Myocardial Material Parameter Estimation—A Comparative Study for Simple Shear

Schmid, Hermann; Nash, Martyn P.; Young, Alistair A.; Hunter, Peter

doi:10.1115/1.2244576

Cited by 95 publications

(85 citation statements)

References 16 publications

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“…This is the tangent model introduced in Schmid et al (2006); see also Schmid et al (2008). We do not consider this model here.…”

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

“…Some of these are inappropriate for modelling myocardial tissue, including the Langevin eightchain based model of Bischoff et al (2002), which, as pointed out by Schmid et al (2008), does not reflect the morphology of the myocardium.…”

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

“…Note that several different forms of this model appear in various papers with or without appropriate modulus signs, and in some cases with b ij set equal to 2 for each i, j pair, as in Schmid et al (2006Schmid et al ( , 2008.…”

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

“…(ii) Fung-type model proposed by Schmid et al (2006) Another Fung-type model consisting of separate exponential terms for each component E ij was introduced by Schmid et al (2006) to decouple the effects of the material parameters in the single-exponential model (4.5) and (4.6). With 12 material parameters, it is given by…”

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

“…Humphrey & Yin 1987;Humphrey et al 1990;Guccione et al 1991;Costa et al 1996) and, more recently, orthotropic models (e.g. Hunter et al 1997;Costa et al 2001;Schmid et al 2006). We review these and several others briefly in §4.…”

Section: Introductionmentioning

confidence: 99%

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Constitutive modelling of passive myocardium: a structurally based framework for material characterization

Holzapfel

Ogden

2009

Phil. Trans. R. Soc. A.

662

835

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In this paper, we first of all review the morphology and structure of the myocardium and discuss the main features of the mechanical response of passive myocardium tissue, which is an orthotropic material. Locally within the architecture of the myocardium three mutually orthogonal directions can be identified, forming planes with distinct material responses. We treat the left ventricular myocardium as a non-homogeneous, thick-walled, nonlinearly elastic and incompressible material and develop a general theoretical framework based on invariants associated with the three directions. Within this framework we review existing constitutive models and then develop a structurally based model that accounts for the muscle fibre direction and the myocyte sheet structure. The model is applied to simple shear and biaxial deformations and a specific form fitted to the existing (and somewhat limited) experimental data, emphasizing the orthotropy and the limitations of biaxial tests. The need for additional data is highlighted. A brief discussion of issues of convexity of the model and related matters concludes the paper.

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“…This is the tangent model introduced in Schmid et al (2006); see also Schmid et al (2008). We do not consider this model here.…”

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

Section: (B) Orthotropic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constitutive modelling of passive myocardium: a structurally based framework for material characterization

Holzapfel

Ogden

2009

Phil. Trans. R. Soc. A.

662

835

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Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments

Holzapfel

2017

Encyclopedia of Computational Mechanics Second Edition

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Computational biomechanics of soft biological tissue is increasing our ability to address multi‐disciplinary problems of academic, industrial, and clinical importance. This chapter reviews parts of our current knowledge of the biomechanics of soft biological tissue such as the arterial wall, the heart wall with the heart valves, and the ligament, as well as some of the available computational methods used to analyze them. The inherent complexities of the biological microstructure and functions of the respective soft tissue are partly reviewed briefly, research effort related to the constitutive modeling is catalogued, and a representative constitutive model for each considered soft tissue is discussed in more detail. An account of residual stresses and biological processes such as growth and remodeling is provided. Finally, a few three‐dimensional finite element models, which attempt to explain the integrated function of the respective soft tissue in terms of geometry, structure, and material properties are emphasized.

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Computational modeling of passive myocardium

Göktepe

Acharya

Wong

et al. 2010

Numer Methods Biomed Eng

122

115

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SUMMARYThis work deals with the computational modeling of passive myocardial tissue within the framework of mixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a threefield Hu-Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler-Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue.

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Myocardial Material Parameter Estimation—A Comparative Study for Simple Shear

Cited by 95 publications

References 16 publications

Constitutive modelling of passive myocardium: a structurally based framework for material characterization

Constitutive modelling of passive myocardium: a structurally based framework for material characterization

Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments

Computational modeling of passive myocardium

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