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

Holzapfel, Gerhard; Ogden, Ray W.

doi:10.1098/rsta.2009.0091

Cited by 632 publications

(808 citation statements)

References 44 publications

(110 reference statements)

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“…Within the same general framework an extension of the model to the passive mechanical response of the myocardium has been developed by Holzapfel & Ogden (2009b). The model embraces the (orthotropic) morphological structure of the myocardium and accounts for the muscle fibre direction and the myocyte sheet structure and fits very well the available simple shear data of Dokos et al (2002).…”

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

“…The model embraces the (orthotropic) morphological structure of the myocardium and accounts for the muscle fibre direction and the myocyte sheet structure and fits very well the available simple shear data of Dokos et al (2002). Figure 7, adopted from Holzapfel & Ogden (2009b), shows a comparison of the constitutive model with simple shear data (Dokos et al 2002) obtained from tests that were conducted on cubeshaped specimens from different orientations within the passive ventricular myocardium from pig hearts. The pairs fs, fn and sn refer to the fibre-sheet, fibre-normal and sheet-normal planes, and the enclosing parentheses indicate the direction of shear within the plane; for example, (fs) indicates shear in the s direction in the fs plane.…”

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

“…Figure 7. Fit of the constitutive model of Holzapfel & Ogden (2009b) to simple shear data obtained from tests that were conducted on cube-shaped specimens from the passive ventricular myocardium of pig hearts; see Dokos et al (2002). The pairs fs, fn and sn refer to the fibre-sheet, fibre-normal and sheet-normal planes, and the direction of shear within each plane is identified by the ordered pair enclosed in parentheses, as described in the text.…”

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

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Constitutive modelling of arteries

2010

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This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thickwalled circular cylindrical tube in order to illustrate its extension-inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

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Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

Section: (B) Modelling Other Soft Tissuesmentioning

confidence: 99%

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Constitutive modelling of arteries

2010

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“…The material is non-linear hyper-elastic, with anisotropic behaviour ruled by the fiber structure. In this work, we use a transversally isotropic material based on [10] and presented in [17].…”

Section: The Electro-mechamical Cardiac Model -Explicit Non-linear Somentioning

confidence: 99%

Alya: Multiphysics engineering simulation toward exascale

Vázquez

Houzeaux

Korić

et al. 2016

Journal of Computational Science

156

106

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Abstract. Alya is a multi-physics simulation code developed at Barcelona Supercomputing Center (BSC). From its inception Alya code is designed using advanced High Performance Computing programming techniques to solve coupled problems on supercomputers efficiently. The target domain is engineering, with all its particular features: complex geometries and unstructured meshes, coupled multi-physics with exotic coupling schemes and physical models, ill-posed problems, flexibility needs for rapidly including new models, etc. Since its beginnings in 2004, Alya has scaled well in an increasing number of processors when solving single-physics problems such as fluid mechanics, solid mechanics, acoustics, etc. Over time, we have made a concerted effort to maintain and even improve scalability for multi-physics problems. This poses challenges on multiple fronts, including: numerical models, parallel implementation, physical coupling models, algorithms and solution schemes, meshing process, etc. In this paper, we introduce Alya's main features and focus particularly on its solvers. We present Alya's performance up to 100.000 processors in Blue Waters, the NCSA supercomputer with selected multi-physics tests that are representative of the engineering world. The tests are incompressible flow in a human respiratory system, low Mach combustion problem in a kiln furnace, and coupled electro-mechanical contraction of the heart. We show scalability plots for all cases and discuss all aspects of such simulations, including solver convergence.Key words. Multi-physics coupling, Parallelisation, Computational Mechanics 1. Introduction. Across a range of engineering fields, the use of computational models is pervasive in the whole design and manufacturing process. In complex systems, High Performance Computing (HPC) plays an essential role in simulation and modelling. Researchers and manufacturing teams depend on HPC to create safe cars and energy-efficient aircraft as well as effective communication systems and efficient supply chain models. Availability of advanced HPC technologies has also fundamentally altered the investigative paradigm in the field of biomechanics. But paradoxically, for many engineers and researchers, the existing hardware and software cannot be used to solve their problems. There are many reasons why this happens, but we focus here in only two. On one hand, current HPC systems lack the computational power, network bandwidth and data storage needed for solving tomorrow's real-world engineering challenges. On the other hand, while emerging peta-scale computing is already a strategic enabler of large-scale simulations in many scientific areas (such as astronomy, biology and chemistry), even the most powerful hardware will fail to deliver on its full potential unless matched with simulation software designed specifically for such environments.Several papers describe the effort of performing large-scale simulations on supercomputers, covering key areas: molecular dynamics [26], mantle convection in solid earth dynami...

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“…The myocardial constitutive model employed in this study is a transversally isotropic version of the Holzapfel and Ogden [12] model. Therefore, the myocardium is considered as a non-homogeneous, non-linearly elastic, slightly compressible material [13].…”

Section: Biomechanicsmentioning

confidence: 99%

Fully-Coupled Electromechanical Simulations of the LV Dog Anatomy Using HPC: Model Testing and Verification

Aguado-Sierra

Santiago

Rivero

et al. 2015

Lecture Notes in Computer Science

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Abstract. Verification of electro-mechanic models of the heart require a good amount of reliable, high resolution, thorough in-vivo measurements. The detail of the mathematical models used to create simulations of the heart beat vary greatly. Generally, the objective of the simulation determines the modeling approach. However, it is important to exactly quantify the amount of error between the various approaches that can be used to simulate a heart beat by comparing them to ground truth data. The more detailed the model is, the more computing power it requires, we therefore employ a high-performance computing solver throughout this study. We aim to compare models to data measured experimentally to identify the effect of using a mathematical model of fibre orientation versus the measured fibre orientations using DT-MRI. We also use simultaneous endocardial stimuli vs an instantaneous myocardial stimulation to trigger the mechanic contraction. Our results show that synchronisation of the electrical and mechanical events in the heart beat are necessary to create a physiological timing of hemodynamic events. Synchronous activation of all of the myocardium provides an unrealistic timing of hemodynamic events in the cardiac cycle. Results also show the need of establishing a protocol to quantify the zero-pressure configuration of the left ventricular geometry to initiate the simulation protocol; however, the predicted zero-pressure configuration of the same geometry was different, depending on the origin of the fibre field employed.

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

Cited by 632 publications

References 44 publications

Constitutive modelling of arteries

Constitutive modelling of arteries

Alya: Multiphysics engineering simulation toward exascale

Fully-Coupled Electromechanical Simulations of the LV Dog Anatomy Using HPC: Model Testing and Verification

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