Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅱ: Cell proliferation

Adam Peddle; William Lee; Tuoi Vo; Adam Peddle; William Lee; Tuoi Vo

doi:10.3934/mbe.2018050

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1117-1135. doi: 10.3934/mbe.2018050

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Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅱ: Cell proliferation

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

Received: 27 April 2017 Accepted: 01 March 2018 Published: 01 October 2018
MSC : Primary: 93M60, 92C50; Secondary: 93A30, 92C35

The aim of a drug eluting stent is to prevent restenosis of arteries following percutaneous balloon angioplasty. A long term goal of research in this area is to use modelling to optimise the design of these stents to maximise their efficiency. A key obstacle to implementing this is the lack of a mathematical model of the biology of restenosis. Here we investigate whether mathematical models of cancer biology can be adapted to model the biology of restenosis and the effect of drug elution. We show that relatively simple, rate kinetic models give a good description of available data of restenosis in animal experiments, and its modification by drug elution.
- Drug-eluting stents,
- drug delivery,
- cell proliferation,
- mathematical modelling,
- parameter estimation
Citation: Adam Peddle, William Lee, Tuoi Vo. Modelling chemistry and biology after implantation of a drug-eluting stent. Part Ⅱ: Cell proliferation[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1117-1135. doi: 10.3934/mbe.2018050

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Abstract

The aim of a drug eluting stent is to prevent restenosis of arteries following percutaneous balloon angioplasty. A long term goal of research in this area is to use modelling to optimise the design of these stents to maximise their efficiency. A key obstacle to implementing this is the lack of a mathematical model of the biology of restenosis. Here we investigate whether mathematical models of cancer biology can be adapted to model the biology of restenosis and the effect of drug elution. We show that relatively simple, rate kinetic models give a good description of available data of restenosis in animal experiments, and its modification by drug elution.

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