A model of stress-induced geometrical remodeling of vessel segments adjacent to stents and artery/graft anastomoses

The mismatch between the elastic properties and initial geometry of a host artery and an implanted stent or graft cause significant stress concentration at the zones close to junctions. This may contribute to the often observed intimal hyperplasia, resulting in late lumen loss and eventual restenosis. This study proposes a mathematical model for stress-induced thickening of the arterial wall at the zones close to an implanted stent or graft. The host artery was considered initially as a cylindrical shell with constant thickness that was clamped to the stent or graft, which was assumed to be non-deformable in the circumferential direction. It was assumed that the abnormal circumferential and axial stresses due to the bending of the arterial wall cause wall thickening that tends to restore the stress state close to that existing far from the junction. The linear equations of a cylindrical shell with variable thickness were coupled to an evolution equation for the wall thickness. These equations were solved numerically and a parametric study was performed using finite difference method and explicit time step. The results show that the remodeling process is self-limiting and leads to local thickening that gradually decreases with distance from the edge of the stent/graft. Model predictions were tested against morphological findings existing in the literature. Recommendations on stent designs that reduce stress concentrations are discussed.