Sebastiaan Annerel

FSI simulation of asymmetric mitral valve dynamics during diastolic filling

In this article, we present a fluid–structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.

A fast strong coupling algorithm for the partitioned fluid-structure interaction simulation of BMHVs.

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluid–structure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time.

The upstream boundary condition influences the leaflet opening dynamics in the numerical FSI simulation of an aortic BMHV

In this paper, the influence of the upstream boundary condition in the numerical simulation of an aortic bileaflet mechanical heart valve (BMHV) is studied. Three three-dimensional cases with different upstream boundary conditions are compared. The first case consists of a rigid straight tube with a velocity profile at its inlet. In the second case, the upstream geometry is a contracting left ventricle (LV), positioned symmetrically with respect to the valve. In the last case, the LV is positioned asymmetrical with respect to the valve. The cases are used to simulate the same three-dimensional BMHV. The change in time of the LV volume is calculated such that the flow rate through the valve is identical in each case. The opening dynamics of the BMHV are modelled using fluid-structure interaction. The simulations show that differences occur in the leaflet movement of the three cases. In particular, with the asymmetric LV, one of the leaflets impacts the blocking mechanism at its open position with a 34% higher velocity than when using the velocity profile, and with an 88% higher velocity than in the symmetric LV case. Therefore, when simulating such an impact, the upstream boundary condition needs to be chosen carefully.

Stability Issues in Partitioned FSI Calculations

In this chapter a short review will be given on stability issues for fluid-structure interaction (FSI) problems we encountered and studied in the last decade. Based on this, the ideas behind two implicit coupling algorithms, developed in the department, will be explained. The first algorithm is the Interface Quasi-Newton coupling method and the second is the Interface Artificial Compressibility coupling method. Most of the applications that are shown are in the biomechanical field. These are representative for more general strongly coupled problems with incompressible fluids and flexible structures.

Validation of a numerical FSI simulation of an aortic BMHV by in vitro PIV experiments

In this paper, a validation of a recently developed fluid-structure interaction (FSI) coupling algorithm to simulate numerically the dynamics of an aortic bileaflet mechanical heart valve (BMHV) is performed. This validation is done by comparing the numerical simulation results with in vitro experiments. For the in vitro experiments, the leaflet kinematics and flow fields are obtained via the particle image velocimetry (PIV) technique. Subsequently, the same case is numerically simulated by the coupling algorithm and the resulting leaflet kinematics and flow fields are obtained. Finally, the results are compared, revealing great similarity in leaflet motion and flow fields between the numerical simulation and the experimental test. Therefore, it is concluded that the developed algorithm is able to capture very accurately all the major leaflet kinematics and dynamics and can be used to study and optimize the design of BMHVs.

Application of a strong FSI coupling scheme for the numerical simulation of bileaflet mechanical heart valve dynamics: study of wall shear stress on the valve leaflets

One of the major challenges in the design of Bileaflet Mechanical Heart Valves (BMHVs) is reduction of the blood damage generated by non-physiological blood flow. Numerical simulations provide relevant insights into the (fluid) dynamics of the BMHV and are used for design optimisation. In this paper, a strong coupling algorithm for the partitioned Fluid-Structure Interaction (FSI) simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using a numerically calculated Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. The developed algorithm is used to simulate the dynamics of a 3D BMHV in three different geometries, allowing an analysis of the solution process. Moreover, the leaflet kinematics and the general flow field are discussed, with special focus on the shear stresses on the valve leaflets.

Evaluation of a new Implicit Coupling Algorithm for the Partitioned Fluid-Structure Interaction Simulation of Bileaflet Mechanical Heart Valves

We present a newly developed Fluid-Structure Interaction coupling algorithm to simulate Bileaflet Mechanical Heart Valves dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This Jacobian is used in the leaflet motion solver when new positions of the leaflets are computed during the coupling iterations. The Jacobian is numerically derived from the flow solver by applying leaflet perturbations. Instead of calculating this Jacobian every time step, the Jacobian is extrapolated from previous time steps and a recalculation of the Jacobian is only done when needed. The efficiency of our new algorithm is subsequently compared to existing algorithms which use fixed relaxation and dynamic Aitken Δ2 relaxation in the coupling iterations when the new positions of the leaflets are computed. Results show that dynamic Aitken Δ2 relaxation outperforms fixed relaxation. Moreover, during the opening phase of the valve, our new algorithm needs fewer subiterations per time step to achieve convergence than the method with Aitken Δ2 relaxation. Thus, our newly developed FSI coupling scheme outperforms the existing coupling schemes.

A multi-solver quasi-Newton method for the partitioned simulation of fluid-structure interaction

In partitioned fluid-structure interaction simulations, the flow equations and the structural equations are solved separately. Consequently, the stresses and displacements on both sides of the fluid-structure interface are not automatically in equilibrium. Coupling techniques like Aitken relaxation and the Interface Block Quasi-Newton method with approximate Jacobians from Least-Squares models (IBQN-LS) enforce this equilibrium, even with black-box solvers. However, all existing coupling techniques use only one flow solver and one structural solver. To benefit from the large number of multi-core processors in modern clusters, a new Multi-Solver Interface Block Quasi-Newton (MS-IBQN-LS) algorithm has been developed. This algorithm uses more than one flow solver and structural solver, each running in parallel on a number of cores. One-dimensional and three-dimensional numerical experiments demonstrate that the run time of a simulation decreases as the number of solvers increases, albeit at a slower pace. Hence, the presented multi-solver algorithm accelerates fluid-structure interaction calculations by increasing the number of solvers, especially when the run time does not decrease further if more cores are used per solver.

State-Of-The-Art Methods for the Numerical Simulation of Aortic BMHVs

Since the first clinical implantation of an artificial aortic valve by Dr. Charles A. Hufnagel in 1952 (Hufnagel et al., 1954), the use of such prostheses has gained strong interest and has become a routine treatment for severe heart valve failure. During the past 60 years, various mechanical heart valve designs have been developed for use in both aortic and mitral positions (Butany et al., 2003; Aslam et al., 2007). Nowadays, bileaflet mechanical heart valves (BMHVs) are widely preferred for aortic valve replacement because of their long lifespan. However, current BMHVs still induce pannus and thromboembolism, among other undesired side effects, which are believed to be due to non-physiological flow and turbulence generated by the valve leaflets (Sotiropoulous & Borazjani, 2009). One way to gain insight into the dynamics of a BMHV in order to improve its design is by experimental testing (Grigioni et al., 2004). Usually, in vitro testing is used, in which the functioning of the valve is assessed, for example, by using Doppler echocardiography (Dumont et al., 2002; Verdonck et al., 2002) or by visualizing the temporal and spatial flow field through velocimetry, like the laser Doppler anemometry (LDA) technique (Browne et al., 2000; Akutsu et al., 2001) or the particle image velocimetry (PIV) technique (Browne et al., 2000; Kaminsky et al., 2007). Also, the spectrum of the valve noise can be analyzed, as is done, for example, in Masson & Rieu (1998). Experimental in vivo testing is another option, using echocardiography and Doppler ultrasound to investigate the behavior of the valve after implantation in human patients (Bech-Hanssen, 2001; Aslam et al., 2007; Aljassim et al., 2008; Zogbi et al., 2009) or in animals (Yin et al., 2006). Numerical (“in silico”) methods can provide an alternative way to obtain relevant and detailed information for valve design optimization, since they are capable of solving the valve dynamics with a high degree of resolution in time and space (Kelly et al., 1999; Grigioni et al., 2004; Yoganathan et al., 2005; Dasi et al., 2009; Sotiropoulous & Borazjani, 2009). Moreover, they are considerably less time-consuming and less expensive during the research and development phase compared with experimental testing (Dasi et al., 2009) and are, therefore, particularly efficient for sensitivity studies (Verdonck, 2002). Unfortunately, the numerical simulation of a BMHV is a complex fluid-structure interaction (FSI) problem

Optimization of a piezoelectric fan using fluid-structure interaction simulation

In this paper, the heat transfer from a single heat fin to the air flow in the wake of a piezoelectric fan (piezofan) is optimised. Both the heat fin and the piezofan are positioned in a channel, which has a significant influence on the flow field. The design variable is the frequency of the voltage applied to the piezofan. The heat transfer for different excitation frequencies is calculated using unsteady fluid-structure interaction simulations. To obtain a modular simulation environment, the flow equations and the structural equations are solved separately. However, the equilibrium on the fluid-structure interface is not satisfied automatically in this partitioned approach. Therefore, the interface quasi-Newton technique with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS) is used to perform coupling iterations between the flow solver and the structural solver in each time step. With the unsteady fluid-structure interaction model, a surrogate model is constructed. The optimization of the surrogate model yields a frequency close to the first eigenfrequency of the structure.