Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovascular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley number, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemodynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pockets in which the direction of the wall shear stress oscillates. Atherosclerotic disease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow. This field is rich with challenging problems in fluid mechanics involving three-dimensional, pulsatile flows at the edge of turbulence.

Blood flow in arteries

Background The ability to assess the patency of coronary arteries by noninvasive means would represent an important advance. We have developed a magnetic resonance imaging (MRI) coronary angiographic technique that permits the display of areas of abnormal coronary blood flow. We have compared this method with conventional contrast angiography for the identification of coronary-artery stenoses. Methods MRI coronary angiography was performed with an electrocardiographically gated sequence in 39 subjects, 33 to 84 years of age, who were scheduled for elective cardiac catheterization with coronary angiography. Sequential overlapping transverse and oblique sections were acquired during periods of breath-holding and were displayed as cine loops for analysis. MRI and conventional angiographic data were compared in a blinded manner. The four major epicardial coronary arteries were classified by MRI coronary angiography as being normal (or having only minimal irregularities) or as having disease that was moderatel...

A preliminary report comparing magnetic resonance coronary angiography with conventional angiography.

The cardiovascular system is an internal flow loop with multiple branches circulating a complex liquid. The hallmarks of blood flow in arteries are pulsatility and branches, which cause wall stresses to be cyclical and nonuniform. Normal arterial flow is laminar, with secondary flows generated at curves and branches. Arteries can adapt to and modify hemodynamic conditions, and unusual hemodynamic conditions may cause an abnormal biological response. Velocity profile skewing can create pockets in which the wall shear stress is low and oscillates in direction. Atherosclerosis tends to localize to these sites and creates a narrowing of the artery lumen--a stenosis. Plaque rupture or endothelial injury can stimulate thrombosis, which can block blood flow to heart or brain tissues, causing a heart attack or stroke. This small lumen and elevated shear rate in a stenosis create conditions that accelerate platelet accumulation and occlusion. The relationship between thrombosis and fluid mechanics is complex, especially in the post-stenotic flow field. New convection models have been developed to predict clinical from platelet thrombosis in diseased arteries. Future hemodynamic studies should address the complex mechanics of flow-induced, large-scale wall motion and convection of semisolid particles and cells in flowing blood.

Fluid Mechanics of Vascular Systems, Diseases, and Thrombosis

Background Experimental studies have shown that fractional flow reserve (defined as the ratio of maximal achievable flow in a stenotic area to normal maximal achievable flow) can be calculated from coronary pressure measurements only. The objectives of this study were to validate fractional flow reserve calculation in humans and to compare this information with that derived from quantitative coronary angiography. Methods and Results Twenty-two patients with an isolated, discrete proximal or mid left anterior descending coronary artery stenosis and normal left ventricular function were studied. Relative myocardial flow reserve, defined as the ratio of absolute myocardial perfusion during maximal vasodilation in the stenotic area to the absolute myocardial perfusion during maximal vasodilation (adenosine 140 mu g.kg(-1).min(-1) intravenously during 4 minutes) in the contralateral normally perfused area, was assessed by O-15-labeled water and positron emission tomography (PET). Myocardial and coronary fractional flow reserve were calculated from mean aortic, distal coronary, and right atrial pressures recorded during maximal vasodilation. Distal coronary pressures were measured by an ultrathin, pressure-monitoring guide wire with minimal influence on the transstenotic pressure gradient. Minimal obstruction area, percent area stenosis, and calculated stenosis flow reserve were assessed by quantitative coronary angiography. There was no difference in heart rate, mean aortic pressure, or rate-pressure product during maximal vasodilation during PET and during catheterization. Percent area stenosis ranged from 40% to 94% (mean, 77+/-13%), myocardial fractional flow reserve from 0.36 to 0.98 (mean, 0.61+/-0.17), and relative flow reserve from 0.27 to 1.23 (mean, 0.60+/-0.26). A close correlation was found between relative flow reserve obtained by PET and both myocardial fractional flow reserve (r=.87) and coronary fractional flow reserve obtained by pressure recordings (r=.86). The correlations between relative flow reserve obtained by PET and stenosis measurements derived from quantitative coronary angiography were markedly weaker (minimal obstruction area, r=.66; percent area stenosis, r=-.70; and stenosis flow reserve, r=.68). Conclusions Fractional flow reserve derived from pressure measurements correlates more closely to relative flow reserve derived from PET than angiographic parameters. This validates in humans the use of fractional flow reserve as an index of the physiological consequences of a given coronary artery stenosis.

Coronary flow reserve calculated from pressure measurements in humans. Validation with positron emission tomography.

The effect of sublingual or intracoronary nitroglycerin (NTG) on luminal caliber in normal and diseased portions of epicardial coronary arteries was determined in 85 lesions from 57 typical patients with ischemic heart disease. Measurements were made from coronary angiograms, using a computer-assisted method and a carefully blinded protocol for analysis of the pre- and post- NTG angiograms. Luminal area in the "normal" portion of the diseased segment and at its maximum constriction and an estimate of flow resistance in the stenosis were computed. Luminal area increased 1.27 mm2 (p less than 0.001) in the "normal" regions, an average increase of 18% over the control area. Dilation with NTG depended strongly on vessel size; area increased 35% in normal vessels of 1.6-2.3 mm luminal diameter and only 9% in vessels 4.0-5.0 mm in diameter. Lesions were grouped into four levels of severity by percent stenosis. Minimum luminal area increased 0.35 mm2 (p less than 0.01) at the narrowest point in moderate lesions, a 22% area increase, and 0.14 mm2 (p less than 0.001) in severe lesions, a 36% area increase. Stenosis dilation resulted in an average 25% reduction (p less than 0.01) in estimated stenosis flow resistance in moderate lesions and a 38% reduction (p less than 0.001) in severe lesions. A statistically significant resistance reduction of greater than 20% occurred in 15 to 20 severe stenoses; only two of 20 showed no measurable dilation. We reviewed recent literature on hemodynamic responses to NTG and determined that changes of this magnitude are among the largest reported. We conclude that vasodilation of epicardial coronary stenosis is usually a major component of the beneficial response to NTG. We support that conclusion by demonstrating a striking improvement in ischemic left ventricular compliance abnormalities after low-dose intracoronary NTG.

The mechanisms of nitroglycerin action: stenosis vasodilatation as a major component of the drug response.

The pressure-flow characteristics of 100 left circumflex stenoses in 10 chronically instrumented unsedated dogs were studied under resting conditions and during pharmacological coronary vasodilation. At rest, the pressure loss (deltaP) due to a stenosis and arterial flow velocity (V) were related by the equation, deltaP = FV + SV2, where F is the coefficient of pressure loss due to viscous friction in the stenotic segment and S is the coefficient of pressure loss due to flow separation at the diverging end of the stenosis. The linear term due to viscous friction accounted for 65% and the nonlinear term due to flow separation accounted for 35% of the total pressure loss at resting coronary flow. At peak coronary flow after coronary vasodilation, the pressure loss due to viscous friction accounted for 33% and pressure loss due to flow separation accounted for 67% of the total pressure loss. The pressure gradient-velocity relationship at high flows was characterized by the same general equation but with proportionately larger values of the coefficient S and therefore greater pressure loss associated with flow separation than predicted by the resting gradient-velocity relationship. The pressure loss predicted for high coronary flow velocities on the basis of the gradient-velocity equation at rest was only 64% of the actual experimentally observed pressure gradient at peak coronary flow. The augmented separation loss following coronary vasodilation probably was due to dilation of the epicardial artery adjacent to the fixed stenotic segment which caused more severe relative percent narrowing and a larger divergence angle at the distal end of the stenosis, the primary geometric determinants of separation losses.

K L Gould

Papers

Pressure-flow characteristics of coronary stenoses in unsedated dogs at rest and during coronary vasodilation.