On the chordae structure and dynamic behaviour of the mitral valve

Multi-Modal in Vitro Experiments Mimicking the Flow Through a Mitral Heart Valve Phantom

PURPOSE

Fluid-structure interaction (FSI) models are more commonly applied in medical research as computational power is increasing. However, understanding the accuracy of FSI models is crucial, especially in the context of heart valve disease in patient-specific models. Therefore, this study aimed to create a multi-modal benchmarking data set for cardiac-inspired FSI models, based on clinically important parameters, such as the pressure, velocity, and valve opening, with an in vitro phantom setup.

METHOD

An in vitro setup was developed with a 3D-printed phantom mimicking the left heart, including a deforming mitral valve. A range of pulsatile flows were created with a computer-controlled motor-and-pump setup. Catheter pressure measurements, magnetic resonance imaging (MRI), and echocardiography (Echo) imaging were used to measure pressure and velocity in the domain. Furthermore, the valve opening was quantified based on cine MRI and Echo images.

RESULT

The experimental setup, with 0.5% cycle-to-cycle variation, was successfully built and six different flow cases were investigated. Higher velocity through the mitral valve was observed for increased cardiac output. The pressure difference across the valve also followed this trend. The flow in the phantom was qualitatively assessed by the velocity profile in the ventricle and by streamlines obtained from 4D phase-contrast MRI.

CONCLUSION

A multi-modal set of data for validation of FSI models has been created, based on parameters relevant for diagnosis of heart valve disease. All data is publicly available for future development of computational heart valve models.

Comparison of Immersed Boundary Simulations of Heart Valve Hemodynamics Against In Vitro 4D Flow MRI Data

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator.

Capturing contact in mitral valve dynamic closure with fluid-structure interaction simulation

PURPOSE

Realistic fluid-structure interaction (FSI) simulation of the mitral valve opens the way toward planning for surgical repair. In the literature, blood leakage is identified by measuring the flow rate, but detailed information about closure efficiency is missing. We present in this paper an FSI model that improves the detection of blood leakage by building a map of contact.

METHODS

Our model is based on the immersed boundary method that captures a map of contact and perfect closure of the mitral valve, without the presence of orifice holes, which often appear with existing methods. We also identified important factors influencing convergence issues.

RESULTS

The method is demonstrated in three typical clinical situations: mitral valve with leakage, bulging, and healthy. In addition to the classical ways of evaluating MV closure, such as stress distribution and flow rate, the contact map provides easy detection of leakage with identification of the sources of leakage and a quality assessment of the closure.

CONCLUSIONS

Our method significantly improves the quality of the simulation and allows the identification of regurgitation as well as a spatial evaluation of the quality of valve closure. Comparably fast simulation, ability to simulate large deformation, and capturing detailed contact are the main aspects of the study.

On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method's performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretization combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta functions). Earlier work with this methodology suggested that such coarse structural meshes can yield improved accuracy for shear-dominated cases and, further, found that accuracy improves when the structural mesh spacing is increased. However, these results were limited to simple test cases that did not include substantial pressure loading on the structure. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations in a broader range of tests. Our results indicate that kernels satisfying a commonly imposed even-odd condition require higher resolution to achieve similar accuracy as kernels that do not satisfy this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, and that structural meshes that are substantially coarser than the Cartesian grid can yield high accuracy for shear-dominated cases but not for cases with large normal forces. We verify our results in a large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a pulse duplicator.

Clinical Impact of Computational Heart Valve Models

This paper provides a review of engineering applications and computational methods used to analyze the dynamics of heart valve closures in healthy and diseased states. Computational methods are a cost-effective tool that can be used to evaluate the flow parameters of heart valves. Valve repair and replacement have long-term stability and biocompatibility issues, highlighting the need for a more robust method for resolving valvular disease. For example, while fluid-structure interaction analyses are still scarcely utilized to study aortic valves, computational fluid dynamics is used to assess the effect of different aortic valve morphologies on velocity profiles, flow patterns, helicity, wall shear stress, and oscillatory shear index in the thoracic aorta. It has been analyzed that computational flow dynamic analyses can be integrated with other methods to create a superior, more compatible method of understanding risk and compatibility.

Automatic extraction of the mitral valve chordae geometry for biomechanical simulation

PURPOSE

Mitral valve computational models are widely studied in the literature. They can be used for preoperative planning or anatomical understanding. Manual extraction of the valve geometry on medical images is tedious and requires special training, while automatic segmentation is still an open problem.

METHODS

We propose here a fully automatic pipeline to extract the valve chordae architecture compatible with a computational model. First, an initial segmentation is obtained by sub-mesh topology analysis and RANSAC-like model-fitting procedure. Then, the chordal structure is optimized with respect to objective functions based on mechanical, anatomical, and image-based considerations.

RESULTS

The approach has been validated on 5 micro-CT scans with a graph-based metric and has shown an [Formula: see text] accuracy rate. The method has also been tested within a structural simulation of the mitral valve closed state.

CONCLUSION

Our results show that the chordae architecture resulting from our algorithm can give results similar to experienced users while providing an equivalent biomechanical simulation.

Fluid-structure interaction in a fully coupled three-dimensional mitral-atrium-pulmonary model

This paper aims to investigate detailed mechanical interactions between the pulmonary haemodynamics and left heart function in pathophysiological situations (e.g. atrial fibrillation and acute mitral regurgitation). This is achieved by developing a complex computational framework for a coupled pulmonary circulation, left atrium and mitral valve model. The left atrium and mitral valve are modelled with physiologically realistic three-dimensional geometries, fibre-reinforced hyperelastic materials and fluid–structure interaction, and the pulmonary vessels are modelled as one-dimensional network ended with structured trees, with specified vessel geometries and wall material properties. This new coupled model reveals some interesting results which could be of diagnostic values. For example, the wave propagation through the pulmonary vasculature can lead to different arrival times for the second systolic flow wave (S2 wave) among the pulmonary veins, forming vortex rings inside the left atrium. In the case of acute mitral regurgitation, the left atrium experiences an increased energy dissipation and pressure elevation. The pulmonary veins can experience increased wave intensities, reversal flow during systole and increased early-diastolic flow wave (D wave), which in turn causes an additional flow wave across the mitral valve (L wave), as well as a reversal flow at the left atrial appendage orifice. In the case of atrial fibrillation, we show that the loss of active contraction is associated with a slower flow inside the left atrial appendage and disappearances of the late-diastole atrial reversal wave (AR wave) and the first systolic wave (S1 wave) in pulmonary veins. The haemodynamic changes along the pulmonary vessel trees on different scales from microscopic vessels to the main pulmonary artery can all be captured in this model. The work promises a potential in quantifying disease progression and medical treatments of various pulmonary diseases such as the pulmonary hypertension due to a left heart dysfunction.

An Immersed Interface Method for Discrete Surfaces

Fluid-structure systems occur in a range of scientific and engineering applications. The immersed boundary (IB) method is a widely recognized and effective modeling paradigm for simulating fluid-structure interaction (FSI) in such systems, but a difficulty of the IB formulation of these problems is that the pressure and viscous stress are generally discontinuous at fluid-solid interfaces. The conventional IB method regularizes these discontinuities, which typically yields low-order accuracy at these interfaces. The immersed interface method (IIM) is an IB-like approach to FSI that sharply imposes stress jump conditions, enabling higher-order accuracy, but prior applications of the IIM have been largely restricted to numerical methods that rely on smooth representations of the interface geometry. This paper introduces an immersed interface formulation that uses only a C 0 representation of the immersed interface, such as those provided by standard nodal Lagrangian finite element methods. Verification examples for models with prescribed interface motion demonstrate that the method sharply resolves stress discontinuities along immersed boundaries while avoiding the need for analytic information about the interface geometry. Our results also demonstrate that only the lowest-order jump conditions for the pressure and velocity gradient are required to realize global second-order accuracy. Specifically, we demonstrate second-order global convergence rates along with nearly second-order local convergence in the Eulerian velocity field, and between first- and second-order global convergence rates along with approximately first-order local convergence for the Eulerian pressure field. We also demonstrate approximately second-order local convergence in the interfacial displacement and velocity along with first-order local convergence in the fluid traction along the interface. As a demonstration of the method's ability to tackle more complex geometries, the present approach is also used to simulate flow in a patient-averaged anatomical model of the inferior vena cava, which is the large vein that carries deoxygenated blood from the lower extremities back to the heart. Comparisons of the general hemodynamics and wall shear stress obtained by the present IIM and a body-fitted discretization approach show that the present method yields results that are in good agreement with those obtained by the body-fitted approach.

Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve

We present a coupled left atrium-mitral valve model based on computed tomography scans with fibre-reinforced hyperelastic materials. Fluid-structure interaction is realised by using an immersed boundary-finite element framework. Effects of pathological conditions, eg, mitral valve regurgitation and atrial fibrillation, and geometric and structural variations, namely, uniform vs non-uniform atrial wall thickness and rule-based vs atlas-based fibre architectures, on the system are investigated. We show that in the case of atrial fibrillation, pulmonary venous flow reversal at late diastole disappears, and the filling waves at the left atrial appendage orifice during systole have reduced magnitude. In the case of mitral regurgitation, a higher atrial pressure and disturbed flows are seen, especially during systole, when a large regurgitant jet can be found with the suppressed pulmonary venous flow. We also show that both the rule-based and atlas-based fibre defining methods lead to similar flow fields and atrial wall deformations. However, the changes in wall thickness from non-uniform to uniform tend to underestimate the atrial deformation. Using a uniform but thickened wall also lowers the overall strain level. The flow velocity within the left atrial appendage, which is important in terms of appendage thrombosis, increases with the thickness of the left atrial wall. Energy analysis shows that the kinetic and dissipation energies of the flow within the left atrium are altered differently by atrial fibrillation and mitral valve regurgitation, providing a useful indication of the atrial performance in pathological situations.

Some Effects of Different Constitutive Laws on FSI Simulation for the Mitral Valve

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.