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.
Peddle, A., Lee, W., & Vo, T. (2018). Modelling chemistry and biology after implantation of a drug-eluting stent. Part II: Cell Proliferation . Mathematical Biosciences and Engineering, 15(5), 1117-1135. https://doi.org/10.3934/mbe.2018050