Wall Shear Stress Gradient Research Articles

Particle image velocimetry measurements of three proximal anastomosis models under a pulsatile flow condition

This study was designed to examine the effects of the anastomotic angle on the flow and haemodynamic parameter distribution patterns of the proximal anastomoses, with emphasis on identifying site-specific haemodynamic features that could reasonably be expected to trigger the initiation and further development of anastomotic intimal hyperplasia. Particle image velocimetry measurements were carried out with three simplified glass proximal models under a physiological flow condition. The results revealed that the disturbed flow and the induced shear stress patterns including low recirculation flow, stagnation point, high wall shear stress, high temporal wall shear stress gradient, low time-averaged wall shear stress (TAWSS), and high oscillating shear index (OSI) occurred around the anastomotic joints and the flow field at proximal anastomosis was strongly affected by the anastomotic angle. Among the three models investigated, the 45 degrees backward anastomosis is found to have a smaller low-recirculation-flow region along the graft inner wall, non-stationary stagnation, and separation points, a higher TAWSS and smaller high-OSI low-TAWSS and low-OSI high-TAWSS regions.

The Flow Field along the Entire Length of Mouse Aorta and Primary Branches

There is a spatial disposition to atherosclerosis along the aorta corresponding to regions of flow disturbances. The objective of the present study is to investigate the detailed distribution of hemodynamic parameters (wall shear stress (WSS), spatial gradient of wall shear stress (WSSG), and oscillatory shear index (OSI)) in the entire length of C57BL/6 mouse aorta with all primary branches (from ascending aorta to common iliac bifurcation). The detailed geometrical parameters (e.g., diameter and length of the vessels) were obtained from casts of entire aorta and primary branches of mice. The flow velocity was measured at the inlet of ascending aorta using Doppler flowprobe in mice. The outlet pressure boundary condition was estimated based on scaling law. The continuity and Navier-Stokes equations were solved using three-dimensional finite element method (FEM). The model prediction was tested by comparing the computed flow rate with the flow rate measured just before the common iliac bifurcation, and good agreement was found. It was also found that complex flow patterns occur at bifurcations between main trunk and branches. The major branches of terminal aorta, with the highest proportion of atherosclerosis, have the lowest WSS, and the relatively atherosclerotic-prone aortic arch has much more complex WSS distribution and higher OSI value than other sites. The low WSS coincides with the high OSI, which approximately obeys a power law relationship. Furthermore, the scaling law between flow and diameter holds in the entire aorta and primary branches of mice under pulsatile blood flow conditions. This model will eventually serve to elucidate the causal relation between hemodynamic patterns and atherogenesis in KO mice.

Flow Structure Around Renal Arterial Branch During Pulsatile Flow

The arterial branch from abdominal artery to renal artery is one of the predilection sites of atherosclerosis. In the present study, we have experimentally clarified the hemodynamic structure such as the velocity profile and the wall shear stress during pulsatile flow in a branch model where the renal artery bifurcates from the abdominal aorta. The hemodynamic structure around the renal arterial branch is characterized the gradient of wall shear stress which distinctly changes around the entrance corner to renal artery. As approaching this corner, the wall shear stress steeply increases, and after passing through this corner it suddenly decreases. Consequently, it would be physiologically suggested that the large gradient of wall shear stress is closely associated with the initiation and the development of atherosclerosis.

708 脳動脈瘤の発生に対する新しい血行力学的指標の提案(J06-2 医療診断のためのマルチスケール血流動態計測と解析(2),ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

We proposed a new hemodynamic indicator for the initiation of cerebral aneurysms, defined by the temporal fluctuations of tension/compression forces acting on endothelial cells. We calculated the proposed hemodynamic indicator and other three hemodynamic quantities (time-averaged wall shear stress (WSS), time-averaged spatial WSS gradient (SWSSG), and potential aneurysm formation indicator (AFI)) for a patient-specific geometry before aneurysm formation by means of computational fluid dynamics technique. The results showed that only the proposed hemodynamic indicator had a significant correlation with the location of aneurysm formation. Our findings suggest that the proposed indicator might be a prospective hemodynamic indicator for the initiation of cerebral aneurysms.

WALL SHEAR STRESS GRADIENT ANALYSIS WITHIN AN IDEALIZED STENOSIS USING NON-NEWTONIAN FLOW

The endothelium is functionally regulated by the magnitude and spatiotemporal gradients of wall shear stress (WSS). Although flow separation and reversal occur beyond high-grade stenoses, little is known of the WSS pattern within clinically relevant mild to moderate stenoses. An axisymmetric geometry with 25, 50, and 75% stenosis criteria (quantified in accordance with the North American Symptomatic Carotid Endarterectomy Trial) was used to generate a high-resolution, hybrid, tetrahedral-hexahedral computational mesh with boundary-layer enrichment to improve near-wall shear stress gradient (WSSG) computation. Time-dependent computational fluid dynamic analysis was performed using a non-Newtonian Carreau-Yasuda model of blood to yield the shear-dependent viscosity. Transition to secondary flow patterns was demonstrated in stenoses of 25, 50, and 75%. A focal region with near-wall flow reversal and retrograde WSS was identified within the stenosis itself and was found to migrate cyclically during the cardiac pulse. A zone of zero WSS and divergent WSSG that shifts in toward the throat with increasing stenotic severity was identified. Focal zones of high WSSG with converging and/or diverging direction were uncovered within the stenosis itself, as were expected changes in the distal poststenotic region. These zones of divergent WSSG shift over a substantial length of the stenosis during the course of the cardiac cycle. Luminal WSS demonstrates dynamic direction reversal and high spatial gradients within the distal stenosis throat of even clinically moderate lesions. These findings shed light on the complex vessel wall hemodynamics within clinical stenoses and reveal a mechanical microenvironment that is conducive to perpetual endothelial functional dysregulation and stenosis progression.

Flow patterns in three-dimensional porcine epicardial coronary arterial tree

The branching pattern of epicardial coronary arteries is clearly three-dimensional, with correspondingly complex flow patterns. The objective of the present study was to perform a detailed hemodynamic analysis using a three-dimensional finite element method in a left anterior descending (LAD) epicardial arterial tree, including main trunk and primary branches, based on computed tomography scans. The inlet LAD flow velocity was measured in an anesthetized pig, and the outlet pressure boundary condition was estimated based on scaling laws. The spatial and temporal wall shear stress (WSS), gradient of WSS (WSSG), and oscillatory shear index (OSI) were calculated and used to identify regions of flow disturbances in the vicinity of primary bifurcations. We found that low WSS and high OSI coincide with disturbed flows (stagnated, secondary, and reversed flows) opposite to the flow divider and lateral to the junction orifice of the main trunk and primary branches. High time-averaged WSSG occurs in regions of bifurcations, with the flow divider having maximum values. Low WSS and high OSI were found to be related through a power law relationship. Furthermore, zones of low time-averaged WSS and high OSI amplified for larger diameter ratio and high inlet flow rate. Hence, different focal atherosclerotic-prone regions may be explained by different physical mechanism associated with certain critical levels of low WSS, high OSI, and high WSSG, which are strongly affected by the diameter ratio. The implications of the flow patterns for atherogenesis are enumerated.

Near-wall scaling for turbulent boundary layers with adverse pressure gradient

A new extended inner scaling is proposed for the wall layer of wall-bounded flows under the influence of both wall shear stress and streamwise pressure gradient. This scaling avoids problems of the classical wall coordinates close to flow separation and reattachment. Based on the proposed extended velocity and length scales a universal nondimensional family of velocity profiles is derived for the viscous region in the vicinity of a wall that depend on wall distance and a parameter α quantifying the importance of the streamwise pressure gradient with respect to the wall shear stress in the momentum balance. The performance of the proposed extended scaling is investigated in two different flow fields, a separating and reattaching turbulent boundary layer and a turbulent flow over a periodic arrangement of smoothly contoured hills. Both flows are results of highly resolved direct numerical simulation (DNS). The results show that the viscous assumptions are valid up to about two extended wall units. If the profiles are scaled by the extended inner coordinates, they seem to behave in a universal way. This gives rise to the hope that a universal behavior of velocity profiles can be found in the proposed extended inner coordinates even beyond the validity of the extended viscous law of the wall.

A parametric numerical investigation on haemodynamics in distal coronary anastomoses

Anastomotic haemodynamics, which plays an important role in the performance of bypass graft, is known to be profoundly affected by the diameter ratio ( Φ) and angle ( α) between the graft and host artery in the peripheral region. We hypothesize that these geometric factors would play similar roles in distal coronary anastomoses and that they could be improved for clinical applications through parametric studies. Anastomotic models covering a range of Φ (1:1, 1.5:1 and 2:1) and α (15°, 30°, 45° and 60°) were investigated numerically in physiological coronary flow conditions. The transient flow patterns, cycle-averaged wall shear stress (WSS), oscillatory shear index (OSI), spatial and temporal WSS gradients (SWSSG and TWSSG) were compared. Results show a stronger influence of Φ than α on haemodynamics in distal coronary artery anastomoses. Substantially higher SWSSG and TSSWG occur on the artery floor when Φ = 1:1 compared to larger Φ. High levels of OSI occur in critical regions when Φ = 1:1 and 2:1. The largest area of high OSI is found in the anastomotic region when α = 15°, whereas the highest level of SWSSG appears on the artery floor when α = 60°. The study suggests the clinical relevance of optimizing geometric parameters of coronary anastomoses to improve their haemodynamic performance. We speculate that for a distal coronary anastomosis with a 20:80 proximal–distal flow division ratio maintained in the host artery, Φ = 1.5 and α = 30–45° would enhance its long-term performance.

Numerical study of hemodynamics comparison between small and large femoral bypass grafts

AbstractThe geometry factors have prominent impacts on the flow patterns of bypass graft. In order to clarify the influence of graft diameter on the hemodynamics of femoral bypass graft, the pulsatile blood flows in three bypassing models with different graft diameters were simulated with finite‐element method. The temporal–spatial distributions of flow patterns, pressure drops, and wall shear stresses were depicted and compared. The results indicated that femoral artery bypassed with a large graft demonstrates relatively better and more profitable hemodynamic phenomena with large longitudinal velocity, uniform wall shear stress, and small wall shear stress gradient. The large model may be effective in decreasing the probability of the initiation and development of postoperative intimal hyperplasia and restenosis. Copyright © 2007 John Wiley & Sons, Ltd.

Non-Newtonian models for molecular viscosity and wall shear stress in a 3D reconstructed human left coronary artery

The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occured at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn–Schneck models over-estimated the non-Newtonian global importance factor I G and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.

PIV-validated numerical modeling of pulsatile flows in distal coronary end-to-side anastomoses

This study employed particle image velocimetry (PIV) to validate a numerical model in a complementary approach to quantify hemodynamic factors in distal coronary anastomoses and to gain more insights on their relationship with anastomotic geometry. Instantaneous flow fields and wall shear stresses (WSS) were obtained from PIV measurement in a modified life-size silastic anastomosis model adapted from a conventional geometry by incorporating a smooth graft–artery transition. The results were compared with those predicted by a concurrent numerical model. The numerical method was then used to calculate cycle-averaged WSS (WSS cyc) and spatial wall shear stress gradient (SWSSG), two critical hemodynamic factors in the pathogenesis of intimal thickening (IT), to compare the conventional and modified geometries. Excellent qualitative agreement and satisfactory quantitative agreement with averaged normalized error in WSS between 0.8% and 8.9% were achieved between the PIV experiment and numerical model. Compared to the conventional geometry, the modified geometry produces a more uniform WSS cyc distribution eliminating both high and low WSS cyc around the toe, critical in avoiding IT. Peak SWSSG on the artery floor of the modified model is less than one-half that in the conventional case, and high SWSSG at the toe is eliminated. The validated numerical model is useful for modeling unsteady coronary anastomotic flows and elucidating the significance of geometry regulated hemodynamics. The results suggest the clinical relevance of constructing smooth graft–artery transition in distal coronary anastomoses to improve their hemodynamic performance.

Computational Study of Flow in a Carotid Bifurcation (Geometry and Flow Ratio Correlations with WSS)

The present study presents a three-dimensional steady numerical simulation of flow through a model of the bifurcation of the common carotid artery (CCA) into the internal (ICA) and external carotid (ECA) arteries. Flow with large inertia bifurcates at the apex (divider tip) and creates a flow recirculation zone associating with very low wall shear stress (WSS) at the outer wall of the ICA sinus where atherosclerotic plaques are localized. The change of both the CCA-ICA and CCA-ECA bifurcation angle has more effect on the distribution of WSS over the outer wall of the sinus. A larger angle of daughter tubes makes the region of low WSS in the ICA sinus narrower in the flow direction, however, makes the WSS gradient in regions surrounding the ICA sinus steeper for a higher volumetric flow ratio of the ICA : ECA. In contrast to the WSS features, the distribution of the axial flow velocity in the plane of symmetry is not very sensitive to the change in both the bifurcation angle and flow ratio between the ICA and ECA.

Time‐resolved 3D quantitative flow MRI of the major intracranial vessels: Initial experience and comparative evaluation at 1.5T and 3.0T in combination with parallel imaging

Exact knowledge of blood flow characteristics in the major cerebral vessels is of great relevance for diagnosing cerebrovascular abnormalities. This involves the assessment of hemodynamically critical areas as well as the derivation of biomechanical parameters such as wall shear stress and pressure gradients. A time-resolved, 3D phase-contrast (PC) MRI method using parallel imaging was implemented to measure blood flow in three dimensions at multiple instances over the cardiac cycle. The 4D velocity data obtained from 14 healthy volunteers were used to investigate dynamic blood flow with the use of multiplanar reformatting, 3D streamlines, and 4D particle tracing. In addition, the effects of magnetic field strength, parallel imaging, and temporal resolution on the data were investigated in a comparative evaluation at 1.5T and 3T using three different parallel imaging reduction factors and three different temporal resolutions in eight of the 14 subjects. Studies were consistently performed faster at 3T than at 1.5T because of better parallel imaging performance. A high temporal resolution (65 ms) was required to follow dynamic processes in the intracranial vessels. The 4D flow measurements provided a high degree of vascular conspicuity. Time-resolved streamline analysis provided features that have not been reported previously for the intracranial vasculature.

Investigations into the relationship between hemodynamics and vascular alterations in an established arteriovenous fistula

Arteriovenous fistula are specific vessels created by a vascular operation in order to provide sufficient blood access for extracorporeal circulation in hemodialysis. They are subject to numerous pathologies that may be caused by hemodynamic effects. To better understand these effects, a specific patient's arteriovenous fistula was reconstructed from computed tomography angiography. Computational fluid dynamics software made it possible to solve fluid mechanics equations under physiological conditions. An accurate map of unsteady velocity profiles and wall shear stress was drawn up. The computed velocity profiles were successfully confronted with Echo Doppler investigation. Selected regions with or without calcification, the end stage of wall alteration, were examined in terms of the mechanical constraints generated by blood flow. In contrast with other authors, we did not observe any association between calcification and areas of oscillating shear stress. Nevertheless, a statistical analysis of the whole vessel envelop and specific sites of calcification suggested a potential association between calcification and high temporal wall shear stress gradients.

Numerical Model Study of Flow Dynamics through an End-to-Side Anastomosis: Choice of Anastomosis Angle and Prosthesis Diameter

The purpose of this numerical model study was to determine the angle of anastomosis and prosthesis-to-artery diameter ratio that theoretically limits development of myointimal hyperplasia (MIH). Blood flow patterns were investigated in a model simulating a distal end-to-side anastomosis on a 2-mm-diameter artery. Tests were carried out under steady and pulsatile flow conditions with and without taking into account the non-Newtonian behavior of blood and compliance. The wall shear stress gradient (WSSG), a potential factor for development of MIH, was analyzed as a function of the angle of anastomosis (18 degrees , 25 degrees , 35 degrees , and 45 degrees ) and prosthesis diameter (4, 5, and 6 mm). The angle of anastomosis that minimized WSSG was 18 degrees . Prosthesis diameter had no effect on WSSG, with similar results for all three diameters. These findings suggest that surgeons should choose as acute an angle of anastomosis as possible. Prosthesis diameter played no role in reducing WSSG values.

A MODEL SYSTEM FOR MAPPING VASCULAR RESPONSES TO COMPLEX HEMODYNAMICS AT ARTERIAL BIFURCATIONS IN VIVO

Cerebral aneurysms are preferentially located at arterial bifurcation apices with complex hemodynamics. To understand disease mechanisms associated with aneurysm initiation, we attempted to establish a causal relationship between local hemodynamics and vascular responses. Arterial bifurcations were surgically created from native common carotid arteries in two dogs, angiographically imaged 2 weeks and 2 months later, and then excised. We characterized local morphological changes in response to specifically manipulated hemodynamics. Computational fluid dynamics simulations were performed on the in vivo images and results mapped onto histological images. Local flow conditions, such as high wall shear stress and high wall shear stress gradient, were found to be associated with vascular changes, including an intimal pad in the flow impingement region and a "groove" bearing the characteristics of an early aneurysm. This novel method of histohemodynamic micromapping reveals a direct correlation between an altered hemodynamic microenvironment and vascular responses consistent with aneurysm development.

Are intramural suction-squeezing effects generated by the variations in radial wall stress during each heart beat the motor of atherosclerosis? A new concept

In the early sixties, the existence of predilection sites for atherosclerotic lesions inside the arterial circulation led to the concept that low wall shear stress (WSS) was responsible, together with systemic factors like high blood pressure, hypercholesterolemia, or diabetes, for the genesis and progression of atherosclerosis. It was found later that oscillating WSS and high WSS gradients could also be incriminated. Yet, this concept, which is broadly accepted today, fails to explains several facts, for instance that some arteries (e.g. epicardial coronary arteries) are more prone to become atherosclerotic than other ones exposed to the same systemic factors (e.g. hepatic and brain arteries). In this paper, we present a quite different concept. It is based on the fact that the increase in intravascular pressure and flow that occur in the arteries during systole generates, at the predilection sites of atherosclerotic lesions (bends, bifurcations, and branchings), an increase of radial wall stress in the outer layers of the arterial wall so that this stress becomes momentarily tensile. These cyclic stress increases have a suction effect that is likely to facilitate the diffusion of atherogenic cells and substances inside the wall. Furthermore, since arteries are not primarily structured to resist inversions of radial stress, they may also create damages (e.g. disruptions of cell membranes and elastic lamellae) followed by inflammations and micro-haemorrhages in the wall. This new concept may provide a complementary (or possibly alternative) explanation of atherosclerosis.

Flow parameters in normal left coronary artery tree. Implication to atherogenesis

The dominant haemodynamic flow parameters of wall pressure (WP), wall shear stress (WSS), molecular viscosity and the spatial gradients: wall pressure gradient (WPG) and wall shear stress gradient (WSSG) along the normal human left coronary artery (LCA) tree are numerically analyzed in relation to atheronegenesis. The LCA tree includes the left main coronary artery, the left anterior descending branch, the left circumflex branch and their major branches. Spatial differentiation indicates that low values of WP (locally), WPG, WSS, WSSG and high molecular viscosity appear opposite flow dividers and this probably correlates to atherosclerosis localization.

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

BackgroundThe success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation.MethodsIn the current investigation, we tested the hypothesis that acute changes in stent-induced regional geometry influence distributions of WSS using 3D coronary artery CFD models implanted with stents that either conformed to or caused straightening of the primary curvature of the left anterior descending coronary artery. WSS obtained at several intervals during the cardiac cycle, time averaged WSS, and WSS gradients were calculated using conventional techniques.ResultsImplantation of a stent that causes straightening, rather than conforms to the natural curvature of the artery causes a reduction in the radius of curvature and subsequent increase in the Dean number within the stented region. This straightening leads to modest skewing of the velocity profile at the inlet and outlet of the stented region where alterations in indices of WSS are most pronounced. For example, time-averaged WSS in the proximal portion of the stent ranged from 8.91 to 11.7 dynes/cm2 along the pericardial luminal surface and 4.26 to 4.88 dynes/cm2 along the myocardial luminal surface of curved coronary arteries as compared to 8.31 dynes/cm2 observed throughout the stented region of a straight vessel implanted with an equivalent stent.ConclusionThe current results predicting large spatial and temporal variations in WSS at specific locations in curved arterial 3D CFD simulations are consistent with clinically observed sites of restenosis. If the findings of this idealized study translate to the clinical situation, the regional geometry established immediately after stent implantation may predispose portions of the stented vessel to a higher risk of neointimal hyperplasia and subsequent restenosis.

Effects of Arterial Bifurcation Geometry on Nucleotide Concentration at the Endothelium

A mathematical and computational analysis of nucleotide concentration for a two-dimensional artery bifurcation has been developed. This region of the vasculature is known to be exposed to spatially varying wall shear stress (WSS), hence the variation of adenosine nucleotides is of interest. A previously derived similarity solution for mass transport in blood boundary layers for arbitrary wall shear stress function has been used. For the analytical model, the geometric condition has been incorporated into the system using the theory for flow past a wedge. As the bifurcation angle varies different characteristics are exhibited, such as maxima in ADP concentration and the existence of a low wall shear stress region around the stagnation point, for large angles. In the limiting case of two-dimensional stagnation point flow the concentration was constant throughout the domain length. The computational simulations provided a more detailed understanding into how nucleotides vary. Similarities existed between the two solution methods in the vicinity of the stagnation point, but deviated as the fully developed condition prevailed. Additionally, the effect of pulsatile flow has been included, leading to considerable gradients in wall shear stress, both temporal and spatial. However, the resulting nucleotide concentration is determined by the time-averaged wall shear stress. The effects of flow-induced ATP release have also been included, leading to significant changes in ATP concentration. Under rapid release, the concentration at the surface increased relative to the bulk concentration.