Mathematical modelling and stability analysis of an inflation of thinwalled hyperelastic tube with applications to abdominal aortic aneurysms

E. V. Nikolova, T. Ivanov

Abstract: In this study we propose a nonlinear second-order ordinary differential equation to describe the radial inflation of the arterial/aneurysmal wall subjected to a pulsatile blood pressure. The arterial/aneurysmal wall is modeled as a thin-walled, incompressible, hyperelastic and isotropic membrane. The hyperelasticity of the wall is presented by the strain energy function (SEF), proposed by Choi and Vito [19], and experimentally verified for healthy abdominal aorta (AA) and abdominal aortic aneurysms (AAAs) by Vande Geest et al. [20]. The aim of this research is to connect the specific material properties of the arterial/aneurysmal wall to its dynamical stability. Applying the methods of nonlinear dynamics to the proposed model, we proved that there is a stable inflation of the AA/AAAs, if they are constructed from Choi and Vito’s material. We support this result by numerical simulations that illustrate stable periodic oscillations (vibrations) of the wall around its stationary state.

Keywords: Abdominal aortic aneurysms; mathematical model; numerical simulations; stability analysis; strain energy function

Date published: 2015-12-10