Amplitude Of Wall Shear Stress Research Articles

Characteristics of the wall shear stress in pulsating wall-bounded turbulent flows

A pulsating turbulent pipe flow has been investigated experimentally using hot-film anemometry and particle image velocimetry. Particularly, a ‘paradoxical phenomenon’ that is known to occur for a range of forcing frequencies and time-averaged Reynolds numbers has been investigated in detail. The paradoxical phenomenon is that the oscillating component of the wall shear stress exhibits a smaller amplitude in a turbulent flow compared to in a laminar flow exposed to the same oscillation in the pressure gradient. In here, the phenomenon is explained by splitting the response of the wall shear stress into one contribution resulting from the imposed pressure gradient τ∼p, and a second contribution resulting from the oscillating Reynolds shear stress, τ∼t. At the conditions of maximum reduction of the wall shear stress amplitude, τ∼p and τ∼t are nearly 136° out of phase. The contributions are thus interfering destructively, this being the ultimate reason for the reduced amplitude. It is also shown that the level of reduction is dependent on the imposed forcing amplitude, this in turn residing from a dependence of the time-development of the oscillating Reynolds shear stress on the forcing amplitude.

High temperature gradient calorimetric wall shear stress micro-sensor for flow separation detection

The paper describes and discusses the design and testing of an efficient and high-sensitivity calorimetric thermal sensor developed for bi-directional wall shear stress measurements in aerodynamic flows. The main technical application targeted is flow separation detection. The measurement principle is based on the forced convective heat transfer from a heater element. The sensor structure is composed of three parallel substrate-free wires presenting a high aspect ratio and supported by periodic perpendicular SiO2 micro-bridges. This hybrid structure takes advantages from both conventional hot-films and hot-wires, ensuring near-wall and non-intrusive measurement, mechanical toughness and thermal insulation to the bulk substrate, and it allowed to add the calorimetric sensor functionality to detect simultaneously the wall shear stress amplitude and direction. The central wire is made of a multilayer structure composed of a heater element (Au/Ti) and a thermistor (Ni/Pt/Ni/Pt/Ni) enabling measurement of the heater temperature and a layer of SiO2 between them for electrical insulation. The upstream and downstream wires are thermistors enabling operation in the calorimetric mode. This design provides a high temperature gradient and a homogeneous temperature distribution along the wires. The sensor operates in both constant current and constant temperature modes, with a feedback on current enabled by uncoupling heating and measurement. Welded on a flexible printed circuit, the sensor was flush mounted on the wall of a turbulent boundary layer wind tunnel. The experiments, conducted in both attached and separated flow configurations, quantify the sensor response to a bi-directional wall shear stress up to 2.4Pa and demonstrate the sensor ability to detect flow separation.

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.

Tortuosity of coronary bifurcation as a potential local risk factor for atherosclerosis: CFD steady state study based on in vivo dynamic CT measurements.

The purpose of the present study was to determine whether in vivo bifurcation geometric factors would permit prediction of the risk of atherosclerosis. It is worldwide accepted that low or oscillatory wall shear stress (WSS) is a robust hemodynamic factor in the development of atherosclerotic plaque and has a strong correlation with the local site of plaque deposition. However, it still remains unclear how coronary bifurcation geometries are correlated with such hemodynamic forces. Computational fluid dynamics simulations were performed on left main (LM) coronary bifurcation geometries derived from CT of eight patients without significant atherosclerosis. WSS amplitudes were accurately quantified at two high risk zones of atherosclerosis, namely at proximal left anterior descending artery (LAD) and at proximal left circumflex artery (LCx), and also at three high WSS concentration sites near the bifurcation. Statistical analysis was used to highlight relationships between WSS amplitudes calculated at these five zones of interest and various geometric factors. The tortuosity index of the LM-LAD segment appears to be an emergent geometric factor in determining the low WSS amplitude at proximal LAD. Strong correlations were found between the high WSS amplitudes calculated at the endothelial regions close to the flow divider. This study not only demonstrated that CT imaging studies of local risk factor for atherosclerosis could be clinically performed, but also showed that tortuosity of LM-LAD coronary branch could be used as a surrogate marker for the onset of atherosclerosis.

Experimental investigation of the wall shear stress in a circular impinging jet

The influence of the large-scale vortical structures on the wall shear stress in a circular impinging jet is investigated experimentally for a Reynolds number of 1260. Time-resolved particle image velocimetry and polarographic measurements are performed simultaneously. It is found that the instantaneous wall shear stress is strongly dependent on the vortex dynamics, particularly for different parts of the transverse vortex. The influence of the vortex ring, the secondary and tertiary vortices on the ejection/sweep process near the wall is the main mechanism involved in the wall shear stress variation. In the region of the boundary layer separation, the wall shear stress amplitude increases just upstream of the separation and dramatically decreases in the recirculation zone downstream from the separation. The interaction between primary and secondary structures and their pairing process with the tertiary structure affects the sweep/ejection process near the wall and subsequently the wall shear stress variation. A comparison between the Finite Time Lyapunov Exponent (FTLE) method and the phase average technique is performed. It is shown that both methods describe the flow dynamics in the impinging region of the vortex ring. However, the FTLE method is more suitable for describing the unsteady separation of the boundary layer.

Characteristics of the response of the iliac artery to wall shear stress in the anaesthetized pig

The functional significance of shear stress-induced vasodilatation in large conduit arteries is unclear since changes in the diameter have little effect on the resistance to blood flow. However, changes in diameter have a relatively large effect on wall shear stress which suggests that the function of flow-mediated dilatation is to reduce wall shear stress. The mean and pulsatile components of shear stress vary widely throughout the arterial system and areas of low mean and high amplitude of wall shear stress are prone to the development of atheroma. In this study, using an in vivo model with the ability to control flow rate and amplitude of flow independently, we investigated the characteristics of the response of the iliac artery to variations in both the mean and amplitude of wall shear stress. The results of this study confirm that increases in mean wall shear stress are an important stimulus for the release of nitric oxide by the endothelium as indicated by changes in arterial diameter and show for the first time, in vivo, that increases in the amplitude of the pulsatile component of shear stress have a small but significant inhibitory effect on this response. A negative feedback mechanism was identified whereby increases in shear stress brought about by increases in blood flow are reduced by the release of nitric oxide from the endothelium causing dilatation of the artery, thus decreasing the stimulus to cell adhesion and, through a direct action of nitric oxide, inhibiting the process of cell adhesion. The results also provide an explanation for the uneven distribution of atheroma throughout the arterial system, which is related to the ratio of pulsatile to mean shear stress and consequent variability in the production of NO.

Near-Wall Deposition Probability of Blood Elements as A New Hemodynamic Wall Parameter

The present study was performed to investigate deposition probability of blood particles on the vessel walls. To track dynamics of movement and adhesion of blood particles in the near wall region, two models such as the particle rolling model (PR-model) and the near wall force model (NWF-model) were employed in the present study. Simulations of the present models for the pre-activated platelets in the stagnated point flow chamber and for the pre-activated monocytes in the stenotic perfusion tube resulted in significant correlations with the experimental data. The proposed near wall deposition probability (NWDP) index exhibited good fits with the experimental data of the stagnation point flow chamber for the platelet. As for the monocyte, the NWDP index exhibited the best fit with the experimental data of the stenotic tube. The new hemodynamic index, NWDP, is different from the wall shear stress (WSS)-based hemodynamic parameters, such as MWSS (Mean Wall Shear Stress), AWSS (Amplitude of Wall Shear Stress), and OSI (Oscillatory Shear Index) in that it locates regions of both the high and low WSS. The proposed NWDP index needs to be tested and compared in real geometries for its effectiveness in locating regions of lesion-prone sites.

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

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

Alteration in fluid mechanics in porcine femoral arteries with atheroma development.

Although the relationship between the local wall shear stresses (WSS) and atheroma development has been previously studied, the effect of variable regional wall distensibility with early atherosclerotic lesions and its effect on local hemodynamics have not been well investigated. We induced early atherosclerotic lesion development in one femoral artery in a Yucatan miniswine model with the contralateral artery serving as control. Eight weeks following atheroma formation, hemodynamic and intravascular ultrasound image data were obtained. Using the measured regional arterial distension as the moving boundary condition, unsteady laminar incompressible computational analysis was performed on the reconstructed arterial segments. With the development of early atherosclerotic lesions, there was increased wall distensibility and an increase in the computed normalized wall shear stress amplitude (NWSA). Alterations in the local fluid mechanics and mass transport at these sites may need to be considered in our understanding of the continued growth of these lesions.

Characteristics of arterial wall shear stress which cause endothelium-dependent vasodilatation in the anaesthetized dog.

1. The effects of changes in the mean and amplitude of arterial wall shear stress on endothelium-dependent arterial dilatation of the iliac artery of the anaesthetized dog were examined. 2. Changes in the mean and amplitude of blood flow and wall shear stress were brought about by varying local peripheral resistance and stroke volume using a distal infusion of acetylcholine and the stimulation of the left ansa subclavia. Changes in the diameter of a segment of the iliac artery with the endothelium intact, relative to a segment with no endothelium, were used as an index of the release of nitric oxide. 3. The increase in mean blood flow was from 84 +/- 12 to 527 +/- 53 ml min-1 and in amplitude was from 365 +/- 18 to 695 +/- 38 ml min-1 (means +/- S.E.M.). The increase in mean wall shear stress was from 1.78 +/- 0.30 to 7.66 +/- 1.01 N m-2 and in amplitude was from 7.37 +/- 0.46 to 13.9 +/- 2.00 N m-2 (means +/- S.E.M.). 4. Increases in mean shear stress caused an increase in the diameter only of the section of artery with endothelium; the slope of the relationship was 0.064 +/- 0.006 mm N-1 m2 (mean +/- S.E.M., P < 0.001); changes in the amplitude of shear stress did not cause an increase in diameter. Changes in both the mean and amplitude of shear stress had no significant effect on the diameter of the section of artery with no endothelium. 5. These findings coupled with the known anti-atheroma effects of nitric oxide and the effect of shear stress on cell adhesion and platelet aggregation offer a possible explanation for the disposition of atheroma in those parts of the arterial system which have low mean and high amplitude of wall shear stress.

Wall Shear Stress Between Compliant Plates Under Oscillatory Flow Conditions: Influence of Wall Motion, Impedance Phase Angle and Non-Newtonian Fluid

The present study investigates flow dynamics between two dimensional compliant plates under sinusoidal flow conditions in order to understand influence of wall motion, impedance phase angle (time delay between pressure and flow waveforms), and non-Newtonian fluid on wall shear stress using computational fluid dynamics. The results showed that wall motion induced additional terms in the streamwise velocity profile and the pressure gradient. These additional terms due to wall motion reduced the amplitude of wall shear stress and also changed the mean wall shear stress. The trend of the changes was very different depending on the impedance phase angle. As the impedance phase angle was changed to more negative values, the mean wall shear stress decreased while the amplitude of wall shear stress increased. As the phase angle was reduced from 0°to -90°under 4% wall motion, the mean wall shear stress decreased by 12% and the amplitude of wall shear stress increased by 9%. Therefore, for hypertensive patients who have large negative phase angles, the ratio of amplitude and mean of the wall shear stress is raised resulting in a more vulnerable state to atherosclerosis according to the low and oscillatory shear stress theory. We also found that non-Newtonian characteristics of the blood protect atherosclerosis by decreasing the oscillatory shear index.

Influence of Blood Viscoelasticity on the Distribution of Wall Shear Stress.

It is well known that blood denotes the viscoelastic property under the unsteady flow conditions. So, we analyzed the unsteady blood flows through the two-dimensional channel with the fixed stenosis to evaluate the effect of blood viscoelasticity on the distribution of wall shear stress. In this study, we adopted the Thurston model to denote the viscoelastic property of blood. The results are summarized as follows : i) The difference among these models appears clearly in the amplitude of wall shear stress. ii) The results based on the Casson model are in qualitative agreement with the results based on the Thurston model, but the Casson model has a tendency to underestimate the amplitude of wall shear stress compared with the Thurston model.

Hemodynamic effects on atherosclerosis-prone coronary artery: wall shear stress/rate distribution and impedance phase angle in coronary and aortic circulation.

The objective of the present study was to evaluate the hemodynamic characteristics of an atherosclerosis-prone coronary artery compared to the aorta. We describe three- dimensional spatial patterns of wall shear stress (WSS) according to the impedance phase angle in pulsatile coronary and aorta models using in vivo hemodynamic parameters and computed numerical simulations both qualitatively and quantitatively. Angiography of coronary arteries and aortas were done to obtain a standard model of vascular geometry. Simultaneously to the physiologic studies, flow-velocity and pressure profiles from in vivo data of the intravascular Doppler and pressure wire studies allowed us to include in vitro numerical simulations. Hemodynamic variables, such as flow-velocity, pressure and WSS in the coronary and aorta models were calculated taking into account the effects of vessel compliance and phase angle between pressure and flow waveforms. We found that there were spatial fluctuations of WSS and in the recirculation areas at the curved outer wall surface of the coronary artery. The mean WSS of the calculated negative phase angle increased in the coronary artery model over that in the aorta model and the phase angle effect was most prominent on the calculated amplitude of WSS of the coronary artery. This study suggests that the rheologic property of coronary circulation, such as the fluctuation of WSS/WSR induces several hemodynamic characteristics. A separation of flow-velocity, a difference in phase between pressure conductance and blood flow and prominent temporal and/or spatial oscillatory fluctuations of the shear forces as a function of pulsatile flow might be important factors in atherogenesis and progression of atherosclerosis.

Corrigenda for vol. 80, Cover legend

Cover legend: In the cover legend for the March and April issues, the starting sentence "Pulsatile pressure-volume relationship..." should read instead "Pulsatile pressure-flow relationship..." Cover legend is reprinted below. Cover: Pulsatile pressure-flow relationship, input impedance, encodes network topology, geometry, and design via reflected pulse waves from distributed branching sites in the pulmonary circulation. Network design is a system property conferring a susceptibility to modulate the amplitude of wall shear stress in vessles with the distribution of blood flow. )From Bennett et al. J. Appl. Physiol. 80: 1033-1056, 1996)

Corrigenda for vol. 80, Cover legend

Cover legend: In the cover legend for the March and April issues, the starting sentence "Pulsatile pressure-volume relationship..." should read instead "Pulsatile pressure-flow relationship..." Cover legend is reprinted below. Cover: Pulsatile pressure-flow relationship, input impedance, encodes network topology, geometry, and design via reflected pulse waves from distributed branching sites in the pulmonary circulation. Network design is a system property conferring a susceptibility to modulate the amplitude of wall shear stress in vessles with the distribution of blood flow. (From Bennett et al. J. Appl. Physiol. 80: 1033-1056, 1996)

Corrigenda for vol. 80, Cover legend

Cover legend: In the cover legend for the March and April issues, the starting sentence “Pulsatile pressure-volume relationship...” should read instead “Pulsatile pressure-flow relationship...” Cover legend is reprinted below. Cover: Pulsatile pressure-flow relationship, input impedance, encodes network topology, geometry, and design via reflected pulse waves from distributed branching sites in the pulmonary circulation. Network design is a system property conferring a susceptibility to modulate the amplitude of wall shear stress in vessles with the distribution of blood flow. (From Bennett et al. J. Appl. Physiol. 80: 1033-1056, 1996)

Corrigenda for vol. 80, Cover legend

Cover legend: In the cover legend for the March and April issues, the starting sentence “Pulsatile pressure-volume relationship...” should read instead “Pulsatile pressure-flow relationship...” Cover legend is reprinted below. Cover: Pulsatile pressure-flow relationship, input impedance, encodes network topology, geometry, and design via reflected pulse waves from distributed branching sites in the pulmonary circulation. Network design is a system property conferring a susceptibility to modulate the amplitude of wall shear stress in vessles with the distribution of blood flow. (From Bennett et al. J. Appl. Physiol. 80: 1033-1056, 1996)

Variation of Wall Shear Stress in Daughter Tube of Asymmetrical Arterial Branch Model.

In the present study, the effect of the flow distribution ratio and the pulsation on the wall shear stress through an asymmetrical branch model has been studied experimentally. The experiment has been carried out for a branch model, such as the inferior mesenteric artery from the abdominal aorta, so that a daughter tube asymmetrically branches out from the parent tube at 45 degrees. The wall shear stress is quite affected by the difference in flow distribution ratio for each downstream tube. In steady flow, the wall shear stress periodically changes along the proximal wall of the daughter tube. In pulsating flow, a< 7, this periodic change in wall shear stress markedly occurs and its magnitude is several times larger than that in the upstream parent tube. The distribution of the amplitude of wall shear stress in pulsating flow at a quasi-steady state is similar to that of wall shear stress in steady flow.