Background: Blood and aortic valve leaflet interactions play a key role in valve dynamics and degeneration. Whereas clinical studies are expensive, time consuming, and limited in spatial as well as temporal resolution, computational models can provide useful insights into valve dynamics and mechanisms for their degeneration. Numerical analysis of the aortic valve dynamics requires a fully coupled model taking into account the interaction between the leaflets and with the surrounding medium, i.e. blood. In fluid-solid interaction (FSI) models, a purely Lagrangian frame is incapable of dealing with strong distortions of the fluid mesh. A purely Eulerian frame for the fluid domain introduces complexity in fluid-solid coupling. Therefore, mixed Lagrangian-Eulerian or Arbitrary Lagrangian Eulerian (ALE) methods are used for kinematical description of the fluid domain. The Eulerian description is used for ‘almost contained' flows and Lagrangian description is used for regions where the mesh would be highly distorted if required to follow fluid motion. In the current study, we developed a FSI model of the aortic valve using the ALE method.

Methods: A fully coupled FSI model of the aortic valve opening phase was developed using Ansys®. The geometry and the boundary conditions are depicted in Fig. 1a. Blood was modeled as Newtonian and the leaflet was isotropic, and incompressible. The Reynold's number for blood flow in the aorta can be as high as 4000, at which viscous forces are dominant(1). In addition, adverse pressure gradients set in during flow deceleration phase, leading to recirculation and formation of vortices in the sinuses(2,3). In the light of these facts, a shear stress transport turbulence model(4) was used for blood flow. The model switches between the standard k- ω and k- ε models near and away from the wall, respectively. A pulsatile pressure was applied at the inlet (Fig. 1b) and stress free boundary conditions at the outlet. The simulation was carried out for the opening phase. Bidirectional fluid-solid coupling was obtained by maintaining displacement and stress continuity at the interface.

Results: The fluid velocity profiles and the valve positions at various time instants are shown in Fig. 2. Initially, the fluid gushes through a very small clearance between the valve tip and the wall, thereby leading to high velocities in the region. This leads to a smaller pressure near the leaflet tip, as compared to that along the remaining length of the leaflet. Also, in the beginning, the fluid velocities and pressures are low near the wall close to the fixed end of the leaflet. This is due to the fact that the simulation starts with quiescent conditions, and the fluid is constrained to move near the leaflet fixed edge due to no-slip at the walls. Therefore, the fluid imparts force to the leaflet such that it deflects the belly before any displacement is imparted to the free edge. Thus, the valve opens by first eliminating the pressure differential along the leaflet length, which is achieved in the first few milliseconds. Beyond this time, the leaflet remains almost straight (unbent) and opens by uniform pressure differential across it due to the forward flow of blood. These results are in accordance with experimental studies of valve dynamics (5).

As the valve opens further, fluid velocities are induced by valve motion, and therefore fluid from the region near the fixed end also rushes past the leaflet, thereby leading to higher velocities in the region. The fluid in the sinus region is almost stagnant until recirculation sets in, leading to vortex formation in the sinuses, during the later part of the valve opening process. Vortices in the sinuses have been observed experimentally(6) and are important in valve closure. The maximum fluid velocity occurs near the leaflet tip, in the gap between the leaflet tip and the wall at all times. During the opening phase, a shortening of the leaflet length is also observed in our simulation, which also confirm the experimental reports (5).

The fluid wall shear was minimum near the leaflet base and maximum near the tip. The von-Mises stresses in the leaflet were maximum near the attachment of the leaflet at the base. Aortic valve degeneration, which is the primary cause of calcific stenosis, occurs in the region near the leaflet attachment to the base. Thus, the spatial distribution of high mechanical stresses and low wall shear stresses correlate with regions of aortic valve calcification, thereby emphasizing the significance of these stresses in the development and progression of the disease. High wall shear stress, which occurs near the leaflet tips, can cause tearing of the leaflet cusps in bioprosthetic heart valves.

Experimental validation of the opening dynamics will be carried out using a pulse duplicator system in which a trileaflet aortic valve of known stiffness will be mounted in the aortic position. The working fluid will be a 40% glycerol solution, whose density and viscosity mimick those of blood. A known pressure pulse will be applied upstream of the valve and the motion of the valve will be tracked using high speed photography. The leaflet opening dynamics will be compared with the simulation results.

Conclusions: A fully coupled FSI model of aortic valve and blood is developed based on ALE method. The model provides results which are in accordance with experimentally published data on aortic valve dynamics and can be used for parametric studies.

References

1. Ku DN. Blood flow in arteries. Annual Reviews in Fluid Mechanics. 1997;29:399-434.

2. Bellhouse BJ, Talbot L. The fluid mechanics of the aortic valve. Journal of Fluid Mechanics. 1969;35:721-735.

3. van Steenhoven AA, van Dongen MEH. Model studies of the closing behavior of the aortic valve. Journal of Fluid Mechanics. 1979;90:21-32.

4. Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. American Institute of Aeronatuics and Astronautics. 1994; 32:1598-1605.

5. Thubrikar M. The Aortic Valve. Boca Raton, FL: CRC Press; 1990.

6. Bellhouse BJ, Talbot L. The fluid mechanics of the aortic valve. Journal of Fluid Mechanics. 1969;35:721-735.