Finite dynamic deformations of a hyperelastic, anisotropic, incompressible and prestressed tube. Applications to in vivo arteries

In this paper, we study the mechanical behavior of a prestressed tube subjected to finite dynamic deformations. The tube is assumed to be made of a hyperelastic, anisotropic and incompressible material. The analysis is carried out by using a Mooney–Rivlin stored energy function augmented with fiber reinforcements in four unidimensional orientations. A semi-analytical solution is proposed to study the radial dynamic mechanical response of an artery by using in vivo data. The optimal model parameters describing the mechanical characteristics of arterial wall microconstituents are obtained by minimizing the difference between computed and measured inner pressures over the cardiac cycle using a nonlinear regression. Theoretical and experimental results on rat carotid elastic arteries are compared in order to assess the validity of the approach by estimating differences of the model parameters and wall stresses with aging.