A biodegradable elastic stent model

Abstract

In this paper we derive and analyse a one-dimensional model of biodegradable elastic stents. The model is given as a nonlinear system of ordinary differential equations on a graph defined by the geometry of stent struts. The unknowns in the problem are the displacement of the middle curve of the struts, the infinitesimal rotation of the cross-sections of the stent struts, the contact couples and contact forces at struts and a function describing the degradation of the stent. The model is based on the one-dimensional model of a biodegradable elastic curved rod model by Tambača and Žugec (‘One-dimensional quasistatic model of biodegradable elastic curved rods’, Zeitschrift für Angewandte Mathematik und Physik 2015; 66(5): 2759–2785) and the ideas from the one-dimensional elastic stent modelling by Tambača et al. (‘Mathematical modeling of vascular stents’, SIAM Journal on Applied Mathematics 2010; 70(6): 1922–1952) used to formulate contact conditions at vertices. We prove the existence and uniqueness results for the model.