A physical corrosion model for bioabsorbable metal stents
Introduction
Coronary stents are small tubular scaffolds that are used in the treatment of coronary heart disease. Coronary stents consisting of bioabsorbable metals are an emerging technology which has the potential to address limitations in the current generation of permanent stents, such as in-stent restenosis and late-stent thrombosis [1], [2], [3]. These devices have shown promise in early clinical trials [4], [5]; however, improvements in device performance are still required prior to their adoption in preference to the current generation of permanent stents.
Computational modelling represents a useful method to improve the currently limited understanding of absorbable metal stent (AMS) performance in the body and can also be used as part of the device design process [6], [7], [8], [9]. In the development of AMSs it is important that the modelling techniques used can account for device corrosion. Previously developed corrosion models for AMS analysis and design have treated the corrosion process in a phenomenological manner. For example, in Grogan et al. [6], [8], uniform corrosion is modelled by specifying a corrosion rate at which the corrosion surface retreats. In order to better understand the corrosion behaviour of AMSs in the body it is important that physical corrosion modelling approaches are also developed for AMSs.
Numerous physical corrosion modelling approaches for metallic alloys have been developed. Many of these rely on the use of boundary element methods and do not consider moving corrosion surfaces [10], [11], [12], [13]. Recently, a number of studies have used finite element analysis and adaptive meshing to physically model corrosion [14], [15], [16]. In these studies the rate of retreat of the corrosion surface depends on species fluxes at the surface. A study of relevance for AMSs is that of Deshpande [17], who considered the corrosion of a magnesium alloy couple using a physical model with adaptive meshing. The aforementioned physical models have typically been applied to relatively simple geometries: two-dimensional (2-D) planar regions, bimetallic interfaces or single corrosion pits. When analysing the corrosion behaviour of an AMS, however, the model must be applied to the complex three-dimensional (3-D) structure of the stent. It is the goal of this study to: (i) develop a finite element based physical corrosion model that is capable of modelling the corrosion of the complex 3-D structure of a stent using adaptive meshing, and (ii) apply the model in assessing the performance of a corroding AMS. The development of such a model addresses a gap between currently available phenomenological corrosion models for AMSs and physical corrosion models for more simple geometric configurations.
Section snippets
Methods
A thin (20–50 nm) oxide film forms on the surface of magnesium and its alloys in atmospheric air [18]. On placement in an aqueous environment the corrosion of magnesium proceeds at local anodes and cathodes on the corrosion surface. For pure magnesium the cathodic regions are often near impurities or rupture locations in the oxide film. Magnesium ions are liberated at the anode and hydrogen gas is evolved at the cathode. The overall electrochemical reaction is:The resulting
Results
Fig. 6 shows a comparison of (a) corrosion surface displacement and (b) magnesium ion concentration predicted by the ALE corrosion model and given by the 1-D analytical model. There is good agreement between the models, verifying the applicability of the ALE adaptive meshing algorithm in Abaqus for Stefan problems of this type.
Fig. 7a shows a contour plot of predicted magnesium ion concentration in the corrosive environment over time. As the device corrodes its dimensions are reduced. The
Discussion
A physical corrosion model is developed here for complex 3-D geometries, based on the use of ALE adaptive meshing. The model, implemented in the Abaqus commercial finite element solver, shows good agreement with the analytical solution of a 1-D moving boundary diffusion corrosion problem and represents a first attempt at modelling the corrosion of AMSs using a physical, rather than a phenomenological, approach. The verification performed here is also the first verification, to the authors’
Limitations
The physical corrosion model developed here gives a number of useful insights into AMS corrosion. However, the assumption of corrosion driven by magnesium diffusion alone limits its applicability.
The assumption of diffusion rather than activation control is based on observations of the formation of stable layers of corrosion product in the body [38], [39], [40] or tissue layers [41] and the known diffusion-controlled corrosion process associated with stable corrosion product layers [21], [22],
Conclusions
A physical model is developed that uses the ALE adaptive meshing method to model the diffusion-controlled corrosion of a 3-D absorbable metal stent (AMS) geometry. Assuming that the corrosion rate is governed by the diffusion of magnesium ions in solution, it is predicted that the mass loss rate from the AMS is inversely proportional to the square root of immersion time. It is predicted that the mass loss rate is proportional to the saturation concentration of magnesium ions in solution and is
Acknowledgements
The authors acknowledge funding through an Irish Research Council (IRC) scholarship (J.A. Grogan) under the EMBARK initiative.
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