Mathematical models of vascular stents with FG bridges aimed on reduction of in‐stent restenosis

Abstract To reduce in‐stent restenosis (ISR), caused by an elastic recoil stent at the initial bend of the artery, it is proposed to use stents with FG bridges, the bending stiffness of which depends on their location. The distribution of bending stiffnesses of FG bridges is studied depending on the initial bend of the artery. The bending of the FG cardiovascular stent is modeled by the bending of a beam with concentrated elastic hinges. Several methods of adapting the stent to the initial bending of the stented section of the vessel were considered: for bridges of the same stiffness, the functional of the squared difference between the deformation of the stent and the initial bending of the artery was minimized; for FG bridges, the flexural compliance of the stent is minimized. Problems are solved based on variational and homogenization approaches. An optimal scheme for the distribution of bending stiffnesses of FG bridges has been found.