A Constitutive Law for Mitral Valve Tissue

May‐Newman, Karen; Yin, F. C. P.

doi:10.1115/1.2834305

Cited by 178 publications

(170 citation statements)

References 23 publications

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“…It is easy to check that S 33 = 0 by inserting (27) 2 into (26) 1 , which shows that the plane stress condition is fulfilled.…”

Section: Stress Tensors and Lagrange Multipliermentioning

confidence: 93%

“…May-Newman and Yin [1] proposed a transversely isotropic material law for mitral valve tissue. It is based on experimental data obtained from biaxial tension tests carried out on porcine mitral valves.…”

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

“…We identified now the material parameters c 0 , c 1 and c 2 of the strain-energy function (15) by fitting the related stress-stretch relations to the stress-stretch relations of the model (14), as proposed by May-Newman and Yin [1], using four sets of biaxial tests (equibiaxial, off-biaxial, strip Table I. Average material parameter values for the strain-energy function by May-Newman and Yin [1] according to Equation (14).…”

Section: Identification Of the Materials Parametersmentioning

confidence: 99%

“…These tests demonstrated that both leaflets are anisotropic and exhibit highly non-linear mechanical response. In [1] the focus was on in vitro biaxial testing of mitral valve tissue, and on the important identification of a strain-energy function and material parameters, but not on its implementation.…”

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

“…The formulation of transversely isotropic hyperelasticity is based on the account provided by Holzapfel [11], and the constitutive models for mitral valves are adopted from May-Newman and Yin [1] and Holzapfel et al [12]. Related stress-strain relationships and their linearizations are provided 989 and implemented in the user-defined subroutine UMAT within the finite element program ABAQUS.…”

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

See 4 more Smart Citations

Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

Prot

Skallerud

Holzapfel

2007

Numerical Meth Engineering

108

129

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SUMMARYThe present study addresses constitutive modelling and implementation of transversely isotropic hyperelastic material models for the analysis of the mitral valve. This valve separates the left atrium and left ventricle in the heart. Two convex strain energy potentials are employed in derivation of stress tensors and elasticity tensors. The plane stress and incompressibility conditions are accounted for directly. The relationships are implemented in an implicit code (ABAQUS) via the user-defined interface. Numerical simulations of the valve motion during a part of the heart cycle are carried out and compared to ultrasound measurements of a healthy human valve. The significance of placement of chordae tendinae is illustrated. The implementation provides a tool for simulations of both healthy and pathological mitral valve conditions.

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“…It is easy to check that S 33 = 0 by inserting (27) 2 into (26) 1 , which shows that the plane stress condition is fulfilled.…”

Section: Stress Tensors and Lagrange Multipliermentioning

confidence: 93%

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

Section: Identification Of the Materials Parametersmentioning

confidence: 99%

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

Section: Prot B Skallerud and G A Holzapfelmentioning

confidence: 99%

See 3 more Smart Citations

Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

Prot

Skallerud

Holzapfel

2007

Numerical Meth Engineering

108

129

View full text Add to dashboard Cite

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Fluid–structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future

Einstein

Jiao

et al. 2009

Numer Methods Biomed Eng

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SUMMARYThe remodeling that occurs after a posterolateral myocardial infarction can alter mitral valve function by creating conformational abnormalities in the mitral annulus and in the posteromedial papillary muscle, leading to mitral regurgitation (MR). It is generally assumed that this remodeling is caused by a volume load and is mediated by an increase in diastolic wall stress. Thus, mitral regurgitation can be both the cause and effect of an abnormal cardiac stress environment. Computational modeling of ischemic MR and its surgical correction is attractive because it enables an examination of whether a given intervention addresses the correction of regurgitation (fluid-flow) at the cost of abnormal tissue stress. This is significant because the negative effects of an increased wall stress due to the intervention will only be evident over time. However, a meaningful fluid-structure interaction model of the left heart is not trivial; it requires a careful characterization of the in-vivo cardiac geometry, tissue parameterization though inverse analysis, a robust coupled solver that handles collapsing Lagrangian interfaces, automatic grid-generation algorithms that are capable of accurately discretizing the cardiac geometry, innovations in image analysis, competent and efficient constitutive models and an understanding of the spatial organization of tissue microstructure. In this manuscript, we profile our work toward a comprehensive fluid-structure interaction model of the left heart by reviewing our early work, presenting our current work and laying out our future work in four broad categories: data collection, geometry, fluid-structure interaction and validation.Keywords biofluid-structure interactions; ischemic mitral regurgitation; imaging based finite element models

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A finite strain nonlinear human mitral valve model with fluid‐structure interaction

Gao

et al. 2014

Numer Methods Biomed Eng

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A computational human mitral valve (MV) model under physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally-based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used to characterize the mechanical behaviour of the MV tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with measurements from in vivo magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet and are concentrated around the annulus trigons and the belly of the leaflet. The results also show that the chordae play an important role in providing a secondary orifice for the flow when the valve opens. Although there are some discrepancies to be overcome in future work, our simulations show that the developed computational model is promising in mimicking the in vivo MV dynamics and providing important information that are not obtainable by in vivo measurements. © 2014 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

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A Constitutive Law for Mitral Valve Tissue

Cited by 178 publications

References 23 publications

Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

Fluid–structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future

A finite strain nonlinear human mitral valve model with fluid‐structure interaction

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