颈动脉血管壁切应力的分析

动脉中管壁的脉动低切应力在动脉粥样硬化形成中起始动和主要的决定作用。本文比较了几种计算血管壁切应力的方法,认为采用有约束的弹性管模型计算获得的动脉壁切应力更适合于临床应用。根据检测得到的正常人和动脉硬化性脑血管病患者的颈动脉血流速度、血管管径等数据,计算两者的颈动脉壁面切应力。研究发现动脉硬化性脑血管病患者的壁面切应力比正常人显著减小。这表明,颈动脉的壁面切应力可以作为动脉硬化性脑血管疾病的早期诊断的重要参考指标。     

Unsteady wall shear stress in a distensible tube

An asymptotic expression of the wall shear stress (WSS) in an elastic tube is deduced for small values of the Womersley parameter. In the case of a rigid tube this asymptotic expression is shown to compare better with the exact solution than Poiseuille's or Lambossy's approximations. Its integration in a one-dimensional model of the internal carotid artery blood flow predicts more marked systolic and less marked diastolic WSS than those predicted by the commonly used Poiseuille's approximation.     

Cell-free layer and wall shear stress variation in microvessels

In this study, we simulated multiple red blood cells flowing through straight microvessels with the immersed-boundary lattice-Boltzmann model to examine the shear stress variation on the microvessel surface and its relation to the properties of cell-free layer. Significant variation in shear stress has been observed due to the irregular configuration of blood cells flowing near the microvessel wall. A low shear stress is typically found at locations where there is a cell flowing close to the wall, and a large shear stress at locations with a relatively wide gap between cell and wall. This relationship between the shear stress magnitude and the distance between cell and wall has been attributed to the reverse pressure difference developed between the front and rear sides of a cell flowing near the vessel wall. We further studied the effects of several hemodynamic factors on the variation of shear stress, including the cell deformability, the flow rate, and the aggregation among red blood cells. These simulations show that the shear stress variation is less profound in situations with wider cell-free layers, since the reverse pressure difference around the edge cells is less evident, and the influence of this pressure difference on wall shear stress becomes weaker. This study also demonstrates the complexity of the flow field in the gap between cell and wall. More precise experimental techniques are required accurately measure such shear stress variation in microcirculation.     

Modeling of mechanosensitive channel gating in response to wall shear stress

The accurate biological function of mechanosensitive (MS) channels is crucial for maintaining the viability of living cells. For instance, in vascular endothelial cells, calcium influx from the extracellular environment into cytoplasm is regulated by stretch-activated channels. However, the mechanism by which cells sense force remains unclear. For this study, we hypothesized that gating of ion channels is simply regulated by the direct mechanical stress induced in a membrane. We modeled a membrane channel using crystallographic data of the bacteria Mycobacterium tuberculosis (Tb-MscL) because MscL homologs are integral membrane proteins with sequence similarity to most known ion channels. Molecular dynamics (MD) simulations were performed to elucidate the gating mechanism of the channel protein in response to the fluid shear stress. Results suggest that the stretched membrane drives the interfacial part of the protein–membrane complex to expand and maintains the stability of the constricted part of the transmembrane pore. Moreover, structural similarities between Tb-MscL and the family of ligand-gated ion channels suggest that the conformational change of this model in response to fluid shear stress is useful for modeling the gating mechanism in a broad class of gated channels.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

A boundary layer model for wall shear stress in arterial stenosis

This paper proposes a model for wall shear stress in arterial stenosis based on boundary layer theory. Wall shear stress estimates are obtained by solving the momentum integral equation using the method proposed by Walz and applying this method to various stenosis geometries for Reynolds numbers (Re) of Re = 59-1000. Elevated wall shear stress may be of importance when considering thrombosis and vascular erosion in stenosis, as well as the potential for debris from the stenotic area to 'break away' and cause further pathology. The values of shear stress obtained using the model in this study agree well with published values of wall shear stress. When compared to a previously published boundary layer model utilizing the Thwaites method (Reese and Thompson, 1998), the model proposed herein performs better at higher Re while the model utilizing the Thwaites method performs better at lower Re. Wall shear stresses are shown to increase with increasing stenosis (increased area reduction) for a given stenosis length, increase with increasing Re for a given stenosis geometry, and increase for steeper stenosis of the same constriction. The boundary layer model proposed can be easily implemented by clinical researchers to provide in vivo estimates of wall shear stress through arterial stenoses.     

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D(1))(z) = (D(2))(z) + (D(3))(z); D(1) is the parent vessel diameter and D(2) and D(3) are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.     

Velocity and wall shear stress patterns in the human right coronary artery.

Blood flow dynamics in the human right coronary artery have not been adequately quantified despite the clinical significance of coronary atherosclerosis. In this study, a technique was developed to construct a rigid flow model from a cast of a human right coronary artery. A laser photochromic method was used to characterize the velocity and wall shear stress patterns. The flow conditions include steady flow at Reynolds numbers of 500 and 1000 as well as unsteady flow with Womersley parameter and peak Reynolds number of 1.82 and 750, respectively. Characterization of the three-dimensional geometry of the artery revealed that the largest spatial variation in curvature occurred within the almost branch-free proximal region, with the greatest curvature existing along the acute margin of the heart. In the proximal segment, high shear stresses were observed on the outer wall and lower, but not negative, stresses along the inner wall. Low shear stress on the inner wall may be related to the preferential localization of atherosclerosis in the proximal segment of the right coronary artery. However, it is possible that the large difference between the outer and inner wall shear stresses may also be involved.     

A numerical assessment of wall shear stress changes after endovascular stenting

This theoretical/numerical study aims at assessing the haemodynamic changes induced by endovascular stenting. By using the classical one-dimensional linear pressure waves theory in elastic vessels, we first show that the modulus of the reflection coefficient induced by an endovascular prosthesis is most likely small since it is proportional to the stent-to-wavelength ratio. As a direct consequence, the wall motion of the elastic (stented) artery can be prescribed a priori and the coupled fluid-structure problem does not have to be solved for assessing the haemodynamic changes due to stenting. Several 2D axisymetric calculations are performed to solve the unsteady incompressible Navier-Stokes equations on moving meshes for different types of (stented) arteries. The numerical results suggest that endovascular stenting increases the systo-diastolic variations of the wall shear stress (by 35% at the middle of the stent, by almost 50% in the proximal transition region). Additional calculations show that over-dilated stents produce less haemodynamic perturbations. Indeed, the increase of the amplitude of the wall shear stress variations over the cardiac cycle is only 10% when the stent radius is equal to the radius of the elastic artery at systole (instead of being equal to the mean artery radius).     

Twenty-fold difference in hemodynamic wall shear stress between murine and human aortas

Endothelial cells regulate vascular tone and mural remodelling in a shear-dependent manner that is commonly assumed to keep wall shear stress constant across arteries and species. Allometric arguments show that aortic flow velocity is constant across species, a deduction that is consistent with much experimental data, but the same arguments also show that the shear stress experienced by aortic endothelium will depend inversely on body mass to the 3/8th power, and hence will be 20-fold higher in mice than in men. This conclusion is robust and has important implications for the study of shear-dependent vascular biology and pathology.     

Maximal wall shear stress in arterial stenoses: application to the internal carotid arteries

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

Exercise-mediated changes in conduit artery wall thickness in humans: role of shear stress

Episodic increases in shear stress have been proposed as a mechanism that induces training-induced adaptation in arterial wall remodeling in humans. To address this hypothesis in humans, we examined bilateral brachial artery wall thickness using high-resolution ultrasound in healthy men across an 8-wk period of bilateral handgrip training. Unilaterally, shear rate was attenuated by cuff inflation around the forearm to 60 mmHg. Grip strength, forearm volume, and girth improved similarly between the limbs. Acute bouts of handgrip exercise increased shear rate (P < 0.005) in the noncuffed limb, whereas cuff inflation successfully decreased exercise-induced increases in shear. Brachial blood pressure responses similarly increased during exercise in both the cuffed and noncuffed limbs. Handgrip training had no effect on baseline brachial artery diameter, blood flow, or shear rate but significantly decreased brachial artery wall thickness after 6 and 8 wk (ANOVA, P < 0.001) and wall-to-lumen ratio after week 8 (ANOVA, P = 0.005). The magnitude of decrease in brachial artery wall thickness and wall-to-lumen ratio after exercise training was similar in the noncuffed and cuffed arms. These results suggest that exercise-induced changes in shear rate are not obligatory for arterial wall remodeling during a period of 8 wk of exercise training in healthy humans.     

Alteration of mean wall shear stress near an oscillating stagnation point.

The site opposite an end-to-side anastomosis, resulting from femoral bypass surgery, and the carotid sinus are two regions well known to be prone to fibrous intimal hyperplasia or atherogenesis, respectively. The blood flow at these two sites features a stagnation point, which oscillates in strength and position. Mathematical models are used to determine some of the features of such a flow; in particular, the mean wall shear stress is calculated. The positional oscillations cause a significant change in the distribution and magnitude of the mean wall shear stress from that of the well-studied case of a stagnation point that oscillates only in strength. It is therefore proposed that the recorded effect of time dependence in the flow upon atherogenesis could still be a result of the distribution of the mean and not the time-varying components of the wall shear stress.     

Common carotid wall shear stress and carotid atherosclerosis in end-stage renal disease patients

Decrease of arterial wall shear stress (WSS) is associated with higher probability of atherosclerotic plaque development in many disease conditions. End-stage renal diseases (ESRD) patients suffer from vascular disease frequently, but its nature differs from general population. This study was aimed at proving an association between common carotid wall shear stress and the presence of carotid bifurcation plaques in a group of ESRD patients. ESRD subjects, planned for the creation of a dialysis access and therapy were included. Wall shear rate (WSR) was used as a surrogate of WSS and was analyzed in the common carotid arteries by duplex ultrasonography. Intima media thickness (IMT) was measured at the same site. The presence/absence of carotid bifurcation plaques was recorded. The endothelial function was estimated by the levels of von Willebrand factor (vWf). 35 ESRD patients were included (19 females, 17 diabetics). Atherosclerotic plaque was present in 53 % of bifurcations. Wall shear rate was lower in arteries with plaques (349+/-148 vs. 506+/-206 s(-1), p=0.005) and was directly related to the height of IMT and inversely to the activity of vWf (r= -0.65, p=0.016). Lower wall shear rate in the common carotid arteries is linked to the endothelial dysfunction and to the presence of atherosclerotic plaques in carotid bifurcations in ESRD subjects. Faster arterial dilatation may facilitate this process in ESRD subjects.     

Quantifying turbulent wall shear stress in a stenosed pipe using large eddy simulation

Large eddy simulation was applied for flow of Re=2000 in a stenosed pipe in order to undertake a thorough investigation of the wall shear stress (WSS) in turbulent flow. A decomposition of the WSS into time averaged and fluctuating components is proposed. It was concluded that a scale resolving technique is required to completely describe the WSS pattern in a subject specific vessel model, since the poststenotic region was dominated by large axial and circumferential fluctuations. Three poststenotic regions of different WSS characteristics were identified. The recirculation zone was subject to a time averaged WSS in the retrograde direction and large fluctuations. After reattachment there was an antegrade shear and smaller fluctuations than in the recirculation zone. At the reattachment the fluctuations were the largest, but no direction dominated over time. Due to symmetry the circumferential time average was always zero. Thus, in a blood vessel, the axial fluctuations would affect endothelial cells in a stretched state, whereas the circumferential fluctuations would act in a relaxed direction.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.