A Next-Generation Mathematical Model for Drug-Eluting Stents

Abstract

We propose a Navier--Stokes--Biot fluid-structure interaction (FSI) model to study the interaction between an incompressible, viscous Newtonian fluid and a poroelastic medium with permeability depending on the volumetric change of pore size. The FSI model is coupled to a set of advection-reaction-diffusion equations defined on moving domains so that we may study the interaction between the blood flow, a stented coronary artery, and time-dependent pharmacokinetics of drug absorption in drug-eluting stents. A monolithic approach is used to implement the proposed problem numerically within the context of finite element discretization. Nitsche's method is employed to enforce one of the coupling conditions at the moving fluid-poroelastic structure interface. Stability analysis is presented, providing conditions on Nitsche's penalty parameter under which the scheme is unconditionally stable. Using 3D simulations, five geometrically different metallic stent platforms are considered with two different pharmacokinetics to show how stent geometry and type of coating impact the biomechanical environment, the local hemodynamics, and the concentration of the pharmacological agents within the vascular wall and artery lumen. It is found that stent implantation changes the permeability properties of the arterial wall, as well as local hemodynamics, which may be responsible for the so-called edge effect, i.e., suboptimal reduction in restenosis rates near the edges of drug-eluting stents. To the best of our knowledge, this is the first study of drug-eluting stents that takes into account fluid-poroelastic structure interaction with permeability depending on the volumetric change of the pore size, coupled to an advection-reaction-diffusion model defined on moving domains.