A Scaling Law for Wall Shear Rate Through an Arterial Stenosis

1994 ◽  
Vol 116 (4) ◽  
pp. 446-451 ◽  
Author(s):  
John M. Siegel ◽  
Christos P. Markou ◽  
David N. Ku ◽  
S. R. Hanson
Keyword(s):  
Shear Rate ◽  
Plaque Rupture ◽  
Scaling Law ◽  
Wall Shear Rate ◽  
Arterial System ◽  
Arterial Stenosis ◽  
Atheromatous Plaque ◽  
High Grade ◽  
Shear Rates ◽  
Wall Shear

Atherosclerosis of the human arterial system produces major clinical symptoms when the plaque advances to create a high-grade stenosis. The hemodynamic shear rates produced in high-grade stenoses are important in the understanding of atheromatous plaque rupture and thrombosis. This study was designed to quantify the physiologic stress levels experienced by endothelial cells and platelets in the region of vascular stenoses. The steady hemodynamic flow field was solved for stenoses with percent area reductions of 50, 75, and 90 percent over a range of physiologic Reynolds numbers (100–400). The maximum wall shear rate in the throat region can be shown to vary by the square root of the Reynolds number. The shear rate results can be generalized to apply to a range of stenosis lengths and flow rates. Using dimensions typical for a human carotid or coronary artery, wall shear rates were found to vary from a maximum of 20,000 s−1 upstream of the throat to a minimum of −630 s−1 in the recirculation zone for a 90 percent stenosis. An example is given which illustrates how these values can be used to understand the relationship between hemodynamic shear and platelet deposition.

Derivation of Shear Rates From Near-Wall LDA Measurements Under Steady and Pulsatile Flow Conditions

1994 ◽  
Vol 116 (3) ◽  
pp. 361-368 ◽  
Author(s):  
Ray S. Fatemi ◽  
Stanley E. Rittgers
Keyword(s):  
Shear Rate ◽  
Linear Approximation ◽  
Curve Fitting ◽  
Pulsatile Flow ◽  
Wall Shear Rate ◽  
Measured Velocity ◽  
Shear Rates ◽  
Wall Shear ◽  
Flow Waveforms ◽  
Near Wall

Atherosclerosis, thrombosis, and intimal hyperplasia are major forms of cardiovascular diseases in the United States. Previous studies indicate a significant correlation between hemodynamics, in particular, wall shear rate, and pathology of the arterial walls. While results of these studies implicate morphologic and functional changes related to wall shear rate magnitude, a standard technique for wall shear rate measurement has not been established. In this study, theoretical and in-vitro experimental fully developed steady and physiologic pulsatile flow waveforms have been used to obtain velocity profiles in the near-wall region. The estimated wall shear rates from these results are compared to the theoretical value to assess the accuracy of the approximating technique. Experimentally obtained results from LDA suggest that in order to minimize the error in velocity data, and subsequently, the wall shear rate, the first measured velocity has to be 500 μm away from the wall. While a linear approximation did not produce errors larger than 16.4 percent at peak systole, these errors substantially increased as the velocity magnitudes decreased during late systole and diastole. Overall, a third degree polynomial curve fit using four points produced the most accurate estimation of wall shear rate through out the cardiac cycle. Results of higher degree curve-fitting functions can be unpredictable due to potential oscillations of the function near the wall. Hence, based on the results of this study, use of a linear approximation is not recommended; a third degree curve-fitting polynomial, using four points provided the most accurate approximation for these flow waveforms.

Wall shear rate in arterioles in vivo: least estimates from platelet velocity profiles

1988 ◽  
Vol 254 (6) ◽  
pp. H1059-H1064 ◽  
Author(s):  
G. J. Tangelder ◽  
D. W. Slaaf ◽  
T. Arts ◽  
R. S. Reneman
Keyword(s):  
Shear Rate ◽  
Velocity Gradient ◽  
Velocity Profiles ◽  
Wall Shear Rate ◽  
Mean Velocity ◽  
Shear Rates ◽  
Spatial Differences ◽  
Data Points ◽  
Wall Shear

Velocity profiles, as determined in vivo in rabbit mesenteric arterioles with fluorescently labeled platelets as natural flow markers, were used to calculate least estimates of the actual wall shear rate in these microvessels (17–32 micron diam). The fit of the velocity data points described the profile as close to the wall as 0.5 micron. To satisfy the no-slip condition, a thin layer of fluid with a steep velocity gradient near the wall was assumed. Least estimates of wall shear rate, as calculated from the fitted platelet-velocity profiles and using the mean velocity gradient in this layer of fluid, ranged from 472 to 4,712 s-1 with a median value of 1,700 s-1. Red blood cell center-line velocities varied between 1.3 and 14.4 mm/s (median 3.4). The wall shear rates were at least 1.46–3.94 (median 2.12) times higher than expected on the basis of a parabolic velocity distribution but with the same volume flow in the vessel. Considerable spatial differences in wall shear rate might exist even within a short segment of a vessel.

scholarly journals Reduced thrombus formation in native blood of homozygous factor VII- deficient patients at high arterial wall shear rate

Blood ◽  
1994 ◽  
Vol 84 (10) ◽  
pp. 3371-3377 ◽  
Author(s):  
RM Barstad ◽  
H Stormorken ◽  
L Orning ◽  
RW Stephens ◽  
LB Petersen ◽  
...  
Keyword(s):  
Shear Rate ◽  
Arterial Wall ◽  
Thrombus Formation ◽  
Wall Shear Rate ◽  
Factor Vii ◽  
High Shear ◽  
Shear Rates ◽  
Perfusion Chamber ◽  
Wall Shear ◽  
Shear Condition

Abstract Inhibition of thrombin formation in flowing native blood reduces thrombus formation on subendothelium, dacron, or collagen fibrils at arterial wall shear rates of 450 to 650 s-1. In the present study, we have investigated the role of low levels of factor VII (FVII) in thrombus formation on collagen fibrils at arterial wall shear rates of 650 s-1 (coronary arteries), 2,600 s-1 (mildly stenosed arteries), and 10,510 s-1 (severely stenosed arteries) in parallel-plate perfusion chambers. In the perfusion chamber with the highest wall shear rate, thrombus formation took place at the apex of an eccentric stenosis, which reduced the cross-sectional area of the blood flow channel by 80%, thus simulating thrombus formation at an atherosclerotic plaque rupture. Native blood from 21 healthy volunteers and 12 homozygous FVII- deficient patients was drawn by a pump directly from an antecubital vein over a surface of fibrillar collagen positioned in the respective perfusion chambers. The patients had FVII coagulant activities ranging from 1.3% to 4.5% and FVII antigen levels of 16% to 23% of normal. Immunoaffinity purification of the patients' FVII followed by electrophoresis (sodium dodecyl sulfate-polyacrylamide gel electrophoresis [SDS-PAGE]) and immunoblotting showed a protein with similar molecular mass as normal FVII. In the perfusion studies, a reduction in thrombus volume of 54% of normal (P < .007) at 10,510 s-1 was observed. The deposition of fibrin on the thrombogenic surface and the plasma level of fibrinopeptide A (FPA) in blood samples collected distal to the perfusion chamber were concomitantly reduced (P < .002 and P < .04, respectively). The plasma FPA level was also reduced at 2,600 s-1 (P < .04), but not at 650 s-1. However, at the lower shear conditions, the thrombus volume and the fibrin deposition were within the ranges observed in normal blood. The platelet-collagen adhesion was not affected at any of the three shear conditions. Thus, low plasma levels of FVII result in significantly less formation of thrombin and fibrin in and around growing platelet masses at high shear condition. This may weaken the thrombus stability and reduce platelet recruitment, thereby lowering thrombus volume. In support of this theory, one patient with afibrinogenemia had an 83% reduction in thrombus volume at this high shear condition.

scholarly journals A Fluid Dynamics Study in a 50 cc Pulsatile Ventricular Assist Device: Influence of Heart Rate Variability

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Jason C. Nanna ◽  
Michael A. Navitsky ◽  
Stephen R. Topper ◽  
Steven Deutsch ◽  
Keefe B. Manning
Keyword(s):  
Heart Rate ◽  
Shear Rate ◽  
Data Collection ◽  
Fluid Mechanics ◽  
Wall Shear Rate ◽  
Ventricular Assist ◽  
Shear Rates ◽  
Penn State ◽  
Wall Shear

Although left ventricular assist devices (LVADs) have had success in supporting severe heart failure patients, thrombus formation within these devices still limits their long term use. Research has shown that thrombosis in the Penn State pulsatile LVAD, on a polyurethane blood sac, is largely a function of the underlying fluid mechanics and may be correlated to wall shear rates below 500 s−1. Given the large range of heart rate and systolic durations employed, in vivo it is useful to study the fluid mechanics of pulsatile LVADs under these conditions. Particle image velocimetry (PIV) was used to capture planar flow in the pump body of a Penn State 50 cubic centimeters (cc) LVAD for heart rates of 75–150 bpm and respective systolic durations of 38–50%. Shear rates were calculated along the lower device wall with attention given to the uncertainty of the shear rate measurement as a function of pixel magnification. Spatial and temporal shear rate changes associated with data collection frequency were also investigated. The accuracy of the shear rate calculation improved by approximately 40% as the resolution increased from 35 to 12 μm/pixel. In addition, data collection in 10 ms, rather than 50 ms, intervals was found to be preferable. Increasing heart rate and systolic duration showed little change in wall shear rate patterns, with wall shear rate magnitude scaling by approximately the kinematic viscosity divided by the square of the average inlet velocity, which is essentially half the friction coefficient. Changes in in vivo operating conditions strongly influence wall shear rates within our device, and likely play a significant role in thrombus deposition. Refinement of PIV techniques at higher magnifications can be useful in moving towards better prediction of thrombosis in LVADs.

scholarly journals Reduced thrombus formation in native blood of homozygous factor VII- deficient patients at high arterial wall shear rate

Blood ◽  
1994 ◽  
Vol 84 (10) ◽  
pp. 3371-3377
Author(s):  
RM Barstad ◽  
H Stormorken ◽  
L Orning ◽  
RW Stephens ◽  
LB Petersen ◽  
...  
Keyword(s):  
Shear Rate ◽  
Arterial Wall ◽  
Thrombus Formation ◽  
Wall Shear Rate ◽  
Factor Vii ◽  
High Shear ◽  
Shear Rates ◽  
Perfusion Chamber ◽  
Wall Shear ◽  
Shear Condition

Inhibition of thrombin formation in flowing native blood reduces thrombus formation on subendothelium, dacron, or collagen fibrils at arterial wall shear rates of 450 to 650 s-1. In the present study, we have investigated the role of low levels of factor VII (FVII) in thrombus formation on collagen fibrils at arterial wall shear rates of 650 s-1 (coronary arteries), 2,600 s-1 (mildly stenosed arteries), and 10,510 s-1 (severely stenosed arteries) in parallel-plate perfusion chambers. In the perfusion chamber with the highest wall shear rate, thrombus formation took place at the apex of an eccentric stenosis, which reduced the cross-sectional area of the blood flow channel by 80%, thus simulating thrombus formation at an atherosclerotic plaque rupture. Native blood from 21 healthy volunteers and 12 homozygous FVII- deficient patients was drawn by a pump directly from an antecubital vein over a surface of fibrillar collagen positioned in the respective perfusion chambers. The patients had FVII coagulant activities ranging from 1.3% to 4.5% and FVII antigen levels of 16% to 23% of normal. Immunoaffinity purification of the patients' FVII followed by electrophoresis (sodium dodecyl sulfate-polyacrylamide gel electrophoresis [SDS-PAGE]) and immunoblotting showed a protein with similar molecular mass as normal FVII. In the perfusion studies, a reduction in thrombus volume of 54% of normal (P < .007) at 10,510 s-1 was observed. The deposition of fibrin on the thrombogenic surface and the plasma level of fibrinopeptide A (FPA) in blood samples collected distal to the perfusion chamber were concomitantly reduced (P < .002 and P < .04, respectively). The plasma FPA level was also reduced at 2,600 s-1 (P < .04), but not at 650 s-1. However, at the lower shear conditions, the thrombus volume and the fibrin deposition were within the ranges observed in normal blood. The platelet-collagen adhesion was not affected at any of the three shear conditions. Thus, low plasma levels of FVII result in significantly less formation of thrombin and fibrin in and around growing platelet masses at high shear condition. This may weaken the thrombus stability and reduce platelet recruitment, thereby lowering thrombus volume. In support of this theory, one patient with afibrinogenemia had an 83% reduction in thrombus volume at this high shear condition.

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

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.

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
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