Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

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.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

Blood flow dynamics in saccular aneurysm models of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.     

The flow of power law fluids in elastic networks and porous media

The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.     

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.     

On the kinematics and efficiency of advective mixing during gastric digestion – A numerical analysis

The mixing performance of gastric contents during digestion is expected to have a major role on the rate and final bioavailability of nutrients within the body. The aim of this study was to characterize the ability of the human stomach to advect gastric contents with different rheological properties. The flow behavior of two Newtonian fluids (10⁻³ Pa s, 1 Pa s) and a pseudoplastic solution (K=0.223 Pa s^0.59) during gastric digestion were numerically characterized within a simplified 3D model of the stomach geometry and motility during the process (ANSYS-FLUENT). The advective performances of each of these gastric flows were determined by analyzing the spatial distribution and temporal history of their stretching abilities (Lagrangian analysis). Results illustrate the limited influence that large retropulsive and vortex structures have on the overall dynamics of gastric flows. Even within the distal region, more than 50% of the flow experienced velocity and shear values lower than 10% of their respective maximums. While chaotic, gastric advection was always relatively poor (with Lyapunov exponents an order of magnitude lower than those of a laminar stirred tank). Contrary to expectations, gastric rheology had only a minor role on the advective properties of the flow (particularly within the distal region). As viscosity increased above 1 St, the role of fluid viscosity became largely negligible. By characterizing the fluid dynamic and mixing conditions that develop during digestion, this work will inform the design of novel in vitro systems of enhanced biomechanical performance and facilitate a more accurate diagnosis of gastric digestion processes.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

Pulsatile flow in fusiform models of abdoiminal aortic aneurysms: flow fields, velocity patterns and flow-induced wall stresses

As one important step in the investigation of the mechanical factors that lead to rupture of abdominal aortic aneurysms, flow fields and flow-induced wall stress distributions have been investigated in model aneurysms under pulsatile flow conditions simulating the in vivo aorta at rest. Vortex pattern emergence and evolution were evaluated, and conditions for flow stability were delineated. Systolic flow was found to be forward-directed throughout the bulge in all the models, regardless of size. Vortices appeared in the bulge initially during deceleration from systole, then expanded during the retrograde flow phase. The complexity of the vortex field depended strongly on bulge diameter In every model, the maximum shear stress occurred at peak systole at the distal bulge end, with the greatest shear stress developing in a model corresponding to a 4.3 cm AAA in vivo. Although the smallest models exhibited stable flow throughout the cycle, flow in the larger models became increasingly unstable as bulge size increased, with strong amplification of instability in the distal half of the bulge. These data suggest that larger aneurysms in vivo may be subject to more frequent and intense turbulence than smaller aneurysms. Concomitantly, increased turbulence may contribute significantly to wall stress magnitude and thereby to risk of rupture.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Leukocytes rolling and recruitment by endothelial cells: hemorheological experiments and numerical simulations

The recruitment of leukocytes from the blood stream and their subsequent adhesion to endothelial walls are essential stages to the immune response system during inflammation. The precise dynamic mechanisms by which molecular mediators facilitate leukocyte arrests are still unknown. In this study combined experimental results and computer simulations are used to investigate localized hydrodynamics of individual and collective behavior of clusters of leukocytes. Leukocyte-endothelial cell interactions in post-capillary venules of Wistar rats cremaster muscle were monitored by intravital microscopy. From these experiments the hemorheologic and hemodynamical measured parameters were used in time dependent three-dimensional computer simulations, using a mesoscopic lattice Boltzmann flow solver for shear thinning fluids. The dynamics of leukocyte clusters under generalized Newtonian blood flow with shear thinning viscosity was computed and discussed. In this paper we present quantified distributions of velocity and shear stress on the surface of leukocytes and near vessel wall attachment points. We have observed one region of maximum shear stress and two regions of minimum shear stress on the surface of leukocytes close to the endothelial wall. We verified that the collective hydrodynamic behavior of the cluster of recruited leukocytes establishes a strong motive for additional leukocyte recruitment. It was found that the lattice Boltzmann solver used here is fully adaptive to the measured experimental parameters. This study suggests that the influence of the leukocytes rolling on the increase of the endothelial wall shear stress may support the activation of more signalling mediators during inflammation.     

Blood's critical Taylor number and its flow behavior at supercritical Taylor numbers

When the inner cylinder of a fluid-filled Couette viscometer is rotated rapidly, a vortical flow pattern develops when a dimensionless value referred to as the critical Taylor number (Tc) is reached. We have determined its magnitude in our viscometer for three Newtonian fluids and for blood at 37 degrees C, using the inflection point of torque/RPM vs. RPM (sudden rise in apparent viscosity). Its position was identified by least squares line fitting. Because blood was studied, the viscosity used in Tc calculation was the apparent bob shear stress/shear rate ratio at the inflection marking vortical flow onset. For glycerol-water mixtures Tc was 41.8 +/- 0.3 (N = 11), for propylene glycol 42.0 +/- 0.2 (N = 14), for silicone oil 41.8 +/- 0.2 (N = 11). For healthy blood Tc was 40.7 +/- 0.9 (N = 140). This evidence against blood's increased resistance to flow instability was accompanied by a slower rate of rise in torque both above and below Tc compared to the three Newtonian fluids. Newtonian fluids and blood both developed wavy vortical flow at a rotation rate moderately higher than Tc. Blood resisted this unstable flow behavior more than the Newtonian fluids but it also experienced a slower rate of rise in torque with increasing rotation rate above the critical Taylor number. Shear-thinning is the simplest explanation for blood's mildly altered Taylor vortex behavior; blood's resistance to flow instability is otherwise not found to be sufficient to affect its flow stability in man.     

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.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Non‐Newtonian rheology in suspension cell cultures significantly impacts bioreactor shear stress quantification

The fields of regenerative medicine and tissue engineering require large‐scale manufacturing of stem cells for both therapy and recombinant protein production, which is often achieved by culturing cells in stirred suspension bioreactors. The rheology of cell suspensions cultured in stirred suspension bioreactors is critical to cell growth and protein production, as elevated exposure to shear stress has been linked to changes in growth kinetics and genetic expression for many common cell types. Currently, little is understood on the rheology of cell suspensions cultured in stirred suspension bioreactors. In this study, we present the impact of three common cell culture parameters, serum content, cell presence, and culture age, on the rheology of a model cell line cultured in stirred suspension bioreactors. The results reveal that cultures containing cells, serum, or combinations thereof are highly shear thinning, whereas conditioned and unconditioned culture medium without serum are both Newtonian. Non‐Newtonian viscosity was modeled using a Sisko model, which provided insight on structural mechanisms driving the rheological behavior of these cell suspensions. A comparison of shear stress estimated by using Newtonian and Sisko relationships demonstrated that assuming Newtonian viscosity underpredicts both mean and maximum shear stress in stirred suspension bioreactors. Non‐Newtonian viscosity models reported maximum shear stresses exceeding those required to induce changes in genetic expression in common cell types, whereas Newtonian models did not. These findings indicate that traditional shear stress quantification of cell or serum suspensions is inadequate and that shear stress quantification methods based on non‐Newtonian viscosity must be developed to accurately quantify shear stress.     

Comparative study of Newtonian and non-Newtonian simulations of drug transport in a model drug-eluting stent

To elucidate the difference between Newtonian and shear thinning non-Newtonian assumptions of blood in the analysis of DES drug delivery, we numerically simulated the local flow pattern and the concentration distribution of the drug at the lumen-tissue interface for a structurally simplified DES deployed in a curved segment of an artery under pulsatile blood flow conditions. The numerical results showed that when compared with the Newtonian model, the Carreau (shear thinning) model could lead to some differences in the luminal surface drug concentration in certain areas along the outer wall of the curved vessel. In most areas of the vessel, however, there were no significant differences between the 2 models. Particularly, no significant difference between the two models was found in terms of the area-averaged luminal surface drug concentration. Therefore, we believe that the shear thinning property of blood may play little roles in DES drug delivery. Nevertheless, before we draw the conclusion that Newtonian assumption of blood can be used to replace its non-Newtonian one for the numerical simulation of drug transport in the DES implanted coronary artery, other more complex mechanical properties of blood such as its thixotropic behavior should be tested.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Dynamics of flow in a mechanical heart valve: the role of leaflet inertia and leaflet compliance

In this work, we examine the dynamics of fluid flow in a mechanical heart valve when the solid inertia and leaflet compliance are important. The fluid is incompressible and Newtonian, and the leaflet is an incompressible neo-Hookean material. In the case of an inertialess leaflet, we find that the maximum valve opening angle and the time that the valve remains closed increase as the shear modulus of the leaflet decreases. More importantly, the regurgitant volume decreases with decreasing shear modulus. When we examined the forces exerted on the leaflet, we found that the downward motion of the leaflet is initiated by a vertical force exerted on its right side and, later on, by a vertical force exerted on the top side of the leaflet. In the case of solid inertia, we find that the maximum valve opening angle and the regurgitant volume are larger than in the case of an inertialess leaflet. These results highlight the importance of solid compliance in the dynamics of blood flow in a mechanical heart valve. More importantly, they indicate that mechanical heart valves with compliant leaflets may have smaller regurgitant volumes and smaller shear stresses than the ones with rigid leaflets.