Background Shear stress is one of the known platelet activating mechanisms that leads to thrombosis. Increased shear stress has also been postulated to reverse the antithrombotic effect of some drugs such as aspirin (ASA).
Methods and Results Experiments were conducted in five dogs to determine the minimal shear stress levels that produce acute platelet thrombus formation in mechanically stenosed arteries and the increase in shear required to reverse the antithrombotic effect of ASA. After intimal and medial damage, stenosis was produced in the circumflex coronary artery. We used the finite-difference numerical solution of the Navier-Stokes equation to determine the wall shear stresses in the area of stenosis. At 70±6% coronary diameter reduction, cyclic flow reductions (CFRs) caused by acute platelet thrombus formation were observed in the stenosed lumen. At this level of stenosis, the shear stress was 144±15 Pa. ASA given at a dose of 5 mg/kg IV inhibited in vivo acute platelet-mediated thrombus formation and abolished CFRs in all dogs. However, increasing the stenosis level to 80±5% caused the CFRs to return. The shear stress increased with the increased level of stenosis to 226±22 Pa. Thus, an average 10% increase in diameter narrowing caused a 56±20% increase in shear stress (P<.005) and renewed platelet activation and thrombus formation despite ASA pretreatment.
Conclusions Individuals who take ASA daily to prevent coronary artery thrombus formation may not be well protected when a change in hemodynamics, such as an acute hypertensive episode, or an increase in stenosis severity due to a ruptured atherosclerotic plaque causes an increase in shear stress.
Recent studies suggest that platelet adhesion and aggregation in a stenosed artery are important factors in the development of atherosclerosis or acute coronary artery thrombosis and myocardial infarction.1 This is thought to occur when a plaque ruptures and there is an acute increase in the degree of stenosis.2 When platelets become hyperactive, they can adhere and aggregate on the coronary artery wall at sites of endothelial injury and stenosis. They also release prostaglandins and thromboxane A2 into the coronary circulation.2 This initiates coronary thrombosis and increases vascular tone, which leads to decreased lumen size and decreased coronary blood flow and is known to cause acute myocardial infarction.3 4 Hemodynamic shear stress, the degree of vascular injury, the amount and geometry of stenosis, and the presence of vWFs are some of the primary determinants in coronary artery thrombosis.1 2 3 4
In vivo methods are needed to study the interaction of platelets with damaged arterial walls. We developed an experimental model for studying platelet accumulation in stenosed and intimally damaged coronary arteries.5 6 This periodic APTF followed by embolization causes CFRs in coronary blood flow. Many agents such as ASA,6 ibuprofen,7 thromboxane synthetase inhibitors,2 8 9 10 serotonin blocking agents,9 11 and ADP antagonists12 abolish APTF in experimentally stenosed arteries. However, increasing the degree of stenosis can reverse the antithrombotic effect of agents such as ASA.6 This phenomenon was originally described by Aiken et al7 when ibuprofen was used to abolish CFRs at a dose of 10 mg/kg. When the stenosis was made more severe such that flow declined by 30% to 40%, CFRs returned.7 Folts5 observed the same effect when using ASA. CFRs were abolished by 5 mg/kg of ASA and returned when the stenosis was increased and flow decreased by 10 to 15 mL/min.5 It is postulated that increasing the amount of stenosis increases the shear forces and enhances the shear-induced aggregation of platelets, which overcomes the antithrombotic effect of ASA. In the present study, our in vivo animal model of coronary artery stenosis was used to study the blood hemodynamics that lead to APTF and CFRs. The numerical solution of the Navier-Stokes equation was used to determine the minimal shear stresses at which we observe APTF inside the arterial stenosis. We also determined the shear stress levels that overcame the antithrombotic effect of ASA and caused the CFRs to return.
Five mongrel dogs (23 to 27 kg) of either sex were anesthetized with sodium pentobarbital (20 mg/kg) and ventilated with room air with a Bird respirator. After a left thoracotomy and removal of the fifth and sixth ribs, the heart was exposed and placed in a pericardial cradle. The left circumflex coronary artery then was dissected out for a length of 2 to 3 cm. Phasic and mean coronary flow were measured by an electromagnetic flow probe positioned on the proximal portion of the artery (Fig 1⇓). Femoral arterial and venous catheters were inserted for blood pressure measurements and drug infusion. A snare occluder was placed on the distal portion of the vessel to periodically produce a temporary 20-second coronary occlusion and produce a reactive hyperemic response. An eight-channel Gould recorder was used to continuously record all measured parameters including the ECG. Arterial blood gases, hematocrit, and body temperature were monitored and kept within normal physiological ranges.
Coronary Artery Stenosis
Intimal and some medial vessel wall damage were produced by carefully squeezing the artery with a 6-mm-wide surgical clamp four times for 3 seconds each. A controlled stenosis was then produced by placing a Lexan plastic cylinder (constrictor) 4 to 5 mm in length around the outside of the coronary artery. The cylinders were made with a range of internal diameters in 0.1-mm increments, with one chosen to cause a fixed mechanical narrowing of the vessel. Some plastic stenosing cylinders were instrumented with two 1×1-mm ultrasound crystals (Titronic Medical Instruments) to measure the velocity inside and distal to the stenosis with a range-gated, pulsed 20-MHz Doppler flowmeter (Bioengineering, the University of Iowa) (Fig 2⇓). The pressure distal to the stenosis was measured using a small, nonobstructing, 21-gauge catheter (Khouri-Gregg) introduced through the wall of the circumflex coronary artery.13 Digital subtraction angiography was used to obtain images of the narrowed circumflex artery at different levels of stenosis. The images were analyzed using a digital video image processor. We used our quantitative arteriography Fourier algorithm to determine the dimensions of the stenosis.14
The amount of coronary artery stenosis was increased in 0.1-mm increments until the reactive hyperemic response to a 20-second complete occlusion was abolished.5 6 At this critical level of stenosis, CFRs caused by platelet thrombi periodically form in the narrowed lumen. The thrombi spontaneously embolize or can be made to break loose and embolize distally by gently shaking the stenosing cylinder. After a 30-minute observation of regular CFRs, a dose of 5 mg/kg of ASA was injected intravenously to decrease platelet activity and abolish thrombus formation.6 Ten to 30 minutes after the CFRs were abolished, the amount of diameter narrowing was then increased by placing a smaller size of stenosing plastic cylinder around the artery until the CFRs returned. This was done by carefully removing one cylinder and replacing it with one of a smaller size in 0.1-mm increments. Care was taken not to produce significant new intimal damage with these maneuvers. Blood volume flow as well as blood pressure proximal and distal to the stenosis were continuously monitored. The stenosis geometry was obtained by digital subtraction angiography arteriograms before and after increasing the stenosis. By use of the hemodynamic measurements, the shear stress corresponding to each level of stenosis was calculated. The duration of these experiments was 6 to 8 hours.
All data values are reported as mean±SD. The statistical significance of the difference between measurements was obtained from the paired Student’s t test and is reported by the probability value.
Theory for Shear Stress Calculation
Blood in all but the smallest vessels (<500 mm) at all but the lowest shear rates (<200 s−1) can be treated as a homogeneous newtonian fluid.15 The shear rate for newtonian, one-directional flow in a cylindrical tube is equal to the velocity gradient with respect to radial position:
where r is the radial distance from the center of the tube.16 The shear stress is the frictional force acting on a unit area of the tube wall and is equal to the product of shear rate and the viscosity μ:
At shear rates higher than 200 s−1, the blood viscosity asymptotically approaches a constant value of about 3 cp.16 For fully developed Poissueille laminar flow, the shear stress at the wall of the tube is related to the volume flow Q and the radius R by
In the case of arterial stenosis, the flow geometry is irregular and cannot be accurately described by the Poisseuille equation. A more adequate model for calculating shear stress in a stenosed vessel is given by the Navier-Stokes equation (see “Appendix”). These equations are difficult to solve analytically for irregular geometries. Finite-difference numerical methods were used to solve them numerically in steady state.
Fig 3⇓ shows typical results from one experiment. At a critical stenosis that abolishes the reactive hyperemic response, platelets adhered to and aggregated in the narrowed and damaged arterial lumen. CFRs caused by APTF occurred and caused volume flow and distal pressure to decline progressively until the artery was totally occluded. Each time the thrombus was dislodged by gently shaking the plastic cylinder, the flow was rapidly restored to control levels (Fig 3⇓). An intravenous infusion of 5 mg/kg of ASA (dissolved in saline) abolished the CFRs in all five dogs within 5 minutes. When the amount of stenosis was increased 15 minutes later, the hemodynamic changes caused the CFRs to return and reversed the antithrombotic effect of ASA.
From the five experiments, the initial percent diameter reduction that was required to produce CFRs was 70±6%. After the ASA infusion had abolished the CFRs, an increase in stenosis, requiring two to four increments of 0.1 mm each, to an average of 80±5% caused the CFRs to return (Fig 4a⇓). Fig 4b⇓ shows the mean volume flow at the apex of the CFRs before and after increasing the stenosis. An average volume flow reduction of 15±4 mL/min occurred (P<.005) with the increase in the amount of stenosis. Increasing the amount of stenosis caused an average increase of 11±7 mm Hg in the pressure gradient measured across the stenosis (P<.005) (Fig 4c⇓).
Using the imaging data and the volume flow measurements as input data to the flow modeling computer program, the values of maximum shear stress inside the stenosis required to produce APTF and CFRs before and after the ASA treatment were obtained. Fig 5⇓ shows the results from the five experiments. The shear stress, with a stenosis of 70±6%, that produced the CFRs before ASA treatment was 144±15 Pa. Increasing the stenosis to 80±5% caused the shear stress to increase to 226±22 Pa (P<.005). This increase was 56±20% higher than the control shear stress level. Since the systemic blood pressure, the heart rate, and the hematocrit were the same before and after increasing the stenosis, the return of the CFRs should be caused only by the hemodynamic changes occurring at the stenosis.
Fig 6⇓ shows the shear stress distribution and diameter variation along the wall of the stenosis. The stenosis diameter is shown in the left y axis and the wall shear stress is shown in the right y axis. The artery diameter starts at about 3.0±0.05 mm, suddenly narrows to about 1±0.05 mm at the stenosis, and then expands after the stenosis, to about 3.0±0.05 mm. The calculated shear stress is very low outside the stenosis, suddenly increases with the narrowing diameter, and reaches a maximum at the smallest diameter inside the stenosis. Distal to the stenosis the flow streamlines separate from the vessel wall, and the fluid adjacent to the wall is forced to flow backward. The fluid in the reverse flow region curls up and forms a vortex. This produces small negative levels of shear stress. The vortex formation causes backflow that can be detected with a range-gated Doppler. Fig 7⇓ shows the variation of aortic blood pressure and phasic blood flow velocity, measured outside the stenosis at a 45° angle, and the phasic volume flow through the stenosis. As one adjusts the range gate to sample away from the outlet of the stenosis, there is flow reversal (see arrow in Fig 7⇓).
ASA is the most widely used antithrombotic agent in acute and chronic coronary artery disease.17 18 ASA has been shown to be very beneficial in treating patients with unstable angina; it decreases mortality in patients with acute myocardial infarction and prevents strokes in patients with transient ischemic attacks.17 18 However, ASA fails to be protective in between 50% to 70% of patients. This may be partly due to the fact that ASA inhibits only one of the many different platelet activation pathways, the one that involves the production of thromboxane A2.19 Hence, it is not surprising that ASA cannot totally prevent platelet-mediated thrombotic events when other platelet activation pathways are involved such as the one that involves shear-induced aggregation.
Recent studies suggest that shear forces can directly expose and/or activate GPIIb/IIIa receptors, with the vWF as the ligand, and cause platelets to aggregate and form thrombi.20 This mechanism of shear-induced platelet activation is not affected by ASA, which inhibits the cyclooxygenase pathway and thromboxane A2 production.20 In a concentric viscometer, it was shown that platelet aggregation in human platelet-rich plasma increased with increasing shear stress from 5 to 46 Pa.21 The addition of ASA did not block shear-induced aggregation.21 The aggregation response to shear forces generated in a cone and plate viscometer showed that neither the mobilization of cytosolic Ca2+ nor the aggregation response to shear stress was inhibited by blocking the platelet cyclooxygenase and thromboxane A2 production with ASA.22 These results suggest that the high levels of shear stress (>30 dyne/cm2) may have induced plasma vWF to bind to platelet GPIb and caused an increase in platelet cytosolic Ca2+ and platelet aggregation, both of which are potentiated by the vWF binding to the platelet GPIIb-IIIa complex.22
Shear-induced aggregation, which is not inhibited by ASA, may mediate platelet aggregation at sites of arterial stenosis where shear stresses are high. In this study, we confirmed that ASA at 5 mg/kg abolishes CFRs due to APTF in the Folts model. We also show that an average 10% decrease in the diameter of the stenosis can cause significant increases (40% to 90%) in shear stress. The increased stenosis and pressure gradient across the stenosis increased the shear stress. This probably enhanced shear-induced aggregation and caused thrombus formation despite pretreatment with ASA. These findings suggest that it might be more beneficial in future studies of antithrombotic therapy to concentrate on blocking the GPIIb/IIIa receptor, which is the final common pathway by which all agonists act to initiate platelet aggregation.17 19 In fact, blocking the GPIIb/IIIa receptor by monoclonal antibodies abolishes APTF in the Folts model in dogs and monkeys despite provocation involving epinephrine infusion, increased intimal damage, and increased stenosis and shear.23 24
It may be that replacing the plastic cylinder several times on the stenosed artery to produce greater degrees of stenosis, even if carefully done, increases the degree of vessel wall damage. This in turn could increase the thrombogenicity of the stenosed lumen by two possible mechanisms. First, increased arterial wall damage could cause intimal thickening caused by interstitial edema, thus adding somewhat to the degree of stenosis. This potential problem should be minimized in the present study because we used repeat arteriograms to determine the internal diameter and stenosis dimension each time. Second, the possibility also exists that we may increase the severity of the intimal and medial damage. We have shown in a previous study that with a 70% stenosis, the CFRs were abolished after ASA. Abruptly increasing to ≈80% stenosis caused the CFRs to return. Quickly going back to a 70% stenosis caused the CFRs to disappear again.6 It is not possible to confirm that the increases in shear stress measured in the present study were the cause of renewed CFRs and coronary thrombosis after ASA treatment; however, this hypothesis is supported by the findings of other in vitro studies.20 21 22
It is likely that with an acute increase in the degree of stenosis caused by rupture of an atherosclerotic plaque, there will also be loss of neointima and an increase in thrombogenicity of the underlying wall. Changes in the stenosis geometry or local flow conditions (likely to occur with an acute hypertensive episode) might produce conditions favorable for shear-induced platelet aggregation. This could produce acute occlusive platelet thrombus formation, leading to myocardial infarction. These events may not be blocked by ASA at any dose. The prevention of shear-induced platelet activation by agents that block the GPIIb-IIIa receptor may prove to be more effective therapeutically than inhibition of ASA-sensitive pathways by ASA or thromboxane synthesis inhibitors and/or thromboxane receptor antagonists.
Selected Abbreviations and Acronyms
|APTF||=||acute platelet-mediated thrombus formation|
|CFR||=||cyclic flow reduction|
|vWF||=||von Willebrand factor|
Assuming that in the case of arterial stenosis we have straight rigid and axisymmetric irregularities, we can simplify the shear stress calculation by using cylindrical coordinates. If u and v are the velocity components in the z and r directions, we can write the cylindrical vorticity stream function form of the Navier-Stokes equation:
where the vorticity and stream function variables ω and ψ are given by
The shear stress along any direction s, making an angle β with the z axis, is given by
To solve the Navier-Stokes equation, the boundary conditions of the control volume must be specified. The no-slip condition at the wall of the vessel is satisfied by letting the velocity components go to zero:
At the inlet of the control volume, far from the stenosis, the velocity can be assumed to be uniform and equal to volume flow divided by the cross-sectional area.
The flow modeling program FLUENT (Creare Inc25 ) was used to numerically solve the Navier-Stokes equations.19 The numerical techniques involve the subdivision of the domain of interest into a grid of small elements or cells. The partial differential equations are expanded over the small elements to obtain sets of simultaneous algebraic equations. A 20×2-mm uniform grid subdivided into 100×40 cells was used. A constant viscosity of 3 cp was assumed, and a blood density of 1.1 kg/L was used. Using the measured volume flow and stenosis geometry, the Navier-Stokes equations were solved iteratively until convergence to a steady state solution.
This study was supported by a grant from the Rennebohm Foundation of Wisconsin and the University of Wisconsin-Madison Department of Medicine Research and Development Fund.
- Received December 20, 1994.
- Accepted February 7, 1995.
- Copyright © 1996 by American Heart Association
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