Fluid-structure interaction modeling of compliant aortic valves using the lattice Boltzmann CFD and FEM methods

Abstract

The lattice Boltzmann method (LBM) has been increasingly used as a stand-alone CFD solver in various biomechanical applications. This study proposes a new fluid-structure interaction (FSI) co-modeling framework for the hemodynamic-structural analysis of compliant aortic valves. Toward that goal, two commercial software packages are integrated using the lattice Boltzmann (LBM) and finite element (FE) methods. The suitability of the LBM-FE hemodynamic FSI is examined in modeling healthy tricuspid and bicuspid aortic valves (TAV and BAV), respectively. In addition, a multi-scale structural approach that has been employed explicitly recognizes the heterogeneous leaflet tissues and differentiates between the collagen fiber network (CFN) embedded within the elastin matrix of the leaflets. The CFN multi-scale tissue model is inspired by monitoring the distribution of the collagen in 15 porcine leaflets. Different simulations have been examined, and structural stresses and resulting hemodynamics are analyzed. We found that LBM-FE FSI approach can produce good predictions for the flow and structural behaviors of TAV and BAV and correlates well with those reported in the literature. The multi-scale heterogeneous CFN tissue structural model enhances our understanding of the mechanical roles of the CFN and the elastin matrix behaviors. The importance of LBM-FE FSI also emerges in its ability to resolve local hemodynamic and structural behaviors. In particular, the diastolic fluctuating velocity phenomenon near the leaflets is explicitly predicted, providing vital information on the flow transient nature. The full closure of the contacting leaflets in BAV is also demonstrated. Accordingly, good structural kinematics and deformations are captured for the entire cardiac cycle.

Keywords: Aortic valve biomechanics; Finite element (FE); Fluid–structure interaction (FSI); Lattice Boltzmann method (LBM).

Fig. 1

(a) TAV parametric multi-scale model geometry with embedded collagen fiber network (b) BAV with 140° non fused cup angle and embedded collagen fiber network parametric multiscale model geometry (c) Calibrated hyperelastic material properties of the aortic root, cusps and the collagen fiber network

Fig. 2

Computational averaged collagen fiber symmetric map embedded inside the aortic valve’s cusp based on images of right, left, and non coronary cusps from five different porcine valves (Marom et al. 2013b; Mega et al. 2016)

Fig. 3

Schematic solution procedure of a single time increment using Lattice Boltzmann Method. Starting from an equilibrium distribution at the current increment (left). Collision and streaming to the next time increment (middle). Calculating the new equilibrium distribution (right) to finish the calculated time increment

Fig. 4

(a) Schematic view of the physical domain of fluid-structure interaction model (b) 3D (upper) and section view (lower) of the numerical domain of FSI model using uniform distribution of unity D3Q27 lattices (c) The effect of the physical domain length on the peak velocity (upper) and grid dependency study examining the effect of the spatial to temporal ratio on the peak velocity and max pressure gradient (lower) (d) Schematic demonstration of the used bounce-back boundary condition

Fig. 5

FSI models using coupled LBM-FE: Flow velocity at representative time-points during TAV cardiac cycle

Fig. 6

TAV velocity field through the cardiac cycle at XZ symmetry plane quantified at 0.5D height from the cusps’ tip for LBM-FE FSI model. In red: diastolic velocity oscillations phenomenon which is explicitly observed using LBM-FE FSI model

Fig. 7

FSI models using coupled LBM-FE: Flow velocity at representative time-points during BAV cardiac cycle

Fig. 8

Maximum principal stress distributions (aortic side view) at peak systole and mid diastole on TAV (upper row) and BAV (lower row) cusps with zoom on the collagen fiber network

Fig. 9

Flow wall shear stress distributions (ventricles side view) at peak systole and mid diastole on TAV (upper row) and BAV (lower row) cusps