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.     

Blood velocity patterns in poststenotic regions and velocity waveforms for myocardial inflow associated with coronary artery stenosis in dogs.

Velocity profiles across a vessel were investigated in poststenotic regions of the canine left coronary artery by our 80-channel 20 MHz ultrasound velocimeter. The velocity waveform in a small artery just before its penetration into myocardium was measured by our laser Doppler method. The poststenotic velocity configuration was characterized by a narrow region of high velocity with diastolic reverse flow near the wall which may dissipate energy. The velocity waveform in the distal small arteries exhibited increased systolic reverse flow with decreased diastolic forward flow, resulting in a remarkable reduction of coronary inflow into the myocardium.     

Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis

Numerical simulations of pulsatile blood flow in straight tube stenosis models were performed to investigate the poststenotic flow phenomena. In this study, three axisymmetrical and three asymmetrical stenosis models with area reduction of 25%, 50% and 75% were constructed. A measured human common carotid artery blood flow waveform was used as the upstream flow condition which has a mean Reynold's number of 300. All calculations were performed with high spatial and temporal resolutions. Flow features such as velocity profiles, flow separation zone (FSZ), and wall shear stress (WSS) distributions in the poststenotic region for all models are presented. The results have demonstrated that the formation and development of FSZs in the poststenotic region are very complex, especially in the flow deceleration phase. In axisymmetric stenoses the poststenotic flow is more sensitive to changes in the degree of stenosis than in asymmetric models. For severe stenoses, the stenosis influence length is shorter in asymmetrical models than in axisymmetrical cases. WSS oscillations (between positive and negative values) have been observed at various downstream locations in some models. The amplitude of the oscillation depends strongly on the axial location and the degree of stenosis.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

Disorder distal to modeled stenoses in steady and pulsatile flow

Measurements of the velocity and energy spectra were made in the distal region of modeled stenoses in a rigid tube with both steady and pulsatile water flows. Reynolds numbers of 318–2540 and a pulsatile flow frequency parameter of 15 were employed. The effects of the degree of stenosis, the stenosis geometry and the presence or absence of the downstream confining wall on the development of flow disturbances were investigated. Visualization of the distal flow patterns in stenotic and free jets illustrated the existence of complex fields which included vortex shedding, highly turbulent regions, and recirculation zones. Significant flow disorder was created by a mild stenosis in pulsatile, but not in steady, flow. Nondimensionalization employing the stenosis diameter and flow velocity in the throat of the constriction correlates the vortex shedding frequency and energy spectra within a limited postestenotic region.     

Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis.

Different shapes of pulsatile flows through a model of stenosis are experimentally and numerically modeled to validate both methods and to determine the wall shear stress temporal evolution downstream from the stenosis. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Finite element package is employed for the transient numerical simulations. Polynomial method, based on the experimental velocity values, is proposed to determine the wall shear stress temporal evolution. There is a good agreement between the numerical and experimental results. The wall shear stress temporal analysis shows oscillating wall shear stress values during the cycle with high wall shear stress values at the throat of about 120 dyn/cm2, and low values downstream from the stenosis of about - 2.5 dyn/cm2. The key result of the study is that the presence of the stenosis leads the artery to work in a direction which is opposite to the direction of a healthy artery.     

Platelet near-wall excess in porcine whole blood in artery-sized tubes under steady and pulsatile flow conditions

Platelet margination (enhanced platelet concentration in the near wall region of a blood vessel) has been well documented in small vessels. In artery-sized vessels margination has only been demonstrated in one study, using ghost cell suspensions and under relatively non-physiologic conditions of steady flow and 50 cm development length. Local sampling experiments were performed to confirm platelet margination in artery-sized stainless steel tubes, for a typical anatomical length and under pulsatile flow, using fresh EDTA-anticoagulated porcine whole blood (N=21). Experiments were designed using three-dimensional Computational Fluid Dynamics (CFD) to model the sample region with greater fidelity. Steady flow experiments in 50 cm long tubes verify published laser Doppler measurements of platelet margination in 3 mm ID tubes at normal arterial shear rate (500 s(-1). Margination persists under pulsatile flow conditions (63.8 pulses/min), but in steady flow at length of 10 cm, margination is reduced. Platelet margination ratio (the ratio of the platelet concentration near the wall to bulk average platelet count) ranges from 1.21 to 2.48. No significant effects of calculated sampling thickness (20 microm and 50 microm) or pulsatility were detected. Hematocrit margination ratio is 0.68 to 0.90. Two model platelet concentration profiles are fit to the experimental results.     

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.     

Laminar-to-turbulent transition in pulsatile flow through a stenosis

Laminar-to-turbulent transition in pulsatile flow through a stenosis is studied by means of three-dimensional numerical simulations. The flow transition is associated with the occurrence of a flow instability initiating in the stenosis region. The instability is manifested by a three-dimensional symmetry-breaking and leads to asymmetric separation and intense swirling motion downstream of the stenosis. The above have profound effects on the wall shear stress (WSS). The simulations reveal that the asymmetric separation is extended several radii downstream of the stenosis with substantial WSS fluctuations, in both space and time, occurring in the poststenotic region.     

Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation

Hemodynamics at the human carotid bifurcation is important to the understanding of atherosclerotic plaque initiation and progression as well as to the diagnosis of clinically important disease. Laser Doppler anemometry was performed in a large scale model of an average human carotid. Pulsatile waveforms and physiologic flow divisions were incorporated. Disturbance levels and shear stresses were computed from ensemble averages of the velocity waveform measurements. Flow in the common carotid was laminar and symmetric. Flow patterns in the sinus, however, were complex and varied considerably during the cycle. Strong helical patterns and outer wall flow separation waxed and waned during each systole. The changing flow patterns resulted in an oscillatory shear stress at the outer wall ranging from -13 to 9 dyn cm-2 during systole with a time-averaged mean of only -0.5 dyn cm-2. This contrasts markedly with an inner wall shear stress range of 17-50, (mean 26) dyn cm-2. The region of transient separation was confined to the carotid sinus outer wall with no reverse velocities detected in the distal internal carotid. Notable disturbance velocities were also time-dependent, occurring only during the deceleration phase of systole and the beginning of diastole. The present pulsatile flow studies have aided in identifying hemodynamic conditions which correlate with early intimal thickening and predict the physiologic level of flow disturbances in the bulb of undiseased internal carotid arteries.     

Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress

Arteries of several species, including man, tend to adjust their diameters such that the mean wall shear stress is in the range of 10-20 dynes cm-2. Additionally, intimal thickening in the human carotid bifurcation correlates well with the reciprocal of wall shear stress as determined in model studies. The correlation indicates that wherever the local mean wall shear stress exceeds approximately 10 dynes cm-2, the artery tends to be spared from intimal thickening. However, it is not known whether mean shear stress, i.e. the time-averaged value, or the instantaneous shear stress is the appropriate correlative variable. Each of these variables suggests different mechanisms for the reaction of the artery wall to its hemodynamic environment. It is therefore important to devise means by which the effects of mean shear and pulsatile shear can be separated in the study of atherogenesis. The present investigation examines the post-stenotic flow field in Plexiglas models under pulsatile conditions approximating those in the aortas of the cynomolgus monkey, an animal often employed in atherogenesis research. Behavior of the core flow and its effects on wall shear stress are studied for stenoses of 75 and 90% area reductions using laser velocimetry. The results show that the post-stenotic field contains regions in which the mean wall shear stress is low, but the pulsatile excursions are large.(ABSTRACT TRUNCATED AT 250 WORDS)     

A numerical and experimental investigation of transitional pulsatile flow in a stenosed channel

In the present paper, a closely coupled numerical and experimental investigation of pulsatile flow in a prototypical stenotic site is presented. Detailed laser Doppler velocimetry measurements upstream of the stenosis are used to guide the specification of velocity boundary conditions at the inflow plane in a series of direct numerical simulations (DNSs). Comparisons of the velocity statistics between the experiments and DNS in the post-stenotic area demonstrate the great importance of accurate inflow conditions, and the sensitivity of the post-stenotic flow to the disturbance environment upstream. In general, the results highlight a borderline turbulent flow that sequentially undergoes transition to turbulence and relaminarization. Before the peak mass flow rate, the strong confined jet that forms just downstream of the stenosis becomes unstable, forcing a role-up and subsequent breakdown of the shear layer. In addition, the large-scale structures originating from the shear layer are observed to perturb the near wall flow, creating packets of near wall hairpin vortices.     

Flow profiles and wall shear stress distribution at a hemodialysis venous anastomosis: preliminary study

The phasic velocity field in the vicinity of the venous anastomosis in a hemodialysis angioaccess arteriovenous fistula loop graft (AVLG) is investigated employing a laser Doppler anemometer (LDA) system. Detailed LDA velocity profiles are obtained by sectional survey performed in a transparent, elastic flow model which was fabricated to represent the geometry of the AVLG system under physiological pressure and flow waveforms. The geometry of the flow model was based on a silicone rubber cast obtained from an experimental dog model. In the present study, detailed distribution of velocity profiles is obtained. The distribution of wall shear stress in the model is computed from the slope of the local velocity profiles near the wall. The relationship between the results obtained by flow visualization and the LDA measurement is discussed.     

Experimental study of physiological pulsatile flow past valve prosthesis in a model of human aorta--II. Tilting disc valves and the effect of orientation

In Part II of this two paper sequence, pulsatile flow development past a tilting disc valve in a model human aorta has been studied using quantitative laser Doppler techniques. The valve was mounted in three different orientations with respect to the aortic root in this study. Under pulsatile flow, the region of flow reversal induced near the wall of the minor flow orifice extends to more than one tissue annulus diameter downstream from the valve into the ascending aorta. In a plane perpendicular to the tilt axis, a bi-helical secondary flow is induced distal to the valve. This secondary flow is further compounded by the multiple curvatures in the aorta. Hence the valve orientation affects the velocity profiles as far downstream as the mid-arch region as well as in the brachio-cephalic arterial branch. In the mid-arch region, a flow reversal along the entire cross-section is observed in early diastole for all the three orientations of the disc valve.     

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic case results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10--100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.     

Relative contribution of wall shear stress and injury in experimental intimal thickening at PTFE end-to-side arterial anastomoses

BACKGROUND: Intimal hyperplastic thickening (IHT) is a frequent cause of prosthetic bypass graft failure. Induction and progression of IHT is thought to involve a number of mechanisms related to variation in the flow field, injury and the prosthetic nature of the conduit. This study was designed to examine the relative contribution of wall shear stress and injury to the induction of IHT at defined regions of experimental end-to-side prosthetic anastomoses. METHODS AND RESULTS: The distribution of IHT was determined at the distal end-to-side anastomosis of seven canine Iliofemoral PTFE grafts after 12 weeks of implantation. An upscaled transparent model was constructed using the in vivo anastomotic geometry, and wall shear stress was determined at 24 axial locations from laser Doppler anemometry measurements of the near wall velocity under conditions of pulsatile flow similar to that present in vivo. The distribution of IHT at the end-to-side PTFE graft was determined using computer assisted morphometry. IHT involving the native artery ranged from 0.0+/-0.1 mm to 0.05+/-0.03 mm. A greater amount of IHT was found on the graft hood (PTFE) and ranged from 0.09+/-0.06 to 0.24+/-0.06 mm. Nonlinear multivariable logistic analysis was used to model IHT as a function of the reciprocal of wall shear stress, distance from the suture line, and vascular conduit type (i.e. PTFE versus host artery). Vascular conduit type and distance from the suture line independently contributed to IHT. An inverse correlation between wall shear stress and IHT was found only for those regions located on the juxta-anastomotic PTFE graft. CONCLUSIONS: The data are consistent with a model of intimal thickening in which the intimal hyperplastic pannus migrating from the suture line was enhanced by reduced levels of wall shear stress at the PTFE graft/host artery interface. Such hemodynamic modulation of injury induced IHT was absent at the neighboring artery wall.     

Computational fluid dynamic analysis of flow velocity waveform notching in umbilical arteries

Umbilical artery Doppler velocimetry waveform notching has long been associated with umbilical cord abnormalities, such as distortion, torsion, and/or compression (i.e., constriction). The physical mechanism by which the notching occurs has not been elucidated. Flow velocity waveforms (FVWs) from two-dimensional pulsatile flows in a constricted channel approximating a compressed umbilical cord are analyzed, leading to a clear relationship between the notching and the constriction. Two flows with an asymmetric, semi-elliptical constriction are computed using a stabilized finite-element method. In one case, the constriction blocks 75% of the flow passage, and in the other the constriction blocks 85%. Channel width and prescribed flow rates at the channel inflow are consistent with typical cord diameters and flow rates reported in the literature. Computational results indicate that waveform notching is caused by flow separation induced by the constriction, giving rise to a vortex (core) wave and associated eddies. Notching in FVWs based on centerline velocity (centerline FVW) is directly related to the passage of an eddy over the point of measurement on the centerline. Notching in FVWs based on maximum cross-sectional velocity (envelope FVW) is directly related to acceleration and deceleration of the fluid along the vortex wave. Results show that notching in envelope FVW is not present in flows with less than a 75% constriction. Furthermore, notching disappears as the vortex wave is attenuated at distances downstream of the constriction. In the flows with 75 and 85% constriction, notching of the envelope FVW disappears at ～3.8 and ～4.3 cm (respectively) downstream of the constriction. These results are of significant medical importance, given that envelope FVW is typically measured by commercial Doppler systems.     

In vitro flow dynamics of four prosthetic aortic valves: a comparative analysis

The velocity fields downstream of four prosthetic heart valves were mapped in vitro over the entire cross-section of a model aortic root using laser Doppler anemometry. THe Bj?rk-Shiley 60 degrees convexo-concave tilting disc valve, the Smeloff-Cutter caged ball valve, the St. Jude Medical bileaflet valve, and the Ionescu-Shiley standard bioprosthesis were examined under both steady and pulsatile flows. Velocity profiles under steady flow conditions were a good approximation for pulsatile profiles only during midsystole. The pulsatile flow characteristics of the four valves showed variation in large scale flow structures. Comparison of the valves according to pressure drop, shear stress and maximum velocities are also provided.     

Hemodynamic stress in lateral saccular aneurysms

The flow velocities in glass and silastic lateral aneurysm models were quantitatively measured with the non-invasive laser Doppler method. The influences of the elasticity of the wall, the pulse wave and the properties of the perfusion medium on the intra-aneurysmal circulation were investigated. As shown previously, the inflow into the aneurysm arose from the downstream lip and was directed toward the center of the fundus. Backflow to the parent vessel took place along the walls of the fundus. With non-pulsatile perfusion, flow velocities in the center of the standardized aneurysms varied between 0.4 and 2% of the maximum velocity in the parent vessel. With pulsatile perfusion, flow velocities in the center of the fundus ranged between 8 and 13% of the flow velocity in the axis of the parent vessel. Flow velocities in the aneurysms were slower with a polymer suspension with blood-like properties compared to a glycerol/water solution. Flow velocity measurements near the aneurysmal wall allowed the estimation of the shear stresses at critical locations. The maximum shear stresses at the downstream lip of the aneurysm were in the range of the stresses measured at the flow divider of an arterial bifurcation. The present results suggest that in human saccular aneurysms intra-aneurysmal flow and shear stress on the wall are directly related to the pulsatility of perfusion, i.e. the systolic/diastolic pressure difference and that the tendency to spontaneous thrombosis depends on the viscoelastic properties of the blood, namely the hematocrit.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.