Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary Lagrangian-Eulerian Techniques for the Mesh Representation

Abstract

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.

Discrete multi-physics: A mesh-free model of blood flow in flexible biological valve including solid aggregate formation

“…As in the previous case, there are some minor differences, but overall the membrane behaviour is well captured by the model. Similar deformation profiles have also been by other studies [15]. …”

“…All the simulations assume blood as liquid medium. Blood is a viscoelastic fluid, but in flow simulations [15, 22, 23] is often considered Newtonian. In our calculations, we also use the Newtonian approximation with ρ = 1056 kg m -3 and μ = 0.0035 Pa s. We consider membranes with different flexural rigidities, the specific value of F , for each case, is given in Section Membrane deformation .…”

“…From this point of view, the fact that we simulate bicuspid valves, while the aortic valve has three leaflets, is not a limitation. Given the same mechanical stress, in fact, deformations are higher in bicuspid valves than in tricuspid valves [15]. Therefore, by forcing velocities that are typical of aortic valves in bicuspid valves, we test our model under conditions that are even more critical (i.e.…”

Numerical investigation on the effect of bileaflet mechanical heart valve's implantation tilting angle and aortic root geometry on intermittent regurgitation and platelet activation

“…Given that the blood flow remains largely laminar for most of the time in the cardiac cycle and undergoes turbulence for a very brief time, previous researchers have modeled blood flow in the aorta as laminar . Hence, laminar flow conditions were adopted in this study.…”

A partition of unity approach to fluid mechanics and fluid–structure interaction

“…While multiple re-meshing techniques [17] have been proposed, the process introduces grid interpolation errors and its computational cost effectiveness is linked to the frequency at which the mesh needs to be adjusted. As shown in [18], where the particular case of cardiac valves is discussed, the ALE based simulations take more time to run than competing interface-capturing methods.…”