Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—II. Results on five models

Turbulent flow simulations are run for five aortic trileaflet valve geometries, ranging from a valve leaflet orifice area of 1.1 cm² (Model A1—very stenotic) to 5.0 cm² (Model A5—natural valve). The simulated data compares well with experimental measurements made downstream of various aortic trileaflet valves by Woo (PhD Thesis, 1984). The location and approximate width and length of recirculation regions are correctly predicted. The less stenotic valve models reattach at the end of the aortic sinus region, 1.1 diameters downstream of the valve. The central jet exiting the less stenotic valve models is not significantly different from fully developed flow, and therefore recovers very quickly downstream of the reattachment point. The more stenotic valves disturb the flow to a greater degree, generating recirculation regions large enough to escape the sinuses and reattach further downstream. Peak turbulent shear stress values downstream of the aortic valve models which approximated prosthetic valves are 125 and 300 N m⁻², very near experimental observations of 150 to 350 N m⁻². The predicted Reynolds stress profiles also present the correct shape, a double peak profile, with the location of the peak occuring at the location of maximum velocity gradient, which occurs near the recirculation region. The pressure drop across model A2 (leaflet orifice area 1.6 cm²) is 20 mmHg at 1.6 diameters downstream. This compares well with values ranging from 19.5 to 26.2 mmHg for valves of similar orifice areas. The pressure drop decreases with decreasing valve stenosis, to a negligible value across the least stenotic valve model. Based on the good agreement between experimental measurements of velocity, shear stress and pressure drop, compared to the simulated data, the model has the potential to be a valuable tool in the analysis of heart valve designs.     

Three-dimensional visualization of velocity fields downstream of six mechanical aortic valves in a pulsatile flow model

Velocity fields downstream of 27 mm Bj?rk-Shiley Standard, Bj?rk-Shiley Convex-Concave, Bj?rk-Shiley Monostrut, Hall-Kaster (Medtronic-Hall), St. Jude Medical and Starr-Edwards Silastic Ball aortic valves were studied in a pulsatile mock circulation. Stroke volume was 70 cm3 and frequency 71 min-1 and 88 min-1. Fluid velocity was measured by a catheter mounted hot-film anemometer probe in a glycerol water mixture one and two diameters downstream of the aortic valve. Velocity fields were dynamically visualized by a three-dimensional technique and revealed qualitative independence of frequency. All profiles were flat in the acceleration phase of systole. From peak systole and throughout the systolic deceleration phase profiles characteristic of the individual valves appeared. The pivoting and tilting disc valves caused a skewed velocity profile with highest velocities downstream of the major orifice and lowest velocities downstream of the minor orifice. The differences between the three investigated Bj?rk-Shiley valves were remarkable. The St. Jude Medical valve generated velocity peaks downstream of the two major orifices and the central slit, and lower velocities in the hinge areas. A rather flat profile with central hollowing was seen downstream of the Starr-Edwards Ball valve. All velocity profiles were more or less dampened two diameters downstream.     

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.     

Predicted wall shear rate gradients in T-type arteriolar bifurcations

The purpose of this study was to examine the theoretical impact of the local bifurcation geometry on the shear rate gradient in a divergent arteriolar-type bifurcation. Newtonian flow through an arteriolar bifurcation was modeled using 3-dimensional computational fluid dynamics (CFD). Branching angles of 30 degrees, 50 degrees, 70 degrees, 90 degrees, 110 degrees, 130 degrees, and 150 degrees were studied at a Reynolds number (Re) of 0.01 in seven separate models. Both the flow split (30%) and the branch to main vessel diameter ratio (4/5) were held constant. Velocity profiles were predicted to deviate significantly from a parabolic form, both immediately before and after the branch. This deviation was shown to be a function of the local bifurcation geometry of each model, which consisted of a branching angle and associated feed-branch intersection shape. Immediately before and after the branch, the shear rate along the lateral branching wall was predicted to exceed (5-fold) that calculated for fully developed flow in the feed. In vivo data were from the anesthetized (pentobarbital, 70 mg/kg) hamster cremaster muscle preparation. Red blood cells were used as flow markers in arteriolar branch points (n = 74) show that a significant gradient in shear rate occurs at the locations and branch shapes predicted by the computational model. Thus, for low Re divergent flow, the gradient in shear rate measured for non-Newtonian conditions, is approximated by a finite element fluid dynamics model of Newtonian flow.     

Experimental study of physiological pulsatile flow past valve prostheses in a model of human aorta--I. Caged ball valves

Pulsatile flow development past a caged ball valve in a model human aorta was studied using laser Doppler anemometry. Velocity profiles measured in the ascending aorta and in the mid-arch region were strongly influenced by the geometry of the valve at the root of the aorta. Velocity profiles distal to the valve were asymmetric with jet-like flow in the peripheral region having larger velocity magnitudes towards the left lateral wall. In early diastole, a streamwise vortex motion was observed throughout the model aorta with fluid moving towards the downstream direction along the left lateral wall and reversed flow along the right lateral wall. With the caged ball valve at the root of the aorta, no reversed flow was observed along the inner wall of curvature in the mid-arch region.     

Velocity profiles in central airways with endotracheal intubation: a model study

Steady inspiratory velocity profiles were measured at two flow rates in a 3:1 scale model of the human central airways in the presence of five modes of endotracheal intubation. The presence of an orifice or a short endotracheal tube had no significant effect on the velocity profiles distal to the carina. Long endotracheal tubes change the profiles in both main bronchi. A significant peak occurred in the frontal plane near the walls, and the maximum velocity in the airway was almost identical to the endotracheal tube center-line velocity. The flow impinging on the medial wall of the main bronchus was redirected up around the anterior and posterior walls yielding bipeak velocity profiles in the sagittal plane. A tube placed eccentrically in the trachea over the right main bronchus did not alter the velocity profiles in the left main bronchus, suggesting a redirection of flow over the carina into the left lung. An endobronchial tube at the mouth of the right main bronchus did change the shape of the velocity profiles in the left main bronchus. In the left upper lobar bronchus the presence of trachea intubation had no effect on the velocity profiles. However, in the right upper lobar bronchus, the long endotracheal tube flattened the velocity profiles from the strongly skewed ones seen in the absence of the endotracheal inserts. These results not only are relevant to distribution of ventilation and aerosol particle deposition, but also have strong implications in intrapulmonary gas mixing, especially when high-frequency low tidal-volume ventilation is involved.     

Comparison of velocity profiles for different flow chamber designs used in studies of microbial adhesion to surfaces

Flow chambers are commonly used to study microbial adhesion to surfaces under environmentally relevant hydrodynamic conditions. The parallel plate flow chamber (PPFC) is the most common design, and mass transport occurs through slow convective diffusion. In this study, we analyzed four different PPFCs to determine whether the expected hydrodynamic conditions, which control both mass transport and detachment forces, are actually achieved. Furthermore, the different PPFCs were critically evaluated based on the size of the area where the velocity profile was established and constant with a range of flow rates, indicating that valid observations could be made. Velocity profiles in the different chambers were calculated by using a numerical simulation model based on the finite element method and were found to coincide with the profiles measured by particle image velocimetry. Environmentally relevant shear rates between 0 and 10,000 s(-1) could be measured over a sizeable proportion of the substratum surface for only two of the four PPFCs. Two models appeared to be flawed in the design of their inlets and outlets and allowed development of a stable velocity profile only for shear rates up to 0.5 and 500 s(-1). For these PPFCs the inlet and outlet were curved, and the modeled shear rates deviated from the calculated shear rates by up to 75%. We concluded that PPFCs used for studies of microbial adhesion to surfaces should be designed so that their inlets and outlets are in line with the flow channel. Alternatively, the channel length should be increased to allow a greater length for the establishment of the desired hydrodynamic conditions.     

Comparison of Velocity Profiles for Different Flow Chamber Designs Used in Studies of Microbial Adhesion to Surfaces

Flow chambers are commonly used to study microbial adhesion to surfaces under environmentally relevant hydrodynamic conditions. The parallel plate flow chamber (PPFC) is the most common design, and mass transport occurs through slow convective diffusion. In this study, we analyzed four different PPFCs to determine whether the expected hydrodynamic conditions, which control both mass transport and detachment forces, are actually achieved. Furthermore, the different PPFCs were critically evaluated based on the size of the area where the velocity profile was established and constant with a range of flow rates, indicating that valid observations could be made. Velocity profiles in the different chambers were calculated by using a numerical simulation model based on the finite element method and were found to coincide with the profiles measured by particle image velocimetry. Environmentally relevant shear rates between 0 and 10,000 s⁻¹ could be measured over a sizeable proportion of the substratum surface for only two of the four PPFCs. Two models appeared to be flawed in the design of their inlets and outlets and allowed development of a stable velocity profile only for shear rates up to 0.5 and 500 s⁻¹. For these PPFCs the inlet and outlet were curved, and the modeled shear rates deviated from the calculated shear rates by up to 75%. We concluded that PPFCs used for studies of microbial adhesion to surfaces should be designed so that their inlets and outlets are in line with the flow channel. Alternatively, the channel length should be increased to allow a greater length for the establishment of the desired hydrodynamic conditions.     

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.     

The flow field downstream of an oscillating collapsed tube

A two-component laser Doppler anemometer was used to determine the velocity of aqueous flow in the region from 0.25 to 2.5 diameters downstream of a collapsible tube while the tube was executing vigorous repetitive flow-induced oscillations. The Reynolds number for the time-averaged flow was 10,750. A simultaneous measurement of the pressure at the downstream end of the tube was used to align all the results in time at sixty locations in each of the two principal planes defined by the axes of collapse of the flexible tube upstream. The raw data of seed-particle velocity were used to create a periodic waveform for each measured velocity component at each location by least-squares fitting of a Fourier series. The results are presented as both velocity vectors and interpolated contours, for each of ten salient instants during the cycle of oscillation. In the plane of the collapse major axis, the dominant feature is the jet which emerges from each of the two tube lobes when it collapses, but transient retrograde flow is observed on both the central and lateral edges of this jet. In the orthogonal, minor-axis plane, the dominant feature is the retrograde flow, which during part of the cycle extends over the whole plane. All these features are essentially confined to the first 1.5 diameters of the rigid pipe downstream of the flexible tube. These data map the temporal and spatial extent of the highly three-dimensional reversing flow just downstream of an oscillating collapsed tube.     

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.     

Two-component laser velocimeter measurements downstream of heart valve prostheses in pulsatile flow

Elevated turbulent shear stresses resulting from disturbed blood flow through prosthetic heart valves can cause damage to red blood cells and platelets. The purpose of this study was to measure the turbulent shear stresses occurring downstream of aortic prosthetic valves during in-vitro pulsatile flow. By matching the indices of refraction of the blood analog fluid and model aorta, correlated, simultaneous two-component laser velocimeter measurements of the axial and radial velocity components were made immediately downstream of two aortic prosthetic valves. Velocity data were ensemble averaged over 200 or more cycles for a 15-ms window opened at peak systolic flow. The systolic duration for cardiac flows of 8.4 L/min was 200 ms. Ensemble-averaged total shear stress levels of 2820 dynes/cm2 and 2070 dynes/cm2 were found downstream of a trileaflet valve and a tilting disk valve, respectively. These shear stress levels decreased with axial distance downstream much faster for the tilting disk valve than for the trileaflet valve.     

Effect of the larynx on oscillatory flow in the central airways: a model study

Measurements were made of the effect of the larynx on the oscillatory flow profiles in a 3:1 scale model of the human central airways. A fixed glottic aperture corresponding to the shape and size at midinspiration was used. Oscillatory airflows at peak Reynolds numbers, similar to those obtained during spontaneous breathing and panting, were studied. The flow distribution to the five lobar bronchi was maintained by distally placed linear resistors. A hot-wire anemometer probe was used to measure the local velocity along two perpendicular diameters at six stations distributed through the model. Near the proximal end of the trachea, the flat velocity profiles at the beginning of the flow cycle peaked at maximum flow because of the jet created by the glottic aperture. This peaked structure was conserved during the latter half of the inspiratory cycle. Close to the carina, the jet had almost dissipated and the entry conditions into the main bronchi corresponded to those in the absence of the laryngeal model. The effect of the glottic aperture on the mean velocity was not felt beyond the carina, and the characteristic skewed profiles seen in oscillatory flows, in the absence of the larynx, were present in the main and lobar bronchi.     

Measurement and calculations of laminar flow in a ninety degree bifurcation

Measurements and numericaL calculations of laminar flow in a plane 90 degrees bifurcation are presented. The corresponding two-dimensional steady flow Navier-Stokes equations solved by a finite-difference procedure employing pressure and velocity as dependent variables. The influence of Reynolds number and mass flow ratio on the velocity field, streamlines, local shear stress and pressure drop are quantified and shown to be substantial. The circulation patterns and shear stresses are examined in view of available data regarding the formation of atherotic plaques in the human circulatory system. The calculated velocity profiles are compared with measurements obtained with laser Doppler anemometry and the agreement is shown to be satisfactory. Calculations outside the range of measurements which are of value to biomechanics are also presented.     

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.     

Finite element analysis of two dimensional steady flow in model arterial bifurcation

The purpose of the investigation reported in this paper is to determine theoretically the fluid dynamic field in models of common iliac arterial bifurcation and to identify the flow features which might influence the predominant occurrence of atherosclerotic lesions at such sites. This has been accomplished by numerically simulating fluid flow through 90 degrees symmetric bifurcations with branch-to-trunk area ratios of 0.8-1.414 and for Reynolds numbers ranging from 100 to 400. The analysis predicts flow reversal along the outer wall in models with area ratios over unity for high Reynolds number range, while no flow reversal occurred in models with area ratio below unity; a low shear zone along the outer wall and high shear stresses at the divider lip. Adverse pressure gradients are observed along the outer wall downstream of the corner point, the magnitudes increased with Reynolds number for a given branch to area ratio. Biological implication of the results is discussed with specific reference to the sites of atherosclerotic lesions found in man for these geometries.     

Velocity field studies at surgically imposed arterial stenoses on the abdominal aorta in pigs

In order to describe velocity profiles and the size of deterministic and non-deterministic velocity disturbances at arterial stenoses, symmetrical and asymmetrical stenoses with intended area reductions of 50% (‘moderate’) and 85% (‘severe’) were applied on the abdominal aorta in six pigs. Blood velocities were registered by hot-film anemometry in 21 measuring points distributed across the vessel cross-sectional area in one pre-stenotic and three post-stenotic positions. Signal analysis included ensemble averaging, the high-pass filtering technique, and three-dimensional visualization. None of the stenoses affected the pre-stenotic velocity field. Downstream moderate stenoses flow separation and vortex formation were present. Moderate asymmetric stenoses induced turbulence in the post-stenotic velocity field. Immediately downstream of severe stenoses a prominent post-stenotic jet was present. Farther downstream, a multitude of coherent vortices and turbulence dominated the flow field. The transverse distribution of turbulence intensity parallelled with the peak systolic velocity profile, whereas transverse profiles of the relative turbulence intensity (turbulence intensity/mean velocity) revealed peak values in flow field locations with high velocity gradients. Velocity parameters for symmetric and asymmetric severe stenoses were highly comparable. However, the exact degree of stenosis was significantly higher for symmetrical (85%) than for asymmetrical (76%) stenoses. Therefore, recalling that stenosis severity strongly influences the development of velocity disturbances, this indicates that asymmetry of a stenosis is a predictor for blood velocity disturbances.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.