Mechanical model of net reinforced blood vessel

Abstract

The mechanical behaviour of a blood vessel, reinforced by a net prosthesis firmly connected to the internal wall of the arteria is studied in this article. The main aim of the net prosthesis insertion is to stop or at least slow down the progressive deformation of the wall owing to the progressive degeneration of the elastic fibers in the aneurysmatic aorta. The analytical approach is performed introducing some simplifying assumptions: from the geometrical point of view, the blood vessel is modelled as a cylindrical tube reinforced by a prosthesis net with rectangular mesh directed along the main axis and, from the mechanical point of view, the artery wall is supposed to be an isotropic membrane with linear elastic constitutive law. At the current stage the entire blood pressure load is assumed to be carried only by the transverse rods of the prosthesis net, disregarding the mechanical contribution due to the longitudinal ones. The structural problem is solved following the hypothesis of small strains but large displacements. Besides the simplified analytical approach a more detailed finite element model is set up. The three fundamental layers along the cross-section of the aorta are described to obey a non-linear stress–strain relationship. The preliminary results obtained seem to encourage deeper investigations both for the surgical and the mechanical aspects.