Sean McGinty

Modelling drug-eluting stents

In this study, we consider a family of mathematical models to describe the elution of drug from polymer-coated stents into the arterial wall. Our models include the polymer layer, the media, the adventitia, a possible topcoat polymer layer and atherosclerotic plaque. We investigate the relative importance of transmural convection, diffusion and drug-dependent parameters in drug delivery and deposition. Furthermore, we investigate how the release rate from the stent can be altered and examine the resulting effect on cellular drug concentrations.

A decade of modelling drug release from arterial stents

Drug-eluting stents have revolutionised the treatment of coronary artery disease. These small medical devices have attracted much interest over the past decade from biologists, clinicians, engineers and mathematicians alike. This article provides a comprehensive review of the modelling of drug release from arterial stents and the subsequent drug transport through arterial tissue, and acts as a useful reference equally for those who are already involved in drug-eluting stents research and for those who are starting out in the field. Assembled in this review are the main models of drug release and arterial drug transport that have been published in the literature to date. Many of the models presented in this paper have evolved from drug transport models in other applications. Furthermore, the ideas presented in this review may also be extended to other drug-delivery applications, such as drug coated balloons, transdermal patches and therapeutic contact lenses.

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

In this paper we present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer. Within the drug coating, our model includes diffusion as well as three different models of dissolution. We show that the model may also be used in cases where dissolution is rapid or not relevant, and additionally when drug release is not limited by its solubility. Within the biological tissue, the model can account for nonlinear saturable reversible binding, with linear reversible binding and linear irreversible binding being recovered as special cases. The generality of our model will allow the simulation of the release from a wide range of drug delivery devices encompassing many different applications. To demonstrate the efficacy of our model we simulate results for the particular application of drug release from arterial stents.

Release mechanism and parameter estimation in drug-eluting stent systems : analytical solutions of drug release and tissue transport

Drug-eluting stents have significantly improved the treatment of coronary artery disease. They offer reduced rates of restenosis compared with their bare-metal predecessors and are the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been approved for use in humans since 2002 and yet, despite the intensive research activity over the past decade, the drug release mechanism(s) and the uptake into the arterial wall are still poorly understood. While stent manufacturers have focussed primarily on empirical methods, several mathematical models have appeared in the literature considering the release problem, the uptake problem and also the coupled problem. However, two significant challenges that remain are in understanding the drug release mechanism(s) and also the determination of the various parameters characterizing the system. These include drug diffusion coefficients and dissolution constants in the stent polymer coating as well as drug diffusion coefficients, binding/uptake rates and the magnitude of the transmural convection in the arterial wall. In this paper we attempt to address these problems. We provide analytical solutions which, when compared with appropriate experiments, may allow the various parameters of the system to be estimated via the inverse problem. The analytical solutions which we provide here for drug release in vitro may thus be used as a tool for providing insights into the mechanism(s) of release.

Modeling Arterial Wall Drug Concentrations Following the Insertion of a Drug-Eluting Stent

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.

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

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.

Modelling the Impact of Atherosclerosis on Drug Release and Distribution from Coronary Stents

Although drug-eluting stents (DES) are now widely used for the treatment of coronary heart disease, there remains considerable scope for the development of enhanced designs which address some of the limitations of existing devices. The drug release profile is a key element governing the overall performance of DES. The use of in vitro, in vivo, ex vivo, in silico and mathematical models has enhanced understanding of the factors which govern drug uptake and distribution from DES. Such work has identified the physical phenomena determining the transport of drug from the stent and through tissue, and has highlighted the importance of stent coatings and drug physical properties to this process. However, there is limited information regarding the precise role that the atherosclerotic lesion has in determining the uptake and distribution of drug. In this review, we start by discussing the various models that have been used in this research area, highlighting the different types of information they can provide. We then go on to describe more recent methods that incorporate the impact of atherosclerotic lesions.

On the role of specific drug binding in modelling arterial eluting stents

In this paper we consider drug binding in the arterial wall following delivery by a drug-eluting stent. Whilst it is now generally accepted that a non-linear saturable reversible binding model is required to properly describe the binding process, the precise form of the binding model varies between authors. Our particular interest in this manuscript is in assessing to what extent modelling specific and non-specific binding in the arterial wall as separate phases is important. We study this issue by extending a recently developed coupled model of drug release and arterial tissue distribution, and comparing simulated profiles of drug concentration and drug mass in each phase within the arterial tissue.

Modeling bispecific monoclonal antibody interaction with two cell membrane targets indicates the importance of surface diffusion

ABSTRACT We have developed a mathematical framework for describing a bispecific monoclonal antibody interaction with two independent membrane-bound targets that are expressed on the same cell surface. The bispecific antibody in solution binds either of the two targets first, and then cross-links with the second one while on the cell surface, subject to rate-limiting lateral diffusion step within the lifetime of the monovalently engaged antibody-antigen complex. At experimental densities, only a small fraction of the free targets is expected to lie within the reach of the antibody binding sites at any time. Using ordinary differential equation and Monte Carlo simulation-based models, we validated this approach against an independently published anti-CD4/CD70 DuetMab experimental data set. As a result of dimensional reduction, the cell surface reaction is expected to be so rapid that, in agreement with the experimental data, no monovalently bound bispecific antibody binary complexes accumulate until cross-linking is complete. The dissociation of the bispecific antibody from the ternary cross-linked complex is expected to be significantly slower than that from either of the monovalently bound variants. We estimate that the effective affinity of the bivalently bound bispecific antibody is enhanced for about 4 orders of magnitude over that of the monovalently bound species. This avidity enhancement allows for the highly specific binding of anti-CD4/CD70 DuetMab to the cells that are positive for both target antigens over those that express only one or the other We suggest that the lateral diffusion of target antigens in the cell membrane also plays a key role in the avidity effect of natural antibodies and other bivalent ligands in their interactions with their respective cell surface receptors.

Medical Stents: State of the Art and Future Directions.

Stents have revolutionised the treatment of arterial disease. Acting as a supporting scaffold, these small mesh devices are now routinely inserted into arteries where the blood flow has become dangerously restricted. While coronary artery stenting is now relatively mature, significant scientific and technological challenges still remain, particularly in relation to arterial restenosis and late stent thrombosis. Overall however, the revolutionary success of coronary artery stenting has led to the emergence of stenting technology for the carotid, neural and peripheral vasculature. And the adaptability of the stent concept has opened horizons beyond the vasculature, with stent technology now being developed for, amongst others, pulmonary, gastro-intestinal and structural heart applications. Given the rapid development of the field, this Special Issue is very timely and it assembles a collection of 27 review articles and original research papers from the top researchers in the field: academics from a variety of disciplines, including those with strong links to industrial application, and clinical practitioners. Through the assembled articles, the Special Issue presents a comprehensive overview and in-depth synthesis of the state of the art and future perspectives for medical stenting science and technology. The Special Issue is structured around the following inter-woven themes that illustrate the complexity and multi-disciplinary character of the modern medical stenting domain: