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.

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.

Preliminary Analysis of the Effects of Blood Vessel Movement on Blood Flow Patterns in the Coronary Arteries

1994 ◽  
Vol 116 (3) ◽  
pp. 302-306 ◽  
Author(s):  
James E. Moore ◽  
Nicolas Guggenheim ◽  
Antonio Delfino ◽  
Pierre-Andre´ Doriot ◽  
Pierre-Andre´ Dorsaz ◽  
...  
Keyword(s):  
Blood Flow ◽  
Shear Rate ◽  
Coronary Arteries ◽  
Cardiac Cycle ◽  
Flow Patterns ◽  
Wall Shear Rate ◽  
Axial Movement ◽  
Wall Shear ◽  
Artery Flow ◽  
Blood Flow Patterns

Blood flow patterns are believed to be involved in the formation and progression of arterial diseases. It is possible that the normal physiologic movement of blood vessels during the cardiac cycle affects blood flow patterns significantly. For example, the contraction of the heart in systole and subsequent relaxation in diastole create movements of the coronary arteries, as evidenced in real-time angiography. The effects of this movement on coronary artery flow patterns have never been previously analyzed. This work was undertaken to provide a preliminary estimate of the importance of the effects of such physiologic movements on blood flow patterns in the coronary arteries. A Womersley-type solution was used to determine the effect of axial movement on the wall shear rate in a simplified model of the coronary arteries. The pulsatile pressure gradient was derived from previously published coronary artery flow waveforms. The axial movement function was obtained from a three-dimensional reconstruction of a biplanar coronary angiogram. Significant changes in wall shear rate were noted when the movement was taken into account. The maximum and minimum wall shear rates were 10 percent smaller and 107 percent larger in magnitude respectively, and the Oscillatory Shear Index (OSI) was doubled. Most of the changes in wall shear rate were observed in systole, when the pressure gradient is minimal and the movement is strongest. The results indicate that blood vessel movement during the cardiac cycle has a significant effect on hemodynamic phenomena which have been associated with the development of atherosclerosis.

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.

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.

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.

Factors Associated with Impaired Arterial Adaptation to Chronically High Wall Shear Rate in the Feeding Artery of PTFE Grafts

2008 ◽  
Vol 28 (5) ◽  
pp. 847-852 ◽  
Author(s):  
Vladimir Tuka ◽  
Marcela Slavikova ◽  
Zdislava Kasalova ◽  
Jan Malik
Keyword(s):  
Shear Rate ◽  
Wall Shear Rate ◽  
Feeding Artery ◽  
Factors Associated ◽  
Wall Shear

A noninvasive method to estimate wall shear rate using ultrasound

1995 ◽  
Vol 21 (2) ◽  
pp. 171-185 ◽  
Author(s):  
Peter J. Brands ◽  
Arnold P.G. Hoeks ◽  
Leo Hofstra ◽  
Robert S. Reneman
Keyword(s):  
Shear Rate ◽  
Wall Shear Rate ◽  
Noninvasive Method ◽  
Wall Shear

scholarly journals In Vivo Vascular Wall Shear Rate and Circumferential Strain of Renal Disease Patients

2013 ◽  
Vol 39 (2) ◽  
pp. 241-252 ◽  
Author(s):  
Dae Woo Park ◽  
Grant H. Kruger ◽  
Jonathan M. Rubin ◽  
James Hamilton ◽  
Paul Gottschalk ◽  
...  
Keyword(s):  
Shear Rate ◽  
Renal Disease ◽  
Circumferential Strain ◽  
Vascular Wall ◽  
Wall Shear Rate ◽  
Wall Shear

On using experimentally estimated wall shear stresses to validate numerically predicted results

2003 ◽  
Vol 217 (2) ◽  
pp. 77-90 ◽  
Author(s):  
M Walsh ◽  
T McGloughlin ◽  
D W Liepsch ◽  
T O'Brien ◽  
L Morris ◽  
...  
Keyword(s):  
Shear Rate ◽  
Laser Doppler Anemometry ◽  
Numerical Models ◽  
Wall Shear Rate ◽  
Shear Stresses ◽  
Velocity Measurements ◽  
Curve Fit ◽  
Wall Shear ◽  
Point Velocity ◽  
Curve Fitting Method

The objective of this investigation was to assess the use of experimentally estimated wall shear stresses to validate numerically predicted results. The most commonly cited haemodynamic factor implicated in the disease initiation and proliferation processes at graft/artery junctions is wall shear stress (WSS). WSS can be determined from the product of the viscosity of the fluid and the wall shear rate. Numerically, the wall shear rate is predicted using velocity values stored in the computational cell near the wall and assuming zero velocity at the wall. Experimentally, the wall shear rate is estimated by applying a curve-fit to near-wall velocity measurements and evaluating the shear rate at a specific distance from the wall. When estimating the wall shear rate from the laser Doppler anemometry (LDA) point velocity measurements, large differences between the experimentally estimated and numerically predicted WSSs were introduced. It was found that the estimated WSS distributions from the experimental results are highly dependent on the curve-fitting method used to calculate the wall shear rate. However, the velocity profiles for both the experimental and numerical investigations show extremely good comparison. It is concluded that numerical models should be validated using unprocessed LDA point velocity measurement and not estimated WSS values.

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