Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain

Math Biosci. 2015 Sep:267:79-96. doi: 10.1016/j.mbs.2015.06.016. Epub 2015 Jul 7.

Abstract

Pharmacokinetics induced by drug eluting stents (DES) in coronary walls is modeled by means of a one-dimensional multi-layered model, accounting for vessel curvature and non-homogeneous properties of the arterial tissues. The model includes diffusion mechanisms, advection effects related to plasma filtration through the walls, and bio-chemical drug reactions. A non-classical Sturm-Liouville problem with discontinuous coefficients is derived, whose closed-form analytical solution is obtained via an eigenfunction expansion. Soundness and consistency of the proposed approach are shown by numerical computations based on possible clinical treatments involving both hydrophilic and hydrophobic drugs. The influence of the main model parameters on drug delivery mechanisms is analyzed, highlighting the effects induced by vessel curvature and yielding comparative indications and useful insights into the concurring mechanisms governing the pharmacokinetics.

Keywords: Advective–diffusive pharmacokinetics; Drug-eluting stents; Multi-layered porous media; Sturm–Liouville problem; Vessel curvature.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cardiovascular Agents / chemistry
  • Cardiovascular Agents / pharmacokinetics
  • Coronary Artery Disease / metabolism
  • Coronary Artery Disease / therapy
  • Coronary Vessels / metabolism*
  • Drug-Eluting Stents* / statistics & numerical data
  • Humans
  • Hydrophobic and Hydrophilic Interactions
  • Mathematical Concepts
  • Models, Cardiovascular

Substances

  • Cardiovascular Agents