Mathematical Modeling of Vascular Stents

We present a mathematical model for a study of the mechanical properties of endovascular stents in their expanded state. The model is based on the theory of slender curved rods. Stent struts are modeled as linearly elastic curved rods that satisfy the kinematic and dynamic contact conditions at the “vertices” where the struts meet. This defines a stent as a mesh of curved rods. A weak formulation for the stent problem is defined and a finite element method for a numerical computation of its solution was developed. Numerical simulations showing the pressure-displacement (axial and radial) relationship for the entire stent are presented. From the numerical data and from the energy of the problem we deduced an “effective” pressure-displacement relationship of the law of Laplace-type for the mechanical behavior of stents, where the proportionality constant in the Laplace law was expressed explicitly in terms of the geometric and mechanic properties of a stent.