Comparison Between Linear Elasticity And
Large Elastic Deformation In The Study Of
The Contraction Of The Myocardium
Author(s)
R. M. Shoucri
Abstract
The purpose of this study is to compare the mathematical formalism obtained by
using linear elasticity with the formalism obtained by using large elastic
deformation in the calculation of the stress in the myocardium. This study is
motivated by previous results based on the theory of linear elasticity that have
shown consistency in the calculation of the stress expressed as a sum of an active
and a passive component. The myocardium is represented as a thick-walled
elastic cylinder contracting symmetrically in which the active force is expressed
as a force/unit volume of the myocardium.
Keywords: cardiac mechanics, mathematical modelling of ventricular
contraction, pressure-volume relation, active force of the myocardium.
1 Introduction
One of the difficulties encountered in the study of stress-strain analysis in the
myocardium is the fact that the myocardium is a composite structure with active
elements generating an active force during the contraction of the myocardium
[1–6]. An approach to solve this problem was to model the active force
generated by the myocardium as force per unit volume of the myocardium. By
using large elastic deformation, this approach was applied to the study of the
pressure-volume relation in the left ventricle [1,2]. By using the linear theory of
elasticity, the concept of active force/unit volume of the myocardium was used to
derive expressions for the active stress due to the muscular fibres and the passive
stress resulting from the deformation of the passive medium of the myocardium
Keywords
cardiac mechanics, mathematical modelling of ventricular
contraction, pressure-volume relation, active force of the myocardium.
Related Book
Other papers in this volume
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