A NUMERICAL ANALYSIS OF THE BLOOD FLOW AROUND THE BILEAFLET MECHANICAL HEART VALVES W ITH DIFFERENT ROTATIONAL IMPLANTATION ANGLES*

HONG Taehyup

Department of Mechanical Engineering, Graduate School, Kyung Hee University,Yongin, Korea, E-mail: hth@khmp.co.kr

KIMChang Nyung

Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Yongin, Korea

A NUMERICAL ANALYSIS OF THE BLOOD FLOW AROUND THE BILEAFLET MECHANICAL HEART VALVES W ITH DIFFERENT ROTATIONAL IMPLANTATION ANGLES*

HONG Taehyup

Department of Mechanical Engineering, Graduate School, Kyung Hee University,Yongin, Korea, E-mail: hth@khmp.co.kr

KIMChang Nyung

Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Yongin, Korea

The effects of implantation angles of Bileaflet Mechanical Heart Valves (BMHVs) on the blood flow and the leafletmotion are investigated in this paper. The physiological blood flow interacting with themoving leaflets of a BMHV is simulated with a strongly coupled implicit Fluid-Structure Interaction (FSI)method based on the Arbitrary-Lagrangian-Eulerian (ALE) approach and the dynam icmeshmethod (remeshing) in Fluent. BMHVs are w idely used to be implanted to replace the diseased heart valves, but the patients would suffer from some complications such as hemolysis, platelet activation, tissue overgrow th and device failure. These complications are closely related to both the flow characteristics near the valves and the leaflet dynam ics. The current numericalmodel is validated against a previous experimental study. The numerical results show that as the rotation angle of BMHV is increased the degree of asymmetry of the blood flow and the leafletmotion is increased, whichmay lead to an unbalanced force acting on the BMHVs. This study shows the applicability of the FSImodel for the interaction between the blood flow and the leafletmotion in BMHVs.

mechanical heart valve, rotational implantation, blood flow, leafletmotion, fluid-structure interaction

Introduction

The heart valvesmaintain a unidirectional blood flow by opening and closing depending on the difference of the pressures in the upstream and downstream sides of the valves. The two sem ilunar valves (aortic valve and pulmonary valve) are present in the arteries and they prevent the blood from flow ing back from the arteries into ventricles.

If the heart valve is seriously deformed or diseased, the native heart valvemay be replaced with a new heart valve，which can be either Biological Heart Valve or Mechanical Heart Valve (BHV or MHV). Mechanical heart valves aremade totally ofmechanical parts, well tolerated by the body. Due to the artificialmaterials involved, the patients withmechanical heart valves w ill have to rely on a lifelong bloodthinner (anticoagulant)medication. Among variousmechanical heart valves, the Bileaflet Mechanical Heart Valves (BMHVs) aremostly used.

Fig.1 Typical flow patterns in different heart valves

Despite the w idespread clinical use ofmechanical valve replacements, the functions of these devices are far from perfect. The primary complications that remain as themajor obstacles toward the idealmechanical heart valve include (1) hemolysis, which is the destruction of red blood cells, (2) platelet des-truction, and (3) thromboembolic events, arising from the formation of clots and their subsequent detachment.

Abnormal blood velocity profiles are associated with allmechanical valves, as a direct result of their nonphysiologic geometries (Fig.1). When the valve is fully opened, high velocity jets through the gap between the leaflets can be readily detected both in vivo and in vitro[1-4]. The leaflets act as an obstruction to the blood flow through the valve, which, coupled with the high velocity jets through the leaflets, causes elevated shear stresses whichmay lead to damages of red blood cells or the platelet activation[2,3,5,6]. The change of flow patterns and leaflet kinematics and the occurrence of high shear stress regions cause an elevated pressure drop, the platelet activation and the hemolysis. Eventually, these complications can lead to the fracture of bileaflet valves and the blood clot formation.

Tight attachment of the valve to the native annulusmay promote distortion of the surrounding tissues. Moreover, surgeons usually attempt to insert as large a prosthesis as possible to counteract the sizem ismatch. More often than not, an unphysiological tilt angle can be resulted[7]. Thus, the bileaflet valvesm ight be implanted with an arbitrarily rotation as well as a tilted angle. When themechanical heart valves are implanted with a rotation, the flow patternsmight also change.

Bluestein et al.[8]performed two-dimensional transient numerical simulations of turbulent pulsatile flows past the fixed bileaflet MHV, and demonstrated the level of the platelet activations in the tilted and untilted valves through the calculation of platelet shear histories. Aemu and Bluestein[9]performed threedimensional transient numerical simulations of a blood flow passing the fixed leaflets with a tilt, and predicted the platelet damage caused by the shear stress. Moreover, there aremany investigations to predict the flow characteristics and the leaflet’s behavior of un-rotated and un-tilted valve implantations using CFD analysis[10,11-13]. Asmentioned before, there were notmany studies of fluid-structure interaction regarding the effects of the rotation of bileaflet MHVs on the characteristics of the leafletmotion and the hemodynamic performances.

To deal with the complications caused by the rotation in the implantation of MHV, it is imperative to understand the leaflets’ kinematics and the detailed blood flow through bileaflet valves. This paper proposes amethod based on a strongly coupled fluid-structure interaction with the Arbirary Lagrangian Eulerian (ALE) frame to study the characteristics of the flow field and the leaflet behavior with different rotation angles of MHV.

1. Numericalmodeling

1.1 Geometry of bileaflet MHV and aortic sinuses

In the present study, themodel geometry of St. Jude Bileaflet heart valves of 25mm diameter (standardmodel) is considered. The three-dimensional geometries of the valve ring and the leaflets are shown in Fig.2. In this valve the fully closed and opened angles are 25oand 85o, respectively.

Fig.2 View of the bileaflet heart valve used in the current numerical calculation

Fig.3 Shape of native aortic valves

The natural aortic valve consists of three leaflets and three aortic sinuses distal to the aortic valve (Fig.3). The size and the shape of three leaflets and sinuses are sim ilar to each other, respectively, with approximately 120orotational symmetry. Therefore, the cross section of the aortic sinus can be approximately described by an epitrochoid. In the present study, the three-dimensional geometry of aortic sinuses ismodeled based on the epitrochoid shown in Fig.4.

Fig.4 Modeled geometry of aortic root

Cases with three different rotation angles (0o, 15oand 30o) of implanted bileaflet valves are considered. When the rotational implantation angle is 0o, the axis of the reflection symmetry of the aortic sinus is parallel to the rotation axis of the two leaflets (Fig.5(a)). A ll calculation cases are shown in Fig.5.

Fig.5 Rotational angles of MHV implantation

1.2 Numericalmethod

Since the leafletsmove in association with the blood flow, the computational grids in the calculation domain are consecutively deformed and regenerated. Therefore, the blood flow can be described by the continuity equation and ALE Reynolds Averaged Navier-Stokes (RANS) equations. Under the assumption of eddy viscosity, these governing equations can be w ritten as follows:

where ν andtν are the lam inar and turbulent kinematic viscosities, respectively. The turbulent kinematic viscosity should be determined by an appropriate turbulencemodel. In this study, the standard k?εmodel is used to determine the turbulent kinematic viscosity. The governing equations for the turbulent kinetic energy k and its dissipation rate of turbulence ε are as follows:

Since the leaflets aremade of carbonmaterial, the leaflets can be assumed to be rigid. A lso, the leaflets are constrained at the hinge axis and can only rotate with only one degree of freedom, therefore, the dynamics of leaflets can be expressed by the Euler equations as follows

where Mis themoment with respect to a hinge axis due to the pressure of the blood acting on a leaflet, I is the rotational inertia of a leaflet and˙ is the angular acceleration of a leaflet.

An accurate solution of the Navier-Stokes equations for deformedmeshes can be provided by the use of the ALE formulation, whichmakes it possible to include grid velocities in themomentum and conti-nuity equations of the fluid domain. The ALE approach is used to simulate the interactions between the blood flow and the leafletsmotion. In this strategy, the fluid and the structural solvers are separately used, with both alternately integrated with time and the fluid-structure interaction in two ways is taken into account by the interface conditions of both the fluid and the solid. The fluid-structure interaction calculation procedure used in this study is shown in Fig.6.

Fig.6 Flow chart of fluid-structure interaction calculation procedure

Fig.7 Volume flow rate[10]for the inlet condition

The fluid domain is solved with the computational code Fluent (Ansys Inc., USA) based on the finite volumemethod, which provides some features well suited to handle the specific problems of rotating boundaries. We use a spring-basedmoving and deform ingmeshmodule, which allows a robustmesh deformation by assuming that themesh element edges behave like an idealized network of interconnected springs. The Fluent remeshing algorithm is adopted to properly treat the degenerated cells, which agglomerates cells that violate the skewness criterion, and locally remeshes the agglomerated cells. If the new cells satisfy the skewness criterion, themesh is locally updated with the new cells, otherw ise, the new cells are discarded. In the current study, the computational domains are basically discretized with around 370 000 hexahedral and tetrahedral cells.

For the boundary condition, the volume blood flow ratemeasured in vitro study[10](Fig.7) is imposed as the inlet condition (the ventricular side) and the pressure at the outlet (the aorta side) is set to be 0mmHg. No-slip conditions are imposed at the vessel walls and the leaflet surface. As for the initial condition, at the beginning of the calculation (t=0 s), the flow is assumed to be at rest and the valve is closed. The time increment is very carefully controlled ranging from 0.01ms to 0.5ms depending on the calculated open angle variance of the leaflet. The time increment for the next step is decided based on the open angle variance (Δθn=θn?θn ?1) at the previous time step, which allows us to keep the variation of the open angle less than 0.4° between two consecutive time steps.

Here, the blood is assumed to be an incompressible New tonian fluid with a density of 1 000 kg/m3 and a dynam ic viscosity of 3.7 kg/ms.

Fig.8(a) Schematic diagram of the experimental layout of Nobili et al.[10]

2. Results and discussions

2.1 Validation of the current calculation

The present FSI calculation on the leafletmotion and the blood flow is validated against an experimental and numerical studies performed by Nobili et al.[1]. Figure 8(a) shows a schematic diagram of the experimental layout. W ith the bileaflet valve installed, its kinematics ismeasured by using the ultrafast cinematographic technique in the pulsatile, open loop,mock circulatory system. Employing the geometric configurations of their experimental studies, Nobili et al.[10]also conducted a numerical analysis of a transient blood flow around the bileaflet valve using anFSI approach.

Fig.8(b) current numerical calculationmodel for validation

Fig.9 Comparison of numerical and experimental transient opening angles

To evaluate the accuracy and applicability of the current numericalmethod, a numerical simulation on the blood flow and the leafletmotion in the same geometric configurations (Fig.8(b)) as those of Nobili et al.[10]was performed. Figure 9 shows the comparison between the numerical and experimental results for the transient angle of the leaflet. Even though there is a slight difference in the leaflet angle in the closing phase of the leaflet, the time duration and the leaflet angle variation against time in the opening phase are predicted very accurately in the present results, show ing that the present numerical results for the angle of the leaflet are in a good agreement with the experimental data. Obviously, it can be shown from the above comparison that the current numericalmethod is applicable to the analyses of the leaflets’motions and the blood flow passing through the bileaflet valves.

2.2 Flow fields

A cycle of the transient blood flow in the present study can be divided into four phases: acceleration phase, peak systole, deceleration phase, regurgitation phase. Several time positions in the flow fields are shown in Fig.10, where time Positions 1 and 2 are in the acceleration phase, time Position 3 is in the peak systole, time Positions 4 and 5 are in the deceleration phase, and time Positions 6, 7, 8 and 9 in the regurgitation phase.

1- 0.010 s in the acceleration phase, 2- 0.015 s in the acceleration phase, 3- 0.090 s in the peak systole, 4- 0.160 s in the deceleration phase, 5- 0.220 s in the deceleration phase,6- 0.300 s in the regurgitation phase, 7- 0.310 s in the regurgitation phase, 8- 0.315 s in the regurgitation phase, 9- 0.319 s in the regurgitation phaseFig.10 Definitions of the time positions

Fig.11 Transient velocity fields in am id-plane perpendicular to the axis of the leaflets

The velocity fields of the blood and the angular positions of the leaflets at different time positions in Case 1 and Case 3 are shown in Fig.11, where1θ and2θ are the opening angles of Leaflet 1 (in theleft) and Leaflet 2 (in the right), respectively. The velocity fields are for am id-plane perpendicular to the axis of the leaflets. The shapes of the twomid-planes of Case 1 and Case 3 are different from each other since the rotational angle of the MHV in the Case 3 is 30o. Here, the velocity in themid-plane in Case 1 is symmetrical with respect to the centerline along the blood vessel, while the velocity in themid-plane in Case 3 is asymmetrical where one sinus is seenmore flat than the other in the plane because of the rotated implantation of MHV. Here, at time Position 2, the blood flows through the regions between a leaflet and a valve ring are noticeable in both cases. At time Position 3, three jet–like blood flows around the valve are seen with high volume flow rates in both cases. At time Position 8, because of the blood flow in the reverse direction and of the asymmetric geometry of the sinus in association with the rotation axis of the leaflets, the blood flow in Case 3 is asymmetric with asymmetric angular positions of the two leaflets, different from the symmetric behaviors of the blood flow and the leafletmotion. In Fig.12 it is clearly seen that the blood passes through the region between the two leaflets and through the regions between one leaflet and the valve ring at the time point of the peak systole. At this time point, asymmetric recirculations in sinuses can be observed in cases of rotation, while the symmetric recirculation is seen in Case 1 without rotation.

Fig.12 Detailed velocity fields around bileaflet MHV at the peak systole (time Position 3)

Fig.13 Detailed velocity fields around bileaflet MHV at time Position 9 in regurgitation phase

At the end of the peak systole, the blood flow around the recirculation region loses itsmomentum, so that it would be easier for the blood near a larger sinus to flow in the reverse direction. Also, when the regurgitation flow starts, the blood near the vessel wall can flow in the reverse directionmore easily than that around the central region since the blood near the vessel wall has, in general, smaller inertia. At time Point 9 in the regurgitation phase (Fig.13), onemay observe that there is a region where themagnitude of the fluid velocity near the leaflets with rotations (15o, 30o) is fairly larger than that in Case 1 (0o) with asymmetric positions of the leaflets, whichmay lead to hemolysis and platelet destruction.

Table 1 shows the transvascular pressure drop averaged in time in the ejection phase with a positive volume flow rate (Fig.7). The averaged pressure dropis generally increased with the rotation angle and the averaged pressure drop in Case 3 is larger by about 7 % than that in Case 1. Larger pressure dropmeans that the heart with MHV prosthesis has to work harder.

Table 1 Transvascular pressure drop averaged in time in different cases

2.3 Motion of the leaflets

Transient variations of the opening angle of the two leaflets with different rotation angles are plotted in Fig.14. A cycle of themotion of each leaflet can be divided into four phases: the fully closed phase, the opening phase, the fully opened phase and the closing phase.

Fig.14 Transient leaflet opening angles for different rotation angles

In Case 1, it is observed that the left and right leaflets behave symmetrically in conjunction with the symmetric geometry. The elapsed time of leaflets’opening and closing in a cycle is 0.31926 s.

In Case 2, the elapsed times for Leaflet 1 and Leaflet 2 to open and close are 0.31849 s and 0.31915 s, respectively. At t =0.31826 s , themaximum difference in the opening angle (8o) is observed in the closing phase with the angles of Leaflet 1 and Leaflet 2 being 26.6oand 34.6o, respectively. A lso the difference in time for the two leaflets to contact the seat is 0.00066 s.

In Case 3, the elapsed time for Leaflet 1 and Leaflet 2 to open and close are 0.31730 s and 0.32376 s, respectively. At t =0.31730 s , the angles of Leaflet 1 and Leaflet 2 are 25.0o(that is, the Leaflet 1 on the seat) and 52.0o, respectively, and themaximum difference in the opening angle (27.0o) is observed in the closing phase. Again, the difference in time for the two leaflets to contact the seat is 0.00245 s.

From the above results, it is seen that, as the rotation angle of MHV increases, the time for Leaflet 1 to finish the closing phase decreases while that for Leaflet 2 increases. A lso, the difference in time for the two leaflets to contact the seat and the difference in the opening angles of the two leaflets in the closing phase increase, which is due to the fact that the degree of asymmetry of the flow domain increases as the rotation angle of MHV increases in the range of the rotation angle of 0o-30o.

Fig.15 Transient leaflet angular velocities for different rotation angles

Figure 15 shows the angular velocities of the leaflets with time. As can be seen, leaflets’ behaviors in different cases are almost the same in the opening phase, but are quite different from each other in the closing phase. In the closing phase, as the rotation angle increases, the asymmetric behavior of the two leaflets becomes notable, the difference in themagnitude of the angular velocities of the two leaflets increases and the time point of the Leaflet 1’s contact with the seat comes earlier. However, the change in the behavior of Leaflet 2 is very complicated as shown in a sub-graph of Fig.15. Themagnitude of themaximum angular velocity of Leaflet 1 is decreased with the rotation angle in the closing phase. This is because the acceleration periods of the leaflets are different from each other due to the difference in time for the two leaflets to contact the valve ring. On the other hand, themagnitude of themaximum angular velocity of Leaflet 2 is increased with the rotation angle. Themagnitude of themaximum angular velocity in Case 3 is 265.1 rad/s, 1.8 times larger than 141.3 rad/s, themagnitude of themaximum angular velocity in Case 1. The reason that themaximum angular velocity of Leaflet 2 in Case 3 is the largest among the cases is that the acceleration period of Leaflet 2 caused by the regurgitation flow in the Case 3 is the longest while the elapsed time for closing of the Leaflet 1 in Case 3 is the smallest.

In Case 1, the behaviors of the two leaflets are symmetric and themagnitudes of both themaximumangular velocities of Leaflet 1 and Leaflet 2 are 141.3 rad/s, as is observed in the closing phase. In Case 2, themagnitudes of themaximum angular velocities of Leaflet 1 and Leaflet 2 are 133.0 rad/s and 241.2 rad/s, respectively. In Case 3, themagnitudes of themaximum angular velocities of Leaflet 1 and Leaflet 2 are 104.7 rad/s and 265.1 rad/s, respectively. Asmentioned above, the difference in themagnitudes of themaximum angular velocities of Leaflet 1 and Leaflet 2 is increased with the rotation angle of the MHV implantation.

Consequently, in the cases of rotated implantation, as one leaflet is closed first, the closing angular velocity of the other leaflet increases and then it causes the increased velocity of the blood around the leaflet and the degree of hemolysis and platelet destruction could be higher than that in Case 1.

3. Conclusions

Bileafletmechanical heart valves are themost commonly implanted prosthetic heart valves to replace disabled native valves. However, the bileaflet valves can be implanted with various rotational angles on account of surgeon’s performance in a surgical operation.

In the present study, the effects of the rotation angle of the MHV implantation on the blood flow and leaflets’ behaviors are investigated using an unsteady, three-dimensional CFD analysis including the FSImethod. The blood flow is symmetrical in the normal MHV implantation, but in case of rotated implantation, the sizes of flow recirculation regions are different in different sinuses, which leads to asymmetrical blood flow near a bileafletmechanical heart valve. This induces asymmetrical behavior of the leaflets, leading to repeated unbalanced forces exerted by the consecutive contacts between the leaflets and the valve ring. Itmay reduce the durability of the bileaflet MHV. Also, the implantation of MHV with rotation can reduce the oxygen supply to a patient body in conjunction with an increased pressure drop across a BMHV and/or a reduced cardiac output.

The developed FSI algorithm in the present study is shown to be very effective inmodeling the interaction of the blood flow and the leafletmotion. The FSImethod can be applied to various dynamics problems where some interactions between the solid bodymotion and the fluid flows exist.

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March 8, 2011, Revised May 2, 2011)

10.1016/S1001-6058(10)60156-4

* Biography: HONG Taehyup (1981-), Male, Bachelor

KIMChang Nyung, E-mail: cnkim@khu.ac.kr