A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation

Abstract

A previous study investigated a number of invariant-based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests and (ii) ‘variability’: how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Keywords:

• inverse parameter estimation
• myocardium
• orthotropic
• transversely isotropic
• polyconvexity

Acknowledgements

The authors would like to thank Socrates Dokos from the University of New South Wales for making the data available. Also Jessica Jor from the Auckland Bioengineering Institute for helping supervise W. Wang's final year project.