Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives.

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.

Mechanical behavior of fully expanded commercially available endovascular coronary stents.

The mechanical behavior of endovascular coronary stents influences their therapeutic efficacy. Through computational studies, researchers can analyze device performance and improve designs. We developed a 1-dimensional finite element method, net-based algorithm and used it to analyze the effects of radial loading and bending in commercially available stents. Our computational study included designs modeled on the Express, Cypher, Xience, and Palmaz stents.We found that stents that did not fully expand were less rigid than the fully expanded stents and, therefore, exhibited larger displacement. Stents with an open-cell design, such as Express-like or Xience-like stents, had a higher bending flexibility. Stents with in-phase circumferential rings, such as the Xience-like stent, had the smallest longitudinal extension when exposed to radial compression forces. Thus, the open-cell model that had in-phase circumferential rings connected by straight horizontal struts exhibited radial stiffness, bending flexibility, and the smallest change in stent length during radial forcing. The Palmaz-like stent was the most rigid of all. These findings are supported by clinical experience.Computer simulations of the mechanical properties of endovascular stents offer sophisticated insights into the mechanical behavior of different stent designs and should be used whenever possible to help physicians decide which stent is best for treating a given lesion. Our 1-dimensional finite element method model is incomparably simpler, faster, and more accurate than the classical 3-dimensional approaches. It can facilitate stent design and may aid in stent selection in the clinical setting.

A comparison between fractured Xience-like and Palmaz-like stents using a novel computational model.

We developed a novel mathematical model to study the mechanical properties of endovascular stents in their expanded state. The model is based on the one-dimensional 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. A Finite Element Method for a numerical computation of its solution was developed and used to study mechanical properties of two commonly used coronary stents (Palmaz-like and Xience-like stent) in their expanded, fractured state. A simple fracture (separation), corresponding to one stent strut being disconnected from one vertex in a stent, was considered. Our results show a drastic difference in the response of the two stents to the physiologically reasonable uniform compression and bending forces. In particular, deformation of a fractured Xience-like stent (with one strut separated from one vertex) is significantly larger than that of a fractured Palmaz-like stent when exposed to uniform compression and bending. This presents conditions which may be a precursor for the clinically observed complications associated with in-stent thrombosis and in-stent restenosis of fractured coronary stents.

Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics, and experimental validation.

The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier-Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, "one-and-a-half dimensional" model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow - vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.