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

Some effects of different constitutive laws on simulating mitral valve dynamics with FSI

In this paper, three different constitutive laws for mitral leaflets and two laws for chordae tendineae are selected to study their effects on mitral valve dynamics with fluid-structure interaction. We first fit these three mitral leaflet constitutive laws and two chordae tendineae laws with experimental data. The fluid-structure interaction is implemented in an immersed boundary framework with finite element extension for solid, that is the hybrid immersed boundary/finite element(IB/FE) method. We specifically compare the fluid-structure results of different constitutive laws since fluid-structure interaction is the physiological loading environment. This allows us to look at the peak jet velocity, the closure regurgitation volume, and the orifice area. Our numerical results show that different constitutive laws can affect mitral valve dynamics, such as the transvalvular flow rate, closure regurgitation and the orifice area, while the differences in fiber strain and stress are insignificant because all leaflet constitutive laws are fitted to the same set of experimental data. In addition, when an exponential constitutive law of chordae tendineae is used, a lower closure regurgitation flow is observed compared to that of a linear material model. In conclusion, combining numerical dynamic simulations and static experimental tests, we are able to identify suitable constitutive laws for dynamic behaviour of mitral leaflets and chordae under physiological conditions

Multiblock High Order Large Eddy Simulation of Powered Fontan Hemodynamics: Towards Computational Surgery

Children born with only one functional ventricle must typically undergo a series of three surgeries to obtain the so-called Fontan circulation in which the blood coming from the body passively flows from the Vena Cavae (VCs) to the Pulmonary Arteries (PAs) through the Total Cavopulmonary Connection (TCPC). The circulation is inherently inefficient due to the lack of a subpulmonary ventricle. Survivors face the risk of circulatory sequelae and eventual failure for the duration of their lives. Current efforts are focused on improving the outcomes of Fontan palliation, either passively by optimizing the TCPC, or actively by using mechanical support. We are working on a chronic implant that would be placed at the junction of the TCPC, and would provide the necessary pressure augmentation to re-establish a circulation that recapitulates a normal two-ventricle circulation. This implant is based on the Von Karman viscous pump and consists of a vaned impeller that rotates inside the TCPC. To evaluate the performance of such a device, and to study the flow features induced by the presence of the pump, Computational Fluid Dynamics (CFD) is used. CFD has become an important tool to understand hemodynamics owing to the possibility of simulating quickly a large number of designs and flow conditions without any harm for patients. The transitional and unsteady nature of the flow can make accurate simulations challenging. We developed and in-house high order Large Eddy Simulation (LES) solver coupled to a recent Immersed Boundary Method (IBM) to handle complex geometries. Multiblock capability is added to the solver to allow for efficient simulations of complex patient specific geometries. Blood simulations are performed in a complex patient specific TCPC geometry. In this study, simulations without mechanical assist are performed, as well as after virtual implantation of the temporary and chronic implants being developed. Instantaneous flow structures, hepatic factor distribution, and statistical data are presented for all three cases

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 fluidstructure 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

Fluid-structure Interaction Simulation of Bileaflet and Monoleaflet Mechanical Heart Valve Flow Dynamics

In this study, opening and closing behavior of monoleaflet and bileaflet prosthetic heart valves was simulated using 2D and 3D Fluid Structure Interaction (FSI) models. The FSI models were based on the arbitrary Lagrangian-Eulerian (ALE) method for moving boundaries. Leaflet and diaphragm motions were described by means of user-defined functions following the experimental setup in a previous study. The hemodynamic performance of monoleaflet valves at the opening angle of 45, 60, 75, 80, and 85 was compared and results from this study demonstrated that the optimal opening angle should fall between 75 and 80. As the opening angle further increased, even though the calculated flow parameters continued to improve, the large angle could prevent the valve to close properly, which might lead to the failure of the heart valve. Furthermore, the hemodynamic performance of bileaflet and monoleaflet heart valves following the design of St. Jude bileaflet valve with 85 of opening angle and Bjork-Shiley monoleaflet valve with 75 of opening angle was compared. Results demonstrated that the flow in the monoleaflet valve design had a lower maximum velocity compared to the bileaflet design during both opening and closing phases which resulted in lower chance for flow to transition to turbulence. The mean pressure gradients across the monoleaflet and bileaflet valves were similar and resulted in an analogous EOA for these valves. According to the results of this study, the bileaflet valve had higher chance of developing cavitation bubbles during the valve closure because of higher pressure drops across the valve.Mechanical & Aerospace Engineerin

Improved acoustic modeling for automatic piano music transcription using echo state networks

Automatic music transcription (AMT) is one of the challenging problems in Music Information Retrieval with the goal of generating a score-like representation of a polyphonic audio signal. Typically, the starting point of AMT is an acoustic model that computes note likelihoods from feature vectors. In this work, we evaluate the capabilities of Echo State Networks (ESNs) in acoustic modeling of piano music. Our experiments show that the ESN-based models outperform state-of-the-art Convolutional Neural Networks (CNNs) by an absolute improvement of 0.5 F-1-score without using an extra language model. We also discuss that a two-layer ESN, which mimics a hybrid acoustic and language model, achieves better results than the best reference approach that combines Invertible Neural Networks (INNs) with a biGRU language model by an absolute improvement of 0.91 F-1-score

Windkessel modeling of the human arterial system

Cardiovascular diseases are a major concern of our society. Millions of patients all around the world are affected by disorders such as arrhythmias or atherosclerosis. Moreover, finding new diagnostic techniques and treatments is of increased difficulty due to the complexity of cardiovascular medicine. In this context, the upcoming generations of experts must be well prepared for overcoming such a challenge. This project aims to develop an educational tool that will allow students to improve their understanding on cardiovascular fluid mechanics and physiology and will allow them to gain practical experience before dealing with real patients. A system modelling the arterial system, available at the Universidad Carlos III de Madrid, is used for this purpose. The educational tool is composed by a theoretical simulation interface and an acquisition and control program, created using MATLAB, and a practical environment based on a physical pneumatic-hydraulic device. A laboratory practice for the students has been developed describing how to work with both platforms.Ingeniería Biomédic