Equivalence Of Two Approaches To Study
The Stress-strain Relation In The Myocardium
Author(s)
R. M. Shoucri
Abstract
A method to study the mechanics of ventricular contraction was developed in
previous publications by the author. In those studies, the active force of the
myocardium is represented as force per unit volume of the myocardium. Other
authors have developed studies in which the active force of the myocardium is
included in the expression of the total stress derived from the constitutive
relations. The purpose of the present study is to show how to make the
connection between these two approaches. Derivation is done in a general way,
expressions for the stress components are derived and application to
experimental data is presented. The possibility of relating the pseudo strain
energy function to the tension generated by the muscular fibre is also shown.
Keywords: cardiac mechanics, mathematical modelling of ventricular
contraction, pressure-volume relation, active force of the myocardium, pseudo
strain energy function.
1 Introduction
In previous studies by the author a method to study the stress-strain relation in
the myocardium was developed in which the active force generated by the
myocardium was represented as force per unit volume of the myocardium [1-6].
This mathematical approach used a cylindrical model of the left ventricle and
was successfully developed by using both large elastic deformation [1, 2] and
linear elasticity [3, 4], the transition from large elastic deformation to linear
elasticity was discussed in [6]. Most other studies that have been developed
focus on the way the expression of the total stress can be derived from the
constitutive relations [9-11].
Keywords
cardiac mechanics, mathematical modelling of ventricular
contraction, pressure-volume relation, active force of the myocardium, pseudo
strain energy function.
Related Book
Other papers in this volume
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