Simulating the Fluid Dynamics of Natural and Prosthetic Heart Valves Using the Immersed Boundary Method

Griffith, Boyce E.; Luo, Xiaoyu; McQueen, David M.; Peskin, Charles S.

doi:10.1142/s1758825109000113

Cited by 164 publications

(171 citation statements)

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“…It may be possible to follow their approach to derive modified staggered-grid finite-difference operators that further improve the volume-conservation properties of the staggered-grid IB method. We anticipate, however, that the unmodified staggered-grid approach will prove more useful in practice both because it is likely to be easier to implement and also because its extensions to cases involving adaptive mesh refinement [23,25,26,28,29] or physical boundary conditions [25,27,29] are significantly more straightforward. Such extensions, which we and others are actively developing, are needed in the context of many of the applications of the IB method to challenging problems of fluid-structure interaction.…”

Section: Discussionmentioning

confidence: 99%

“…Approximate projection methods alleviate many of the difficulties of exact projection methods, although they do so at the price of yielding velocity fields that generally are not discretely divergence free. Approximate projection methods have been used with the IB method previously [22][23][24][25][26]; however, to date, there appear to have been few detailed comparisons between IB methods based on exact and approximate projections. Herein, we seek to quantify the extent to which using an approximate projection method affects the volume-conservation properties of the IB method.…”

Section: Introductionmentioning

confidence: 99%

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On the Volume Conservation of the Immersed Boundary Method

Griffith

2012

Commun. comput. phys.

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Abstract.The immersed boundary (IB) method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid. It is well known that some versions of the IB method can suffer from poor volume conservation. Methods have been introduced to improve the volume-conservation properties of the IB method, but they either have been fairly specialized, or have used complex, nonstandard Eulerian finite-difference discretizations. In this paper, we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method. We consider both collocated and staggered-grid discretization methods. For the tests considered herein, the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods, and in many cases considered in this work, the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes. We also compare the performance of cell-centered schemes that use either exact or approximate projection methods. We find that the volumeconservation properties of approximate projection IB methods depend strongly on the formulation of the projection method. When used with the IB method, we find that pressure-free approximate projection methods can yield extremely poor volume conservation, whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Volume Conservation of the Immersed Boundary Method

Griffith

2012

Commun. comput. phys.

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“…For non-periodic systems, one must generalize the definition of J and S in the case when the particle overlaps a physical boundary [79]. Even if a particle does not overlap a boundary, however, it will feel the boundary hydrodynamically and therefore both J PS and J L −1 S will depend on the proximity of the particle to physical boundaries.…”

Section: Translational Invariancementioning

confidence: 99%

Inertial coupling method for particles in an incompressible fluctuating fluid

Usabiaga

Delgado‐Buscalioni

Griffith

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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155

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We develop an inertial coupling method for modeling the dynamics of point-like "blob" The coupling between the fluid and the blob is based on a no-slip constraint equating the particle velocity with the local average of the fluid velocity, and conserves momentum and energy. We demonstrate that the formulation obeys a fluctuation-dissipation balance, owing to the non-dissipative nature of the no-slip coupling. We develop a spatiotemporal discretization that preserves, as best as possible, these properties of the continuum formulation. In the spatial discretization, the local averaging and spreading operations are accomplished using compact kernels commonly used in immersed boundary methods. We find that the special properties of these kernels allow the blob to provide an effective model of a particle; specifically, the volume, mass, and hydrodynamic properties of the blob are remarkably grid-independent. We develop a second-order semi-implicit temporal integrator that maintains discrete fluctuation-dissipation balance, and is not limited in stability by viscosity. Furthermore, the temporal scheme requires only constant-coefficient Poisson and Helmholtz linear solvers, enabling a very efficient and simple FFT-based implementation on GPUs. We numerically investigate the performance of the method on several standard test problems. In the deterministic setting, we find the blob to be a remarkably robust approximation to a rigid sphere, at both low and high Reynolds numbers. In the stochastic setting, we study in detail the short and long-time behavior of the velocity autocorrelation function and observe agreement with all of the known behavior for rigid sphere immersed in a fluctuating fluid. The proposed inertial coupling method provides a low-cost coarse-grained (minimal resolution) model of particulate flows over a wide range of time-scales ranging from 2 Brownian to convection-driven motion.

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“…Let V * (t) be the volume of blood in the ventricle during the heart cycle, with a maximum V 274 V. Meschini, M. D. de Tullio, G. Querzoli and R. Verzicco & Tonti (2010) and Querzoli et al (2010) have underlined the strong influence the mitral valve has on the diastolic flow structure, and Einstein et al (2005), Wattona et al (2008) and Griffith et al (2009) have focused on the dynamics of mitral valve leaflets. Moreover, McQueen & Peskin (2000) and Mihalef et al (2011) have studied the effect of combining realistic intra-ventricular flow with a physiological mitral valve using patient-specific models without fluid-structure interaction.…”

mentioning

confidence: 99%

Flow structure in healthy and pathological left ventricles with natural and prosthetic mitral valves

Meschini

Tullio²,

Querzoli

et al. 2017

J. Fluid Mech.

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In this paper, the structure and the dynamics of the flow in the left heart ventricle are studied for different pumping efficiencies and mitral valve types (natural, biological and mechanical prosthetic). The problem is investigated by direct numerical simulation of the Navier-Stokes equations, two-way coupled with a structural solver for the ventricle and mitral valve dynamics. The whole solver is preliminarily validated by comparisons with ad hoc experiments. It is found that the system works in a highly synergistic way and the left ventricular flow is heavily affected by the specific type of mitral valve, with effects that are more pronounced for ventricles with reduced pumping efficiency. When the ventricle ejection fraction (ratio of the ejected fluid volume to maximum ventricle volume over the cycle) is within the physiological range (50 %-70 %), regardless of the mitral valve geometry, the mitral jet sweeps the inner ventricle surface up to the apex, thus preventing undesired flow stagnation. In contrast, for pathological ejection fractions ( 40 %), the flow disturbances introduced by the bileaflet mechanical valve reduce the penetration capability of the mitral jet and weaken the recirculation in the ventricular apex. Although in clinical practice the fatality rates in the five-year follow-ups for mechanical and biological mitral valve replacements are essentially the same, a breakdown of the deaths shows that the causes are very different for the two classes of prostheses and the present findings are consistent with the clinical data. This might have important clinical implications for the choice of prosthetic device in patients needing mitral valve replacement.

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Simulating the Fluid Dynamics of Natural and Prosthetic Heart Valves Using the Immersed Boundary Method

Cited by 164 publications

References 50 publications

On the Volume Conservation of the Immersed Boundary Method

On the Volume Conservation of the Immersed Boundary Method

Inertial coupling method for particles in an incompressible fluctuating fluid

Flow structure in healthy and pathological left ventricles with natural and prosthetic mitral valves

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