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

Sean McGinty, Sean McKee, Roger Wadsworth, Christopher McCormick

Research output: Contribution to journalArticle

22 Citations (Scopus)
58 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)2004-2028
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume73
Issue number6
Early online date12 Nov 2013
DOIs
Publication statusPublished - 2013

Keywords

  • drug-eluting stent
  • atherosclerosis
  • Laplace transforms
  • branch points
  • analytial solutions
  • Volterra integral equations

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