An intricate interplay between stent drug dose and release rate dictates arterial restenosis.

Since the introduction of percutaneous coronary intervention (PCI) for the treatment of obstructive coronary artery disease (CAD), patient outcomes have progressively improved. Drug eluting stents (DES) that employ anti-proliferative drugs to limit excess tissue growth following stent deployment have proved revolutionary. However, restenosis and a need for repeat revascularisation still occurs after DES use. Over the last few years, computational models have emerged that detail restenosis following the deployment of a bare metal stent (BMS), focusing primarily on contributions from mechanics and fluid dynamics. However, none of the existing models adequately account for spatiotemporal delivery of drug and the influence of this on the cellular processes that drive restenosis. In an attempt to fill this void, a novel continuum restenosis model coupled with spatiotemporal drug delivery is presented. Our results indicate that the severity and time-course of restenosis is critically dependent on the drug delivery strategy. Specifically, we uncover an intricate interplay between initial drug loading, drug release rate and restenosis, indicating that it is not sufficient to simply ramp-up the drug dose or prolong the time course of drug release to improve stent efficacy. Our model also shows that the level of stent over-expansion and stent design features, such as inter-strut spacing and strut thickness, influence restenosis development, in agreement with trends observed in experimental and clinical studies. Moreover, other critical aspects of the model which dictate restenosis, including the drug binding site density are investigated, where comparisons are made between approaches which assume this to be either constant or proportional to the number of smooth muscle cells (SMCs). Taken together, our results highlight the necessity of incorporating these aspects of drug delivery in the pursuit of optimal DES design.

Mathematical modelling of endovascular drug delivery: Balloons versus stents.

The most common treatment for obstructive coronary artery disease (CAD) is the implantation of a permanent drug-eluting stent (DES). Not only has this permanency been associated with delayed healing of the artery, but it also poses challenges when treating subsequent re-narrowing due to in-stent restenosis (ISR). Drug-coated balloons (DCBs) provide a potential solution to each of these issues. While their use has been primarily limited to treating ISR, in recent years, DCBs have emerged as an attractive potential alternative to DESs for the treatment of certain de novo lesions. However, there remain a number of concerns related to the safety and efficacy of these devices. Firstly, unlike DESs, DCBs necessitate a very short drug delivery window, favouring a higher drug loading. Secondly, while the majority of coronary DCBs in Europe are coated with paclitaxel, the potential mortality signal raised with paclitaxel DCBs in peripheral interventions has shifted efforts towards the development of limus-eluting balloons. The purpose of this paper is to provide a computational model that allows drug delivery from DCBs and DESs to be investigated and compared. We present a comprehensive computational framework that employs a 2D-axisymmetric geometry, incorporates two nonlinear phases of drug binding (specific and non-specific) and includes the influence of diffusion and advection, within a multilayer arterial wall. We utilise this framework to (i) simulate drug delivery from different types of balloon platform; (ii) explore the influence of DCB application time; (iii) elucidate the importance on release kinetics of elevated pressure during DCB application; (iv) compare DCB delivery of two different drugs (sirolimus and paclitaxel) and; (v) compare simulations of DESs versus DCBs. Key measures of comparison are related to safety (drug content in tissue, DC) and efficacy (specific binding site saturation, %SBSS) markers. Our results highlight the pros and cons of each device in terms of DC and %SBSS levels achieved and, moreover, indicate the potential for designing a DCB that gives rise to sufficiently similar safety and efficacy indicators as current commercial DESs.

Do we really understand how drug eluted from stents modulates arterial healing?

The advent of drug-eluting stents (DES) has revolutionised the treatment of coronary artery disease. These devices, coated with anti-proliferative drugs, are deployed into stenosed or occluded vessels, compressing the plaque to restore natural blood flow, whilst simultaneously combating the evolution of restenotic tissue. Since the development of the first stent, extensive research has investigated how further advancements in stent technology can improve patient outcome. Mathematical and computational modelling has featured heavily, with models focussing on structural mechanics, computational fluid dynamics, drug elution kinetics and subsequent binding within the arterial wall; often considered separately. Smooth Muscle Cell (SMC) proliferation and neointimal growth are key features of the healing process following stent deployment. However, models which depict the action of drug on these processes are lacking. In this article, we start by reviewing current models of cell growth, which predominantly emanate from cancer research, and available published data on SMC proliferation, before presenting a series of mathematical models of varying complexity to detail the action of drug on SMC growth in vitro. Our results highlight that, at least for Sodium Salicylate and Paclitaxel, the current state-of-the-art nonlinear saturable binding model is incapable of capturing the proliferative response of SMCs across a range of drug doses and exposure times. Our findings potentially have important implications on the interpretation of current computational models and their future use to optimise and control drug release from DES and drug-coated balloons.

Influence of vessel curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation.

In the last decade, many computational models have been developed to describe the transport of drug eluted from stents and the subsequent uptake into arterial tissue. Each of these models has its own set of limitations: for example, models typically employ simplified stent and arterial geometries, some models assume a homogeneous arterial wall, and others neglect the influence of blood flow and plasma filtration on the drug transport process. In this study, we focus on two common limitations. Specifically, we provide a comprehensive investigation of the influence of arterial curvature and plaque composition on drug transport in the arterial wall following drug-eluting stent implantation. The arterial wall is considered as a three-layered structure including the subendothelial space, the media and the adventitia, with porous membranes separating them (endothelium, internal and external elastic lamina). Blood flow is modelled by the Navier-Stokes equations, while Darcy's law is used to calculate plasma filtration through the porous layers. Our findings demonstrate that arterial curvature and plaque composition have important influences on the spatiotemporal distribution of drug, with potential implications in terms of effectiveness of the treatment. Since the majority of computational models tend to neglect these features, these models are likely to be under- or over-estimating drug uptake and redistribution in arterial tissue.

How does stent expansion alter drug transport properties of the arterial wall?

Stents have become the most successful device to treat advanced atherosclerotic lesions. However, one of the main issues with these interventions is the development of restenosis. The coating of stents with antiproliferative substances to reduce this effect is now standard, although such drugs can also delay re-endothelialization of the intima. The drug release strategy is therefore a key determinant of drug-eluting stent efficacy. Many mathematical models describing drug transport in arteries have been developed and, usually separately, models describing the mechanics of arterial tissue have been devised. However, the literature is lacking a comprehensive model that adequately takes into account both the mechanical deformation of the porous arterial wall and the resulting impact on drug transport properties. In this paper, we provide the most comprehensive study to date of the effect of stent mechanical expansion on the drug transport properties of a three-layer arterial wall. Our model incorporates the state-of-the art description of the mechanical properties of arterial tissue though an anisotropic, hyperelastic material model and includes a nonlinear saturable binding model to describe drug transport in the arterial wall. We establish relationships between mechanical force generated through device expansion and alteration in diffusion within the arterial wall and perform simulations to elucidate the impact of such alterations in spatio-temporal drug release and tissue uptake. Mechanical deformation of the arterial wall results in modified drug transport properties and tissue drug concentrations, highlighting the importance of coupling solid mechanics with drug transport.

Mathematical modelling of the restenosis process after stent implantation.

The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion-reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.