Modeling the transport of drugs eluted from stents: physical phenomena driving drug distribution in the arterial wall

Optimization of polymer coating thickness and strut width in drug Eluting stents using Magnetic field

The transport of drug/magnetic particle (MP) conjugates in the presence of a Magnetic Field (MF) in Drug Eluting Stents (DESs) is modeled numerically using the Finite Volume Method (FVM). The effects of physiological conditions corresponding to different degrees of calcification, drug particles sizes and hematocrit level, were analyzed by investigating the roles of the tissue permeability, its anisotropy and the plasma viscosity. It was found that both in the absence and presence of the MF, as the tissue permeability decreases or the plasma viscosity increases, the free-phase drug and Extracellular Matrix (ECM)-bound phase contents increase. Stronger tissue anisotropy leads to a decrease of the free-phase drug content and an increase of the ECM-bound phase content. Within the explored ranges, the Specific Receptor (SR)-bound phase of the drug was found to be insensitive to the tissue permeability and plasma viscosity, and to be larger in anisotropic tissues. The activation of the MF leads systematically to larger free-phase drug contents, with the increases most prominent at smaller tissue permeability, anisotropy and plasma viscosity. On the other hand, the effects on the ECM-bound phase content are found to be stronger at larger permeability, smaller plasma viscosity and lower tissue anisotropy. For an isotropic tissue, the MF induces a decrease of the ECM-bound phase content at early times, followed by an increase at later times. For the considered ranges of permeability and viscosity, the MF does not seem to have any noticeable effects on the SR-bound phase. However, this phase of the drug tends to increase with the activation of the MF in isotropic tissues and is unchanged in anisotropic ones. These reported effects of the MF hold promise for alleviating two factors contributing to In-Stent Restenosis, namely the polymer coating width and thickness. The study reveals that a narrower or thinner polymer layer, in combination with the MF, can mimic the drug release dynamics of a wider or thicker polymer layer in the absence of the MF. The corresponding width and thickness of the magnetized stents, that we referred to as the equivalent polymer width (EPW) and equivalent polymer thickness (EPT) were determined and their dependence on the tissue permeability, isotropy and the plasma viscosity, was investigated. The study shows that it is possible to achieve the same drug delivery with polymer coating of half the width or half the thickness of the non-magnetized stent when an electric intensity of 3A is used.

AnXplore: a comprehensive fluid-structure interaction study of 101 intracranial aneurysms

Advances in computational fluid dynamics continuously extend the comprehension of aneurysm growth and rupture, intending to assist physicians in devising effective treatment strategies. While most studies have first modelled intracranial aneurysm walls as fully rigid with a focus on understanding blood flow characteristics, some researchers further introduced Fluid-Structure Interaction (FSI) and reported notable haemodynamic alterations for a few aneurysm cases when considering wall compliance. In this work, we explore further this research direction by studying 101 intracranial sidewall aneurysms, emphasizing the differences between rigid and deformable-wall simulations. The proposed dataset along with simulation parameters are shared for the sake of reproducibility. A wide range of haemodynamic patterns has been statistically analyzed with a particular focus on the impact of the wall modelling choice. Notable deviations in flow characteristics and commonly employed risk indicators are reported, particularly with near-dome blood recirculations being significantly impacted by the pulsating dynamics of the walls. This leads to substantial fluctuations in the sac-averaged oscillatory shear index, ranging from -36% to +674% of the standard rigid-wall value. Going a step further, haemodynamics obtained when simulating a flow-diverter stent modelled in conjunction with FSI are showcased for the first time, revealing a 73% increase in systolic sac-average velocity for the compliant-wall setting compared to its rigid counterpart. This last finding demonstrates the decisive impact that FSI modelling can have in predicting treatment outcomes.

Investigating the effect of drug release on in-stent restenosis: A hybrid continuum - agent-based modelling approach

BACKGROUND AND OBJECTIVE

In-stent restenosis (ISR) following percutaneous coronary intervention with drug-eluting stent (DES) implantation remains an unresolved issue, with ISR rates up to 10%. The use of antiproliferative drugs on DESs has significantly reduced ISR. However, a complete knowledge of the mechanobiological processes underlying ISR is still lacking. Multiscale agent-based modelling frameworks, integrating continuum- and agent-based approaches, have recently emerged as promising tools to decipher the mechanobiological events driving ISR at different spatiotemporal scales. However, the integration of sophisticated drug models with an agent-based model (ABM) of ISR has been under-investigated. The aim of the present study was to develop a novel multiscale agent-based modelling framework of ISR following DES implantation.

METHODS

The framework consisted of two bi-directionally coupled modules, namely (i) a drug transport module, simulating drug transport through a continuum-based approach, and (ii) a tissue remodelling module, simulating cellular dynamics through an ABM. Receptor saturation (RS), defined as the fraction of target receptors saturated with drug, is used to mediate cellular activities in the ABM, since RS is widely regarded as a measure of drug efficacy. Three studies were performed to investigate different scenarios in terms of drug mass (DM), drug release profiles (RP), coupling schemes and idealized vs. patient-specific artery geometries.

RESULTS

The studies demonstrated the versatility of the framework and enabled exploration of the sensitivity to different settings, coupling modalities and geometries. As expected, changes in the DM, RP and coupling schemes illustrated a variation in RS over time, in turn affecting the ABM response. For example, combined small DM - fast RP led to similar ISR degrees as high DM - moderate RP (lumen area reduction of ∼13/17% vs. ∼30% without drug). The use of a patient-specific geometry with non-equally distributed struts resulted in a heterogeneous RS map, but did not remarkably impact the ABM response.

CONCLUSION

The application to a patient-specific geometry highlights the potential of the framework to address complex realistic scenarios and lays the foundations for future research, including calibration and validation on patient datasets and the investigation of the effects of different plaque composition on the arterial response to DES.

How does the Nature of an Excipient and an Atheroma Influence Drug-Coated Balloon Therapy?

The advent of drug-eluting stents and drug-coated balloons have significantly improved the clinical outcome of patients with vascular occlusions. However, ischemic vascular disease remains the most common cause of death worldwide. Improving the current treatment modalities demands a better understanding of the processes which govern drug uptake and retention in blood vessels. In this study, we evaluated the influence of urea and butyryl-trihexyl citrate, as excipients, on the efficacy of drug-coated balloon therapy. An integrated approach, utilizing both in-vitro and in-silico methods, was used to quantify the tracking loss, vessel adhesion, drug release, uptake, and distribution associated with the treatment. Moreover, a parametric study was used to evaluate the potential influence of different types of lesions on drug-coated balloon therapy. Despite the significantly higher tracking loss (urea: 35.5% vs. butyryl-trihexyl citrate: 8.13%) observed in the urea-based balloons, the drug uptake was almost two times greater than with its hydrophobic counterpart. Non-calcified lesions were found to delay the transmural propagation of sirolimus while calcification was shown to limit the retentive potential of lesions. Ultimately this study helps to elucidate how different excipients and types of lesions may influence the efficacy of drug-coated balloon therapy.

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.

An Overview of In Vitro Drug Release Methods for Drug-Eluting Stents

The drug release profile of drug-eluting stents (DESs) is affected by a number of factors, including the formulation, design, and physicochemical properties of the utilized material. DES has been around for twenty years and despite its widespread clinical use, and efficacy in lowering the rate of target lesion restenosis, it still requires additional development to reduce side effects and provide long-term clinical stability. Unfortunately, for analyzing these implants, there is still no globally accepted in vitro test method. This is owing to the stent's complexity as well as the dynamic arterial compartments of the blood and vascular wall. The former is the source of numerous biological, chemical, and physical mechanisms that are more commonly observed in tissue, lumen, and DES. As a result, universalizing bio-relevant apparatus, suitable for liberation testing of such complex implants is difficult. This article aims to provide a comprehensive review of the methods used for in vitro release testing of DESs. Aspects related to the correlation of the release profiles in the cases of in vitro and in vivo are also addressed.

Evolution of drug-eluting coronary stents: a back-and-forth journey from the bench-to-bedside

Coronary stents have revolutionized the treatment of coronary artery disease. Compared with balloon angioplasty, bare-metal stents effectively prevented abrupt vessel closure but were limited by in-stent restenosis due to smooth muscle cell proliferation and neointimal hyperplasia. The first-generation drug-eluting stent (DES), with its antiproliferative drug coating, offered substantial advantages over bare-metal stents as it mitigated the risk of in-stent restenosis. Nonetheless, they had several design limitations that increased the risk of late stent thrombosis. Significant advances in stent design, including thinner struts, enhanced polymers' formulation, and more potent antiproliferative agents, have led to the introduction of new-generation DES with a superior safety profile. Cardiologists have over 20 different DES types to choose from, each with its unique features and characteristics. This review highlights the evolution of stent design and summarizes the clinical data on the different stent types. We conclude by discussing the clinical implications of stent design in high-risk subsets of patients.

An Implantable Artificial Atherosclerotic Plaque as a Novel Approach for Drug Transport Studies on Drug-Eluting Stents

Atherosclerotic arteries are commonly treated using drug-eluting stents (DES). However, it remains unclear whether and how the properties of atherosclerotic plaque affect drug transport in the arterial wall. A limitation of the currently used atherosclerotic animal models to study arterial drug distribution is the unpredictability of plaque size, composition, and location. In the present study, the aim is to create an artificial atherosclerotic plaque-of reproducible and controllable complexity and implantable at specific locations-to enable systematic studies on transport phenomena of drugs in stented atherosclerosis-mimicking arteries. For this purpose, mixtures of relevant lipids at concentrations mimicking atherosclerotic plaque are incorporated in gelatin/alginate hydrogels. Lipid-free (control) and lipid-rich hydrogels (artificial plaque) are created, mounted on DES and successfully implanted in porcine coronary arteries ex-vivo. Matrix-assisted laser desorption ionization mass spectrometry imaging (MALDI-MSI) is used to measure local drug distribution in the arterial wall behind the prepared hydrogels, showing that the lipid-rich hydrogel significantly hampers drug transport as compared to the lipid-free hydrogel. This observation confirms the importance of studying drug transport phenomena in the presence of lipids and of having an experimental model in which lipids and other plaque constituents can be precisely controlled and systematically studied.

Specific and nonspecific binding of drug eluted from a half-embedded stent in presence of atherosclerotic plaque

This study is dealt with the two-phase binding (specific and nonspecific) of drug eluted from a half- embedded drug-eluting stent in presence of atherosclerotic plaque. The specific binding due to the interaction of drug molecules with specific receptors and nonspecific binding caused by the trapping of drug in the extra-cellular matrix have been paid due attention. An idealised wall consisting of a plaque and a healthy tissue region has been considered. Moreover, a Dirichlet release condition is imposed on the strut surface. In this investigation, a two-dimensional model governing drug transport and its two-phase binding in cylindrical polar coordinate system has been solved numerically by a finite-difference method. Our simulation predicts that plaque behaves like a physical barrier in two types of the binding process and there is an inverse relationship between bound drug concentration and plaque thickness. Simulations show that a single peak profile of drug is noted when the struts are situated one-strut radius apart and as the inter-strut distance increases, the peak concentration falls and distinct peak profiles over each strut are visualised. The model also reveals that in the region downstream of a strut, the concentration of both bound drug forms in the plaque and healthy regions increases, and eventually, the saturation length of binding sites increases. Predicted results show for smaller Damköhler number, the rapid saturation of binding sites takes place and the stent having thinner strut may perform well in terms of effectiveness as well as efficacy in the stent-based delivery.

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.

The Use of Bioactive Polymers for Intervention and Tissue Engineering: The New Frontier for Cardiovascular Therapy

Coronary heart disease remains one of the leading causes of death in most countries. Healthcare improvements have seen a shift in the presentation of disease with a reducing number of ST-segment elevation myocardial infarctions (STEMIs), largely due to earlier reperfusion strategies such as percutaneous coronary intervention (PCI). Stents have revolutionized the care of these patients, but the long-term effects of these devices have been brought to the fore. The conceptual and technologic evolution of these devices from bare-metal stents led to the creation and wide application of drug-eluting stents; further research introduced the idea of polymer-based resorbable stents. We look at the evolution of stents and the multiple advantages and disadvantages offered by each of the different polymers used to make stents in order to identify what the stent of the future may consist of whilst highlighting properties that are beneficial to the patient alongside the role of the surgeon, the cardiologist, engineers, chemists, and biophysicists in creating the ideal stent.

A Thesis Proposal Development Course for Engineering Graduate Students

Helping engineering graduate students to write their thesis can be a difficult and time-consuming undertaking for a thesis advisor. Efficiency can be gained by having an experienced graduate student thesis advisor help multiple students at the same time. This article describes the philosophy, methods, and course design details used to develop and conduct a graduate level course on "thesis proposal development" for engineering students. The course provides structure to encourage students to engage in research and write their thesis proposal. The thesis proposal contains the student's detailed research plans and serves as the foundation for the student's final thesis. Each element of the course is described in detail with enough information that readers can implement the course at their own institution using this article as a guide. It includes detailed descriptions of individual assignments, reasons for including the assignment in the course, and Supplemental Material on the ASME Digital Collection which is downloadable from the journal. Since implementing this at our university, we have observed improvements in graduate student research projects, better written theses, and earlier thesis defense dates. The changes were implemented without altering the number of credit hours needed to graduate and we believe that the change has been beneficial.

Computational model of stent-based delivery from a half-embedded two-layered coating

An attempt is made in the present investigation to develop a computational model for the purpose of studying the effect of interstitial flow in the porous media on the distribution of drug eluted from a half-embedded drug-eluting stent and its retention in the presence of two-layered coating of the stent. The transport of free drug inside the coatings is considered as an unsteady diffusion process while that in the tissue as an unsteady convection-diffusion-reaction process. The bound drug is governed by an unsteady reaction process only. Immersed boundary method (IBM) in the staggered grid formulation, popularly known as marker and cell (MAC) method, has been leveraged to tackle numerically the governing equations. This model highlights the benefits of consideration of two-layered coating and does predict underlying mechanism for better efficacy by tweaking the kinetics parameters. Comparisons are also made with the results available for stent-based delivery.

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.

Stability analysis of drug dynamics model: A mathematical approach

In this paper, a mathematical model of drug release from polymeric matrix and consequent intracellular drug transport is proposed and analyzed. Modeling of drug release is done through solubilization dynamics of drug particles, diffusion of the solubilized drug through the polymeric matrix in addition to reversible dissociation/recrystallization process. The interaction between drug-receptor, drug-plasma proteins along with other intracellular endosomal events is modeled. This leads to a mixed system of partial and ordinary differential equations with associated pertinent set of initial and boundary conditions. Furthermore, besides the stability of the proposed model, several sub-models are also studied for their stability criteria. Prominence is provided to the reduced model system having requisite relevance to the original system where quasi steady state approximation (QSSA) theory is utilized. For the model to be potent enough to generate appropriate predictive results for drug delivery, the stability properties of equilibrium in the mathematical model are analyzed both analytically and numerically. Numerical simulation in the embodiment of graphical representations speaks about various vital characteristics of the underlying physical phenomena along with the importance and sensitized impact of the model parameters controlling significant biological functions. Probed new therapies and clinical procedures could be assessed considering the present mathematical model and its analysis as the basis framework in order to effectively enhance therapeutic efficacy and improved patient compliance. The present study confirms the necessity of stability analysis study so that advocated mathematical model can effectively complement the real physiological behavior of pharmacokinetics.

Delivery of magnetic micro/nanoparticles and magnetic-based drug/cargo into arterial flow for targeted therapy

Magnetic drug targeting (MDT) and magnetic-based drug/cargo delivery are emerging treatment methods which attracting the attention of many researchers for curing different cancers and artery diseases such as atherosclerosis. Herein, computational studies are accomplished by utilizing magnetic approaches for cancer and artery atherosclerosis drug delivery, including nanomagnetic drug delivery and magnetic-based drug/cargo delivery. For the first time, the four-layer structural model of the artery tissue and its porosity parameters are modeled in this study which enables the interaction of particles with the tissue walls in blood flow. The effects of parameters, including magnetic field strength (MFS), magnet size, particle size, the initial position of particles, and the relative magnetic permeability of particles, on the efficacy of MDT through the artery walls are characterized. The magnetic particle penetration into artery layers and fibrous cap (the covering layer over the inflamed part of the artery) is further simulated. The MDT in healthy and diseased arteries demonstrates that some of the particles stuck in these tissues due to the collision of particles or blood flow deviation in the vicinity of the inflamed part of the artery. Therefore the geometry of artery and porosity of its layers should be considered to show the real interaction of particles with the artery walls. Also, the results show that increasing the particles/drug/cargo size and MFS leads to more particles/drug/cargo retention within the tissue. The present work provides insights into the decisive factors in arterial MDT with an obvious impact on locoregional cancer treatment, tissue engineering, and regenerative medicine.

Combining mathematical modelling with in vitro experiments to predict in vivo drug-eluting stent performance

In this study, we developed a predictive model of in vivo stent based drug release and distribution that is capable of providing useful insights into performance. In a combined mathematical modelling and experimental approach, we created two novel sirolimus-eluting stent coatings with quite distinct doses and release kinetics. Using readily measurable in vitro data, we then generated parameterised mathematical models of drug release. These were then used to simulate in vivo drug uptake and retention. Finally, we validated our model predictions against data on drug kinetics and efficacy obtained in a small in vivo evaluation. In agreement with the in vivo experimental results, our mathematical model predicted consistently higher sirolimus content in tissue for the higher dose stents compared with the lower dose stents. High dose stents resulted in statistically significant improvements in three key efficacy measures, providing further evidence of a basic relationship between dose and efficacy within DES. However, our mathematical modelling suggests a more complex relationship is at play, with efficacy being dependent not only on delivering an initial dose of drug sufficient to achieve receptor saturation, but also on the consequent drug release rate being tuned to ensure prolonged saturation. In summary, we have demonstrated that our combined in vitro experimental and mathematical modelling framework may be used to predict in vivo DES performance, opening up the possibility of an in silico approach to optimising the drug release profile and ultimately the effectiveness of the device.

Targeted Delivery of Bioactive Molecules for Vascular Intervention and Tissue Engineering

Cardiovascular diseases are the leading cause of death in the United States. Treatment often requires surgical interventions to re-open occluded vessels, bypass severe occlusions, or stabilize aneurysms. Despite the short-term success of such interventions, many ultimately fail due to thrombosis or restenosis (following stent placement), or incomplete healing (such as after aneurysm coil placement). Bioactive molecules capable of modulating host tissue responses and preventing these complications have been identified, but systemic delivery is often harmful or ineffective. This review discusses the use of localized bioactive molecule delivery methods to enhance the long-term success of vascular interventions, such as drug-eluting stents and aneurysm coils, as well as nanoparticles for targeted molecule delivery. Vascular grafts in particular have poor patency in small diameter, high flow applications, such as coronary artery bypass grafting (CABG). Grafts fabricated from a variety of approaches may benefit from bioactive molecule incorporation to improve patency. Tissue engineering is an especially promising approach for vascular graft fabrication that may be conducive to incorporation of drugs or growth factors. Overall, localized and targeted delivery of bioactive molecules has shown promise for improving the outcomes of vascular interventions, with technologies such as drug-eluting stents showing excellent clinical success. However, many targeted vascular drug delivery systems have yet to reach the clinic. There is still a need to better optimize bioactive molecule release kinetics and identify synergistic biomolecule combinations before the clinical impact of these technologies can be realized.

Non-polymer drug-eluting coronary stents

Cardiovascular complications are leading causes of most fatalities. Coronary artery disease and surgical failures contribute to the death of the majority of patients. Advanced research in the field of medical devices like stents has efficiently resolved these problems. Clinically, drug-eluting stents have proven their efficacy and safety compared to bare metal stents, which have problems of in-stent restenosis. However, drug-loaded stents coated with polymers have shown adverse effects related to the stability and deterioration of the polymer coating over time. This results in late stent thrombosis and immunogenicity. These reasons laid the foundation for the development of non-polymeric drug-eluting stents. This review focuses on non-polymer drug-eluting stents loaded with different drugs like anti-inflammatory agents, anti-thrombotic, anti-platelet agents, immune suppressants and others. Surface modification techniques on stents like crystalline coating; microporous, macroporous, and nanoporous coatings; and chemically modified self-assembled monolayers are described in detail. There is also an update on clinically approved products and those under development.

A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix

The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tissue. The model embodies drug diffusion, dissolution, solubilization, polymer degradation and dissociation/recrystallization phenomena in the polymeric matrix accompanied by diffusion, advection, reaction, internalization and specific/nonspecific binding in the biological tissue. The model is formulated through a system of nonlinear partial differential equations which are solved numerically in association with pertinent set of initial, interface and boundary conditions using suitable finite difference scheme. After spatial discretization, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is subsequently solved by the fourth-order Runge-Kutta method. The model simulations deal with the comparison between a drug delivery from a biodegradable polymeric matrix and that from a biodurable polymeric matrix. Furthermore, simulated results are compared with corresponding existing experimental data to manifest the efficaciousness of the advocated model. A quantitative analysis is performed through numerical computation relied on model parameter values. The numerical results obtained reveal an estimate of the effects of biodegradable and biodurable polymeric matrices on drug release rates. Furthermore, through graphical representations, the sensitized impact of the model parameters on the drug kinetics is illustrated so as to assess the model parameters of significance.

Cardiovascular stents: overview, evolution, and next generation

Compared to bare-metal stents (BMSs), drug-eluting stents (DESs) have been regarded as a revolutionary change in coronary artery diseases (CADs). Releasing pharmaceutical agents from the stent surface was a promising progress in the realm of cardiovascular stents. Despite supreme advantages over BMSs, in-stent restenosis (ISR) and long-term safety of DESs are still deemed ongoing concerns over clinically application of DESs. The failure of DESs for long-term clinical use is associated with following factors including permanent polymeric coating materials, metallic stent platforms, non-optimal drug releasing condition, and factors that have recently been supposed as contributory factors such as degradation products of polymers, metal ions due to erosion and degradation of metals and their alloys utilizing in some stents as metal frameworks. Discovering the direct relation between stent materials and associating adverse effects is a complicated process, and yet it has not been resolved. For clinical success it is of significant importance to optimize DES design and explore novel strategies to overcome all problems including inflammatory response, delay endothelialization, and sub-acute stent thrombosis (ST) simultaneously. In this work, scientific reports are reviewed particularly focusing on recent advancements in DES design which covers both potential improvements of existing and recently novel prototype stent fabrications. Covering a wide range of information from the BMSs to recent advancement, this study mostly sheds light on DES's concepts, namely stent composition, drug release mechanism, and coating techniques. This review further reports different forms of DES including fully biodegradable DESs, shape-memory ones, and polymer-free DESs.

Modelling drug release from polymer-free coronary stents with microporous surfaces

Traditional coronary drug-eluting stents (DES) are made from metal and are coated with a permanent polymer film containing an anti-proliferative drug. Subsequent to stent deployment in a diseased coronary artery, the drug releases into the artery wall and helps prevent restenosis by inhibiting the proliferation of smooth muscle cells. Although this technology has proven to be remarkably successful, there are ongoing concerns that the presence of a polymer in the artery can lead to deleterious medical complications, such as late stent thrombosis. Polymer-free DES may help overcome such shortcomings. However, the absence of a rate-controlling polymer layer makes optimisation of the drug release profile a particular challenge. The use of microporous stent surfaces to modulate the drug release rate is an approach that has recently shown particularly promising clinical results. In this study, we develop a mathematical model to describe drug release from such stents. In particular, we develop a mathematical model to describe drug release from microporous surfaces. The model predicts a two-stage release profile, with a relatively rapid initial release of most of the drug, followed by a slower release of the remaining drug. In the model, the slow release phase is accounted for by an adsorption/desorption mechanism close to the stent surface. The theoretical predictions are compared with experimental release data obtained in our laboratory, and good agreement is found. The valuable insights provided by our model will serve as a useful guide for designing the enhanced polymer-free stents of the future.

Effect of Interstitial Fluid Flow on Drug-Coated Balloon Delivery in a Patient-Specific Arterial Vessel with Heterogeneous Tissue Composition: A Simulation Study

Angioplasty with drug-coated balloons (DCBs) using excipients as drug carriers is emerging as a potentially viable strategy demonstrating clinical efficacy and proposing additional compliance for the treatment of obstructive vascular diseases. An attempt is made to develop an improved computational model where attention has been paid to the effect of interstitial flow, that is, plasma convection and internalization of bound drug. The present model is capable of capturing the phenomena of the transport of free drug and its retention, and also the internalization of drug in the process of endocytosis to atherosclerotic vessel of heterogeneous tissue composition comprising of healthy tissue, as well as regions of fibrous cap, fibro-fatty, calcified and necrotic core lesions. Image processing based on an unsupervised clustering technique is used for color-based segmentation of a patient-specific longitudinal image of atherosclerotic vessel obtained from intravascular ultrasound derived virtual histology. As the residence time of drug in a stent-based delivery within the arterial tissue is strongly influenced by convective forces, effect of interstitial fluid flow in case of DCB delivery can not be ruled out, and has been investigated by modeling it through unsteady Navier-Stokes equations. Transport of free drug is modeled by considering unsteady advection-reaction-diffusion process, while the bound drug, assuming completely immobilized in the tissue, by unsteady reaction process. The model also takes into account the internalization of drug through the process of endocytosis which gets degraded by the lysosomes and finally recycled into the extracellular fluid. All the governing equations representing the flow of interstitial fluid, the transport of free drug, the metabolization of free drug into bound phase and the process of internalization along with the physiologically realistic boundary and initial conditions are solved numerically using marker and cell method satisfying necessary stability criteria. Simulated results obtained predict that faster drug transfer promotes rapid saturation of binding sites despite perivascular wash out and the concentrations of all drug forms are modulated by the presence of interstitial flow. Such premier attempt of its kind would certainly be of great help in the optimization of therapeutic efficacy of drug.

Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found.

Assessing the potential of mathematical modelling in designing drug-releasing orthopaedic implants

Orthopaedic implants have been the subject of intense research in recent years, with academics, clinicians and industrialists seeking to broaden our understanding of their function and potential consequences within the human body. Current research is focussed on ways to improve the integration of an orthopaedic device within the body, whether it be to encourage better osseointegration, combat possible infection or stem the foreign body response. A key emerging strategy is the controlled delivery of therapeutics from the device, which may take the form of, for example, antibiotics, analgesics, anti-inflammatories or growth factors. However, the optimal device design that gives rise to the desired controlled release has yet to be defined. There are many examples in the literature of experimental approaches which attempt to tackle this issue. However, the necessity of having to conduct multiple experiments to test different scenarios is a major drawback of this approach. So enter stage left: mathematical modelling. Using a mathematical modelling approach can provide much more than experiments in isolation. For instance, a mathematical model can help identify key drug release mechanisms and uncover the rate limiting processes; allow for the estimation of values of the parameters controlling the system; quantify the effect of the interaction with the biological environment; and aid with the design of optimisation strategies for controlled drug release. In this paper we review current experimental approaches and some relevant mathematical models and suggest the future direction of such approaches in this field.

Computational Model of Drug-Coated Balloon Delivery in a Patient-Specific Arterial Vessel with Heterogeneous Tissue Composition

Balloon angioplasty followed by local delivery of antiproliferative drugs to target tissue is increasingly being considered for the treatment of obstructive arterial disease, and yet there is much to appreciate regarding pharmacokinetics in arteries of non-uniform disease. We developed a computational model capable of simulating drug-coated balloon delivery to arteries of heterogeneous tissue composition comprising healthy tissue, as well as regions of fibrous, fibro-fatty, calcified and necrotic core lesions. Image processing using an unsupervised clustering technique was used to reconstruct an arterial geometry from a single, patient-specific color image obtained from intravascular ultrasound-derived virtual histology. Transport of free drug was modeled using a time-dependent reaction-diffusion model and the bound, immobilized drug using the time-dependent reaction equation. The governing equations representing the transport of free as well as bound drug along with a set of initial settings and boundary conditions were solved numerically using an explicit finite difference scheme that satisfied the Courant-Friedrichs-Lewy stability criterion. Our results support previous findings related to the transport and binding of drug in arteries where tissue retention is strongly dependent on local pharmacologic properties. Additionally, modeling results indicate that non-uniform disease composition leads to heterogeneous arterial drug distribution patterns, although further validation using animal studies is required to fully appreciate pharmacokinetics in disease-laden arteries.

Numerical simulation on the effects of drug-eluting stents with different bending angles on hemodynamics and drug distribution

Implantation of drug-eluting stents in curved blood vessels may cause changes in hemodynamics and drug distribution, and even provoke in-stent restenosis. Due to the complexity of building three-dimensional (3-D) curved stent model, few studies have gone through such numerical simulations. In this study, three virtual stent models with different bending angles (0°, 30° and 90°) were developed to numerically investigate the distribution of wall shear stress (WSS) and drug concentration. The results showed that (1) the low-WSS regions in the inner bend of the stent models increased with the bending angles; (2) the drug concentration differed between the inner and outer bends of the stents but irrespective to the changes of bending angle; (3) the pattern of drug concentration for the curved stents found similar to that of the straight stents, and the phenomenon, 'proximal part low and distal part high' in the drug concentration showed in both the straight and curved stents. The increase in bending angles from 30° to 90° had little effect on the WSS and drug concentration; however, the largest effect of the curved stents was the remarkable difference of drug concentration between the inner and outer bends of the stents-about 20 %. Hence, it is feasible that quick analysis focused on the straight stents instead of the curved stents.

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.

Drug-Eluting Stent Design is a Determinant of Drug Concentration at the Endothelial Cell Surface

Although drug-eluting stents (DES) have greatly reduced arterial restenosis, there are persistent concerns about stent thrombosis. DES thrombosis is attributable to retarded vascular re-endothelialization due to both stent-induced flow disturbance and the inhibition by the eluted drug of endothelial cell proliferation and migration. The present computational study aims to determine the effect of DES design on both stent-induced flow disturbance and the concentration of eluted drug at the arterial luminal surface. To this end, we consider three closed-cell stent designs that resemble certain commercial stents as well as three "idealized" stents that provide insight into the impact of specific characteristics of stent design. To objectively compare the different stents, we introduce the Stent Penalty Index (SPI), a dimensionless quantity whose value increases with both the extent of flow disturbance and luminal drug concentration. Our results show that among the three closed-cell designs studied, wide cell designs lead to lower SPI and are thus expected to have a less adverse effect on vascular re-endothelialization. For the idealized stent designs, a spiral stent provides favorable SPI values, whereas an intertwined ring stent leads to an elevated SPI. The present findings shed light onto the effect of stent design on the concentration of the eluted drug at the arterial luminal surface, an important consideration in the assessment of DES performance.

Integrated Stent Models Based on Dimension Reduction: Review and Future Perspectives

Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this work, we aim at reviewing dimensional model reduction of stent mechanics and drug release. Firstly, we address model reduction techniques for the description of stent mechanics, aiming to illustrate how a three-dimensional stent model can be transformed into a collection of interconnected one-dimensional rods, called a "stent net". Secondly, we review available model reduction methods similarly applied to drug release, in which the "stent net" concept is adopted for modeling of drug elution. As a result, drug eluting stents are described as a distribution of concentrated drug release sources located on a graph that fully represents the stent geometry. Lastly, new results about the extension of these model reduction approaches to biodegradable stents are also discussed.