Atherosclerosis, the leading cause of death in the developed world and
nearly the leading cause in the developing world, is associated with systemic
risk factors including hypertension, smoking, hyperlipidemia, and diabetes
mellitus, among others. Nonetheless, atherosclerosis remains a geometrically
focal disease, preferentially affecting the outer edges of vessel bifurcations.
In these predisposed areas, hemodynamic shear stress, the frictional force
acting on the endothelial cell surface as a result of blood flow, is weaker
than in protected regions. Studies have identified hemodynamic shear stress
as an important determinant of endothelial function and phenotype. Arterial-level
shear stress (>15 dyne/cm2) induces endothelial quiescence and
an atheroprotective gene expression profile, while low shear stress (<4
dyne/cm2), which is prevalent at atherosclerosis-prone sites, stimulates
an atherogenic phenotype. The functional regulation of the endothelium by
local hemodynamic shear stress provides a model for understanding the focal
propensity of atherosclerosis in the setting of systemic factors and may help
guide future therapeutic strategies.

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Hemodynamic shear stress and its role in atherosclerosis.

Mechanical forces associated with blood flow play important roles in the acute control of vascular tone, the regulation of arterial structure and remodeling, and the localization of atherosclerotic lesions. Major regulation of the blood vessel responses occurs by the action of hemodynamic shear stresses on the endothelium. The transmission of hemodynamic forces throughout the endothelium and the mechanotransduction mechanisms that lead to biophysical, biochemical, and gene regulatory responses of endothelial cells to hemodynamic shear stresses are reviewed.

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Flow-mediated endothelial mechanotransduction

Fluid velocities were measured by laser Doppler velocimetry under conditions of pulsatile flow in a scale model of the human carotid bifurcation. Flow velocity and wall shear stress at five axial and four circumferential positions were compared with intimal plaque thickness at corresponding locations in carotid bifurcations obtained from cadavers. Velocities and wall shear stresses during diastole were similar to those found previously under steady flow conditions, but these quantities oscillated in both magnitude and direction during the systolic phase. At the inner wall of the internal carotid sinus, in the region of the flow divider, wall shear stress was highest (systole = 41 dynes/cm2, diastole = 10 dynes/cm2, mean = 17 dynes/cm2) and remained unidirectional during systole. Intimal thickening in this location was minimal. At the outer wall of the carotid sinus where intimal plaques were thickest, mean shear stress was low (-0.5 dynes/cm2) but the instantaneous shear stress oscillated between -7 and +4 dynes/cm2. Along the side walls of the sinus, intimal plaque thickness was greater than in the region of the flow divider and circumferential oscillations of shear stress were prominent. With all 20 axial and circumferential measurement locations considered, strong correlations were found between intimal thickness and the reciprocal of maximum shear stress (r = 0.90, p less than 0.0005) or the reciprocal of mean shear stress (r = 0.82, p less than 0.001). An index which takes into account oscillations of wall shear also correlated strongly with intimal thickness (r = 0.82, p less than 0.001). When only the inner wall and outer wall positions were taken into account, correlations of lesion thickness with the inverse of maximum wall shear and mean wall shear were 0.94 (p less than 0.001) and 0.95 (p less than 0.001), respectively, and with the oscillatory shear index, 0.93 (p less than 0.001). These studies confirm earlier findings under steady flow conditions that plaques tend to form in areas of low, rather than high, shear stress, but indicate in addition that marked oscillations in the direction of wall shear may enhance atherogenesis.

Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress.

Vascular endothelial cells (ECs) are exposed to hemodynamic forces, which modulate EC functions and vascular biology/pathobiology in health and disease. The flow patterns and hemodynamic forces are not uniform in the vascular system. In straight parts of the arterial tree, blood flow is generally laminar and wall shear stress is high and directed; in branches and curvatures, blood flow is disturbed with nonuniform and irregular distribution of low wall shear stress. Sustained laminar flow with high shear stress upregulates expressions of EC genes and proteins that are protective against atherosclerosis, whereas disturbed flow with associated reciprocating, low shear stress generally upregulates the EC genes and proteins that promote atherogenesis. These findings have led to the concept that the disturbed flow pattern in branch points and curvatures causes the preferential localization of atherosclerotic lesions. Disturbed flow also results in postsurgical neointimal hyperplasia and contributes to pathophysiology of clinical conditions such as in-stent restenosis, vein bypass graft failure, and transplant vasculopathy, as well as aortic valve calcification. In the venous system, disturbed flow resulting from reflux, outflow obstruction, and/or stasis leads to venous inflammation and thrombosis, and hence the development of chronic venous diseases. Understanding of the effects of disturbed flow on ECs can provide mechanistic insights into the role of complex flow patterns in pathogenesis of vascular diseases and can help to elucidate the phenotypic and functional differences between quiescent (nonatherogenic/nonthrombogenic) and activated (atherogenic/thrombogenic) ECs. This review summarizes the current knowledge on the role of disturbed flow in EC physiology and pathophysiology, as well as its clinical implications. Such information can contribute to our understanding of the etiology of lesion development in vascular niches with disturbed flow and help to generate new approaches for therapeutic interventions.

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Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives

The distribution of nonstenosing, asymptomatic intimal plaques in 12 adult human carotid bifurcations obtained at autopsy was compared with the distribution of flow streamline patterns, flow velocity profiles, and shear stresses in corresponding scale models. The postmortem specimens were fixed while distended to restore normal in vivo length, diameter, and configuration. Angiograms were used to measure branch angles and diameters, and transverse histological sections were studied at five standard sampling levels. Intimal thickness was determined at 15 degrees intervals around the circumference of the vessel sections from contour tracings of images projected onto a digitizing plate. In the models, laser-Doppler anemometry was used to determine flow velocity profiles and shear stresses at levels corresponding to the standard specimen sampling sites under conditions of steady flow at Reynolds numbers of 400, 800, and 1200, and flow patterns were visualized by hydrogen bubble and dye-washout techniques. Intimal thickening was greatest and consistently eccentric in the carotid sinus. With the center of the flow divider as the 0 degree index point, mid-sinus sections showed minimum intimal thickness (0.05 +/- 0.02 mm) within 15 degrees of the index point, while maximum thickness (0.9 +/- 0.1 mm) occurred at 161 +/- 16 degrees, i.e., on the outer wall opposite the flow divider. Where the intima was thinnest, along the inner wall, flow streamlines in the model remain axially aligned and unidirectional, with velocity maxima shifted toward the flow divider apex. Wall shear stress along the inner wall ranged from 31 to 600 dynes/cm2 depending on the Reynolds number. Where the intima was thickest, along the outer wall opposite the flow divider apex, the pattern of flow was complex and included a region of separation and reversal of axial flow as well as the development of counter-rotating helical trajectories. Wall shear stress along the outer wall ranged from 0 to -6 dynes/cm2. Intimal thickening at the common carotid and distal internal carotid levels of section was minimal and was distributed uniformly about the circumference. We conclude that in the human carotid bifurcation, regions of moderate to high shear stress, where flow remains unidirectional and axially aligned, are relatively spared of intimal thickening. Intimal thickening and atherosclerosis develop largely in regions of relatively low wall shear stress, flow separation, and departure from axially aligned, unidirectional flow. Similar quantitative evaluations of other atherosclerosis-prone locations and corresponding flow profile studies in geometrically accurate models may reveal which of these hemodynamic conditions are most consistently associated with the development of intimal disease.

Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress.

Steady flow in a model of the human carotid bifurcation. Part I--flow visualization.

Steady flow in a model of the human carotid bifurcation. Part II—Laser-Doppler anemometer measurements

Boundary layer separation in a plexiglass model carotid bifurcation was investigated in relation to the origin of atherosclerotic plaque clinically found in this region. Our model was comparable to a human carotid in both dimensions and geometry. Water flowed through the model at Reynolds numbers from 200 to 1200 under steady and pulsatile flow conditions, with outflow through the external and internal branches varied. The near-wall flow was visualized by slow injection of dye through ports machined in the model. Under steady flow at a physiological Reynolds number of 500 and a flow split at the bifurcation similar to that of a human carotid at rest, boundary layer separation was found to occur in a carotid sinus across from the external carotid origin, forming a shell of slowly moving fluid around the bifurcation. The rapidly moving mainstream impinged directly on the flow divider. The location of atherosclerotic plaque correlates best with the low shear region of separation and not with the region of high shear at the flow divider. Preliminary studies with pulsatile flow demonstrated little change from the steady flow results.

Flow studies in a model carotid bifurcation.

This work presents a general boundary-integral-equation methodology for the solution of the wave equation around objects moving in arbitrary motion, with applications to compressible potential aerodynamics of airplanes and helicopters. The paper includes the derivation of the boundary integral equation for the wave equation, in a frame of reference moving in arbitrary motion (in particular, in translation and in rotation). The formulation is then applied to study unsteady potential compressible aerodynamic flows around streamlined bodies, such as airplanes and helicopters. The formulation is given in terms of the velocity potential, for which an explicit treatment of the wake is required; a discussion of the formulation for the wake transport is included. The advantages of the velocity-potential formulation over the acceleration-potential formulation are discussed. The boundary-element algorithm used for the computational implementation is briefly outlined. Validation of the formulation is presented for airplane wings and helicopter rotors in hover. The test cases fall into two categories. prescribed-wake and free-wake analyses. The validation of the prescribed-wake analysis is presented for compressible flows, subsonic for helicopter rotors, transonic for airplanes. The numerical validation of the free-wake analysis of helicopter rotors is presented for incompressible flows.

B. K. Bharadvaj

Papers

Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress.

Steady flow in a model of the human carotid bifurcation. Part I--flow visualization.

Steady flow in a model of the human carotid bifurcation. Part II—Laser-Doppler anemometer measurements

Flow studies in a model carotid bifurcation.

Boundary integral equation for wave equation with moving boundary and applications to compressible potential aerodynamics of airplanes and helicopters