Comparison Between Linear Elasticity And Large Elastic Deformation In The Study Of The Contraction Of The Myocardium
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R. M. Shoucri
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
cardiac mechanics, mathematical modelling of ventricular contraction, pressure-volume relation, active force of the myocardium.