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Biomedical Engineering

Transient, Three-Dimensional Flow Field Simulation through a Mechanical, Trileaflet Heart Valve Prosthesis

Kaufmann, Tim A. S.; Linde, Torsten; Cuenca-Navalon, Elena; Schmitz, Christoph; Hormes, Marcus; Schmitz-Rode, Thomas; Steinseifer, Ulrich

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doi: 10.1097/MAT.0b013e318222849c
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Abstract

Thromboembolic events are one of the major challenges faced by designers of blood-contacting artificial organs, for example, artificial heart valves.1 Approximately 2–4 thromboembolic complications occur per 100 patient-years after heart valve replacement.2 In total, 75% of all complications experienced by heart valve patients are related to thromboembolic events and anticoagulant-related bleedings.3 More than 300,000 cases of aortic valve replacement have been reported in the United States between 1991 and 2003. Approximately 64% of implants were mechanical heart valves.4 Analysis of mechanical heart valves is, therefore, of high clinical relevance.

To reduce the risk of thromboemboli in heart valves and other blood-contacting artificial organs, computational fluid dynamics (CFD) is a well-known tool that can provide insight into blood flow conditions, fluid stresses, and fluid exposure times.5,6

Although experimental analysis is often limited by the maximal resolution of the analysis device (e.g., 0.44 × 0.44 × 3 mm for magnetic resonance imaging), the spatial resolution of simulations is only limited by the meshing size. Thus, it can be customized for different applications.

Besides being limited to flow field analysis, most experimental studies on heart valves such as particle image velocimetry (PIV) analyses are performed in the vicinity of the valves (upstream [US] or downstream [DS]) but not within the hinges themselves. For the evaluation of potential thrombogenic areas, these regions are of primary interest. Using CFD, the flow and stress in pivot regions can be calculated in high resolution. Therefore, additional knowledge about the damage to blood cells and thrombosis generation to subsequently optimize settings and boundaries for mechanical heart valve applications can be achieved using CFD.

In many applications of mechanical heart valves, the opening and closing events are critical due to cavitation and compressed and accelerated flow in small gaps and between leaflets during the end stage of valve closing, shortly before the impact, and when the valve opens.7–11 Additionally, the flow is dependent on the chronological sequence. Thus, a transient simulation is needed to gain the necessary information about flow, pressure, and stress for each point in time. In doing so, the temporal resolution is only limited by the time step of the simulation.

In this work, the novel trileaflet mechanical valve “Triflo” (Triflo Inc.) was simulated in the THIA II12 (Thrombosis Tester Helmholtz Institute Aachen) test configuration. The THIA II is a test rig for in vitro assessment of the thrombogenic potential and blood damage of heart valves. The Triflo valve has leaflets made of pyrolytic carbon connected to a titanium alloy ring. The valve was experimentally tested and simulated in a preclinical configuration (Figure 1).

Figure 1.
Figure 1.:
Triflo trileaflet valve (Triflo Inc.), THIA II.

The simulation boundary conditions for inlet flow and pressure profile were adjusted to the experimentally routed leaflet motion, thus coupling the numerical simulation to experimental analysis of leaflet kinematics. These experimental measurements include pressure profiles and high-speed videos of the valve. Thus, a one-way fluid-structure-interaction model was used. Also, additional simulations of the tester geometry without an installed valve were conducted to increase the accuracy of boundary conditions.

The main goal of this project was to mimic the exact settings of the THIA II to be able to compare numerical simulations with experimental results.

Materials and Methods

A detailed schematic of the THIA II thrombosis tester including the pneumatic drive system is depicted in Figure 2. The solenoid valve switches to the inlet during systole, and air passes though throttle 1 into the US air chamber. The polyurethane membrane bulges to the inside, and fluid is pushed though the valve prosthesis.

Figure 2.
Figure 2.:
Schematic of THIA II.

During diastole, the solenoid valve switches to the outlet, and the fluid in the water chamber is pushed back, driven by pressure in the DS compliance. Thus, blood flows through the bypass to the US chamber.

The THIA II tester operating point was set to an approximate cycle time of 0.8 seconds with an average systole time of approximately 0.28 seconds, 75 bpm, and a pressure setting of 140/70 mm Hg.

Simulations were performed with ANSYS CFX 11.0 (Ansys Europe Ltd.). A Newtonian blood model was used to represent the settings given from THIA II, where water-glycerine (42%/58% by mass fraction) was used as fluid. Dynamic viscosity was set to a constant value of 3.6 mPa·s, and fluid density was assumed to be 1,059 kg/m3, corresponding to the THIA II test fluid. Shear stress transport with an automated blending function was chosen as turbulence model, and time step size was set to 1/30 seconds, providing a temporal resolution of approximately 33 ms.

The smallest symmetrical element (SSE) of the simulated geometry consists of one sixth of the Triflo valve, thus half a leaflet, half a bulb, and part of a conical inlet (Figure 3). Only these parts of the geometry were considered for the simulations.

Figure 3.
Figure 3.:
Smallest symmetrical element of the geometry: 1/6 of Inlet, valve, bulbs.

Tetrahedral elements, which are best suited to represent the complex geometry of the Triflo valve, were created during the meshing process. Additionally, three layers of prismatic elements were generated around the leaflets (ANSYS ICEM CFD 11.0, Ansys Europe Ltd.). After a mesh independency study, the final mesh for the SSE consisted of approximately 900,000 elements. As this SSE is 1/6 of the whole geometry, approximately 5.4 million elements represent the whole geometry including valve, bulbs, and inlet.

To achieve the best possible adjustment of flow boundary conditions, the flow field during systole was simulated in a separate simulation of THIA II with no installed valve. For diastole, measured pressure curves were used to adjust the flow boundaries.

To represent the exact boundary conditions of THIA II, the valve movement was measured in an experiment and fit to experimental data of flow through the valve.

For the first step, a high-speed video (2,000 fps) of the valve motion was taken for several cycles from DS the valve by an endoscope applied to THIA II. The distance between the leaflet tips and the central point was measured for each frame using self-developed software based on LabView 7.1.1 (National Instruments Inc.), which detects the leaflet tips by brightness comparison and calculates the opening angle of the valve from this information. Thus, the exact leaflet position is known for each point. Simultaneously, pressures upward and downward of the Triflo valve were measured.

The movement of leaflets within the numerical simulation was described by mesh deformation, as movement of nodes and thereby distortion of mesh elements, according to the experimentally recorded data. Thus, a one-way fluid-structure interaction model was used.

To be able to move the leaflets by mesh deformation, mesh elements have to be created in each point in the geometry. In particular, every small region between leaflet and wall has to contain enough elements to allow deformation and, thus, leaflet rotation. Therefore, no contact between the three leaflets and between the leaflets and the ring was assumed. Possible inaccuracy caused by this gap, especially during diastole, is discussed later.

To be able to simulate a whole cycle of systole and diastole with the leaflet rotation of 48° in both directions without extreme mesh distortion, it has to be split up in single simulations of three degrees of rotation each. If the leaflets get to close to or in contact with the ring, the simulation stops and the leaflet position was adjusted. The mesh for every single simulation was created separately, and results from one simulation were used as initial data for the next one. Each separate simulation was performed as a transient simulation with the same timestep size, so that 32 simulations complete a whole cycle of systole and diastole.

To achieve independency on the initial guess, a sequence of several cycles was simulated until no changes occurred in each cycle. This was achieved after four full cycles.

A very important part of the mesh generation is meshing of small volumes between leaflets and ring, where high shear rates and velocity gradients are expected. The highest mesh deformation occurs in these parts where the relative change of volume is maximal. The location of these areas varies for different leaflet positions. At fully closed valve position, the leaflets are in contact with the ring and the lower part of the bearing. Therefore, they are moved a bit to the side, away from the ring. Fully opened, the leaflets stuck to the upper bearing, so they are moved a bit downward into the free volume. The narrow gap that was described earlier is assumed in both cases but in different positions. An optimization of the mesh was performed for each single simulation separately, to make sure that the leaflets at no point get in contact with the walls but stay in free volume.

In addition to many elements of highest possible quality, prism layers around the leaflets were used to move the mesh deformation from the walls into the volume. Also, the mesh stiffness was adjusted, so that the distortion of elements would occur in areas with high-quality elements and expected low gradients. Therefore, the mesh stiffness proximal to the leaflets was assumed to be 10 times higher than in free volume.

However, this cannot avoid distortion, and, thereby, element quality loss in important and critical areas where the relative change of mesh is maximal. Analysis of these gaps is, therefore, most important during postprocessing. Also, flow and stress in bearing positions are of high importance for mechanical heart valve applications, because measurements in these areas are hardly possible and thrombocyte accumulation is very likely.13,14

Results

The ANSYS solver (ANSYS CFX 11.0, Ansys Europe Ltd.) delivered converging results for each single simulation. Run time for a whole cycle was 36 hours with a parallelization to eight cores. A periodical steady state could be achieved after four cycles.

The flow field during systole and diastole for the same leaflet position is shown in Figure 4.

Figure 4.
Figure 4.:
Simulated flow field for systole (top) and diastole (bottom).

During systole, a vortex behind the Triflo valve occurs. This vortex moves downward behind the leaflets during diastole. The highest velocities appear in the middle of the leaflets and in the bearing positions, where also the highest shear rates appear. High gradients in the small volumes between leaflets and ring can be observed as expected.

The pressure distribution during systole is depicted in Figure 5.

Figure 5.
Figure 5.:
Pressure distribution at peak systole.

The simulated pressure was read out US and DS the valve and compared with experimental results from the THIA-II (Figure 6).

Figure 6.
Figure 6.:
Simulated pressure curve upstream (US) and downstream (DS), close to the leaflet.

Shear rates were analyzed in the whole volume. Approximately 0.7% of volume fraction during valve opening and 0.5% during valve closing are exposed to shear rates above 1,125 s−1. Additionally, shear rates above 10,000 s−1 appear at the edges of leaflets and in bearing positions, as shown in Figure 7.

Figure 7.
Figure 7.:
High shear rates at different points of the cycle.

Discussion

The vortex behind the Triflo valve, which occurs during systole, stabilizes the flow into aorta. During diastole, it channels fluid onto the backside of the leaflets, supporting the closing procedure. The same vortex structure has been found in experimental studies.7 It corresponds to the pressure distribution, which shows good agreement with experimental data.

Nevertheless, the pressure before the Triflo valve starts to open is too high. This might be due to a wrong assumption in the inlet flow field simulation. A new driving system including chamber geometry will be implemented in the next version of THIA II to provide a better established flow profile with a circular flow field that is more accurate to describe in a numerical simulation. For the rest of systole, simulated and measured pressure profiles are in good agreement. The average deviation of pressure difference between simulations and experiments is approximately ±3 mm Hg (2.5%). This confirms that the use of a simulated flow field as inlet boundary condition delivers feasible results for that part of the cycle.

The pressure difference between simulations and experiments at the end of diastole is approximately 15 mm Hg (25%). This might be due to the assumed gap between the leaflets and between the leaflets and the ring. The actual leakage flow through the Triflo valve cannot be measured in THIA II. The next model of the tester will permit leakage measurements; therefore, an analysis of leakage flow compared with the gap can be undertaken.

The highest velocity gradients appear in the middle of the leaflets and in the pivot regions, where also the highest shear rates appear. This area is especially important, because it contains the mesh elements with highest distortion and, hence, worst quality. Possible inaccuracy in these elements may be transported into the whole geometry through the high velocity gradients. To achieve the highest possible mesh quality, preliminary studies were performed in which mesh distortion due to leaflet motion was analyzed, while the fluid itself was neglected. Based on these simulations, the rotation of three degrees for each simulation was chosen. Another important aspect of the meshing is the y+ value for turbulence consideration. The different meshes have y+ values between 7 and 15. Shear stress transport was used as turbulence model, because it uses a blending function between wall functions and low Reynolds formulations for 2 < y+ < 11. In this range, it has a performance superior to the k-epsilon or the k-omega model, while for y+ > 11 its performance is similar to k-epsilon. Using these settings, analysis of the bearing is possible with feasible accuracy.

A main goal of the THIA II application is to study the activation of thrombocytes and their deposition on different mechanical heart valves. In this case, the simulation can help to find shear rates and thus gain inside into platelet activation. According to Hellums,15 the threshold for platelet activation is described by a stress exposure-time product of 35 dyn·s/cm2. As a whole cycle equals 0.8 seconds, activation can occur for shear rates equal or higher than 1,125 s−1. Only 0.7% of volume fraction during valve opening and 0.5% during valve closing are exposed to such shear rates. However, very high shear rates in the order of 10,000 s−1 may cause immediate platelet activation. Those rates occur mainly in pivot regions and directly at the leaflets. Finally, to study the activation of a single platelet, particle tracking is necessary.16 This is not included in the model, but qualitative information about the level of activation can be obtained from the maximal shear rates that appear and the regions where activation is most likely to occur can be identified.

Conclusion

A transient simulation of flow through a trileaflet, mechanical heart valve was successfully undertaken. A novel method was developed using experimentally defined boundary conditions to describe the valve movement. The results permit analysis of flow, pressure, stress rates, and shear rates for each leaflet position. Additionally, bearing positions can be studied. Activation of platelets by the Triflo valve will be performed in the future after detailed information is obtained in continued experimental studies.

The chosen boundary conditions allow a transfer of this method to other mechanical heart valves and applications, but new supporting measurements have to be done for each new setting. The simulation is limited due to technical limitations of the THIA II such as leakage flow measurement and driving system, both of which will be changed in the next version of the tester.

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