The Guccione Constitutive Material Law
Vijayaraghavan
Rajagopal
Auckland Bioengineering Institute, The University of Auckland
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ABSTRACT: The central problem in modelling the multi-dimensional mechanics of the heart is in identifying functional forms and parameters of the constitutive equations, which describe the material properties of the resting and active, normal and diseased myocardium. The constitutive properties of myocardium are three dimensional, anisotropic, nonlinear and time dependent. Formulating useful constitutive laws requires a combination of multi-axial tissue testing in vitro, microstructural modelling based on quantitative morphology, statistical parameter estimation, and validation with measurements from intact hearts. Recent models capture some important properties of healthy and diseased myocardium including: the nonlinear interactions between the responses to different loading patterns; the influence of the laminar myofibre sheet architecture; the effects of transverse stresses developed by the myocytes; and the relationship between collagen fibre architecture and mechanical properties in healing scar tissue after myocardial infarction.
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 Auckland Bioengineering Institute, The University of Auckland.
For additional information on implementation of cellML files in CMISS, please refer to the following Link.
The 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. (no PubMed ID)
$q=\mathrm{bff}\mathrm{E11}^{2}+\mathrm{bss}\mathrm{E22}^{2}+\mathrm{bnn}\mathrm{E33}^{2}+2\mathrm{bfn}\mathrm{E13}^{2}+2\mathrm{bfs}\mathrm{E12}^{2}+2\mathrm{bns}\mathrm{E23}^{2}$
$\mathrm{Tdev11}=a\mathrm{bff}\mathrm{E11}e^{q}$
$\mathrm{Tdev22}=a\mathrm{bss}\mathrm{E22}e^{q}$
$\mathrm{Tdev33}=a\mathrm{bnn}\mathrm{E33}e^{q}$
$\mathrm{Tdev12}=a\mathrm{bfs}\mathrm{E12}e^{q}$
$\mathrm{Tdev13}=a\mathrm{bfn}\mathrm{E13}e^{q}$
$\mathrm{Tdev23}=a\mathrm{bns}\mathrm{E23}e^{q}$
Auckland Bioengineering Institute
University of Auckland
Auckland Bioengineering Institute
Holger
Schmid
h.schmid@auckland.ac.nz
h.schmid@auckland.ac.nz
In this simple model we only have one component, which holds the
six equations.
Modelling Cardiac Mechanical Properties In Three Dimensions
359
1233
1250
James
Lawson
Richard
A
McCulloch
D
This file contains a CellML description of the Orthotropic Exponential Constitutive relationship proposed by Costa et. al. (2001), it deals with the situation of modelling the three dimensional mechanical properties of cardiac tissue.
Updated documentation
2005-07-30T00:00:00+00:00
This is a CellML version of the Costa constitutive material law, defining the relation between the six independent strain components
and the stress components. It is assumed that the strain components
will be controlled externally by the application using this CellML
model.
Vignesh Kumar
J
Holmes
W
Catherine
Lloyd
M
2009-06-08T12:51:49+12:00
Vignesh Kumar
K
Costa
D
Vignesh
Kumar
Holger
Schmid
2007-12-04T12:21:03+13:00
Philosophical Transactions of The Royal Society
keyword
costa law
mechanical constitutive laws
cardiac mechanics
Added metadata to the model.
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2004-02-18
The University of Auckland
The Bioengineering Institute
2001-06-15 00:00
updated curation status
2003-12-28