Measurement of wall motion and wall shear in a compliant arterial cast

Initial measurements of the time-varying wall shear rate at two sites in a compliant cast of a human aortic bifurcation are presented. The shear rates were derived from flow velocities measured by laser Doppler velocimetry (LDV) near the moving walls of the cast. To derive these shear rate values, the distance from the velocimeter sampling volume to the cast wall must be known. The time variation of this distance was obtained from LDV measurements of the velocity of the wall itself.     

Alternate method for the analysis of residual strain in the arterial wall

If an artery is cut transversely into rings, and the rings are then cut radially, they spring open into sectors. This phenomenon implies the existence of residual stresses and strains in the arterial wall in the non-loaded state. In the present paper, we propose a new method to calculate the residual strain from the measured wall dimensions and a polar angle of a specimen in the stress-free state, assuming that the wall is homogeneous and incompressible, and that a radially cut, stress-free specimen forms a circular sector. For this analysis, edge angles were measured at the edges of the opened-up specimen. Residual strains were obtained for the descending thoracic aorta, the common carotid artery, and the femoral artery in the rabbit. The results obtained indicated that the magnitude of residual strain was largest in the femoral artery and smallest in the aorta among the three arteries. The opening angle did not depend upon the length of a ring specimen if the ratio of the length to the diameter was ≤ 3.     

Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability

A better understanding of how hemodynamic factors affect the integrity and function of the vascular endothelium is necessary to appreciate more fully how atherosclerosis is initiated and promoted. A novel technique is presented to assess the relation between fluid dynamic variables and the permeability of the endothelium to macromolecules. Fully anesthetized, domestic swine were intravenously injected with the albumin marker Evans blue dye, which was allowed to circulate for 90 min. After the animals were euthanized, silicone casts were made of the abdominal aorta and its iliac branches. Pulsatile flow calculations were subsequently made in computational regions derived from the casts. The distribution of the calculated time-dependent wall shear stress in the external iliac branches was directly compared on a point-by-point basis with the spatially varying in vivo uptake of Evans blue dye in the same arteries. The results indicate that in vivo endothelial permeability to albumin decreases with increasing time-average shear stress over the normal range. Additionally, endothelial permeability increases slightly with oscillatory shear index.     

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.     

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.     

Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model

The structure of pulsatile blood flow and wall shear stress in a 90° T-bifurcation model is analysed numerically. The nonlinear Navier-Stokes equations for time-dependent incompressible Newtonian fluid flow are approximated using a newly developed pressure correction, finite element method. The wall shear stress is calculated from the finite element velocity field. The investigation shows viscous flow phenomena such as flow separation and stagnation and the distribution of high and low wall shear stress during the pulse cycle. Furthermore, the effect of a sharp corner the bifurcation edge on the wall shear stress is analysed. Detailed local flow investigation is required to examine fluid dynamic contribution to the development of arterial diseases such as atherosclerosis and thrombosis.     

Unsteady near wall residence times and shear exposure in model distal arterial bypass grafts

Building on previous studies of unsteady flow within model distal bypass grafts we analyse the near wall residence times and shear exposure in a 45 degrees anastomosis under symmetrical and symmetry breaking geometric configurations. We define residence time as the minimum time for a particle to exit a spherical region and shear exposure as a temporal integral of the Huber-Henky-von-Mises criterion along a particle path over a fixed time interval. Decomposing the pulsatile cycle into four equal intervals we find that the interval of peak residence time in the host vessel is from mid-deceleration to peak diastole and peak diastole to mid-acceleration. The asymmetric model is shown to have a significantly lower residence time during these intervals. Considering the shear exposure prior to the residence time evaluation we determine that a higher average shear exposure exists in the asymmetric model associated with the upstream geometry modification. Analysis of the regions of high residence time and shear exposure suggests that the "toe" region and the interface between the "heel" and bulk flow are more significant than the bed and heel region. Although the asymmetric model considered in this study reduces residence times in the host artery, the product of the measure of shear exposure and residence time is not found to be preferable. If shear exposure were to be considered as an important factor in particle activation, the findings imply that for junction optimisation, greater consideration needs to be given both to the local junction asymmetry and upstream influence on the shear history.     

Shear strain in the adventitial layer of the arterial wall facilitates development of vulnerable plaques

Myocardial infarction and stroke are two of the leading causes of death and primarily triggered by destabilization of atherosclerotic plaques. Fatty streaks are known to develop at sites in the arterial wall where shear stress is low. These fatty streaks can develop into more advanced plaques that are prone to rupture. Rupture leads to thrombus formation, which may subsequently result in a myocardial infarction or stroke. The relation between shear stress on the inner (endothelial) layer of the arterial wall in relation to plaque development has been studied extensively. However, a causal relation between adventitial shear forces and atherosclerosis development has never been considered.Arterial stiffening increases with age and may facilitate an increase in shear strain in the adventitial layer, an axial shear between artery and surrounding tissue. In the adventitial layer, a large number of inflammatory cells and perivascular structures are present that are subjected to shear strain. Cyclic strain applied to endothelial cells stimulates neovascularisation via different pathways. The conduit arteries in the human body (e.g. coronary and carotid artery) have their own nutrition supply: the vasa vasorum, which is located in the adventitial layer and sprouts into the intimal layer when atherosclerotic plaque develops. Increased plaque neovascularisation makes the plaques more prone to rupture. Therefore we hypothesize that increased shear strain facilitates the development of vulnerable plaques by stimulation of atherosclerotic plaque neovascularisation that sprouts from the adventitial vasa vasorum. Validation of this hypothesis paves the road to the use of adventitial shear strain (measured using a noninvasive ultrasound technique) as risk assessment in plaque.     

Longitudinal displacement and intramural shear strain of the porcine carotid artery undergo profound changes in response to catecholamines

The effects of catecholamines on longitudinal displacements and intramural shear strain of the arterial wall are unexplored. Therefore, the common carotid artery of five anaesthetized pigs was investigated using an in-house developed noninvasive ultrasonic technique. The study protocol included intravenous infusion of low-dose epinephrine (β-adrenoceptor activation), as well as intravenous boluses of norepinephrine (α-adrenoceptor activation). Further, the effects of β-blockade (metoprolol) were studied. There were significant positive correlations between pulse pressure and longitudinal displacement of the intima-media complex (r = 0.72; P < 0.001), as well as between pulse pressure and intramural shear strain (r = 0.48; P < 0.001). Following administration of norepinephrine, the longitudinal displacement of the intima-media complex and intramural shear strain profoundly increased (median 190%, range 102-296%, and median 141%, range 101-182%, respectively, compared with baseline), also when given during β-blockade (median 228%, range 133-266%, and median 158%, range 152-235%, respectively). During infusion of low-dose epinephrine, the longitudinal displacement of the intima-media complex and intramural shear strain decreased (median 88%, range 69-122%, and median 69%, range 47-117%, respectively, compared with baseline). In conclusion, the present study shows, for the first time, that the longitudinal displacement and intramural shear strain of the porcine carotid artery undergo profound changes in response to catecholamines. Increase in longitudinal displacements seems to be strongly related to α-adrenoceptor activation. Thus metoprolol is insufficient to counteract a profound increase in longitudinal displacement and intramural shear strain following a surge of norepinephrine.     

Numerical simulation of wall shear stress conditions and platelet localization in realistic end-to-side arterial anastomoses

Research studies over the last three decades have established that hemodynamic interactions with the vascular surface as well as surgical injury are inciting mechanisms capable of eliciting distal anastomotic intimal hyperplasia (IH) and ultimate bypass graft failure. While abnormal wall shear stress (WSS) conditions have been widely shown to affect vascular biology and arterial wall self-regulation, the near-wall localization of critical blood particles by convection and diffusion may also play a significant role in IH development. It is hypothesized that locations of elevated platelet interactions with reactive or activated vascular surfaces, due to injury or endothelial dysfunction, are highly susceptible to IH initialization and progression. In an effort to assess the potential role of platelet-wall interactions, experimentally validated particle-hemodynamic simulations have been conducted for two commonly implemented end-to-side anastomotic configurations, with and without proximal outflow. Specifically, sites of significant particle interactions with the vascular surface have been identified by a novel near-wall residence time (NWRT) model for platelets, which includes shear stress-based factors for platelet activation as well as endothelial cell expression of thrombogenic and anti-thrombogenic compounds. Results indicate that the composite NWRT model for platelet-wall interactions effectively captures a reported shift in significant IH formation from the arterial floor of a relatively high-angle (30 deg) graft with no proximal outflow to the graft hood of a low-angle graft (10 deg) with 20% proximal outflow. In contrast, other WSS-based hemodynamic parameters did not identify the observed system-dependent shift in IH formation. However, large variations in WSS-vector magnitude and direction, as encapsulated by the WSS-gradient and WSS-angle-gradient parameters, were consistently observed along the IH-prone suture-line region. Of the multiple hemodynamic factors capable of eliciting a hyperplastic response at the cellular level, results of this study indicate the potential significance of platelet-wall interactions coinciding with regions of low WSS in the development of IH.     

Effects of arterial compliance and non-Newtonian rheology on correlations between intimal thickness and wall shear.

A minimally diseased (mean intimal thickness = 56 microns) human aortic bifurcation was replicated in rigid and compliant flow-through casts. Both casts were perfused with physiological flow waves having the same Reynolds and unsteadiness numbers; the pulse pressure in the compliant cast produced radial strains similar to those expected from post-mortem measurements of the compliance of the original tissue. The compliant cast was perfused with a Newtonian fluid and one whose rheology was closer to that of blood. Wall shear rate histories were estimated from near-wall velocities obtained by laser Doppler velocimetry at identical sites in both casts. Intimal thickness was measured at corresponding sites in the original vessel and linear regressions were performed between these thicknesses and several normalized shear rate measures obtained from the histories. The correlations showed a positive slope--that is, the intima was thicker at sites exposed to higher shear rates--consistent with earlier results for relatively healthy vessels, but their significance was often poor. There was no significant effect of either model compliance or fluid rheology on the slopes of the correlations of intimal thickness against any normalized shear rate measure.     

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.     

Measurement of the transverse strain tensor in the coronary arterial wall from clinical intravascular ultrasound images

Atherosclerotic plaque rupture is the major cause of acute coronary syndromes. Currently, there is no reliable diagnostic tool to predict plaque rupture. Knowledge of plaque mechanical properties based on local artery wall strain measurements would be useful for characterizing its composition and predicting its vulnerability. Due to cardiac motion, strain estimation in clinical intravascular ultrasound (IVUS) images is extremely challenging. A method is presented to estimate cross-sectional coronary artery wall strain in response to cardiac pulsatile pressure using clinically acquired IVUS images, which are acquired in continuous pullback mode. First, cardiac phase information is retrieved retrospectively from an IVUS image sequence using an image-based gating method, and image sub-sequences at systole and diastole are extracted. Then, images at branch sites are used as landmarks to align the two image sub-sequences. Finally, the paired images at each site are registered to measure the 2D strain tensor of the coronary artery cross-section. This method has been successfully applied to IVUS images of a left anterior descending (LAD) coronary artery acquired clinically during a standard procedure. Such complete strain information should be useful for identifying vulnerable plaque.     

Isotropy and anisotropy of the arterial wall

The passive biomechanical response of intact cylindrical rat carotid arteries is studied in vitro and compared with the mechanical response of rubber tubes. Using true stress and natural strain in the definition of the incremental modulus of elasticity, the tissue wall properties are analyzed over wide ranges of simultaneous circumferential and longitudinal deformations. The type of loading chosen is 'physiological' i.e. symmetric: the cylindrical segments are subjected to internal pressure and axial prestretch without torsion or shear. Several aspects pertaining to the choice of parameters characterizing the material are discussed and the analysis pertaining to the deformational behavior of a hypothetical compliant tube with Hookean wall material is presented. The experimental results show that while rubber response can be adequately represented as linearly elastic and isotropic, the overall response of vascular tissue is highly non-linear and anisotropic. However, for states of deformation that occur in vivo, the elasticity of arteries is quite similar to that of rubber tubes and as such the arterial wall may be viewed as incrementally isotropic for the range of deformations that occur in vivo.     

Relative contribution of wall shear stress and injury in experimental intimal thickening at PTFE end-to-side arterial anastomoses

BACKGROUND: Intimal hyperplastic thickening (IHT) is a frequent cause of prosthetic bypass graft failure. Induction and progression of IHT is thought to involve a number of mechanisms related to variation in the flow field, injury and the prosthetic nature of the conduit. This study was designed to examine the relative contribution of wall shear stress and injury to the induction of IHT at defined regions of experimental end-to-side prosthetic anastomoses. METHODS AND RESULTS: The distribution of IHT was determined at the distal end-to-side anastomosis of seven canine Iliofemoral PTFE grafts after 12 weeks of implantation. An upscaled transparent model was constructed using the in vivo anastomotic geometry, and wall shear stress was determined at 24 axial locations from laser Doppler anemometry measurements of the near wall velocity under conditions of pulsatile flow similar to that present in vivo. The distribution of IHT at the end-to-side PTFE graft was determined using computer assisted morphometry. IHT involving the native artery ranged from 0.0+/-0.1 mm to 0.05+/-0.03 mm. A greater amount of IHT was found on the graft hood (PTFE) and ranged from 0.09+/-0.06 to 0.24+/-0.06 mm. Nonlinear multivariable logistic analysis was used to model IHT as a function of the reciprocal of wall shear stress, distance from the suture line, and vascular conduit type (i.e. PTFE versus host artery). Vascular conduit type and distance from the suture line independently contributed to IHT. An inverse correlation between wall shear stress and IHT was found only for those regions located on the juxta-anastomotic PTFE graft. CONCLUSIONS: The data are consistent with a model of intimal thickening in which the intimal hyperplastic pannus migrating from the suture line was enhanced by reduced levels of wall shear stress at the PTFE graft/host artery interface. Such hemodynamic modulation of injury induced IHT was absent at the neighboring artery wall.     

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。