Elliptic st. jude bileaflet mechanical heart valves

St. Jude Medical (SJM) bileaflet mechanical valves were approved by the Food and Drug Administration in 1977. The SJM valve design consists of two semicircular leaflets which pivot on hinges. Compared to other mechanical heart valve prostheses such as ball and cage and tilting disk prosthetic valves, it provides good central flow, the leaflets open completely, and the pressure drop across the valve is trivial. However, non-physiological hemodynamics around these valves may lead to red blood cells lysis and therombigenic complications. Also, the regurgitation-flow inSJM valves is almost twice that of the native valves in the aortic position. In this study, we suggest a new design for the stent (housing) of SJM valves in which 15% ovality is applied to the stent whereas its perimeter remains constant. In a pilot study, the hemodynamic performance of the proposed design is analyzed in the closing phaseand compared to that of conventional SJM models. Results show that while the elliptic SJM model offers a shorter closing phase (9.7% shorter), the regurgitation flow remains almost unchanged. In other words, even though the dynamic response of the valve is improved, the regurgitation flow is not decreased. Thus, a more efficient effective orifice area (EOA) is shown to be provided by the proposed model. The preliminary calculations presented in this study justify an improved hemodynamics of elliptic SJM valves compared to conventional models; the proposed design shows promise and merits further development.


Introduction
Bileaflet mechanical heart valves (MHVs) are used extensively due to their great hemodynamic performance, as indicated by a uniform flow profile, free central flow and considerably higher level of durability. However, thrombogenicity is an issue with the bileaflet MHVs due to a non-physiological hemodynamics around the valve [1][2][3]. More than 300,000 replacement heart valves are implanted annually worldwide and mechanical heart valves are used to replace diseased human heart valves in approximately 50% of these interventions. In addition, two million patients receive St. Jude Medical (SJM) valves worldwide each year [4,5]. In our previous studies, we extensively assessed the hemodynamic performance of the SJM valve in the opening phase using computational fluid dynamics (CFD). Results suggested that SJM valves may be associated with thrombogenic complications around the hinges, on the leading edge of the leaflets and at the sinuses, possibly because of high blood shear stresses, turbulence, and the overall complexity of the hemodynamics in MHVs [6,7].
In this study, we propose a design modification on SJM valves. We hypothesize that 15% ovality on the housing while its perimeter remains constant may result in an improved hemodynamics around the SJM valves. In a pilot study, we study the hemodynamic performance of the proposed design to evaluate its regurgitation flow and its velocity and the leaflet tip velocity in the closing phase. We apply a quick but novel numerical model which is sufficiently accurate to estimate the overall performance of the new design. The numerical model uses the finite strips method to solve the equations of motion. The computations run on an Intel (R) Core (TM) i7-4500u CPU @1.80 GHz & 1.80 GHz processors with 16.0 Gb of RAM.

Methods
The SJM model considered in this study has an inner diameter of 25 mm as shown in Figures 1a and 1b. In the proposed design, the perimeter of the housing remains constant. The housing is elliptic with a major diameter of 27 mm and a minor diameter of 23 mm as shown in Figures 1c and 1d. Due to the leaflet's rotation, the computational domain is defined as a control volume (CV) with moving boundaries as shown in Figures 2a and 2b. In order to simplify the computational process, flow is assumed to be unidirectional in the direction of the major axis and the projected area between the leaflets and the aortic wall is assumed to be rectangular at various positions during the closing phase [5]. The flow is considered inviscidsuch that velocity is uniform at every cross section in the CVand the inlet [8,9]. The regurgitation flow is divided into two regimes through the minor and major orifices at the entrance of each section. When the valve is fully open, it is assumed that the aortic pressure (P ao ) and the ventricular pressure (P v ) are both uniform and equal. This is because the valve remains fully open during the systole with almost no forward flow. The control volume is ABCD, where AB is the leaflet, o is the pivot, and EF is an arbitrary section. U AD , U BC , and U EF are the velocities of blood at the entrance (AD), at the outlet (BC) and at the arbitrary section (EF), respectively. The distance from the EF section with respect to the inlet section is denoted as Y. l AD , l bc and l EF are the length of the inlet and the outlet and the arbitrary sections which are time dependent but their width (w) remains constant (Figure 2). Velocities and pressures vary constantly through the sections AD to BC. Mass is conserved within the CV such that the velocity at the EF section (V EF ) is calculated with respect to the inlet velocity (V AD ) or the outlet velocity (V BC ) in the CV. It should be noted that the velocity of blood in the vicinity of the leaflet tips and at the EF section is higher than the axial velocity of the leaflet tip (V tAD ,V tBC ) and the axial velocity of the leaflet at the EF section (V tEF ), respectively. The unsteady continuity equation on the CV takes the form: where A AD (w l AD ) and A EF (w l EF ) are cross sectional areas at the sections AD and EF, respectively. The axial velocities of the leaflet at A and E are and , where r is the radius of the leaflet in the circular SJM valve and the major radius of the leaflet in the elliptic SJM valve. l is the axial distance from the pivot to the major leaflet tip, b is the axial distance of the pivot to the minor leaflet tip, ω is the angular velocity of the leaflet, and θ is the angle between the AD and the leaflet. (a). The control volume used in this study. (b). AB is the leaflet, o is the pivot, AD is the inlet, BC is the outlet, Pv is the ventricular pressure, Aao is the aortic pressure, Freac is the force applied on the control volume by the leaflets, EF is an arbitrary section between the inlet and the outlet and the control volume used for force and momentum balance equations [5]. where P AD is the aortic pressure and P EF is the pressure at the section EF. Y EF is the axial distance between AD and FE. Assuming ( ) as: Then the term of the right part of equation is expressed: where the subscript "t", "t-δt" represents the value at time t, and t-δt, respectively, δt is the time increment and where N is the number of strips. The set of equations of 3 to 5 gives the pressure at an arbitrary section (P EF ) which is used to calculate The two approaches used to calculate reac

Results
The hemodynamic performance of proposed design including the velocity of the blood and the velocity of the leaflets and the regurgitation flow volume are calculated with respect to time in the beginning of the diastolic phase, i.e., the closing phase. The time increment δt is chosen to be 0.05 ms. Also, mentioned above, reac F is calculated using the two approaches in order to calculate the inlet velocity. The converging criterion specified is that the calculated reac F from the two approaches should be less than or equal to 0.001 (N). When the leaflet angle is less than 1 degree, it is assumed that the leaflet is very close to the final closed position. Time, t, is selected to be zero at the moment where backflow is initiated and it is assumed that the initial velocity of the fluid is zero. The leaflet is divided into 30 strips of equal width. The governing equations of motion for the leafletare solved by fourth order Runge-Kutta method. The heart rate and cardiac output were selected to be 70 beats per minute (bmp) and 6 lit/min, respectively [10]. The ventricular pressure is assumed to decrease from a value equal to the aortic pressure (when the valve is fully opened) and the average aortic pressure is considered to be 16.0 kPa, i.e., 120 mmHg in the closing phase and is assumed to be constant all along. The velocity of the leaflet tip, the velocity of the blood flow in the vicinity of the leaflet tip and the regurgitation flow volume of the conventional SJM valves obtained in this study and those reported before [5,11] are consistent. Figure 3 shows the velocity of the leaflet tip in the closing phase for both designs. The velocity of the leaflet tip in the elliptic design is higher than that of the conventional design. It also shows that the closing phase in the elliptic design is 9.7% lower. calculate the regurgitation flow volume is (1) the closing phase time and (2) the velocity of the blood which is shown in Figure 5. Results show that even though the velocity of the regurgitation flow in the elliptic SJM model is higher than that of the conventional SJM model, the backflow volume in the two models is comparable and equal (<0.05% error).

Conclusion
In this study, we proposed a design modification to the SJM conventional valves and developed a numerical tool that can quickly assess the hemodynamic performance of bileaflet mechanical heart valves in general and the elliptic SJM valve proposed in this study in particular. Results of the current study suggest a clear improvement in the hemodynamic performance of elliptic SJM valves over the conventional models. A comprehensive set of experimental and computational studies in the opening and closing phases will further address the hemodynamic performance of the proposed elliptic SJM valve.