Costa, Holmes, McCulloch, 2001

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Model Structure

The mechanics of the heart are multi-dimensional by nature, the constitutive properties of myocardium are three dimensional; anisotropic, nonlinear and time dependent. The significance of this is that the forces generated by the ventricular sarcomeres (basic functional units of muscle) are converted to chamber pressures in the heart. These forces and chamber pressures are in turn dependant on the three-dimensional geometry and myofibre architecture of the ventricular myocardium.

One of the main problems in modeling the heart and its mechanical properties is its inherent multi-dimensional nature; the foremost issues of concern include identifying functional forms and parameters of the constitutive equations, which describe the material properties of the resting and active, normal and diseased myocardium.

Formulating useful constitutive laws are the key to solving the problem of modelling cardiac mechanics, and requires a combination of things. Such as multi-axial tissue testing in vitro, microstructural modelling based on quantitative morphology, statistical parameter estimation, and validation with measurements from intact hearts.

The inability to simplify myocardium mechanics to a 2D level requires a more rigorous approach, and so mathematical models are needed to interpret experimental and clinical observations on regional myocardial deformations.

Because the problem of modelling cardiac mechanics is nonlinear, dynamic and three-dimensional, numerical methods are essential for accurate quantitative analysis. Many aspects of the problem are covered elsewhere: LeGrice et al. (2001) and Guccione et al. (1991) .

In the paper described here, Kevin Costa, Jeffrey Holmes and Andrew McCulloch review a critical challenge in myocardial mechanics: developing accurate constitutive models that describe how the structure and biophysics of the normal and diseased myocardium give rise to the mechanical responses of the intact tissue.

While much of the work in this field builds on uniaxial and two-dimensional studies, the authors focus primarily on three-dimensional measurements and models.

The model was implemented in a manner that could be used for peforming finite element model simulations on the CMISS software program developed at the Bioengineering Institute, University of Auckland.

For additional information on implementation of cellML files in CMISS, please refer to the following Link.

The complete original paper reference is cited below:

Modelling cardiac mechanical properties in three dimensions, K.D. Costa, J.W. Holmes and A. D. McCulloch, 2001. Philosophical Transactions of The Royal Society , 359, 1233-1250. PubMed ID: Unknown