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Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅰ: Drug transport

1. Mathematics Applications Consortium for Science and Industry, University of Limerick, Castletroy, Co. Limerick, Ireland
2. Department of Mathematics, University of Portsmouth, Winston Churchill Ave, Portsmouth PO1 2UP, United Kingdom
3. College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Exeter, Devon, EX4 4QF, United Kingdom
4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found.

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