Flow measurements in a highly curved atherosclerotic coronary artery cast of man.

Flow visualization and wall pressure measurements were made in a polyurethane cast of a cadaver coronary artery with a significant "s" shaped reverse curvature. A sucrose solution was used to simulate the kinematic viscosity of blood, with flow rates in the physiologic range. Flow visualization demonstrated significant secondary flow patterns in the wall vicinity, which increased with increasing Reynolds number. Random dye dispersion was observed at a Reynolds number of about 400, but not at 200. Dye filament patterns in the transition between the first and second curved region were predominantly influenced by the second curved region at lower Reynolds numbers, and by the first curved region at higher Re. Local wall pressure measurements demonstrated a significant centrifugal effect with large radial pressure differences across the casting. Flow resistances for the casting were considerably greater than reference Poiseuille flow values, and increased further with pulsatile flow.     

Wall shear rate measurements in an elastic curved artery model

Since atherosclerotic lesions tend to be localized at bends and branching points, knowledge of wall shear rate patterns in models of these geometries may help elucidate the mechanism of atherogenesis. This study uses the photochromic method of flow visualization to determine both the mean and amplitude of the wall shear rate waveform in straight and curved elastic arterial models to demonstrate the effects of curvature, elasticity, and the phase angle between the flow and pressure waveforms (impedance phase angle). Under sinusoidal flow conditions characteristic of large arteries, the mean shear rate at the inner wall of the curved tube is reduced 40–56% from its steady flow value, depending on the phase angle. Wall shear rate amplitudes in the curved tube are significantly reduced by wall motion (36–55% of the Womersley amplitude for a straight rigid tube). The shear rate amplitude at the outer wall decreases 30% as the phase angle is reduced from −20° to −66°, while the shear rate amplitude at the inner wall increases 45%. As a result, the oscillatory nature of flow at the outer wall decreases with decreasing negative phase angle, but flow at the inner wall becomes much more oscillatory. At large negative phase angles, characteristic of hypertension or vasoactive agents, the shear rate at the inner wall has a small mean and cycles through positive and negative values; the shear rate at the outer wall remains positive throughout the flow cycle. Thus, the impedance phase angle could affect atherogenesis along the inner wall if temporal and directional changes in wall shear rate play a role.     

Flow measurements in a human femoral artery model with reverse lumen curvature

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.     

Flow in a catheterized curved artery with stenosis

The fluid mechanics of blood flow in a catheterized curved artery with stenosis is studied through a mathematical analysis. Blood is modelled as an incompressible Newtonian fluid and the flow is assumed to be steady and laminar. An approximate analytic solution to the problem is obtained through a double series perturbation analysis for the case of small curvature and mild stenosis. The effect of catheterization on various physiologically important flow characteristics (i.e. the pressure drop, impedance and the wall shear stress) is studied for different values of the catheter size and Reynolds number of the flow. It is found that all these flow characteristics vary markedly across a stenotic lesion. Also, increase in the catheter size leads to a considerable increase in their magnitudes. These results are used to obtain the estimates of increased pressure drop across an arterial stenosis when a catheter is inserted into it. Our calculations, based on the geometry and flow conditions existing in coronary arteries, suggest that, in the presence of curvature and stenosis, and depending on the value of k (ratio of catheter size to vessel size) ranging from 0.1 to 0.4, the pressure drop increases by a factor ranging from 1.60 to 5.16. But, in the absence of curvature and stenosis, with the same range of catheter size, this increased factor is about 1.74-4.89. These estimates for the increased pressure drop can be used to correct the error involved in the measured pressure gradients using catheters. The combined effects of stenosis and curvature on flow characteristics are also studied in detail. It is found that the effect of stenosis is more dominant than that of the curvature. Due to the combined effect of stenosis, curvature and catheterization, the secondary streamlines are modified in a cross-sectional plane. The insertion of a catheter into the artery leads to the formation of increased number of secondary vortices.     

Flow-pressure drop measurement and calculation in a tapered femoral artery of a dog

This study describes the in vivo measurement of pressure drop and flow during the cardiac cycle in the femoral artery of a dog, and the computer simulation of the experiment based on the use of the measured flow, vessel dimensions and blood viscosity. In view of the experimental uncertainty in obtaining the accurate velocity profile at the wall region, the velocity pulse at the center was measured and numerical calculations were performed for the center Une instantaneous velocity and within the two limits of spatial distribution of inlet flow conditions: uniform and parabolic. Temporal and spatial variations of flow parameters, i.e., velocity profile, shear rate, non-Newtonian viscosity, wall shear stress, and pressure drop were calculated. There existed both positive and negative shear rates during a pulse cycle, i.e., the arterial wall experiences zero shear three times during a cardiac cycle. For the parabolic inlet condition, the taper of the artery not only increased the magnitude of the positive and negative shear rates, but caused a steep gradient in shear rate, a phenomenon which in turn affects wall shear stress and pressure. In contrast, for the uniform inlet condition, the flow through the tapered artery was predominantly the developing type, which resulted in reduction in magnitude of wall shear rate along the axial direction.     

Phasic and spatial pressure measurements in a femoral artery branch model for pulsatile flow

Phasic and spatial time-averaged pressure distributions were measured in a 60-deg femoral artery branch model over a large range of branch flow ratios and at physiological Reynolds numbers of about 120 and 700. The results obtained with an in-vivo like flow wave form indicated spatial adverse time average pressure gradients in the branch vicinity which increased in magnitude with branch flow ratio, and the importance of the larger inertial effects at the higher Reynolds numbers. Pressure losses in the branch entrance region were relatively large, and corresponding flow resistances may limit branch flow, particularly at higher Reynolds numbers. The effect of branch flow was to reduce the pressure loss in the main lumen.     

Pulse velocities in cylindrical,tapered and curved anisotropic elastic arteries

Modified Moens-Korteweg formulae have been developed for the pulse velocities in anisotropic elastic arteries of varying geometries. In particular, cylindrical straight, tapered and curved tubes have been considered. Numerical results indicate that the cylindrical tube formula can be applied in all cases and that the circumferential elastic modulus is the dominant elastic parameter.     

Medial and adventitial macrophages are associated with expansive atherosclerotic remodeling in rabbit femoral artery

Expansive vascular remodeling is considered a feature of vulnerable plaques. Although inflammation is upregulated in the media and adventitia of atherosclerotic lesions, its contribution to expansive remodeling is unclear. We investigated this issue in injured femoral arteries of normo- and hyperlipidemic rabbits fed with a conventional (CD group; n=20) or a 0.5% cholesterol (ChD group; n=20) diet. Four weeks after balloon injury of the femoral arteries, we examined vascular wall alterations, localization of macrophages and matrix metalloproteases (MMP)-1, -2, -9, and extracellular matrix. Neointimal formation with luminal stenosis was evident in both groups, while expansive remodeling was observed only in the ChD group. Areas immunopositive for macrophages, MMP-1, -2 and -9 were larger not only in the neointima, but also in the media and/or adventitia in the injured arterial walls of the ChD, than in the CD group. Areas containing smooth muscle cells (SMCs), elastin and collagen were smaller in the injured arterial walls of the ChD group. MMP-1, -2 and -9 were mainly localized in infiltrating macrophages. MMP-2 was also found in SMCs and adventitial fibroblasts. Vasa vasorum density was significantly increased in injured arteries of ChD group than in those of CD group. These results suggest that macrophages in the media and adventitia play an important role in expansive atherosclerotic remodeling via extracellular matrix degradation and SMC reduction.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Far-field dosimetric measurements in a full-sized man model at 2.0 GHz

Electromagnetic dosimetry was conducted in a tissue-equivalent full-sized model of man irradiated at 2 GHz inside a microwave-anechoic chamber. A nonperturbing temperature probe and a gradient-layer calorimeter were used to determine local and whole-body specific absorption rate (SAR), respectively. Relatively high SAR values were found in the limbs compared to the axis of the trunk of the model. The calorimeter experiments yielded an average SAR about three times higher than that estimated theoretically for a prolate spheroidal model of man. It is suggested that resonant interactions involving the limbs may be responsible for the disparity between theory and experiment.     

Estrogens, progestins, and coronary artery reactivity in atherosclerotic monkeys

It has been known for many years that sex hormones modulate vasodilator responses of arteries supplying the uterus with blood. Recently, it has been shown that sex hormones such as estrogen modulate vasomotor responses of other arteries, including coronary arteries. It is thought that modulation of vasodilator and constrictor responses of coronary arteries may be one mechanism by which estrogen affects the risk of coronary heart disease. Although several studies have examined the effects (and potential mechanisms) of estrogen on vasodilator responses of nonatherosclerotic arteries, few have focused on estrogen's effects on atherosclerotic coronary arteries. In studies of ovariectomized atherosclerotic female cynomolgus monkeys, both long-term (2 years) and short-term (20 min) estradiol treatment augments dilator responses to acetylcholine, but not nitroglycerin. Presumably, this indicates an effect of estradiol on endothelium-mediated dilator responses of coronary arteries. Addition of the progestin medroxyprogesterone acetate diminishes the beneficial effect of conjugated equine estrogens on these dilator responses. This is significant because a progestin is usually added to estrogen replacement to reduce the risk of endometrial and breast cancer associated with unopposed estrogen therapy. However, it would seem that not all progestins act similarly on vascular reactivity. Studies in monkeys indicate that addition of progesterone or the progestin medroxyprogesterone acetate does not diminish the beneficial effects of estrogen on coronary dilator responses. Thus it would appear that different estrogen/progestin combinations may affect vascular reactivity in different manners, There is also an effort being made to examine the potential of different kinds of estrogens on cardiovascular risk. Studies in monkeys indicate that one of the estrogens found in conjugated equine estrogens (17 alpha-dihydroequilenin) has estrogen effects on vascular reactivity without having detrimental effects on uterine pathology. The isoflavones “plant estrogens” found in soy protein also have estrogenic effects on vascular reactivity and inhibition.     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flow investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.     

The impedance of curved artery models

The impedance (pressure drop/flow rate) of four curved artery models has been determined experimentally for steady and periodic flows simulating conditions in the aortic arch. Steady flow results indicate that very short entry lengths are required for flow development in curved artery models, and impedance is elevated above straight tube values by a factor of 3-4 for mean flow conditions in the aortic arch. Results for periodic flow with a nonzero mean show a significant elevation of mean flow impedance relative to values for steady flow at the mean flow rate--a factor of 2-3 for aortic arch flow conditions. The impedance of the first harmonic of periodic flows follows straight tube theory at high values of the unsteadiness parameter in agreement with available theory for curved tubes. The implications of the impedance measurements for wall shear stress in the aortic arch are discussed.