Fluid-Structure Interaction Study of Transcatheter Aortic Valve Dynamics Using Smoothed Particle Hydrodynamics

Abstract

Computational modeling of heart valve dynamics incorporating both fluid dynamics and valve structural responses has been challenging. In this study, we developed a novel fully-coupled fluid-structure interaction (FSI) model using smoothed particle hydrodynamics (SPH). A previously developed nonlinear finite element (FE) model of transcatheter aortic valves (TAV) was utilized to couple with SPH to simulate valve leaflet dynamics throughout the entire cardiac cycle. Comparative simulations were performed to investigate the impact of using FE-only models vs. FSI models, as well as an isotropic vs. an anisotropic leaflet material model in TAV simulations. From the results, substantial differences in leaflet kinematics between FE-only and FSI models were observed, and the FSI model could capture the realistic leaflet dynamic deformation due to its more accurate spatial and temporal loading conditions imposed on the leaflets. The stress and the strain distributions were similar between the FE and FSI simulations. However, the peak stresses were different due to the water hammer effect induced by the fluid inertia in the FSI model during the closing phase, which led to 13-28% lower peak stresses in the FE-only model compared to that of the FSI model. The simulation results also indicated that tissue anisotropy had a minor impact on hemodynamics of the valve. However, a lower tissue stiffness in the radial direction of the leaflets could reduce the leaflet peak stress caused by the water hammer effect. It is hoped that the developed FSI models can serve as an effective tool to better assess valve dynamics and optimize next generation TAV designs.

Keywords: Bioprosthetic heart valve; Finite element method; Fluid–structure interaction; Hemodynamics; Smoothed particle hydrodynamics; Transcatheter aortic valve.

Figure 1

A 2D illustration of the basic principle of the smoothed particle hydrodynamics methodology. The property A of particle ‘a’ is determined by the properties of its neighboring particles, for example, ‘b’, based on an interpolating kernel function (W) which is a function of the smoothing length, h, and the distance between particle ‘a’ and its neighboring particle ‘b’.

Figure 2

(a) GLBP equi-biaxial response from Sun’s thesis (Sun 2004) (open circles), with anisotropic MHGO model fit (black lines), and the averaged response (red squares) with isotropic Ogden model fit (red line). (b) Diagram of the leaflet material orientations and the fiber orientations, m₀₁ and m₀₂, drawn on the 2D leaflet schematic.

Figure 3

Three-dimensional FE-SPH model for TAV opening and closing simulations. The model consists of a 36.8 mm diameter rigid tubular structure, a rigid gasket and skirt to seal the gap between the tube and valve, two rigid plates at the aortic and ventricular sides respectively, blood particles (half SPH particles are shown in the fluid domain for clarity), and three flexible TAV leaflets.

Figure 4

(a) Wiggers diagram representing physiological pressure waveforms at a heart rate of 75 bpm (Wiggers). (b) Pressure boundary conditions applied to the plates.

Figure 5

(a) Time-dependent radial position of the midpoint of leaflet free edge during a cardiac cycle. (b) Time-dependent GOA of TAV during a cardiac cycle. Note for the sake of clarity, a full cardiac cycle was truncated to show the variation from 0 s to 0.4 s.

Figure 6

A series of the time-dependent leaflet deformed shape (the red curve in the center inset) is depicted with respect to the perpendicular bisection plane of the leaflet. The red curves represent the opening profiles, and the blue curves represent the closing profiles. (a) FSI-Ogden model. (b) FSI-MHGO model. (c) FE-Ogden model. (d) FE-MHGO model.

Figure 7

Opening and closing of TAV leaflets colored by the maximum principal strain from the FE-MHGO model. Note the different scale for each time instance.

Figure 8

Opening and closing of TAV leaflets colored by the maximum principal strain from the FSI-MHGO model. Note the different scale for each time instance.

Figure 9

Opening and closing of TAV leaflets colored by the maximum principal strain from the FSI-Ogden model. Note the different scale for each time instance.

Figure 10

Contour plots of the maximum principal stress (in MPa) for each valve in the fully-open (t = 40 ms) and fully-closed (t = 300 ms) configurations. (a) FE-Ogden model. (b) FSI-Ogden model. (c) FE-MHGO model. (d) FSI-MHGO model.

Figure 11

Comparison of (a) transvalvular pressure gradient, (b) hydrodynamic force acting on the leaflets (the dotted line represent the maximum hydrostatic pressure force in diastole), (c) maximum velocity at 15 mm downstream the TAV annulus (basal ring), (d) flow rate through the TAV in a cardiac cycle between the FSI-Ogden and FSI-MHGO models. For the sake of clarity, only a partial cardiac cycle from 0 s to 0.4 s is shown.

Figure 12

Blood velocity vector fields at different time instances for the FSI-Ogden (the left hand side) and FSI-MHGO (the right hand side) models. Note the color legend on the top applies to the first four time instances, while the bottom legend corresponds to the last two instances.