Some design considerations for polymer-free drug-eluting stents: A mathematical approach

Abstract

In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug.

A general model of coupled drug release and tissue absorption for drug delivery devices

“…In this case, if the resulting Damköhler number is so large that binding is diffusion limited, the concentrations of free and bound drug may exist in quasi-equilibrium and the model may be simplified. For further details the reader is referred to [21,28]. It is noted, however, that the low computational cost of the numerical method described in this paper means that the solving of the full model (even if binding is fast) does not significantly add to the computation time.…”

“…Whilst the three-dimensional geometry of the device may vary widely (Fig. 1), we can exploit the fact that the coating layer is usually thin relative to its lateral dimensions, with the result being that the drug release predominantly takes place in the direction normal to the device surface [8,21]. This provides justification for an idealized one-dimensional model.…”

Asymptotic analysis of drug dissolution in two layers having widely differing diffusivities

“…In Stage 2, the moving boundary has tracked back to x = a and the drug then proceeds to dissolve from the rough surface region where it is released at a slower rate. For Stage 1 (s (t) > a), [9] wrote down an analytical solution, the derivation of which may be found in [4]. The solution is given by…”

Application of underdamped Langevin dynamics simulations for the study of diffusion from a drug-eluting stent

“…The PDEs are often solved by separation of variables, or numerically through some kind of a discretization scheme, e.g., finite elements, finite differences, and the marker cell method. Noteworthy exceptions include analytical Laplace transform solutions [27], Boltzmann reductions [11], and numerically solved Voltera integral equations [23]. Experimental data is also available [31][32][33], and has been used to test and validate theoretical models.…”