An intergral method for the analysis of flow in arterial stenoses

An approximate solution is presented to the problem of incompressible flow through an axisymmetric constriction. The geometry is intended to simulate an arterial stenosis, and the solution is applicable to both mild and severe stenoses for Reynolds numbers below transition. Theoretical results obtained for specific geometries are given for the velocity distribution, pressure drop, wall shearing stress, and separation phenomena. These results reveal the significant alterations in flow caused by a stenosis. Experiments using model stenoses are described and compared with the theoretical results. Theoretical predictions of pressure drop and separation characteristics are in reasonably good agreement with the experimental observations.     

Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: Steady flows

Effects of the non-Newtonian viscosity of blood on a flow in a coronary arterial casting of man were studied numerically using a finite element method. Various constitutive models were examined to model the non-Newtonian viscosity of blood and their model constants were summarized. A method to incorporate the non-Newtonian viscosity of blood was introduced so that the viscosity could be calculated locally. The pressure drop, wall shear stress and velocity profiles for the case of blood viscosity were compared for the case of Newtonian viscosity (0.0345 poise). The effect of the non-Newtonian viscosity of blood on the overall pressure drop across the arterial casting was found to be significant at a flow of the Reynolds number of 100 or less. Also in the region of flow separation or recirculation, the non-Newtonian viscosity of blood yields larger wall shear stress than the Newtonian case. The origin of the non-Newtonian viscosity of blood was discussed in relation to the viscoelasticity and yield stress of blood.     

Effects of surface irregularities on flow resistance in differently shaped arterial stenoses

The combined influence of an asymmetric shape and surface irregularities has been explored in a computational study of flow through arterial stenoses with 48% areal occlusion. Contrary to the conclusion of an earlier investigation, namely that the resistance to laminar flow through a stenosed artery is being reduced in the presence of surface irregularities, the present predictions demonstrate that the flow resistance is practically unaffected by surface irregularities at low Reynolds numbers, whereas an excess pressure drop up to 10% above that for a smooth stenosis is observed for higher Reynolds numbers. For a given areal occlusion, the flow resistance is reduced with increasing degree of stenosis asymmetry and this effect may more than outweigh the influence of surface irregularities. This effect is moreover prevailing throughout the entire range of Reynolds numbers considered.     

A 3D unsteady flow analysis in a doubly constricted arterial vessel

The aim of this study is to examine the interaction between two mild atherosclerotic proliferations spaced apart by a distance S by analyzing their influence on flow structure, pressure drop and stress field in an arterial vessel under pulsatile flow conditions. This has been achieved numerically by employing a time accurate, cell centered finite volume method in solving the Navier-Stokes equations governing the 3D unsteady flow dynamics in a conceptual model of an multiply constricted arterial vessel. In comparison to the pressure drop across a single stenosis, nearly a 50% increase in the late systolic and early diastolic pressure drops has been observed across the two mild constrictions when they are spaced within a distance of S相似文献   

Estimated flow resistance increase in a spiral human coronary artery segment

Coronary flow estimates were made for a spiral coronary artery segment (identified from a post-mortem replica casting) by using a modified Dean number based on the approximate coil radius of curvature, as suggested earlier. The estimates were found to correlate experimental pressure drop data for helical coiled tubes. Over a physiological range of mean Reynolds numbers from 100 to 400 for blood flow through main coronary arteries, estimates of the flow resistance increase relative to a straight lumen segment ranged from about 20 to 80 percent, and were of similar magnitude to those found in a flow study in a sinuous coronary vessel segment with no spiral.     

Hemodynamic characteristics of flow around a deformable stenosis

Clinical studies reported that some vulnerable stenoses deformed their shape in a blood vessel based on flow condition. However, the effects of shape variation on flow characteristics remain unclear. The flow characteristics are known to affect vulnerable stenosis rupture and fractional flow reserve (FFR) value which has been widely used as a diagnostic tool for stenosis. Vulnerable stenosis rupture occurs when the structural stress exerted on a fibrous cap exceeds its tolerable threshold. The stress magnitude is determined from the spatial distribution of static pressure around the stenosis. In the present study, the static pressure distribution and the FFR value in deformable stenosis were investigated with related other flow characteristics. Two phantom models were fabricated to mimic deformable and nondeformable stenoses using polydimethylsiloxane. The flow characteristics were observed under a steady-flow condition at three Reynolds numbers (Re = 500, 1000, 1500) using a particle image velocimetry. The pressure drop across the stenosis models were measured using a pressure sensor to determine effects of shape deformation on FFR value. Shape variations and jet deflections were clearly observed in the deformable stenosis model, and the effective severity of the stenosis increased up to 17.2%. The shape variations of deformable stenosis model increased the static pressure difference at the upstream and downstream sides of the stenosis. The pressure drop across the deformable stenosis model was significantly higher than that of the nondeformable stenosis model. The present results substantiate that stenosis deformability should be carefully considered to diagnose the rupture of vulnerable stenosis.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Flow measurements in an atherosclerotic curved, tapered femoral artery model of man

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiogram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.     

Catheter obstruction effect on pulsatile flow rate--pressure drop during coronary angioplasty.

The coupling of computational hemodynamics to measured translesional mean pressure gradients with an angioplasty catheter in human coronary stenoses was evaluated. A narrowed flow cross section with the catheter present effectively introduced a tighter stenosis than the enlarged residual stenoses after balloon angioplasty; thus elevating the pressure gradient and reducing blood flow during the measurements. For resting conditions with the catheter present, flow was believed to be about 40 percent of normal basal flow in the absence of the catheter, and for hyperemia, about 20 percent of elevated flow in the patient group. The computations indicated that the velocity field was viscous dominated and quasi-steady with negligible phase lag in the delta p(t)-u(t) relation during the cardiac cycle at the lower hydraulic Reynolds numbers and frequency parameter. Hemodynamic interactions with smaller catheter-based pressure sensors evolving in clinical use require subsequent study since artifactually elevated translesional pressure gradients can occur during measurements with current angioplasty catheters.     

Hemodynamic diagnostics of epicardial coronary stenoses: <Emphasis Type="Italic">in-vitro</Emphasis> experimental and computational study

Background  

The severity of epicardial coronary stenosis can be assessed by invasive measurements of trans-stenotic pressure drop and flow. A pressure or flow sensor-tipped guidewire inserted across the coronary stenosis causes an overestimation in true trans-stenotic pressure drop and reduction in coronary flow. This may mask the true severity of coronary stenosis. In order to unmask the true severity of epicardial stenosis, we evaluate a diagnostic parameter, which is obtained from fundamental fluid dynamics principles. This experimental and numerical study focuses on the characterization of the diagnostic parameter, pressure drop coefficient, and also evaluates the pressure recovery downstream of stenoses.     

Physiological flow simulation in residual human stenoses after coronary angioplasty

To evaluate the local hemodynamic implications of coronary artery balloon angioplasty, computational fluid dynamics (CFD) was applied in a group of patients previously reported by [Wilson et al. (1988), 77, pp. 873-885] with representative stenosis geometry post-angioplasty and with measured values of coronary flow reserve returning to a normal range (3.6 +/- 0.3). During undisturbed flow in the absence of diagnostic catheter sensors within the lesions, the computed mean pressure drop delta p was only about 1 mmHg at basal flow, and increased moderately to about 8 mmHg for hyperemic flow. Corresponding elevated levels of mean wall shear stress in the midthroat region of the residual stenoses, which are common after angioplasty procedures, increased from about 60 to 290 dynes/cm2 during hyperemia. The computations (Ree approximately equal to 100-400; alpha e = 2.25) indicated that the pulsatile flow field was principally quasi-steady during the cardiac cycle, but there was phase lag in the pressure drop-mean velocity (delta p - u) relation. Time-averaged pressure drop values, delta p, were about 20 percent higher than calculated pressure drop values, delta ps, for steady flow, similar to previous in vitro measurements by Cho et al. (1983). In the throat region, viscous effects were confined to the near-wall region, and entrance effects were evident during the cardiac cycle. Proximal to the lesion, velocity profiles deviated from parabolic shape at lower velocities during the cardiac cycle. The flow field was very complex in the oscillatory separated flow reattachment region in the distal vessel where pressure recovery occurred. These results may also serve as a useful reference against catheter-measured pressure drops and velocity ratios (hemodynamic endpoints) and arteriographic (anatomic) endpoints post-angioplasty. Some comparisons to previous studies of flow through stenoses models are also shown for perspective purposes.     

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.     

An artifacts removal post-processing for epiphyseal region-of-interest (EROI) localization in automated bone age assessment (BAA)

Background

Guidewire (GW) size and stenosis dimensions are the two major factors affecting the translesional pressure drop. Studying the combined effect of these parameters on the mean pressure drop (Δp) across the stenosis is of high practical importance.

Methods

In this study, time averaged mass and momentum conservation equations are solved analytically to obtain pressure drop-flow, Δp-Q, curves for three different percentage area blockages corresponding to moderate (64%), intermediate (80%), and severe (90%) stenoses. Stenosis is considered to be axisymmetric consisting of three different sections namely converging, throat, and diverging regions. Analytical expressions for pressure drop are obtained for each of these regions separately. Using this approach, effects of lesion length and GW insertion on the mean translesional pressure drop and its component (loss due to momentum change and viscous loss) are analyzed.

Results and Conclusion

It is observed that for a given percent area stenosis (AS), increase in the throat length only increases the viscous loss. However, increase in the severity of stenosis and GW insertion increase both loss due to momentum change and viscous loss. GW insertion has greater contribution to the rise in viscous loss (increase by 2.14 and 2.72 times for 64% and 90% AS, respectively) than loss due to momentum change (1.34% increase for 64% AS and 25% decrease for 90% AS). It also alters the hyperemic pressure drop in moderate (48% increase) to intermediate (30% increase) stenoses significantly. However, in severe stenoses GW insertion has a negligible effect (0.5% increase) on hyperemic translesional pressure drop. It is also observed that pressure drop in a severe stenosis is less sensitive to lesion length variation (4% and 14% increase in Δp for without and with GW, respectively) as compared to intermediate (10% and 30% increase in Δp for without and with GW, respectively) and moderate stenoses (22% and 48% increase in Δp for without and with GW, respectively). Based on the contribution of pressure drop components to the total translesional pressure drop, it is found that viscous losses are dominant in moderate stenoses, while in severe stenoses losses due to momentum changes are significant. It is also shown that this simple analytical solution can provide valuable information regarding interpretation of coronary diagnostic parameters such as fractional flow reserve (FFR).     

Modeling the bifurcating flow in a human lung airway

The inspiratory flow characteristics in a three-generation lung airway have been numerically investigated using a control volume method to solve the fully three-dimensional laminar Navier-Stokes equations. The three-generation airway is extracted from the fifth to seventh branches of the model of Weibel (Morphometry of the Human Lung, Academic Press, New York, Springer, Berlin, 1963) with in-plane and 90 degrees off-plane configurations. Computations are carried out in the Reynolds number range of 200-1600, corresponding to mouth-air breathing rates ranging from 0.27 to 2.16l/s, or an averaged height of a man breathing from quiet to vigorous state. Particular attention is paid to establishing relations between the Reynolds number and the overall flow characteristics, including flow patterns and pressure drop. The ratio of airflow rate through the medial branch to that of the lateral branch for an in-plane airway increases as Re(0.227). However, the total pressure drop coefficient varies as Re(-0.497) for an in-plane airway and as Re(-0.464) for an off-plane airway. These pressure drop results are in good agreement with the experimentally measured behavior of Re(-0.5) and are more accurate than the numerically determined behavior of Re(-0.61) assuming the airways to be approximated by two-dimensional channels.     

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.     

Effects of diagnostic guidewire catheter presence on translesional hemodynamic measurements across significant coronary artery stenoses

This study gains insight on the nature of flow blockage effects of small guidewire catheter sensors in measuring mean trans-stenotic pressure gradients Deltap across significant coronary artery stenoses. Detailed pulsatile hemodynamic computations were made in conjunction with previously reported clinical data in a group of patients with clinically significant coronary lesions before angioplasty. Results of this study ascertain changes in hemodynamic conditions due to the insertion of a guidewire catheter (di=0.46 mm) across the lesions used to directly determine the mean pressure gradient (Deltap) and fall in distal mean coronary pressure (pr). For the 32 patient group of Wilson et al. [1988] (minimal lesion diameter dm=0.95 mm; 90% mean area stenosis; proximal measured coronary flow reserve (CFR) of 2.3 in the abnormal range) the diameter ratio of guidewire catheter to minimal lesion was 0.48, causing a tighter "artifactual" mean area stenosis of 92.1%. The results of the computations indicated a significant shift in the Deltap-Q relation due to guidewire induced increases in flow resistances (R=Deltap/Q) of 110% for hyperemic flow, a 35% blockage in hyperemic flow (Qh) and a phase shift of the coronary flow waveform to systolic predominance. These alterations in flow resulted in a fall in distal mean coronary pressure (at lower mean flow rates) below the patho-physiological range of prh approximately 55 mmHg, which is known to cause ischemia in the subendocardium (Brown et al. [1984]) and coincides with symptomatic angina. Transient wall shear stress levels in the narrow throat region (with flow blockage) were of the order of levels during hyperemic conditions for patho-physiological flow. In the separated flow region along the distal vessel wall, vortical flow cells formed periodically during the systolic phase when instantaneous Reynolds numbers Ree(t) exceeded about 110. For patho-physiological flow without the presence of the guidewire these vortical flow cells were much stronger than in the more viscous flow regime with the guidewire present. The non-dimensional pressure data given in tabular form may be useful in interpretation of guidewire measurements done clinically for lesions of similar geometry and severity.     

Flow disturbance measurements through a constricted tube at moderate Reynolds numbers

Instantaneous velocities in the field distal to contoured axisymmetric stenoses were measured with a laser Doppler anemometer. Upstream flow conditions were steady and spanned a range of Reynolds numbers from 500 to 2000. Autocorrelation functions and spectra of the velocity were employed to describe the nature of fluid dynamic disturbances. Depending upon the degree of stenosis and the Reynolds number, the flow field contained disturbances of a discrete oscillation frequency, of a turbulent nature, or both. If turbulence was detected in a given experiment, it was always preceded upstream by velocity oscillations at discrete frequency arising from vortex shedding. For mild degrees of stenosis (50% area reduction or less) the intensity of flow disturbances was relatively low until the Reynolds number exceeded 1000, thus highlighting difficulties to be expected in employing flow disturbance detection as a diagnostic tool in the recognition of early atherosclerosis in major arteries. In view of the relatively high noise levels inherent in noninvasive Doppler ultrasound systems employed clinically, it seems unlikely that detection of stenoses of less than 50% area reduction is feasible unless the Reynolds numbers exceed 1000 or unless pulsatility introduces new unsteady flow features beyond those studied here.     

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.     

Simulation of pressure drop and energy dissipation for blood flow in a human fetal bifurcation.

The pressure drop from the umbilical vein to the heart plays a vital part in human fetal circulation. The bulk of the pressure drop is believed to take place at the inlet of the ductus venosus, a short narrow branch of the umbilical vein. In this study a generalized Bernoulli formulation was deduced to estimate this pressure drop. The model contains an energy dissipation term and flow-scaled velocities and pressures. The flow-scaled variables are related to their corresponding spatial mean velocities and pressures by certain shape factors. Further, based on physiological measurements, we established a simplified, rigid-walled, three-dimensional computational model of the umbilical vein and ductus venosus bifurcation for stationary flow conditions. Simulations were carried out for Reynolds numbers and umbilical vein curvature ratios in their respective physiological ranges. The shape factors in the Bernoulli formulation were then estimated for our computational models. They showed no significant Reynolds number or curvature ratio dependency. Further, the energy dissipation in our models was estimated to constitute 24 to 31 percent of the pressure drop, depending on the Reynolds number and the curvature ratio. The energy dissipation should therefore be taken into account in pressure drop estimates.     

Pulsatile flow and mass transport over an array of cylinders: gas transfer in a cardiac-driven artificial lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.