/*
 * The Guccione Constitutive Material Law
 * 
 * Model Status
 * 
 * ValidateCellML verifies this model as valid CellML with consistent
 * units.
 * 
 * Model Structure
 * 
 * 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)
 */

import nsrunit;
unit conversion on;
unit strain=1  dimensionless;
unit stress=1  dimensionless;

math main {
	//Warning:  the following variables were set 'extern' or given
	//  an initial value of '0' because the model would otherwise be
	//  underdetermined:  E11, E12, E13, E22, E23, E33
	extern real E11 strain;
	extern real E12 strain;
	extern real E13 strain;
	extern real E22 strain;
	extern real E23 strain;
	extern real E33 strain;
	real a strain;
	a=0;
	real bff strain;
	bff=0;
	real bfn strain;
	bfn=0;
	real bfs strain;
	bfs=0;
	real bnn strain;
	bnn=0;
	real bns strain;
	bns=0;
	real bss strain;
	bss=0;
	real Tdev11 stress;
	real Tdev12 stress;
	real Tdev13 stress;
	real Tdev22 stress;
	real Tdev23 stress;
	real Tdev33 stress;
	real q strain;

	// <component name="interface">

	// <component name="equations">
	q=(bff*E11^2+bss*E22^2+bnn*E33^2+2*bfn*E13^2+2*bfs*E12^2+2*bns*E23^2);
	Tdev11=(a*bff*E11*exp(q));
	Tdev22=(a*bss*E22*exp(q));
	Tdev33=(a*bnn*E33*exp(q));
	Tdev12=(a*bfs*E12*exp(q));
	Tdev13=(a*bfn*E13*exp(q));
	Tdev23=(a*bns*E23*exp(q));
}