The Separated Fung Law
Holger
Schmid
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model was implemented in a manner that could be used for performing finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland.
Model Structure
ABSTRACT: The study of ventricular mechanics-analyzing the distribution of strain and stress in myocardium throughout the cardiac cycle-is crucially dependent on the accuracy of the constitutive law chosen to represent the highly nonlinear and anisotropic properties of passive cardiac muscle. A number of such laws have been proposed and fitted to experimental measurements of stress-strain behavior. Here we examine five of these laws and compare them on the basis of (i) "goodness of fit:" How well they fit a set of six shear deformation tests, (ii) "determinability:" How well determined the objective function is at the optimal parameter fit, and (iii) "variability:" How well determined the material parameters are over the range of experiments. These criteria are utilized to discuss the advantages and disadvantages of the constitutive laws.
The original paper reference is cited below:
Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear, H. Schmid, M. P. Nash, A. A. Young and P. J. Hunter, 2006. Journal of Biomechanical Engineering, 128(5), 742-750. PubMed ID: 16995761
$\mathrm{Tdev11}=e^{\mathrm{bff}\mathrm{E11}^{2}}\mathrm{aff}\mathrm{bff}\mathrm{E11}$
$\mathrm{Tdev22}=e^{\mathrm{bss}\mathrm{E22}^{2}}\mathrm{ass}\mathrm{bss}\mathrm{E22}$
$\mathrm{Tdev33}=e^{\mathrm{bnn}\mathrm{E33}^{2}}\mathrm{ann}\mathrm{bnn}\mathrm{E33}$
$\mathrm{Tdev12}=e^{\mathrm{bfs}\mathrm{E12}^{2}}\mathrm{afs}\mathrm{bfs}\mathrm{E12}$
$\mathrm{Tdev13}=e^{\mathrm{bfn}\mathrm{E13}^{2}}\mathrm{afn}\mathrm{bfn}\mathrm{E13}$
$\mathrm{Tdev23}=e^{\mathrm{bns}\mathrm{E23}^{2}}\mathrm{ans}\mathrm{bns}\mathrm{E23}$
P
Hunter
J
Added metadata to the model.
Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear
128(5)
742
750
Journal of Biomechanical Engineering
Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear (Separated Fung Law)
Auckland Bioengineering Institute
H
Schmid
Updated documentation
In this simple model we only have one component, which holds the
six equations.
Holger
Schmid
2007-12-05T13:30:52+13:00
2004-02-18
Vignesh Kumar
h.schmid@auckland.ac.nz
M
Nash
P
This is a CellML version of the Separated Fung 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.
Holger
Schmid
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
The University of Auckland
Auckland Bioengineering Institute
A
Young
A
h.schmid@auckland.ac.nz
keyword
separated fung law
mechanical constitutive laws
simple shear
constitutive material law
2003-07-30T00:00:00+12:00
This file contains a CellML description of the Separated Fung Law, that defines the higly nonlinear and anisotropic properties of (passive) cardiac muscle
The University of Auckland
The Bioengineering Institute
Vignesh
Kumar
Catherine
Lloyd
M
2003-12-28
2006-10-01 00:00
16995761
Vignesh Kumar