Flow investigations in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Part I

Together with biochemical factors, fluid mechanical factors play a role in atherogenesis and the deposition of blood platelets at bends and bifurcations in human arteries. Hence, flow patterns were investigated in a simplified 3-dimensional model of a human renal artery bifurcation using Newtonian (aqueous glycerol) and non-Newtonian (aqueous solution of polyacrylamide) fluids. Studies were carried out in steady as well as pulsatile flow at inflow Reynolds numbers of 498 and 951 with flow rate ratios main tube V1: right branch V4: left branch V3 of 1: 0.25: 0.25 and 1: 0.18: 0.18 respectively. The velocity distribution proximal and distal to the bifurcations was measured using a laser-Doppler anemometer. In steady flow, zones of flow separation and reverse flow were observed distal to the bifurcations. In pulsatile flow using non-Newtonian fluids, there was a significant enlargement of these zones. Differences between the Newtonian and non-Newtonian fluids occurred especially distal to the bifurcations. Shear stresses along all measuring positions were computed from the velocity gradients.     

Numerical simulation of steady flow fields in a model of abdominal aorta with its peripheral branches

In the present study, a numerical calculation procedure based on a finite volume method was developed to simulate steady flow fields in a model of abdominal aorta with its peripheral branches. The study focused on the steady baseline flow fields and the wall shear stress (WSS) distribution as well as the localization of the reversed flow regions and results were compared to those obtained by other investigators. In the case of resting conditions, the existence of a region of reversed flow of about one to two diameters in size and next to the renal arteries and along the posterior wall as observed by other researchers was confirmed. However, under the exercise conditions this region could be wiped out. The flow reversal along the lateral walls proximal to the bifurcation persisted in both rest and exercise conditions. The WSS distribution and the wall shear stress gradient distribution were obtained. The lowest WSS occurred near the ostia of the renal arteries and the lateral walls of the iliac arteries. And the highest is always at the turn to the branch. The results were generally consistent with those obtained experimentally and numerically by other investigators. It was also shown that the steady flow might be used to depict the averaged behavior of pulsatile flow. The present computer code provides a platform for the future more realistic simulations.     

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.     

Role of blood cell-wall interactions in thrombogenesis and atherogenesis: a microrheological study

The relationship between blood flow and the localization of thrombosis and atherosclerosis in vivo was investigated using the approach and techniques of microrheology. The flow patterns and wall-adhesion of platelets were studied in the captive annular vortex formed at a sudden tubular expansion at various hematocrits in steady and pulsatile flow. The adhesion density exhibited a peak within the vortex and just downstream of the reattachment point, which is also a stagnation point. The peaks flattened out with increasing Reynolds number in steady flow and also in pulsatile flow. Platelet adhesion increased markedly with increasing hematocrit. The localization of adhesion peaks was explained by curvature of the streamlines carrying platelets to the wall on either side of the reattachment point. The relevance of these results to the circulation is that stagnation points are found in regions of disturbed flow at various sites in the arterial and venous circulations. This was shown in experiments using a technique whereby flow was visualized in isolated transparent natural blood vessels prepared from dogs and humans postmortem. In dog saphenous vein bileaflet valves, there was a large primary spiral vortex as well as a smaller secondary vortex, the latter acting as a trap and generator of thrombi. Recirculation zones also existed in the dog aorta at T-junctions of the celiac, cranial mesenteric and renal arteries. Finally, in the human carotid bifurcation, a large standing recirculation zone consisting of spiral secondary flows formed in the carotid sinus at physiological flow conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Spiral blood flow in aorta–renal bifurcation models

The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta–renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta–renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta–renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.     

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.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions

We present a one-dimensional (1D) fluid dynamic model that can predict blood flow and blood pressure during exercise using data collected at rest. To facilitate accurate prediction of blood flow, we developed an impedance boundary condition using morphologically derived structured trees. Our model was validated by computing blood flow through a model of large arteries extending from the thoracic aorta to the profunda arteries. The computed flow was compared against measured flow in the infrarenal (IR) aorta at rest and during exercise. Phase contrast-magnetic resonance imaging (PC-MRI) data was collected from 11 healthy volunteers at rest and during steady exercise. For each subject, an allometrically-scaled geometry of the large vessels was created. This geometry extends from the thoracic aorta to the femoral arteries and includes the celiac, superior mesenteric, renal, inferior mesenteric, internal iliac and profunda arteries. During rest, flow was simulated using measured supraceliac (SC) flow at the inlet and a uniform set of impedance boundary conditions at the 11 outlets. To simulate exercise, boundary conditions were modified. Inflow data collected during steady exercise was specified at the inlet and the outlet boundaries were adjusted as follows. The geometry of the structured trees used to compute impedance was scaled to simulate the effective change in the cross-sectional area of resistance vessels and capillaries due to exercise. The resulting computed flow through the IR aorta was compared to measured flow. This method produces good results with a mean difference between paired data to be 1.1 +/- 7 cm(3) s(- 1) at rest and 4.0 +/- 15 cm(3) s(- 1) at exercise. While future work will improve on these results, this method provides groundwork with which to predict the flow distributions in a network due to physiologic regulation.     

Some flow visualization and laser-Doppler-velocity measurements in a true-to-scale elastic model of a human aortic arch--a new model technique.

Flow studies were done in an elastic true-to-scale silicone rubber model of an aortic arch to study further hemodynamic influences on atherosclerosis. The model was prepared from a cast of a young woman. A revised model technique was used. The model had a compliance similar to that of the human aortic arch. Velocity measurements were done in the model with a two component laser-Doppler-anemometer in steady and pulsatile flow using a calcium chloride solution with a viscosity of eta = 3.18 mPas and density of rho = 1.28 kg/m3 at 20 degrees C. The time average Reynolds numbers over a whole cycle in the ascending aorta was Re = 1350. The Womersley parameter for pulsatile flow was a = 20. The pulse wave velocity in the ascending aorta was about c = 5.4 m/sec. The secondary flow behavior was discussed for steady and pulsatile flow. Reverse flows were found, especially along the inner radius of the aortic arch in the descending aorta in steady and pulsatile flow and also in small areas of the ascending aorta and at the branches of the aortic arch. The formation of atherosclerotic plaques at preferred local flow regions is discussed.     

Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier-Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.     

Influence of the renal artery ostium flow diverter on hemodynamics and atherogenesis

The structure and function of the renal artery ostium flow diverter on the caudal side of the renal branch point were previously reported; in this study, we further evaluate the diverter?s possible functions. The protrusion of this structure into the abdominal aorta suggests that the diverter may preferentially direct blood flow to the renal arteries, and that it may also influence flow patterns and recirculation known to be involved in atherogenesis. Three-dimensional computational fluid dynamics (CFD) simulations of steady and pulsatile blood flow are performed to investigate the influence of diverter size and position, and vascular geometry, on the flow patterns and fluid mechanical forces in the neighborhood of the diverter. CFD results show that the flow diverter does affect the blood distribution; depending on the diverter?s position, the flow to the renal arteries may be increased or reduced. Calculated results also demonstrate the diverter?s effect on the wall shear stress (WSS) distribution, and suggest that the diverter contributes to an atherogenic environment in the abdominal aorta, while being atheroprotective in the renal arteries themselves. These results support previous clinical findings, and suggest directions for further clinical study. The results of this work have direct implications in understanding the physiological significance of the diverter, and its potential role in the pathophysiological development of atherosclerosis.     

Finite element models of total shoulder replacement: Application of boundary conditions

We present a one-dimensional (1D) fluid dynamic model that can predict blood flow and blood pressure during exercise using data collected at rest. To facilitate accurate prediction of blood flow, we developed an impedance boundary condition using morphologically derived structured trees. Our model was validated by computing blood flow through a model of large arteries extending from the thoracic aorta to the profunda arteries. The computed flow was compared against measured flow in the infrarenal (IR) aorta at rest and during exercise. Phase contrast-magnetic resonance imaging (PC-MRI) data was collected from 11 healthy volunteers at rest and during steady exercise. For each subject, an allometrically-scaled geometry of the large vessels was created. This geometry extends from the thoracic aorta to the femoral arteries and includes the celiac, superior mesenteric, renal, inferior mesenteric, internal iliac and profunda arteries. During rest, flow was simulated using measured supraceliac (SC) flow at the inlet and a uniform set of impedance boundary conditions at the 11 outlets. To simulate exercise, boundary conditions were modified. Inflow data collected during steady exercise was specified at the inlet and the outlet boundaries were adjusted as follows. The geometry of the structured trees used to compute impedance was scaled to simulate the effective change in the cross-sectional area of resistance vessels and capillaries due to exercise. The resulting computed flow through the IR aorta was compared to measured flow. This method produces good results with a mean difference between paired data to be 1.1 ± 7 cm³ s^? 1 at rest and 4.0 ± 15 cm³ s^? 1 at exercise. While future work will improve on these results, this method provides groundwork with which to predict the flow distributions in a network due to physiologic regulation.     

Pulsatile flow of non-Newtonian fluid in distensible models of human arteries

In addition to biochemical factors, hydromechanical influences are responsible for atherogenesis and deposits of blood platelets at bends and bifurcations of human arteries. Hence the flow patterns were simulated in a true-to-scale three-dimensional bifurcation of a human renal artery model and of an arterial femoralis with Newtonian and non-Newtonian blood like fluid. Investigations were made with steady and pulsatile flow. The velocity profiles (at physiological Re-numbers) were measured after the bifurcations with a laser-Doppler-anemometer. In previous works Newtonian fluids were used to investigate the flow in bends and bifurcations of rigid and elastic simplified models. In this paper, emphasis is placed on the difference between rigid and elastic models and also Newtonian and non Newtonian flow behavior. Differences between Newtonian and non Newtonian fluids may especially be expected to occur after branches where the flow has local strong convective elements such as in reverse zones and flow separation points.     

Recirculation zone length in renal artery is affected by flow spirality and renal-to-aorta flow ratio

Haemodynamic perturbations such as flow recirculation zones play a key role in progression and development of renal artery stenosis, which typically originate at the aorta-renal bifurcation. The spiral nature of aortic blood flow, division of aortic blood flow in renal artery as well as the exercise conditions have been shown to alter the haemodynamics in both positive and negative ways. This study focuses on the combinative effects of spiral component of blood flow, renal-to-aorta flow ratio and the exercise conditions on the size and distribution of recirculation zones in renal branches using computational fluid dynamics technique. Our findings show that the recirculation length was longest when the renal-to-aorta flow ratio was smallest. Spiral flow and exercise conditions were found to be effective in reducing the recirculation length in particular in small renal-to-aorta flow ratios. These results support the hypothesis that in renal arteries with small flow ratios where a stenosis is already developed an artificially induced spiral flow within the aorta may decelerate the progression of stenosis and thereby help preserve kidney function.     

Visualization and finite element analysis of pulsatile flow in models of the abdominal aortic aneurysm

Pulsatile flows in glass models simulating fusiform and lateral saccular aneurysms were investigated by a flow visualization method. When resting fluid starts to flow, the initial fluid motion is practically irrotational. After a short period of time, the flow began to separate from the proximal wall of the aneurysm. Then the separation bubble or vortex grew rapidly in size and filled the whole area of the aneurysm circumferentially. During this period of time, the center of the vortex moved from the proximal end to the distal point of the aneurysm. The transient reversal flow, for instance, which may occur at the end of the ejection period, passed between the wall of the aneurysm and the centrally located vortex. When the rate and pulsatile frequency of flow were high, the vortex broke down into highly disturbed flow (or turbulence) at the distal portion of the aneurysm. The same effect was observed when the length of the aneurysm was increased. A reduction in pulsatile amplitude made the flow pattern close to that in steady flow. A finite element analysis was made to obtain velocity and pressure fields in pulsatile flow through a tube with an axisymmetric expansion. Calculations were performed with the pulsatile flows used in the visualization experiment in order to study the effects of change in the pulsatile wave form by keeping the time-mean Reynolds number and Womersley's parameter unchanged. Calculated instantaneous patterns of velocity field and stream lines agreed well with the experimental results. The appearance and disappearance of the vortex in the dilated portion and its development resulted in complex distributions of pressure and shear fields. Locally minimum and maximum values of wall shear stress occurred at points just upstream and downstream of the distal end of the expansion when the flow rate reached its peak.     

Steady flow visualization in a rigid canine aortic cast

Steady flow studies were conducted in a transparent canine aortic cast. The cast segment stretched from the aortic valve to beyond the renal arteries and included all major branches. Flow was visualized by analysis of dye streaklines. Flow rates for basal and exercising cardiovascular states were simulated. The Reynolds numbers in the ascending aorta for basal and exercising conditions were 900 and 1587 respectively. Aortic core flow was laminar in basal simulations. Disturbed flow commenced in the upper descending aorta with exercising flow rates. Separation zones existed along the inner curvature of the aortic arch and the proximal walls of the brachiocephalic, left subclavian, and coeliac arteries. Such zones may exist over a portion of the cardiac cycle. If either renal artery was occluded, then a vortex formed. This vortex is associated with high shear regions which correlate well with sites where sudanophilic lesions have been reported in cholesterol-fed nephrectomized rabbits.     

Vortex generation in pulsatile flow through arterial bifurcation models including the human carotid artery

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.     

Patterns of flow in the left coronary artery

The purpose of this investigation is to describe our preliminary observations of the overall pattern of flow in a mold of the left coronary artery of a pig. Flow in the coronary mold was visualized by the injection of dye into the sinus of Valsalva. Studies were performed during steady flow at rates of 100, 200, 300, 400, and 500 mL/min. Studies were also performed during pulsatile flow, using a pulse duplicator that simulated the magnitude and phasic pattern of coronary flow at rest and during reactive hyperemia. At conditions that simulated rest, mean coronary flow was adjusted to 121 mL/min of which 24 mL/min (20 percent) was systolic. During simulated reactive hyperemia, mean flow was 440 mL/min. Visualization of flow revealed the absence of disturbances of turbulence during both steady and pulsatile flow in the left anterior descending (LAD) and left circumflex (CIRC) coronary arteries throughout the entire range of flow studied. Prominent spiraling of flow occurred during steady and pulsatile flow. Spiraling of flow was not observed in the LAD at rest during pulsatile flow, but developed during simulated reactive hyperemia. Helical flows were observed in the CIRC both during simulated rest and reactive hyperemia. These observations suggest that helical flows may be characteristic features of flow in the left coronary artery; whereas turbulence may not be a feature of this flow field. Whether the spiraling of flow that we observed related to the spiral distribution of early atheroma reported by others, is undetermined.     

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.     

In vitro pulsatile flow velocity and shear stress measurements in the vicinity of mechanical mitral heart valve prostheses

A three beam laser Doppler anemometer system was used to study the flow fields created by various types of mitral heart valve prostheses under physiological pulsatile flow conditions. The prosthetic valves studied were: Beall caged disc valve, Bjork-Shiley tilting disc valve, Medtronic-Hall tilting disc valve and St. Jude bileaflet valve. The results indicate that all four prosthetic valve designs studied create very disturbed flow fields with elevated turbulent shear stresses and regions of flow separation and/or stagnation. The observed elevated turbulent shear stresses could cause sublethal and/or lethal damage to red cells and platelets. The regions of flow separation and/or stagnation, could lead to thrombus formation and/or tissue overgrowth on the valve structure, as observed on clinically recovered prosthetic valves.