This is the code created by Vijay Rajgopal and used in CM.
Update 09 November 2015: A combination effort from Jagir Hussan, Vicky Wang, and David Nickerson to check the model and get it working in passive elasticity simulations in OpenCMISS. Model also simplified by Vicky to clarify the equations.
This is an example of how CellML can be used to describe a material law which models the passive, mechanical behaviour of a material. The material law is to calculate the stress induced in a body when a certain amount of deformation (strain) is imposed on it. The calculated stresses are used to solve a system of equations that govern the mechanics of large deformations. This is an example of how CellML can be used to describe a material law. The example presented is the Guccione constitutive material law, which defines the relationship between six independent strain components and the stress components.
The Guccione material law was developed by Guccione et al. to model the passive material (mechanical) properties of intact ventricular myocardium.They approximated the equatorial region of the canine left ventricle as a thich-walled cylinder made of incompressible (volume is conserved during deformation), hyperelastic (stores energy during deformation) and homogeneous (made of same material) myocardium. Biaxial tests have shown that passive myocardium exhibits anisotropy due to the fibre orientation and structure of myocardial tissue (Guccione et al. 1991). Here, Guccione et al. assumed transverse isotropy (behaviour is independent of all directions of loading perpendicular to one direction). For further details refer to Guccione et al. 1991.
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. Examples of how the CellML model is used can seen here.
The complete original paper reference is cited below:
Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model, J. M. Guccione, A. D. McCulloch, and L. K. Waldman, 1991. Journal of Biomechanical Engineering , 113, 42-55. PubMed ID: 2020175