Wall Shear Rate Distribution in an Abdominal Aortic Bifurcation Model: Effects of Vessel Compliance and Phase Angle Between Pressure and Flow Waveforms

1997 ◽  
Vol 119 (3) ◽  
pp. 333-342 ◽  
Author(s):  
C. S. Lee ◽  
J. M. Tarbell
Keyword(s):  
Shear Rate ◽  
Phase Angle ◽  
Wall Motion ◽  
Outer Wall ◽  
Wall Shear Rate ◽  
Rate Distribution ◽  
Abdominal Aortic ◽  
The Mean ◽  
Wall Shear ◽  
Low Shear

The goal of this study was to determine how vessel compliance (wall motion) and the phase angle between pressure and flow waves (impedance phase angle) affect the wall shear rate distribution in an atherogenic bifurcation geometry under sinusoidal flow conditions. Both rigid and elastic models replicating the human abdominal aortic bifurcation were fabricated and the wall shear rate distribution in the median plane of the bifurcation was determined using the photochromic flow visualization method. In the elastic model, three phase angle conditions were simulated (+12, −17, −61 deg), and the results compared with those obtained in a similar rigid model. The study indicates a very low (magnitude close to zero) and oscillatory wall shear rate zone within 1.5 cm distal to the curvature site on the outer (lateral) wall. In this low shear rate zone, unsteadiness (pulsatility) of the flow greatly reduces the mean (time-averaged) wall shear rate level. Vessel wall motion reduces the wall shear rate amplitude (time-varying component) up to 46 percent depending on the location and phase angle in the model. The mean wall shear rate is less influenced by the wall motion, but is reduced significantly in the low shear region (within 1.5 cm distal to the curvature site on the outer wall), thus rendering the wall shear rate waveform more oscillatory and making the site appear more atherogenic. The effect of the phase angle is most noteworthy on the inner wall close to the flow divider tip where the mean and amplitude of wall shear rate are 31 and 23 percent lower, respectively, at the phase angle of −17 deg than at −61 deg. However, the characteristics of the wall shear rate distribution in the low shear rate zone on the outer wall that are believed to influence localization of atherosclerotic disease, such as the mean wall shear rate level, oscillation in the wall shear rate waveform, and the length of the low and oscillatory wall shear rate zone, are similar for the three phase angles considered. The study also showed a large spatial variation of the phase angle between the wall shear stress waveform and the circumferential stress waveform (hoop stress due to radial artery expansion in response to pressure variations) near the bifurcation (up to 70 deg). The two stresses became more out of phase in the low mean shear rate zone on the outer wall (wall shear stress wave leading hoop stress wave as much as 125 deg at the pressure-flow phase angle of −61 deg) and were significantly influenced by the impedance phase angle.

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

Frequency Dependence of Dynamic Curvature Effects on Flow Through Coronary Arteries

2000 ◽  
Vol 123 (2) ◽  
pp. 129-133 ◽  
Author(s):  
James E. Moore, ◽  
Erlend S. Weydahl ◽  
Aland Santamarina
Keyword(s):  
Shear Rate ◽  
Mean Curvature ◽  
Flow Patterns ◽  
Wall Shear Rate ◽  
Radius Of Curvature ◽  
Time Varying ◽  
Static Approach ◽  
Flow Through ◽  
The Mean ◽  
Wall Shear

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (δ), normalized change in radius of curvature (ε), and a Womersley parameter (α). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of εδα>0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.

A COMPUTATIONAL STUDY ON AXISYMMETRIC ABDOMINAL AORTIC ANEURYSM MODELS USING FLUID-STRUCTURE INTERACTIONS UNDER PULSATILE FLOW CONDITIONS

2002 ◽  
Vol 02 (03n04) ◽  
pp. 211-230 ◽  
Author(s):  
YOUNG-HO KIM
Keyword(s):  
Abdominal Aortic Aneurysm ◽  
Shear Rate ◽  
Aortic Aneurysm ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Distal Region ◽  
Wall Shear Rate ◽  
Aneurysm Wall ◽  
Abdominal Aortic ◽  
Wall Shear

Fluid-structure interaction study was performed on various abdominal aortic aneurysm (AAA) models under the pulsatile flow condition. Eight aneurysm models were made with four different dilatation sizes and two different wall thickness. Von Mises stress increased at the proximal and distal region (± 1D) of the aneurysm as well as the maximum dilatation, where both change in diameter and radial movement were larger than any other site with more dilated models. In spite of considerable radial movements, axial movements of the aneurysm wall were dominant and were larger in the proximal region of the aneurysm than in the distal region of the aneurysm. Wall shear rate, in general, increased further for uniform wall thickness models and for less dilated models, which means that wall shear rate is closely related to the motion of the wall. We confirmed the phase delay between the pressure gradient and wall shear rate. Throughout the entire pulsatile cycle, a weak recirculating vortex near the proximal end moved further distally in the aneurysm with increase in size and strength. Larger and stronger vortex was dominant inside the aneurysm with more dilated models and decelerating pressure gradient had a relatively stronger effect on the flow.

In Vitro Evaluation of Flow Divertors in an Elastase-Induced Saccular Aneurysm Model in Rabbit

2007 ◽  
Vol 129 (6) ◽  
pp. 863-872 ◽  
Author(s):  
Jaehoon Seong ◽  
Ajay K. Wakhloo ◽  
Baruch B. Lieber
Keyword(s):  
Shear Rate ◽  
Kinetic Energy ◽  
Wall Shear Rate ◽  
Endovascular Coiling ◽  
Aneurysm Neck ◽  
The Mean ◽  
Wall Shear ◽  
Aneurysm Model

Endovascular coiling is an acceptable treatment of intracranial aneurysms, yet long term follow-ups suggest that endovascular coiling fails to achieve complete aneurysm occlusions particularly in wide-neck and giant aneurysms. Placing of a stentlike device across the aneurysm neck may be sufficient to occlude the aneurysm by promoting intra-aneurysmal thrombosis; however, conclusive evidence of its efficacy is still lacking. In this study, we investigate in vitro the efficacy of custom designed flow divertors that will be subsequently implanted in a large cohort of animals. The aim of this study is to provide a detailed database against which in vivo results can be analyzed. Six custom designed flow divertors were fabricated and tested in vitro. The design matrix included three different porosities (75%, 70%, and 65%). For each porosity, there were two divertors with one having a nominal pore density double than that of the other. To quantify efficacy, the divertors were implanted in a compliant elastomeric model of an elastase-induced aneurysm model in rabbit and intra-aneurysmal flow changes were evaluated by particle image velocimetry (PIV). PIV results indicate a marked reduction in intra-aneurysmal flow activity after divertor implantation in the innominate artery across the aneurysm neck. The mean hydrodynamic circulation after divertor implantation was reduced to 14% or less of the mean circulation in the control and the mean intra-aneurysmal kinetic energy was reduced to 29% or less of its value in the control. The intra-aneurysmal wall shear rate in this model is low and implantation of the flow divertor did not change the wall shear rate magnitude appreciably. This in vitro experiment evaluates the characteristics of local flow phenomena such as hydrodynamic circulation, kinetic energy, wall shear rate, perforator flow, and changes of these parameters as a result of implantation of stentlike flow divertors in an elastomeric replica of elastase-induced saccular aneurysm model in rabbit. These initial findings offer a database for evaluation of in vivo implantations of such devices in the animal model and help in further development of cerebral aneurysm bypass devices.

Atheroma and arterial wall shear - Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis

1971 ◽  
Vol 177 (1046) ◽  
pp. 109-133 ◽  
Keyword(s):  
Shear Rate ◽  
Mass Transport ◽  
Concentration Gradient ◽  
Arterial Wall ◽  
Wall Shear Rate ◽  
Main Stream ◽  
High Shear ◽  
Wall Shear ◽  
Dependent Mass ◽  
Low Shear

On the basis of various observations, we argue that there is spatial variation of the time averaged wall shear rate in arteries, both overall and locally. From our own observations, and those of others, we show that the distribution of early atheroma in man is coincident with those regions in which arterial wall shear rate is expected to be relatively low, while the development of lesions is inhibited or retarded in those regions in which wall shear rate is expected to be relatively high. Such a correlation is inconsistent with a proposal, made by several workers, that there is a causative relation between arterial blood mechanics and the development of atheroma, i. e. that atheroma is associated with wall damage due to the motion of blood. Instead it immediately suggests that the process is associated with shear dependent mass transport phenomena. It has been demonstrated by others that mass transport, in the inner part of the arterial wall, is dominantly to and from blood flowing within the lumen. We review theory relevant to diffusional mass transport across such a sheared interface, and examine available experimental evidence, relating to normally occurring (quasi-steady state) and experimentally induced (transient-type) atheroma, as well as the distribution of cholesterol in arteries. These results are considered in the light of simple theoretical schemes which we develop for the movement of cholesterol, in particular, although the arguments may also be relevant to other diffusing species. Shear enhances mass transport by means of a steepening effect on the concentration gradient, thus diffusion of material from a wall is promoted when material which has already diffused is swept rapidly away, so that the concentration gradient leading to further diffusion remains steep. However, the influence of shear on the diffusion of a species, say, from just within the wall of an artery to fluid in the main stream, depends upon the relative resistances to its diffusion from within the wall to surface fluid (wall phase) and from surface fluid to fluid in the main stream (blood phase); diffusion is not appreciably shear dependent if the latter resistance is small compared with the former. Assuming simplified flow conditions and that as suggested by others cholesterol is transported in blood in association with plasma protein, we can estimate resistance for diffusion of this species in the blood phase, for different stations in the arterial system. However, we possess no definite comparable information for the wall phase; we conjecture that this resistance is relatively small, and assume shear dependence of diffusional transport of cholesterol between arterial walls and intraluminal blood. We find that a net flux of cholesterol from blood to wall, as has been suggested by others, cannot account, in terms of the proposed schemes, for the observed normally occurring (quasi-steady state) distribution of atheromatous lesions in man and in animals; mass transport is inhibited in low shear regions by the thick diffusional boundary layer. Instead it appears that cholesterol, which has been shown by others to be synthesized in arterial walls, accumulates in low shear regions because its local diffusional efflux from wall to blood is inhibited by the reduced concentration gradient. Given suitable values for relevant parameters, the theoretical schemes are also able to account for adequacy of supply of precursor to the wall for cholesterol synthesis, for the preferential occurrence that we now recognize of lesions in high shear regions in response to sudden natural or experimental elevation of blood cholesterol, and for the responses to administration of labelled cholesterol (transient type phenomena); it appears therefore possible, in terms of these schemes, to unify naturally occurring and experimentally induced atheroma. It is reported by others that platelets are associated only with advanced lesions; the correlation of naturally occurring atheroma with low shear regions, and transient type lesions with high shear regions, with the fluid mechanics being unaltered in the two situations, provides no support for the implication of platelets in the development of early atheroma. It appears that wall shear rate may be a major controlling factor in the development of atheroma, i.e. that high shear, such as is associated for example with increased cardiac output in exercise, will retard progression of the process. Its progression will also be retarded by any means which reduces the accumulation of atheromatous material, by influencing its rate of net production or diffusion.

scholarly journals Importance of Primary Capture and L-Selectin–Dependent Secondary Capture in Leukocyte Accumulation in Inflammation and Atherosclerosis in Vivo

2001 ◽  
Vol 194 (2) ◽  
pp. 205-218 ◽  
Author(s):  
Einar E. Eriksson ◽  
Xun Xie ◽  
Joachim Werr ◽  
Peter Thoren ◽  
Lennart Lindbom
Keyword(s):  
Shear Rate ◽  
Leukocyte Recruitment ◽  
Wall Shear Rate ◽  
Free Flow ◽  
Initial Contact ◽  
Atherosclerotic Lesions ◽  
Leukocyte Accumulation ◽  
Wall Shear ◽  
Rolling Leukocytes

In the multistep process of leukocyte extravasation, the mechanisms by which leukocytes establish the initial contact with the endothelium are unclear. In parallel, there is a controversy regarding the role for L-selectin in leukocyte recruitment. Here, using intravital microscopy in the mouse, we investigated leukocyte capture from the free flow directly to the endothelium (primary capture), and capture mediated through interactions with rolling leukocytes (secondary capture) in venules, in cytokine-stimulated arterial vessels, and on atherosclerotic lesions in the aorta. Capture was more prominent in arterial vessels compared with venules. In venules, the incidence of capture increased with increasing vessel diameter and wall shear rate. Secondary capture required a minimum rolling leukocyte flux and contributed by ∼20–50% of total capture in all studied vessel types. In arteries, secondary capture induced formation of clusters and strings of rolling leukocytes. Function inhibition of L-selectin blocked secondary capture and thereby decreased the flux of rolling leukocytes in arterial vessels and in large (&gt;45 μm in diameter), but not small (&lt;45 μm), venules. These findings demonstrate the importance of leukocyte capture from the free flow in vivo. The different impact of blockage of secondary capture in venules of distinct diameter range, rolling flux, and wall shear rate provides explanations for the controversy regarding the role of L-selectin in various situations of leukocyte recruitment. What is more, secondary capture occurs on atherosclerotic lesions, a fact that provides the first evidence for roles of L-selectin in leukocyte accumulation in atherogenesis.

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