The Guccione Constitutive Material Law
Vijayaraghavan
Rajagopal
Bioengineering Institute, University of Auckland
Model Status
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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
$q=\mathrm{bff}\mathrm{E11}^{2}+\mathrm{bss}\mathrm{E22}^{2}+\mathrm{bnn}\mathrm{E33}^{2}+2\mathrm{bfn}\mathrm{E13}^{2}+2\mathrm{bfs}\mathrm{E12}^{2}+2\mathrm{bns}\mathrm{E23}^{2}$
$\mathrm{Tdev11}=a\mathrm{bff}\mathrm{E11}e^{q}$
$\mathrm{Tdev22}=a\mathrm{bss}\mathrm{E22}e^{q}$
$\mathrm{Tdev33}=a\mathrm{bnn}\mathrm{E33}e^{q}$
$\mathrm{Tdev12}=a\mathrm{bfs}\mathrm{E12}e^{q}$
$\mathrm{Tdev13}=a\mathrm{bfn}\mathrm{E13}e^{q}$
$\mathrm{Tdev23}=a\mathrm{bns}\mathrm{E23}e^{q}$
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.
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
2004-02-18
The University of Auckland
The Bioengineering Institute
2001-06-15 00:00
updated curation status
2003-12-28