title: Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives.
abstract: Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.
authors.affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 604 Benedum Hall, 3700 O'Hara street, Pittsburgh, 15261, PA, USA. paz13@pitt.edu.|MOX, Modeling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Milan, Italy. paz13@pitt.edu.
authors.forename: Paolo
authors.initials: P
authors.lastname: Zunino
authors.affiliation: Department of Mathematics, University of Zagreb, Zagreb, Croatia.
authors.forename: Josip
authors.initials: J
authors.lastname: Tambača
authors.affiliation: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering 'Giulio Natta', Politecnico di Milano, Milan, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Cutrì
authors.affiliation: Department of Mathematics, University of Houston, Houston, 77204, TX, USA.
authors.forename: Suncica
authors.initials: S
authors.lastname: Čanić
authors.affiliation: MOX, Modeling and Scientific Computing, Department of Mathematics, Politecnico di Milano, Milan, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Formaggia
authors.affiliation: Laboratory of Biological Structure Mechanics, Department of Chemistry, Materials and Chemical Engineering 'Giulio Natta', Politecnico di Milano, Milan, Italy.
authors.forename: Francesco
authors.initials: F
authors.lastname: Migliavacca
mesh_terms: D000818:Animals; D054855:Drug-Eluting Stents; D006801:Humans; D008962:Models, Theoretical; D010599:Pharmacokinetics; D011474:Prosthesis Design
keywords: Biodegradable stents; Dimensional model reduction; Drug eluting stents; Mathematical modeling; Medical stents; Stent mechanics