Computational Mechanics of the Heart
 M. P. Nash,
 P. J. Hunter
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Finite elasticity theory combined with finite element analysis provides the framework for analysing ventricular mechanics during the filling phase of the cardiac cycle, when cardiac cells are not actively contracting. The orthotropic properties of the passive tissue are described here by a “pole–zero” constitutive law, whose parameters are derived in part from a model of the underlying distributions of collagen fibres. These distributions are based on our observations of the fibroussheet laminar architecture of myocardial tissue. We illustrate the use of high order (cubic Hermite) basis functions in solving the Galerkin finite element stress equilibrium equations based on this orthotropic constitutive law and for incorporating the observed regional distributions of fibre and sheet orientations. Pressure–volume relations and 3D principal strains predicted by the model are compared with experimental observations. A model of active tissue properties, based on isolated muscle experiments, is also introduced in order to predict transmural distributions of 3D principal strains at the end of the contraction phase of the cardiac cycle. We end by offering a critique of the current model of ventricular mechanics and propose new challenges for future modellers.
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 Title
 Computational Mechanics of the Heart
 Journal

Journal of elasticity and the physical science of solids
Volume 61, Issue 13 , pp 113141
 Cover Date
 20000701
 DOI
 10.1023/A:1011084330767
 Print ISSN
 03743535
 Online ISSN
 15732681
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 finite elastic deformation
 cardiac mechanics
 orthotropic constitutive relations
 fibroussheet tissue structure
 Industry Sectors
 Authors

 M. P. Nash ^{(1)}
 P. J. Hunter ^{(2)}
 Author Affiliations

 1. University Laboratory of Physiology, University of Oxford, Parks Road, Oxford, OX1 3PT, U.K.
 2. Department of Engineering Science, The University of Auckland, Auckland, New Zealand