The Effect of Mitral Valve on Left Ventricular Flow

Transcription

1 The Effect of Mitral Valve on Left Ventricular Flow Fortini S. 1, Querzoli G. 2, Cenedese A. 1, Marchetti M. 1 1: Department of Idraulica Trasporti e Strade - Sapienza University of Rome, Italy; stefania.fortini@uniroma1.it 2: Department of Ingegneria del Territorio - University of Cagliari, Italy Abstract Mechanical heart valves implanted in mitral position modify deeply the ventricular flow during the diastole. The changes include the modification of the vortical structures and the onset of turbulence, possibly affecting the energetic efficiency of the heart pump or causing damage to blood cells. The objective of this study is to describe the hemodynamics characteristics in the LV when the inflow is altered: we document the results obtained from time resolved velocity measurements in a flexible model ventricle by means of an image analysis technique, i.e. Feature Tracking. The laboratory is designed to be able to reproduce any arbitrarily assigned law of variation of the ventricular volume with time. In the present experiment, a physiologically shaped curve has been used. Firstly, a one-way, hydraulic valve has been inserted upstream of the mitral orifice in order to obtain a uniform velocity profile at the ventricular inlet. This condition is not so different from the inflow generated by the natural valve. Secondly a monoleaflet and a bileaflet valve has been inserted in the mitral orifice and compared with the former. For each inlet condition, two different cardiac outputs have been considered by changing the stroke volume. Vortex formation and interaction are two important physical phenomena that dominate the filling of the ventricle. They have been studied by comparing the vorticity maps. The possible consequences of the change in the structure of the diastolic flow on the hemolysis was analyzed by looking at the shear stresses and at the onset of turbulence, that was described in terms of turbulent kinetic energy and Reynolds stresses. 1. Introduction The complexity of the left ventricular flows in the human heart is further increased in the presence of a diseased condition, such as unhealthy or prosthetic heart valves. Replacement of defective heart valves with artificial prostheses is a safe and routine surgical procedure worldwide. Over the past three decades, many old heart valves have been discarded, redesigned, or re-evaluated with the emergence of new technology and increasing expertise. The choice of the type of the prosthesis (mechanical or biological) is left to the surgeon appreciation depending on the patient (Senthilnathan et al., 1999). The main problem associated with implantable valve prostheses is their compatibility with the surrounding natural environment; the medical development has started to show, during last years, an increasing interest in quantitative and systematic approaches in support to the diagnostic and therapeutic activities. According to Grigioni et al. (02), the replacement of natural heart valves by artificial mechanical heart valves (MHV) induces blood damage and sthenosis, of a degree mainly depending on the design of the valves. It is also widely agreed that the damage to the blood depends on the high level of turbulence and strong velocity gradients and it is reported that the mechanical hemolysis has the shear stress threshold in the range [Pa] (Lee et al., 03; Grigioni et al., 1999). So, there is a continual obligation to better understand the mechanical behavior of MHVs, to study the effects and presence of thrombosis, hemolysis, cavitation, transvalvular pressure fluctuations, high levels of shear stress and certainly the association and interaction of all these conditions. Laboratory investigations can help assessing the origin of the anomalies observed in vivo by addressing the ventricular flow dynamics induced by a particular artificial valve. They are often - 1 -

2 schematic in the reproduction of the geometry and of the mechanical characteristics of the cardiac apparatus, but, on the other hand, the flow can be investigated in detail, using techniques that are not feasible in vivo (Chew et al., 01). Most in vitro studies of the flow downstream of MHVs have been conducted with the valve in the aortic position (Chandran et al. (1985), Reul et al. (1981), Yoganathan et al. (1986), Hasenkam et al. (1988), Lim et al. (1998)). Lim et al. (1998) used particle image velocimetry (PIV) in the investigation of flow past artificial heart valves (using a rigid aortic root). However, their work was limited to rigid models. Bluestein et al. (00) used a numerical simulation and digital particle image velocimetry (DPIV) to reveal intricate patterns of interacting shed vortices downstream of the aortic valve and demonstrated that blood elements exposed to the high shear stresses in the immediate proximity of the MHV could be trapped within these vortices and lead to emboli formation. In vitro experimental studies of the flow downstream of a MHV in the mitral position are fewer and more complicated due to the dynamically changing LV geometry. A number of laboratory models of the left heart have been developed in the last few decades. Some of them reproduce only the flow though an orifice, without a ventricle (Kini et al. (01), while others simplified the problem by employing rigid models of ventricles (Woo et al. (1986), Schoephoerster et al. (1993)). Garitey et al. (1995) employed a flexible ventricle model of the LV, and made extensive pressure measurements and used pulsed ultrasound Doppler Velocimetry to record one component of the velocity. They captured the activity of vortical structures in the ventricular chamber and compared the effects of three bileaflet valves and their orientation when mounted on their model. The complexity of the geometry combined with the pulsatile character of the flow, the interaction of the jets with the LV flexible walls and the unsteady motion of the leaflets generate intrinsically complicated turbulent flow structures. As a result, conventional, time averaged or point measurement methods, such as the ones employed in previous studies, would fail to reveal the underlying character of the flow demonstrating the need for global, time resolved measurement techniques. In this effort, time resolved Feature Tracking (FT) results in a flexible, transparent LV are presented and turbulence during a complete cardiovascular cycle is investigated. The aim of the present work is to compare the flows generated by three configurations of the mitral orifice in order to investigate how it affects the characteristics of the velocity field and, in particular, the onset of turbulence. In the first case a fuse valve was placed upstream enough to the inlet be completely open, generating a spatially uniform inflow, in the second and third series of experiments, a tilting disk and a bileaflet mechanical valve was placed in mitral position, respectively. The flow is described in terms of instantaneous maps of quantities describing both properties of the phase averaged field and of the turbulent fluctuations - computed as the deviations from the phased average over 100 heart-cycles. The shear strain rate and the turbulent shear stresses are represented in a form that is not depending on the orientation of the reference frame on the measuring plane (Grigioni et al., 1999). Finally, the time evolution of integral quantities, obtained from the time resolved velocity measurements, are used to describe globally the vortex dynamics, the shear rate, and turbulence in the different test conditions. 2. Methods and materials The ventricular flow was simulated by means of the laboratory model shown in figure 1. The model left-ventricle was a conical sack made of silicone rubber in order to be at the same time flexible and transparent. The sack was secured on a circular plate, 56 mm in diameter, connected by means of two Plexiglas conduits to a constant head reservoir. Along the outlet (aortic) conduit a one-way valve was mounted, whereas the valve placed on the inlet (mitralic) conduit, was changed during the experiments. In the first series of runs, the inlet was set-up to obtain a nearly uniform velocity profile at the mitral orifice. To this aim, the function of the mitral valve was performed by - 2 -

3 a one-way valve, placed upstreams along the inlet conduit. During the other series of runs the check valve was removed and mono- or bi-leaflet prosthetic valves were placed at the mitral orifice, namely a Bjork-Shiley Monostrut and a Bicarbon, both 27 mm in nominal diameter. I H C L F D A E B Figure 1. Experimental model. A: Ventricle chamber; B: Laser; C: Mirror; D: Compliance; E: motor; F: pressure transducer; G: position transducer; H: fast camera; I: Tank; L: Head losses The circulatory system was reproduced globally by two adjustable head losses (L) and a compliance chamber (D) inserted along the conduits. The compliance chamber was made of a sealed Plexiglas cylinder, partially filled with air, and connected to the aortic conduit by means of a T-joint. A rectangular tank (A) with transparent, Plexiglas walls housed the left-ventricular model. The volume of the ventricle was changed by moving the piston (F), placed on the side of the tank. The piston was driven by a linear motor (E), controlled by a personal computer. A physiologicallyshaped law of variation of the ventricular volume was used during the tests. In figure 2, its time derivative, i.e. the flow-rate, q, is plotted as a function of time. The flow rate is nondimensionalised by means of the period of the cardiac cycle, T, and the stroke volume SV. q(t) represents the flow rate through the mitral during the diastole (0.00T 0.75T), and through the aortic valve during the systole (0.75T 1.00T). G 1 V Q(t) Diastole Systole T/t Figure 2. Time law of variation of ventricular volume (black line) and flow-rate: (blue line) The vertical mid-plane of the ventricular cavity was illuminated by a 12 W, infrared laser. The working fluid inside the ventricle (distilled water) was seeded with neutrally buoyant particles. The - 3 -

4 average particle diameter was 30 µ m. A high-speed digital camera (250 frames/s, 480x4 pixel resolution) was synchronized with the motor to capture the time evolution of the phenomenon at known instants of the cycle. The acquired images were analyzed to measure the velocity fields on a regular grid (51x51 knots) by means of a Feature Tracking algorithm (Cenedese et al., 05). The spatio-temporal resolution was high enough to identify the vortical structures generated in the left ventricle and to follow their evolution during the whole cardiac cycle. The geometric aspect-ratio was 1:1, whereas the duration of the cycle, T, was adjusted in order to keep the Womersley number: Wo = T ν and the Reynolds number: U D Re = ν in the physiological range. In the above definitions D indicates the maximum diameter of the ventricle, ν the kinematic viscosity and U the peak average velocity through the mitral orifice. Aiming to characterise the influence of the variation of stroke volume on the flow structure, for each inflow condition, two series runs have been done, varying the stroke volume from 64 ml to 80 ml, the period T =6 s being fixed. Each series consisted of 100 runs that have been used to compute the phased averages and the statistics of the fluctuations around these averages. The main experiments parameters are listed in table 1. 2 D SV [ml] T [s] U [m/s] Re Wo Results Table 1. Main parameters describing the experiments Average flow Streamlines Changing the mitral valve influences both the velocity distribution and the initial direction of the fluid entering the ventricle during the diastole. These variations in the inflow affect, in turn, the nature of the coherent structures which are generated during the E-wave and the way in which they interact with fluid entering during the succeeding A-wave. Figure 3 shows the streamlines of the phase averaged velocity fields with stroke volume SV = 64 ml, and period T = 6 s. For each inflow condition, two salient instants of the diastole have been chosen: the end of the E-wave (t/t = 0.7) and the end of the diastasis (t/t = 0.573). In the first column of figure 3, the flow generated in absence of any obstacle at the mitral orifice is shown. That configuration is a rough approximation of the physiological condition and the starting jet entering the ventricle at the beginning of the diastole generates a vortex ring. The vortex ring is generated during the E-wave as is clearly shown by the streamlines plotted at t/t = 0.7. During its propagation through the ventricle, the part of the vortex ring that is closer to the wall (the right vortex in the plot) tends to move slower and to dissipate its energy due to the viscous interaction with the ventricular wall. At the same time, the opposite part of the vortex, can move and increase its size without obstacles. Therefore, at the end of the diastasis, it takes up all the ventricle and its centre is in the apical region (lower plot). The A-wave does not break the coherence of the vortex. Conversely it tends to increase the vortex strength as the new - lateral - injection of fluid, is - 4 -

5 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics deflected toward the posterior ventricular wall (right side of the plot) and contributes to increase the momentum of the vortical fluid t/t: 0.7 t/t: 0.7 t/t: t/t: t/t: t/t: Figure 3. Streamlines at two instants of the cycle in case of SV = 64 ml, and period T = 6 s. The first column corresponds to uniform inflow, the second to the tilting-disk valve, and the third to the bileaflet valve. The scenario is completely different when a tilting-disk valve is inserted in mitral position (Second column of figure 3). During the E-wave, the tilted disk of the valve parts the inflow in two jets: a main jet with a leading vortex ring, directed towards the anterior wall, and a secondary jet on the posterior side of the ventricle. At the end of the E-wave (t/t = 0.7), three vortex are clearly recognizable on the measurement plane: the two traces of the vortex ring leading the main jet, and only one vortex on the posterior side of the secondary jet. In this case, the main vortex ring has already reached the opposite wall, meaning a higher propagation velocity compared with the case of the uniform inflow. During the diastasis the two vortices of the main jet tend to separate, moving along the ventricular walls, whereas the third vortex dissipates because of the interaction with the ventricular wall. At the same time, the vortex on the left side of the plot increases in size. At the end of the diastasis (t/t = 0.573), the flow is dominated two vortices: one just below the mitral valve and the other on the opposite wall, closer to the apex. An intermediate situation is shown by the plots representing the flow generated by the bileaflet valve (third column of figure 3): during the E-wave, the inflow is divided into three jets moving straight downwards. On average, they produce a single, wide, stream moving downwards below the mitral and a large, clockwise, vortex located below the aortic valve (upper plot). During the diastasis the vortex increases in size and its core moves to the centre of the ventricle. Therefore, at the end of the diastasis the streamline pattern is basically similar to the one observed in case of uniform inflow (first column of figure 3) Vorticity map The description of time evolution of the phenomenon with uniform inflow, at 64ml stroke volume and 6 s period, is shown in Figure 4, where phase averaged on 100 cycles of velocity and vorticity fields are plotted. The nine most meaningful stages were chosen, and each figure reports nondimensional time with respect to cycle period and, at bottom left, the flow-rate plot with a red dot indicating the current instant. At t/t = 0.174, corresponding to the E-wave peak, the vorticity layer at the jet edges has begun to roll itself up to create a vortex ring which moves through the ventricle main axis. Two peaks are observed in the vorticity map (A, B) and the measured vorticity reaches at that point of the cycle its -5-

6 maximum value. At t/t = 0.2 the vortex B begins to interact with the ventricle wall; the non-slip condition determines a negative vortex layer at the wall, which tends to slow down the vortex B in its downward motion, and to increase the dissipating effects due to high velocity gradients. At the end of E-wave (t/t = 0.237), the vortex ring separates from the vorticity layer generated by the trailing jet (the so called pinch-off). Vortex B, which is slower, covered a shorter distance, while vortex A has now propagated to the centre of the ventricle, becoming sensitively larger than vortex B. At t/t = 0.307, vortex A reaches the bottom wall of the ventricle in proximity of the ventricle apex, its dimension being still increased; even vortex B has reached the wall and begins to go back upwards, while its dimensions tend to diminish. Instant t/t = corresponds to the center of the diastasis, that is the time interval during which the ventricle volume remains constant. At this stage the structures, being generated during the first diastolic peak, almost completely vanish; both velocity and vorticity do not have meaningful features except for the presence of vortex A, extremely weak, which remains in proximity of the ventricle apex. At last, during the systolic peak (t/t=0.867), any flow structure is destroyed and an exit flow is generated; there is still a partial memory of diastolic flow and in fact it is possible to recognize a main circulation upwards along the walls and to the aortic valve. Figure 4. Velocity (black arrows) and vorticity (scale of colour) field in the case of 64 ml stroke volume and simulation period of 6 s, in presence of the uniform mitral inflow. In Figure 5, the temporal evolution of the flow in presence, tilting-disk, cardiac valve is shown for comparison. The stroke volume is 64 ml and the simulation period is 6 s as above. During the accelerated ejection (t/t=0.117), at the beginning of the E-wave, only the jet generated by the main orifice is developed. Only at (t/t = 0.174), two jets are generated on the two sides of the tilting disk as is clearly visible by the four peaks in the vorticity map (A, B, C and D): the left jet (vorticity peaks A and B) is the strongest, both because it comes from the largest portion of the inlet and because it is deflected by the curvature of the disk. At t/t = 0.4 peaks A and B reach the bottom wall of the ventricle; the vortex C is slowed down by the presence of the wall. The plot at t/t = shows the vorticity field at the end of the E-wave; the velocity field mainly consists of two rotating structures, one on the left, with negative vorticity, and one on the right. At that stage, the vortices are wider but less intense than before. At the second diastolic peak (A-wave) originating from the contraction of the atrium, a similar, but less intense, phenomenon is observed At the A-peak, t/t=0.687, though the inlet velocity is a relative maximum, the two vortex rings had not yet time to develop completely. At the systolic peak (t/t=0.867), only an exit flow is recognizable as the vortical structures generated during the diastole are almost completely vanished

7 Figure 5. Velocity field (black arrows) and vorticity (scale of colour) in the case of 64 ml stroke volume and simulation period of 6 s in presence of the mono-leaflet valve in mitral position. Finally, in Figure 6 the temporal evolution of the flow in presence of a bileaflet, cardiac valve is shown for the last comparison. As clearly shown by the plot at t/t = 0.127, the valve opening and the consequent leaflets movements generates a first vortex ring (peaks A end B in the vorticity map). The vortex ring is followed by three jets (C, D, E) which begin to develop as soon as the valve has completely opened. The two lateral jets develop slightly earlier than the central one. At the first diastolic peak (t/t = 0.174) the two side jets generated vortex structures move downwards, while the central one gets weaker and weaker in vorticity. At t/t = the vortex E reaches the side-wall of the ventricle in proximity of the apex, changes its shape lengthening in the direction parallel to the wall and its maximum vorticity diminishes. Figure 6. Velocity field (black arrows) and vorticity (scale of colour) in the case of 64 ml stroke volume and simulation period of 6 s in presence of the bileaflet valve in mitral position. Oppositely to the flow examined in Figure 5, the pinch-off does not take place. At t/t = only the vortex E can be still individuated, It is in proximity of the wall assuming again a round shape. At t/t = takes place the second diastolic peak: the developing of three jets (F, G, H) with six vortex stripes moving towards the center of the ventricle are similar to the previous one but less intense. Again, during the systolic peak (t/t=0.867), any flow structure is destroyed and an exit flow is generated. Figures 7 and 8 below exhibit the time history of the total circulation, Γ, computed by integration of the component of the vorticity orthogonal to the measurement plane over the whole interrogation area. It is remarkable that monoleaflet valve and uniform inflow give the same peak circulation at - 7 -

8 the E-wave, both at 64 ml and 80 ml stroke volume, whereas the bileaflet valve yields a lower peak value. The reason seems to be that in the firsts two cases the flow is characterised by large vortical structures that propagate, with moderate dissipation, through the ventricle. Comparing figure 7 and 8 it is apparent that the peak circulation is proportional to the stroke volume. The bileaflet valve, instead, generates three parallel jets with small, highly dissipative structures between them that cannot be assimilated to vortex rings Γ sv 64 ml uniform flow Γ sv 64 ml bileaflet Γ sv 64 ml monoleaflet Γ sv 80 ml uniform flow Γ sv 80 ml monoleaflet Γ sv 80 ml bileaflet t/t t/t Figure 7. Total circulation for all configurations at stroke volume 64 ml. Figure 8. Total circulation for all configurations at stroke volume 80 ml Viscous shear stresses It was reported in literature that the quantities more likely related to blood cells damages are the viscous shear stresses. The continuous damaging of the red cells (hemolysis) requires al long term therapy based on anticoagulant. The expression used for the evaluation of the maximum shear stress, ν max, at a given location is (Grigioni et al., (02): τ = ( τ τ ) / 2 = µ ( e e ) max taking unto account only the in plane velocity field. The phase-averaged maximum shear stress was calculated and made dimensionless by means of the scale ρ U 2 in the six investigated conditions. In Figure 9, these values are shown during three significant points of the cycle with the same period and stroke volume as above. In the three upper plot (a.1, a.2 and a.3), referred to the uniform inflow, the higher shear stresses are located at the jet lateral boundaries, along the vortical layer linking the mitralic orifice boundaries to the vortex ring (plots a.1 and a.2). The peak corresponding to the mitralic orifice is due to noise in the velocity measurement. At t/t = 0.177, a high value zone begins to develop around the vortex ring itself and at t/t=0.234 (a.3), shear stresses high values surround the vortical ring. A low stress line joining the two vorticity peaks is observed. That line persists during the whole evolution of the vortex ring, until its interaction with the ventricular boundary. Shear stresses significant values are measured at the same instant for the tests effectuated with the tilting-disk and bileaflet valves, as shown in the three plots b.1, b.2, b.3 and c.1, c.2, c.3. The flow generated by the tilting-disk valve is characterized by remarkably high values of the shear stresses during the early diastolic peak. These high values are located at the boundaries of the main jet. After the jet impacts the opposite ventricular wall, a significant shear layer is generated also at the ventricular wall. The presence of the bileaflet valve determines a complex texture of high shear streaks, due to the development of three, parallel jets

9 Figure 9. Maximum viscous stresses during the series at stroke volume 64 ml and simulation period T=6 s with uniform inflow (up), monoleaflet valve (centre) and bileaflet valve (down). In order to compare the overall shear level during the whole cycle in the different conditions, the maximum shear stress presented above was averaged over the investigated area of the ventricle. Results are non-dimensionally plotted in figure 10. The highest values are given by the series with stroke volume 80 ml and using the tilting-disk valve. The values measured for this case are globally higher than those with bileaflet valve at least of 10.5% and than those with the hydraulic valve of 88%. Even with stroke volume 64 ml the highest values are found using the tilting-disk valve, and they are higher than those with uniform inflow also at the higher stroke volume, exceeding the case with bileaflet valve at the same stroke volume of 16.8% and than those with the hydraulic valve of 105% Turbulence Figure 10. Comparison among the viscous shear stresses during the different cycles. The flow is characterized by a strong variability in time, with remarkably high velocities during the cardiac cycle. So, it is important to determine if and when turbulent characteristics arise. Using the - 9 -

10 same formulation as above, but with the Reynolds stress tensor, the maximum turbulent shear stresses have been computed (Figure 11). In case of tilting-disk valve, high turbulent shear stresses are found during the E-wave in correspondence with the shear layer generated on the sides of the jets. At t/t=0.190, while in the case of uniform inflow we observe a high value zone at the jet leading edge (A.1, A.2, A.3), in the case of the mono-leaflet valve, Reynolds stresses high values are located along the four stripes corresponding to the boundaries of the two jets (B.1, B.2, B.3) and along the six streaks due to the three jets in the case of the bileaflet valve (C.1, C.2, C.3). Figure 11. Maximum turbulent shear stresses during the series at stroke volume 64 ml and simulation period T=6 s uniform inflow (up), monoleaflet valve (centre) and bileaflet valve (down). Figure 12. Comparison among the turbulent shear stresses. Comparing the values averaged over the interrogation region for the six different conditions (Figure 12), it is apparent that the non-dimensional Reynolds shear stresses are more influenced by the valve model, rather than by the stroke volume. In fact, the curves corresponding the same valve are very similar whatever the stroke volume. This fact confirms that the turbulent stresses are well scaled by the squared peak velocity. As expected, higher values are associated to the tilting-disk

11 valve, whereas the lower ones are given by the uniform inflow. The analysis of the fraction of the turbulent kinetic energy (TKE) that can be calculated on the basis of the two measured velocity components, and normalised by the velocity scale U: ( u ' ) 2 + v ' 2 Et = 2 U is shown in Figure 13 for the test with stroke volume 64 ml and period T = 6 s. Figure 13. TKE during the series at stroke volume 64 ml and simulation period T=6 s with uniform inflow (up), tilting-disk valve (centre) and bileaflet valve (down). The first two plots, corresponding to the uniform inflow, show high turbulence levels at the center of the vortices and at the leading edge of the jet. These are zones of high velocity gradients, where a small oscillation of the coherent structures causes high velocity fluctuations. As a consequence, as confirmed by visual inspection of the time series, those values cannot be related to presence real turbulence. The diffuse zone of relatively high levels, observed in the third plot, corresponds to the instabilization of the vortical structures occurring after the impact with the ventricular wall. The two flows generated by MHVs, exhibit zones of turbulence at the boundaries of the jets, possibly generated by the Kelvin-Helmholtz instabilities. Also in those cases, a diffuse zone of relatively high turbulence kinetic energy is observed after the impact on the ventricular wall. 4. Conclusions An experimental model of a ventricle allowed a detailed analysis of the cardiac flow during the entire cycle, and the analysis of the consequence of the variation of the transmitral flow. An image analysis technique, i.e. Feature Tracking, was employed to measure time resolved velocity fields. The phase-averaged velocity and vorticity fields were analyzed in order to investigate the evolution of the vortical structures. Different experiments were developed changing the stroke volume and the inflow: uniform inflow conditions, tilting-disk and bileaflet valves in mitral position were used. The

12 effects on velocity and vorticity and the onset of turbulence were investigated. In particular, both for uniform inflow and tilting-disk valve, large vortical structures are observed to propagate through the ventricle, whereas in the case of the bileaflet valve a three jets structure, characterized by four vorticity streaks dominates the flow during the diastolic peaks. During their evolution, the vortical structures assume a complex three-dimensional shape because of their interaction with the ventricle boundaries. In all cases, after the impact of the jet(s) on the ventricular wall, the flow reorganises in a single, large vortex in the proximity of the apical region. The analysis of the non-dimensional viscous stresses and measured turbulent kinetic energy shows that the first ones are influenced both by the stroke volume and by the inflow, whereas the turbulence characteristics seems to be quite insensitive to the variation of the stroke volume, indicating that it is well scaled by the squared peak velocity. Finally, the peak values of the circulation attain more or less the same values for the tilting-disk and uniform inflow case, and these values are proportional to the stroke volume, whereas the different flow structure generated by the bileaflet valve yields lower values since no large vortical structure have the possibility to develop. References Senthilnathan V., Treasure T., Grunkemeier G., Starr A., (1999) Heart Valve: which is the best choice? Cardiovascular Surgery, 7 (4), pp Grigioni M., Daniele C., D Avenio V., Barbaro V., (02) Evaluation of the surface-averaged load exerted on a blood element by the Reynolds shear stress field provided by artificial cardiovascular devices J. Biomechanics, 35, pp Chew Y. T., Chew T. C., Low H. T., Lim W. L., (01) Techniques of determination of the flow effectiveness of heart valve prostheses CRC Press, Boca Raton, Florida. Kini V., Bachmann C., Fontaine A., Deutsh S., Tarbell J.M., (01) Integrating particle image velocimetry and laser Doppler velocimetry measurements of the regurgitant flow field past mechanical heart valves Artif. Organs, 25(2), pp Chandran K. B., Khaloghi B., and Chen C. J., (1985) Experimental Study of Physiological Pulsatile Flow Past Valve Prostheses in a Model of Human Aorta: I. Caged Ball Valves J. Biomechanics, 18 (10), pp Reul, H., Talukder, N. and Müller, E. W., 1981, Fluid Mechanics of the Natural Mitral Valve'' J. Biomechanics, 14 (5), pp Yoganathan, A. P., Woo, Y., and Sung, H., (1986) Turbulent Shear Stress Measurements in the Vicinity of Aortic Heart Valve Prostheses J. Biomechanics, 19(6), pp Hasenkam JM, Westphal D., Wygaard H., Reul H., Giersiepen M., Stodkilde-Jorgensen H., In vitro stress measurements in the vicinity of six mechanical aortic valves using hot-film anemometry in steady flow J. Biomechanics, 21 (3), pp Lim W. L., Chew Y. T., Chew T. C. and Low H. T., (1998) Steady flow dynamics of prosthetic aortic heart valves: a comparative evaluation with PIV techniques J. Biomechanics, 31, pp Woo Y. and Yoganathan, A. P., (1986) In vitro Pulsatile Flow Velocity and Shear Stress Measurements in the Vicinity of Mechanical Mitral Heart Valve Prostheses J. Biomechanics, 19 (6), pp Schoephoerster, R. T., Oynes, F., Numez, H., Kapadvanjwala, M., and Dewanjee, M. K., (1993) Effects of Local Geometry and Fluid Dynamics on Regional Platelet Deposition on Artificial Surfaces, Arterioscler. Thromb., 12, pp Garitey, V., Gandelheid, T., Fusezi, J., Pelissier, R., and Rieu, R., (1995) Ventricular Flow Dynamic Past Bileaflet Prosthetic Heart Valves Int. J. Artificial Organs, 18 (7), pp Bluestein, D., Rambod, E., and Gharib, M., (00) Vortex Shedding as a Mechanism for Free Emboli Formation in Mechanical Heart Valves J. Biomech. Eng., 122, pp Grigioni M., Daniele C., D Avenio V., Barbaro V., (1999) A discussion on the threshold limit for hemolysis related to Reynolds shear stress J. Biomechanics, 32, pp Cenedese A., Del Prete Z., Miozzi M., Querzoli G., (05) A laboratory investigation of the flow in the left ventricle of a human heart with prosthetic, tilting-disk valves Experiments in Fluids, 39. pp Lee S. S., Kim N., Lee Sa., Sun K., Goedhart P. T., Hardeman M. R., Ahn K. H., Lee S. J., (03) Shear induced preconditioning effect of red blood cell damage Summer Bioengineering Conference, Sonesta Beach Resort in Key Biscayne, Florida. Grigioni M., Daniele C., D Avenio V., Barbaro V., (1999) A discussion on the threshold limit for hemolysis related to Reynolds shear stress J. Biomechanics, 32, pp