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Modelling arterial wall drug concentrations following the insertion of a drug-eluting stent

McGinty, Sean and McKee, Sean and Wadsworth, Roger and McCormick, Christopher (2013) Modelling arterial wall drug concentrations following the insertion of a drug-eluting stent. SIAM Journal on Applied Mathematics, 73 (6). pp. 2004-2028. ISSN 0036-1399

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A mathematical model of a drug-eluting stent is proposed. The model considers a polymer region, containing the drug initially, and a porous region consisting of smooth muscle cells embedded in an extracellular matrix. An analytical solution is obtained for the drug concentration both in the target cells and the interstitial region of the tissue in terms of the drug release concentration at the interface between the polymer and the tissue. When the polymer region and the tissue region are considered as a coupled system it can be shown, under certain assumptions, that the drug release concentration satisfies a Volterra integral equation which must be solved numerically in general. The drug concentrations, both in the cellular and extracellular regions, are then determined from the solution of this integral equation and used in deriving the mass of drug in the cells and extracellular space.