Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds numbers

The velocity field in the neighborhood of axisymmetric constrictions in rigid tubes was investigated using laser Doppler anemometry and flow visualization. Upstream flow conditions were steady; and Reynolds numbers were in the range 500-2000, values which are representative of the larger arteries in humans. Stenoses of 25, 50 and 75% area reduction were studied. Velocity profiles are presented in sufficient detail to allow comparison with computational biofluid dynamics models. Wall shear stresses were estimated from the near wall velocity gradient, and the nature of observed poststenotic flow disturbances is discussed. Results indicate that flow disturbances of discrete oscillation frequency may be more valuable than turbulence as an indicator of early stages of stenosis development. Additionally, despite the fact that poststenotic turbulence exists for the higher degrees of stenosis and Reynolds numbers, the resulting wall shear stresses are only three to four times greater than the Poiseuille value and are considerably less than the wall shear stress within the stenosis itself.     

Influence of cardiac flow rate on turbulent shear stress from a prosthetic heart valve

Elevated turbulent shear stresses associated with sufficient exposure times are potentially damaging to blood constituents. Since these conditions can be induced by mechanical heart valves, the objectives of this study were to locate the maximum turbulent shear stress in both space and time and to determine how the maximum turbulent shear stress depends on the cardiac flow rate in a pulsatile flow downstream of a tilting disk valve. Two-component, simultaneous, correlated laser velocimeter measurements were recorded at four different axial locations and three different flow rates in a straight tube model of the aorta. All velocity data were ensemble averaged within a 15 ms time window located at approximately peak systolic flow over more than 300 cycles. Shear stresses as high as 992 dynes/cm2 were found 0.92 tube diameters downstream of the monostrut, disk valve. The maximum turbulent shear stress was found to scale with flow rate to the 0.72 power. A repeatable starting vortex was shed from the disk at the beginning of each cycle.     

The congenital bicuspid aortic valve can experience high-frequency unsteady shear stresses on its leaflet surface

The bicuspid aortic valve (BAV) is a common congenital malformation of the aortic valve (AV) affecting 1% to 2% of the population. The BAV is predisposed to early degenerative calcification of valve leaflets, and BAV patients constitute 50% of AV stenosis patients. Although evidence shows that genetic defects can play a role in calcification of the BAV leaflets, we hypothesize that drastic changes in the mechanical environment of the BAV elicit pathological responses from the valve and might be concurrently responsible for early calcification. An in vitro model of the BAV was constructed by surgically manipulating a native trileaflet porcine AV. The BAV valve model and a trileaflet AV (TAV) model were tested in an in vitro pulsatile flow loop mimicking physiological hemodynamics. Laser Doppler velocimetry was used to make measurements of fluid shear stresses on the leaflet of the valve models using previously established methodologies. Furthermore, particle image velocimetry was used to visualize the flow fields downstream of the valves and in the sinuses. In the BAV model, flow near the leaflets and fluid shear stresses on the leaflets were much more unsteady than for the TAV model, most likely due to the moderate stenosis in the BAV and the skewed forward flow jet that collided with the aorta wall. This additional unsteadiness occurred during mid- to late-systole and was composed of cycle-to-cycle magnitude variability as well as high-frequency fluctuations about the mean shear stress. It has been demonstrated that the BAV geometry can lead to unsteady shear stresses under physiological flow and pressure conditions. Such altered shear stresses could play a role in accelerated calcification in BAVs.     

Fluid-Structure Interaction Analysis of Pulsatile Flow within a Layered and Stenotic Aorta

In this paper, the hemodynamic characteristics of blood flow and stress distribution in a layered and stenotic aorta are investigated. By introducing symmetrical and unsymmetrical stenosis, the influence of stenosis morphology and stenotic ratio on the coupled dynamic responses of aorta is clarified. In the analysis, the in-vivo pulsatile waveforms and fully fluid–structure interaction (FSI) between the layered elastic aorta and the blood are considered. The results show that the fluid domain is abnormal in the stenotic aorta, and the whirlpool forms at the obstructed and downstream unobstructed regions. The maximum wall shear stresses appear at the throat of the stenosis. Downstream region appears low and oscillated shear stresses. In addition, along with the increase of the stenotic ratio, the amplitude of the maximum shear stress will be intensively increased and localized, and the sensitivity is also increased. In the aorta with unsymmetrical stenosis, the Von Mises stresses reach the peak value at the side with the surface protuberance, but they are reduced at the side with no protuberance. The sign variation of the layer interface shear stresses near the throat indicates the variation of the shear direction which increases the opportunity of shear damage at the transition plane. Moreover, the shear stress levels at the fluid-solid and intima-media interfaces are higher than that at the media-adventitia interface. The unsymmetrical stenosis causes higher stresses at the side with the surface protuberance than symmetrical one, but lower at the side with no protuberance. These results provide an insight in the influence of the stenosis, as well as its morphology, on the pathogenesis and pathological evolution of some diseases, such as arteriosclerosis and aortic dissection.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.     

Computer modeling of fluid dynamics related to a myocardial bridge in a coronary artery

Fluid mechanics associated with blood flows induced by the so-called myocardial bridge (MB) has been studied systematically using a computational fluid dynamic modeling of the Newtonian, incompressible, two-dimensional, unsteady flow in a channel with a time-dependently flushing in/out indentation. During each cycle, a train of vortex wave flow was observed downstream of the phasic stenosis and both upper and lower walls suffer severely from consistently high, oscillating wall shear stresses (WSS). Extensive studies were conducted on the influence of the Reynolds number, the geometry and the Strouhal number of the MB movement on the nature of the vortex flow and the time-dependent wall shear stress distribution. Special attention was drawn to the relationship between the vortex wave and the pressure distribution. It was found that the pressure gradient changed markedly during one cycle, which was apparently dominated by the dynamics of the indentation. A steep, adverse pressure gradient was observed when the indentation was flushing out, which corresponded to the existence of the most developing vortices. It implies the possibility that the MB in a coronary artery can produce an extremely low pressure region immediately downstream of the phasic stenosis, where elastic choking or collapse of the coronary artery might occur.     

Two-dimensional color-mapping of turbulent shear stress distribution downstream of two aortic bioprosthetic valves in vitro.

Since artificial heart valve related complications such as thrombus formation, hemolysis and calcification are considered related to flow disturbances caused by the inserted valve, a thorough hemodynamic characterization of heart valve prostheses is essential. In a pulsatile flow model, fluid velocities were measured one diameter downstream of a Hancock Porcine (HAPO) and a Ionescu-Shiley Pericardial Standard (ISPS) aortic valve. Hot-film anemometry (HFA) was used for velocity measurements at 41 points in the cross-sectional area of the ascending aorta. Three-dimensional visualization of the velocity profiles, at 100 different instants during one mean pump cycle, was performed. Turbulence analysis was performed as a function of time by calculating the axial turbulence energy within 50 ms overlapping time windows during the systole. The turbulent shear stresses were estimated by using the correlation equation between Reynolds normal stress and turbulent (Reynolds) shear stress. The turbulent shear stress distribution was visualized by two-dimensional color-mapping at different instants during one mean pump cycle. Based on the velocity profiles and the turbulent shear stress distribution, a relative blood damage index (RBDI) was calculated. It has the feature of combining the magnitude and exposure time of the estimated shear stresses in one index, covering the entire cross-sectional area. The HAPO valve showed a skewed jet-type velocity profile with the highest velocities towards the left posterior aortic wall. The ISPS valve revealed a more parabolic-shaped velocity profile during systole. The turbulent shear stresses were highest in areas of high or rapidly changing velocity gradients. For the HAPO valve the maximum estimated turbulent shear stress was 194 N m-2 and for the ISPS valve 154 Nm-2. The RBDI was the same for the two valves. The turbulent shear stresses had magnitudes and exposure times that might cause endothelial damage and sublethal or lethal damage to blood corpuscules. The RBDI makes comparison between different heart valves easier and may prove important when making correlation with clinical observations.     

Local hemodynamics affect monocytic cell adhesion to a three-dimensional flow model coated with E-selectin.

Monocyte adhesion to the endothelium depends on concentrations of receptors/ligands, local concentrations of chemoattractants, monocyte transport to the endothelial surface and hemodynamic forces. Monocyte adhesion to the inert surface of a three-dimensional perfusion model was shown to correlate inversely with wall shear stress, but was also affected by flow patterns which influenced the near-wall cell availability. We hypothesized that (a) under the same flow conditions, insolubilized E-selectin on the model's surface may mediate adhesive interactions at higher wall shear stresses, compared to an uncoated model, and (b) pulsatile flow may modify the adhesion profile obtained under steady flow. An axisymmetric flow model with a stenosis and a sudden expansion produced a range of wall shear stresses and a separated flow with recirculation and reattachment. Pre-activated U937 cells were perfused through the model under either steady (Re = 100, 140) or pulsatile (Remean = 107) flow. The velocity field was characterized through computational fluid dynamics and validated by inert particle tracking. Surface E-selectin greatly increased cell adhesion in all regions at Re = 100 and 140, compared to an uncoated model under the same flow conditions. In regions where the cells near the wall were abundant (taper and stenosis), adhesion to E-selectin correlated with the reciprocal of local wall shear stress when flow was steady. Pulsatile flow distributed the adherent cells more evenly throughout the coated model. Hence, characterizing both the local hemodynamics and the biological activity on the vessel wall is important in leukocyte adhesion.     

Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.     

A two-dimensional numerical analysis of unsteady flow in the carotid artery bifurcation. A comparison with three-dimensional in-vitro measurements and the influence of minor stenoses

In the present study a two-dimensional finite element model for incompressible Newtonian flow is applicated to the modelling of carotid artery flow. In earlier studies, the numerical model was validated experimentally for several flow configurations. In general the pulsatile flow is characterized by reversed flow regions at the non-divider side walls of both the internal and external carotid arteries. The unsteadiness of the flow is associated with rather complex spatial and temporal velocity distributions and leads to temporal variations of the location and length of the reversed flow regions. As a consequence, pronounced spatial and temporal variations in the wall shear stresses are found. At the non-divider side walls, wall shear stresses are relatively low and exhibits an oscillatory behaviour in space and time. At the divider side walls, wall shear stresses are relatively high and approximately follow the flow rate distribution in time. The aim of this study is not only to present two-dimensional calculations but also to compare the calculated two-dimensional velocity profiles with those from three-dimensional experiments. It is observed that in the common carotid artery and in the proximal parts of the internal and external carotid arteries, the two-dimensional numerical model provides valuable information with respect to the three-dimensional configuration. In the more distal parts of especially the internal carotid artery, deviations are found between the two-dimensional numerical and three-dimensional experimental model. These deviations can mainly be attributed to the neglect of the secondary velocity distribution in the two-dimensional model. In the two-dimensional numerical model the influence of a minor stenosis in the internal carotid artery is hardly distinguishable from a minor geometrical variation without stenosis. Full three-dimensional analyses of the influence of minor stenoses are needed to prove numerically whether in-vivo measurements of the axial velocity distribution are useful in the detection of minor stenoses.     

Laser anemometry measurements of pulsatile flow past aortic valve prostheses

Experimental results are presented on physiological pulsatile flow past caged ball and tilting disc aortic valve prostheses mounted in an axisymmetric chamber incorporated in a mock circulatory system. The measurements of velocity profiles and turbulent normal stresses during several times in a cardiac cycle were obtained using laser-Doppler anemometry. Our results show that with increased angle of opening for the tilting disc valves, a large but locally confined vortex is observed along the wall in the minor flow region throughout most of the cardiac cycle. The turbulent normal stresses measured downstream to the tilting disc in the minor flow region parallel to the tilt axis were found to be larger than those measured downstream to the caged ball valves. Comparison of measurements with steady flow at flow rates comparable to peak pulsatile flow rate show that the turbulent normal stresses are larger by a factor of two in pulsatile flow with a frequency of 1.2 Hz.     

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.     

Flow of couple stress fluid through stenotic blood vessels

The effects of an axially symmetric mild stenosis on the flow of blood, when blood is represented by a couple stress fluid model, have been studied. It is found that, for a fixed stenosis size, the resistance to flow and wall shear stress increase as the couple stress parameter eta decreases from unity. A comparison of the results with those of the Newtonian case shows that the magnitude of resistance to flow and wall shear under a given set of conditions, is greater in the case of the couple stress fluid model. It is seen that even in the case of a mild stenosis (19% area reduction), resistance to flow and wall shear values are increased over those for no stenosis by 60% and 62%, respectively, when compared with the case of a Newtonian fluid.     

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery.

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.     

A nonlinear axisymmetric model with fluid-wall interactions for steady viscous flow in stenotic elastic tubes.

Arteries with high-grade stenoses may compress under physiologic conditions due to negative transmural pressure caused by high-velocity flow passing through the stenoses. To quantify the compressive conditions near the stenosis, a nonlinear axisymmetric model with fluid-wall interactions is introduced to simulate the viscous flow in a compliant stenotic tube. The nonlinear elastic properties of the tube (tube law) are measured experimentally and used in the model. The model is solved using ADINA (Automatic Dynamic Incremental Nonlinear Analysis), which is a finite element package capable of solving problems with fluid-structure interactions. Our results indicate that severe stenoses cause critical flow conditions such as negative pressure and high and low shear stresses, which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The pressure filed near a stenosis has a complex pattern not seen in one-dimensional models. Negative transmural pressure as low as -24 mmHg for a 78 percent stenosis by diameter is observed at the throat of the stenosis for a downstream pressure of 30 mmHg. Maximum shear stress as a high as 1860 dyn/cm2 occurs at the throat of the stenoses, while low shear stress with reversed direction is observed right distal to the stenosis. Compressive stresses are observed inside the tube wall. The maximal principal stress and hoop stress in the 78 percent stenosis are 80 percent higher than that from the 50 percent stenosis used in our simulation. Flow rates under different pressure drop conditions are calculated and compared with experimental measurements and reasonable agreement is found for the prebuckling stage.     

Stenosis severity effects for unbalanced simple-pulsatile bifurcation flow

A numerical finite-difference analysis is made of a plane simple-pulsatile flow past a symmetrical bifurcation which contains an asymmetrical smooth-contoured stenosis in the trunk. In essence, such a situation could represent a stenosed common carotid artery immediately upstream from the carotid junction. The flow is unbalanced; two-thirds of it exits or enters through the lower branch. The effect on various flow parameters of the stenosis itself and on changes in its severity is investigated by comparing the results for a severe stenosis, a mild stenosis, and no stenosis. The simple-pulsatile forcing function is specified in terms of an oscillatory and a steady Karman number. To obtain a significant amount of backflow, the oscillatory trunk Karman number is taken as 1000 compared to the steady value of 250. The frequency of oscillation is stipulated by a trunk Stokes number of 10 pi. The numerical procedures utilize the vorticity-transport version of the Navier-Stokes governing equations. A non-orthogonal coordinate transform allows the calculations to be made in a rectangular grid where the central difference expressions are easily applied. The results are presented in terms of both kinematic and kinetic parameters. The variation in the basic kinematic variables of stream function and vorticity is shown by temporal sequences of contour plots at times of peak flow and during the flow reversal stages as well as by several velocity vector plots. Kinetic results are given in terms of the temporal variation in shear stresses along boundaries. The peak shears are found to occur at the zenith of the stenosis at times of peak flow: the value for the severe stenosis is twice as large as that for the mild stenosis. The midline pressure distribution in the trunk and the centerline pressure distributions in the branches are also included.     

MRI-based quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries

Accurate assessment of wall shear stress (WSS) is vital for studies on the pathogenesis of atherosclerosis. WSS distributions can be obtained by computational fluid dynamics (CFD) using patient-specific geometries and flow measurements. If patient-specific flow measurements are unavailable, in- and outflow have to be estimated, for instance by using Murray’s Law. It is currently unknown to what extent this law holds for carotid bifurcations, especially in cases where stenoses are involved. We performed flow measurements in the carotid bifurcation using phase-contrast MRI in patients with varying degrees of stenosis. An empirical relation between outflow and degree of area stenosis was determined and the outflow measurements were compared to estimations based on Murray’s Law. Furthermore, the influence of outflow conditions on the WSS distribution was studied.For bifurcations with an area stenosis smaller than 65%, the outflow ratio of the internal carotid artery (ICA) to the common carotid artery (CCA) was 0.62±0.12 while the outflow ratio of the external carotid artery (ECA) was 0.35±0.13. If the area stenosis was larger than 65%, the flow to the ICA decreased linearly to zero at 100% area stenosis. The empirical relation fitted the flow data well (R²=0.69), whereas Murray’s Law overestimated the flow to the ICA substantially for larger stenosis, resulting in an overestimation of the WSS. If patient-specific flow measurements of the carotid bifurcation are unavailable, estimation of the outflow ratio by the presented empirical relation will result in a good approximation of calculated WSS using CFD.     

Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture

Flow patterns and flow-related stresses contribute to the characterization of health risks, particularly the risk of plaque rupture, posed by a particular atherosclerotic stenosis. Blood flow in the presence of significant plaque deposits is investigated, and the influence of factors such as stenosis morphology and surface irregularity is evaluated. Solutions for three-dimensional, unsteady flow in these stenotic vessels are obtained for an incompressible, Newtonian fluid. The equations of motion are solved numerically using a finite volume formulation. The resulting flow patterns and shear and normal stresses are interpreted with respect to diagnostic implications, including the possibility of plaque rupture. The inadequacy of "percent stenosis" to characterize the risks posed by a particular plaque is demonstrated. Surface irregularity, stenosis aspect ratio, and the shape of the pulsatile waveform all have considerable influence on the flow field and on the stresses on the plaque. A measure of surface irregularity or plaque symmetry, in particular, may complement percent stenosis in diagnosing the risk of plaque rupture.     

Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses

Hemodynamics factors and biomechanical forces play key roles in atherogenesis, plaque development and final rupture. In this paper, we investigated the flow field and stress field for different degrees of stenoses under physiological conditions. Disease is modelled as axisymmetric cosine shape stenoses with varying diameter reductions of 30%, 50% and 70%, respectively. A simulation model which incorporates fluid-structure interaction, a turbulence model and realistic boundary conditions has been developed. The results show that wall motion is constrained at the throat by 60% for the 30% stenosis and 85% for the 50% stenosis; while for the 70% stenosis, wall motion at the throat is negligible through the whole cycle. Peak velocity at the throat varies from 1.47 m/s in the 30% stenosis to 3.2m/s in the 70% stenosis against a value of 0.78 m/s in healthy arteries. Peak wall shear stress values greater than 100 Pa were found for > or =50% stenoses, which in vivo could lead to endothelial stripping. Maximum circumferential stress was found at the shoulders of plaques. The results from this investigation suggest that severe stenoses inhibit wall motion, resulting in higher blood velocities and higher peak wall shear stress, and localization of hoop stress. These factors may contribute to further development and rupture of plaques.     

The hemodynamic and embolizing forces acting on thrombi--II. The effect of pulsatile blood flow

A previous analysis (Basmadjian, J. Biomechanics 17, 287-298, 1984) of the embolizing forces acting on thrombi in steady Poiseuille flow has been extended to pulsatile blood flow conditions in the major blood vessels. We show that for incipient and small compact thrombi up to 0.1 mm height, the maximum embolizing stresses can be calculated from the corresponding 'quasi-steady' viscous drag forces and measured maximum wall shear. Their magnitude is from 5 to 30 times (tau w)Max, the maximum wall shear stress during the cardiac cycle in the absence of thrombi. For larger thrombi, inertial and 'history' effects have to be taken into account, leading to embolizing stresses in excess of 100 Pa (1000 dyn cm-2).