Design of a fourth generation prosthetic heart valve: tri-leaflet valve

Transcription

1 Design of a fourth generation prosthetic heart valve: tri-leaflet valve Esquivel C., Rosenberger M., Gueijman S., Schvezov C., Amerio O. Fac. de Cs. Ex., Qcas y Nat., Universida Nacional de Misiones, Argentina; Sanatorio Integral (IOT), Posadas, Misiones, Argentina. ASBTRACT Introduction: The interest in developing a prosthetic heart tri-laeflet valve is based on the durability of mechanical prosthesis; the good hemodynamic performance of bio-prosthesis due to the central flow, its perfect closure, the negligible thrombogenic index, and the negligible perception of its presence by the user. Objectives: Develop a mathematical model of a fourth generation prosthetic heart valve or tri-leaflet valve. Obtain an optimal design through numerical modeling using computational fluid dynamics. Modeling procedure: Tri- and Bi-leaflet valves were designed schematically. Each model valve was situated in the center of a cylindrical tube. The fluid was assumed to be incompressible, newtonian, isothermal and stationary. Meshing and Finite Element modeling was performed using Gambit (R) 1.2 and Fidap (R) 8.5 from Fluent Inc. The model was validated mathematically comparing our results with the results available in the literature for bi-leaflet prosthesis. Results: The flow in the tri-leaflet valve is mainly central, with an 86% to 95% of the total flow. The effective surface area for flow is 67.4% of the total section, 32.6% of the surface area is obstructed by pivot system (11%) and the leaves (21.6%). The shear stresses are lower than the values reported as lower limit for hemolysis by foreign bodies. Discussion: The amount of central flow in the tri-leaflet valve is high, similar to the center flow in natural valves and much higher than in a bi-leaflet valve. The design based in peripheral pivots gives good aperture characteristics that avoid the immobilization of the leaves by invasive tissue. The flow under maximum aperture is affected mainly by the pivot systems and the curvature of the leaves. Conclusions: Modeling results of a tri-leaflet valve indicate the presence of a high amount of central flow. The design may be improved by modeling modifying the pivot systems and the curvature of the leaves. INTRODUCTION The interest in developing a prosthetic heart tri-laeflet valve is based on the durability of mechanical prosthesis; the good hemodynamic performance of bio-prosthesis due to the central flow, its perfect closure, the negligible thrombogenic index, and the negligible perception of its presence by the user. OBJECTIVES Develop a mathematical model of a fourth generation prosthetic heart valve or tri-leaflet valve. Obtain an optimal design through numerical modeling using computational fluid dynamics. MODELING PROCEDURE Two mathematical models based in 3-D computational fluid dynamics were developed; one of a tri-leaflet valve and another of a typical flat bi-leaflet valve with a maximum aperture of 85º. In both cases the models were axis-symmetric following the real physical symmetry. This assumption permitted to take into account in the model, only a sixth and a fourth of the cylindrical section for the tri- and bi-leaflet valves respectively. In such way the number of elements and calculation efforts were significantly reduced. The blood was assumed to be a Newtonian fluid and incompressible, isothermal and in a steady state of flow. For solving the reduced Navier-Stokes equations a finite element method was used and the domain was discretized using isoparametric hexahedric elements. Figure 1.a shows a schematic array of the tri-leaflet valve model and figure 1.c indicates the sixth-part of the valve, which was actually modeled. In the figure it is observed that the valve was located in a cylindrical tube with rigid walls. This configuration permitted to analyze the flow in any perpendicular section before and after the blood passes the valve [1,2].

2 Figure 1: Schematic of the tri-leaflet valve model. (a) position with respect to the blood flow; (b) view of the whole leaves in three different positions: closed, partially open and at the maximum opening; (c) Section of the valve considered in the model. The blood as a fluid was characterized employing the typical Reynolds number (Re), which was calculated as it is shown in Table I. List of equations and parameters used for modeling. The physical parameters used to simulate the blood flow were the viscosity, density, flow rate which were assigned to have the following values Pa.s, 1.050g/cm 3 and 5,000cm 3 /min respectively, these values are the average flow for an adult under normal conditions. The internal diameter of the tube was 27mm [3,4]. For these values the corresponding Re has a value of In order to analyze the valve behavior, the models were run for Re in the range of 100 to The discretization of the model domain was done using Gambit 1.2 (R). The finite element models were developed using Fidap 8.5 (R). The model results were mathematically validated comparing the results obtained with the present model for the bi-leaflet valve and those reported in the literature for the same valve [1,2].

3 RESULTS The results show two very different flow patterns between the bi- and tri-leaflet valves. Both flows can be observed in figures 3 and 4 for the bi- and tri-leaflet valves respectively. The opening for the bi-leaflet valve is 85º and for the tri-leaflet valve is 65 º. In both cases the flow patterns correspond to cross sections at 2mm from the valve plates. In both cases the Re number is The main characteristic of each flow are as follows. In the case of the bi-leaflet valve the flow occurs mainly through two parallel and lateral channels (79.3%) with a narrow central section responsible of 20.7% of the flow. The flow has a perfect two-folds symmetry, as expected. Figure 2: Percentage of central flow with respect to the total flow as a function on Re number for the tri- an bileaflet valve designs. Figure 3: Flow velocities in a cross section located at a distance 1/10 of the valve diameter away from the bileaflet valve exit. Re = 1000 the largest velocity is 2.25 m/s.

4 Figure 4: Flow velocities in a cross section located at a distance 1/10 of the valve diameter away from the trileaflet valve exit. Re = 1000 the largest velocity is 2.64 m/s. In the case of the tri-leaflet valve shown in figure 4 it is observed that the flow occurs through three symmetric areas near the valve periphery which are located between each leaflet and the valve ring. The central flow has a three-fold symmetry and occupies a wide area of the valve. In addition, it is noted that there is little velocity gradient in the radial direction as it can be inferred by the same color in the figure. Another related aspect which is different for both, is the free surface area for flow which is taken as the objectfree projection in the axial direction. In the case of the bi-leaflet valve the free surface area is 78.6% whereas in the tri-leaflet valve is lower, at 67.4%, the 32.6% surface area is obstruction, and accounts for the proper leaves (21.6%) and the pivot (11%). In some areas of any valve there are regions where the shear stress can reach high values, enough to produce platelet aggregations in presence of foreign bodies [5]. The critical shear stress limit tc as reported by Brown et al. [5] is about 5 N/m 2. This critical value is compared with the shear stress for the bi- and tri-leaflet valves in figure 5 and 6 respectively. In the figures the abscise corresponds at the non-dimensional stress and the ordinate corresponds to the cumulative surface area fraction. It is observed, comparing figures 5 and 6, that for Re numbers from 100 to 2000 the shear stress behaves in similar way for both valves and they are below tc in more than 80% of the surface area.

5 Figure 5: Shear stress levels in the leaves and the ring valve for the bi-leaflet valve model as function of the cumulative surface area for different Re numbers. The non-dimensional critical stress is 240,000. Figure 6: Shear stress levels in the leaves and the ring valve for the tri-leaflet valve model as function of the cumulative surface area for different Re numbers. The non-dimensional critical stress is 240,000. DISCUSSION The main characteristics of the tri-leaflet valve presented in this report are that the three leaves when are completely open (65%) present a large central area for flow and therefor present a configuration with small resistance for blood flow. This large opening is the results of the location of the pivots which are the closest possible to the ring and the flow avoid the overgrow of natural tissue which way immobilize the leaves. The large central free region described above permits a flow which is more similar to the natural valve than

6 the bi-leaflet valve. The main advantage of the present design is not only this central flow but also the related fact that, as a result the velocity gradient in any radial direction is small compared to the bi-leaflet valve. In the case of the tri-leaflet valve, most of the central region has a high range of velocities between m/s as shown in figure 4, while in the bi-leaflet valve the main flow given by the highest velocity is dispersed in three regions, two regions symmetric to the leaves and one central region, as can be seen in figure 3, in all three cases the velocity gradient is high. In such case the effect of any local disturbance in the flow has a much larger impact than in the tri-leaflet valve design. Comparing the flows in the tri-leaflet valve Re = 1000 is 85.7% central whereas in the bi-leaflet valve 79.3% of the flow is lateral and 20.7% is central. Another characteristic of the tri-leaflet valve design which is noticed here, is the relatively large area taken for the pivot system, occupying 11% of the surface area, despite the fact that they do not present a high resistance to the blood flow, the present design can be improved by moving the pivot system closer to the valve ring and away from the center of the valve. In this way the surface area for central flow will be larger and the lateral flow smaller. In addition, the present design of the leaves are such that they represent a 21.6% of the whole valve surface area blocking the blood flow. This relative surface area can be reduced by reducing the curvature of the leaves; The limit is a flat leave configuration, which present a 12% surface area blocking blood flow. The resulting flow will be the determining fact for a right design. With respect to the shear stress it has been shown in figures 5 and 6 that the values for a Re=2000 are similar for both valve designs and that an 80% of the surface area of the tri-leaflet valve is subject to shear stresses less than 240,000. It is important to note that the shear stress value increases with the value of the Re number and in the actual blood flow there are instant velocities which are much larger than those used here. Finally, despite the simplifications of the model resulting from the assumptions, the results obtained here are useful for comparison purposes; however, it is important to note that the flow conditions are far from the nonsteady pulse flow in a real aortic o mitral cardiac valve. Those models will be necessary to developed in the future at a much higher cost in time and more powerful computers. CONCLUSION The conclusions of the present investigation can be summarized as follows: Steady state models of bi- and tri-leaflet valves have been developed following standard steady state equation for flow. The model results indicate that the tri-leaflet valve has a flow which is mainly central. The shear stress for both models are similar and mostly below the critical value reported by Brown et al [5]. The tri-leaflet valve design can be improved by modifying the pivot system and the curvature of the leaves. BIBLIOGRAPHY 1. Dubini, G.; Pietrabissa, R.; Fumero, R. - Computational fluid dynamics of artificial heart valves. Int. Jou. Artif. Org., vol 14, n 6 (1991) Kelly, S.G.D.; Verdonck, P.R.; Vierendeels, J.A.M.; Riemslagh, K.; Dick, E.; Van Nooten, G.G. A three-dimensional analysis of flow in the pivot regions of an ATS bileaflet valve. Int. Jou. Artif. Org., vol 22, n 11 (1999) Selkurt, E.; "Fisiologia", Editorial El Ateneo. Buenos Aires King, M.J.; David, T.; Fisher, J. An initial parametric study on fluid flow through bileaflet mechanical heart valves using computational fluid dynamics. - Jou. Engineering in Medicine, vol 208, part. H (1994) Brown, C.H. 3d.; Leverett, L.B.; Lewis, C.W.; Alfrey, C.P. Jr., Hellums, J.D. - Morphological, biochemical, and functional changes in human platelets subjected to shear stress. J.Lab. Clin. Med., 86(3) (1975) Your questions, contributions and commentaries will be answered by the authors in the Medical Informatics list. Please fill in the form and press the "Send" button.

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