Research Article

A numerical model of elasticity for cardiovascular system that includes 2/3D displacements and deformations

Finance, Entrepreneurship and Development Laboratory, Faculty of Legal, Economic and Social Sciences of SALE, Mohammed V University, Rabat, Morocco

^* e-mail: ayoubsaha@gmail.com

Received: 13 June 2020
Accepted: 30 July 2020

Abstract

In this work, we deal an elasticity model in 2D and 3D dimension for deformation under constraint by taking into account the direction of the deformation displacement. This work is a result of an article [A. Azzayani et al., Br. J. Math. Comput. Sci. (2016)] in which we use the same mathematical model by fixing the fiber orientation. Then, if we considered the case of eignvalue and eigenvector, and which is the case of this work, we can be able to control the deformation of the heart in the image processing. This mathematical model can be used to describe the heart deformation taking into account the orientation of the fibers for estimating global and regional parameters of the left ventricular function. In first, we start by presenting the proposed mathematical model on a domain Ω ⊂ ℝⁿ (n = 2 or 3), and we give the existence and uniqueness of solution to the mathematical model is given (in both 2D and 3D dimension). Secondly, we give numerical simulations with FreeFem software, simulations results and comments are given in the end. In the end, we will discuss about the image treatment with this model and its feasibility to help doctors in the diagnosis of heart disease.