, ramp loading with a constant rate, and cyclic loadings. We observed that the failure time and number of cycles to failure during cyclic loadings are correlated to the duration of loading and magnitude of the prescribed mechanical loads. A scalar degradation variable is also introduced in order to determine the severity of the degradation in the materials, which is useful to predict the lifetime of the structures subject to various loading histories during the structural design stage.