Modelling the effect of a functional endothelium on the development of in-stent restenosis

Impact of Tissue Damage and Hemodynamics on Restenosis Following Percutaneous Transluminal Angioplasty: A Patient-Specific Multiscale Model

Multiscale agent-based modeling frameworks have recently emerged as promising mechanobiological models to capture the interplay between biomechanical forces, cellular behavior, and molecular pathways underlying restenosis following percutaneous transluminal angioplasty (PTA). However, their applications are mainly limited to idealized scenarios. Herein, a multiscale agent-based modeling framework for investigating restenosis following PTA in a patient-specific superficial femoral artery (SFA) is proposed. The framework replicates the 2-month arterial wall remodeling in response to the PTA-induced injury and altered hemodynamics, by combining three modules: (i) the PTA module, consisting in a finite element structural mechanics simulation of PTA, featuring anisotropic hyperelastic material models coupled with a damage formulation for fibrous soft tissue and the element deletion strategy, providing the arterial wall damage and post-intervention configuration, (ii) the hemodynamics module, quantifying the post-intervention hemodynamics through computational fluid dynamics simulations, and (iii) the tissue remodeling module, based on an agent-based model of cellular dynamics. Two scenarios were explored, considering balloon expansion diameters of 5.2 and 6.2 mm. The framework captured PTA-induced arterial tissue lacerations and the post-PTA arterial wall remodeling. This remodeling process involved rapid cellular migration to the PTA-damaged regions, exacerbated cell proliferation and extracellular matrix production, resulting in lumen area reduction up to 1-month follow-up. After this initial reduction, the growth stabilized, due to the resolution of the inflammatory state and changes in hemodynamics. The similarity of the obtained results to clinical observations in treated SFAs suggests the potential of the framework for capturing patient-specific mechanobiological events occurring after PTA intervention.

Haemodynamics of stent-mounted neural interfaces in tapered and deformed blood vessels

The endovascular neural interface provides an appealing minimally invasive alternative to invasive brain electrodes for recording and stimulation. However, stents placed in blood vessels have long been known to affect blood flow (haemodynamics) and lead to neointimal growth within the blood vessel. Both the stent elements (struts and electrodes) and blood vessel wall geometries can affect the mechanical environment on the blood vessel wall, which could lead to unfavourable vascular remodelling after stent placement. With increasing applications of stents and stent-like neural interfaces in venous blood vessels in the brain, it is necessary to understand how stents affect blood flow and tissue growth in veins. We explored the haemodynamics of a stent-mounted neural interface in a blood vessel model. Results indicated that blood vessel deformation and tapering caused a substantial change to the lumen geometry and the haemodynamics. The neointimal proliferation was evaluated in sheep implanted with an endovascular neural interface. Analysis showed a negative correlation with the mean Wall Shear Stress pattern. The results presented here indicate that the optimal stent oversizing ratio must be considered to minimise the haemodynamic impact of stenting.

Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation

Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.

Chitosan-salvianolic acid B coating on the surface of nickel-titanium alloy inhibits proliferation of smooth muscle cells and promote endothelialization

Introduction: Intracranial stents are of paramount importance in managing cerebrovascular disorders. Nevertheless, the currently employed drug-eluting stents, although effective in decreasing in-stent restenosis, might impede the re-endothelialization process within blood vessels, potentially leading to prolonged thrombosis development and restenosis over time. Methods: This study aims to construct a multifunctional bioactive coating to enhance the biocompatibility of the stents. Salvianolic acid B (SALB), a bioactive compound extracted from Salvia miltiorrhiza, exhibits potential for improving cardiovascular health. We utilized dopamine as the base and adhered chitosan-coated SALB microspheres onto nickel-titanium alloy flat plates, resulting in a multifunctional drug coating. Results: By encapsulating SALB within chitosan, the release period of SALB was effectively prolonged, as evidenced by the in vitro drug release curve showing sustained release over 28 days. The interaction between the drug coating and blood was examined through experiments on water contact angle, clotting time, and protein adsorption. Cellular experiments showed that the drug coating stimulates the proliferation, adhesion, and migration of human umbilical vein endothelial cells. Discussion: These findings indicate its potential to promote re-endothelialization. In addition, the bioactive coating effectively suppressed smooth muscle cells proliferation, adhesion, and migration, potentially reducing the occurrence of neointimal hyperplasia and restenosis. These findings emphasize the exceptional biocompatibility of the newly developed bioactive coating and demonstrate its potential clinical application as an innovative strategy to improve stent therapy efficacy. Thus, this coating holds great promise for the treatment of cerebrovascular disease.

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.

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.

A predictive multiscale model of in-stent restenosis in femoral arteries: linking haemodynamics and gene expression with an agent-based model of cellular dynamics

In-stent restenosis (ISR) is a maladaptive inflammatory-driven response of femoral arteries to percutaneous transluminal angioplasty and stent deployment, leading to lumen re-narrowing as consequence of excessive cellular proliferative and synthetic activities. A thorough understanding of the underlying mechanobiological factors contributing to ISR is still lacking. Computational multiscale models integrating both continuous- and agent-based approaches have been identified as promising tools to capture key aspects of the complex network of events encompassing molecular, cellular and tissue response to the intervention. In this regard, this work presents a multiscale framework integrating the effects of local haemodynamics and monocyte gene expression data on cellular dynamics to simulate ISR mechanobiological processes in a patient-specific model of stented superficial femoral artery. The framework is based on the coupling of computational fluid dynamics simulations (haemodynamics module) with an agent-based model (ABM) of cellular activities (tissue remodelling module). Sensitivity analysis and surrogate modelling combined with genetic algorithm optimization were adopted to explore the model behaviour and calibrate the ABM parameters. The proposed framework successfully described the patient lumen area reduction from baseline to one-month follow-up, demonstrating the potential capabilities of this approach in predicting the short-term arterial response to the endovascular procedure.

Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling

In-stent restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for in-stent restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cell bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximum relative area loss in a vessel. Owing to the high computational cost required for uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed and subsequently used for model response evaluation in the uncertainty quantification. A detailed analysis of the uncertainty propagation is presented. Around 11% and 16% uncertainty is observed on the two quantities of interest, respectively, and the uncertainty estimates show that a higher fenestration mainly determines the uncertainty in the neointimal growth at the initial stage of the process. The uncertainties in blood flow velocity and endothelium regeneration time mainly determine the uncertainty in the quantities of interest at the later, clinically relevant stages of the restenosis process.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

A homogenized constrained mixture model of restenosis and vascular remodelling after balloon angioplasty

Restenosis is one of the main adverse effects of the treatment of atherosclerosis through balloon angioplasty or stenting. During the intervention, the arterial wall is overstretched, causing a cascade of cellular events and subsequent neointima formation. This mechanical stimulus and its mechanobiological effects can be reproduced in biomechanical simulations. The aim of these models is to predict the long-term outcome of these procedures, to help increase the understanding of restenosis formation and to allow for in silico optimization of the treatment. We propose a predictive finite-element model of restenosis, using the homogenized constrained mixture modelling framework designed to model growth and remodelling in soft tissues. We compare the results with clinical observations in human coronary arteries and experimental findings in non-human primate models. We also explore the model's clinical relevance by testing its response to different balloon loads and to the use of drug-eluting balloons. The comparison of the results with experimental data shows the relevance of the model. We show its ability to predict both inward and outward remodelling as observed in vivo and we show the importance of an improved understanding of restenosis formation from a biomechanical point of view.

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.

Effects of local coronary blood flow dynamics on the predictions of a model of in-stent restenosis

Computational models are increasingly used to study cardiovascular disease. However, models of coronary vessel remodelling usually make some strong assumptions about the effects of a local narrowing on the flow through the narrowed vessel. Here, we test the effects of local flow dynamics on the predictions of an in-stent restenosis (ISR) model. A previously developed 2D model of ISR is coupled to a 1D model of coronary blood flow. Then, two different assumptions are tested. The first assumption is that the vasculature is always able to adapt, and the volumetric flow rate through the narrowed vessel is kept constant. The second, alternative, assumption is that the vasculature does not adapt at all, and the ratio of the pressure drop to the flow rate (hydrodynamic resistance) stays the same throughout the whole process for all vessels unaffected by the stenosis, and aortic or venous blood pressure does not change either. Then, the dynamics are compared for different locations in coronary tree for two different reendothelization scenarios. The assumptions of constant volumetric flow rate (absolute vascular adaptation) versus constant aortic pressure drop and no adaptation do not significantly affect the growth dynamics for most locations in the coronary tree, and the differences can only be observed at the locations where a strong alternative flow pathway is present. On the other hand, the difference between locations is significant, which is consistent with small vessel size being a risk factor for restenosis. These results suggest that the assumption of a constant flow is a good approximation for ISR models dealing with the typical progression of ISR in the most often stented locations such as the proximal parts of left anterior descending (LAD) and left circumflex (LCX) arteries.

The Combined Contribution of Vascular Endothelial Cell Migration and Adhesion to Stent Re-endothelialization

Coronary stent placement inevitably causes mechanical damage to the endothelium, leading to endothelial denudation and in-stent restenosis (ISR). Re-endothelialization depends mainly on the migration of vascular endothelial cells (VECs) adjacent to the damaged intima, as well as the mobilization and adhesion of circulating VECs. To evaluate the combined contribution of VEC migration and adhesion to re-endothelialization under flow and the influence of stent, in vitro models were constructed to simulate various endothelial denudation scales (2 mm/5 mm/10 mm) and stent deployment depths (flat/groove/bulge). Our results showed that (1) in 2 mm flat/groove/bulge models, both VEC migration and adhesion combined completed the percentage of endothelial recovery about 27, 16, and 12%, and migration accounted for about 21, 15, and 7%, respectively. It was suggested that the flat and groove models were in favor of VEC migration. (2) With the augmentation of the injury scales (5 and 10 mm), the contribution of circulating VEC adhesion on endothelial repair increased. Taken together, endothelial restoration mainly depended on the migration of adjacent VECs when the injury scale was 2 mm. The adhered cells contributed to re-endothelialization in an injury scale-dependent way. This study is helpful to provide new enlightenment for surface modification of cardiovascular implants.

NUMERICAL INVESTIGATION ON INFLUENCE OF VASCULAR STENOSIS RATE AND CURVATURE RADIUS ON PLAQUE VULNERABILITY IN STENTED VESSELS

The high stresses on plaque wall experienced by stent implantation into a stenotic artery can go beyond the material strength of plaque tissue, potentially leading to plaque rupture. Two non-commercial stents with different link structures called S-type and N-type were taken into account, respectively. A non-linear finite element model was developed to investigate the influence of the stenosis level (i.e., 24%, 40%, and 50%) and arterial curvature radius (i.e., 6, 10, and 20[Formula: see text]mm) on the stress induced within the plaque tissue during stent expansion. The numerical results indicated that the severer stenosis level and more tortuous artery caused the higher stress on plaque wall. The maximal stresses on the plaque wall were in the fracture level of 1.79[Formula: see text]MPa for N-type stent, and 1.82[Formula: see text]MPa for S-type stent under the 50% stenosis rate and 6[Formula: see text]mm curvature radius. Due to smaller compliance mismatch to the curved vessel, the N-type stent was founded to induce less stress gradient on the plaque wall than that by the S-type stent. This suggests a lower risk of the plaque rupture for the N-type stent. This study showed how the arterial curvature radius and stenosis level were correlated with the plaque vulnerability. Therefore, it is possible to choose a suitable stent in terms of arterial stenosis geometry and thereby optimize the outcome of stenting procedure.

Mechanistic evaluation of long-term in-stent restenosis based on models of tissue damage and growth

Development and application of advanced mechanical models of soft tissues and their growth represent one of the main directions in modern mechanics of solids. Such models are increasingly used to deal with complex biomedical problems. Prediction of in-stent restenosis for patients treated with coronary stents remains a highly challenging task. Using a finite element method, this paper presents a mechanistic approach to evaluate the development of in-stent restenosis in an artery following stent implantation. Hyperelastic models with damage, verified with experimental results, are used to describe the level of tissue damage in arterial layers and plaque caused by such intervention. A tissue-growth model, associated with vessel damage, is adopted to describe the growth behaviour of a media layer after stent implantation. Narrowing of lumen diameter with time is used to quantify the development of in-stent restenosis in the vessel after stenting. It is demonstrated that stent designs and materials strongly affect the stenting-induced damage in the media layer and the subsequent development of in-stent restenosis. The larger the artery expansion achieved during balloon inflation, the higher the damage introduced to the media layer, leading to an increased level of in-stent restenosis. In addition, the development of in-stent restenosis is directly correlated with the artery expansion during the stent deployment. The correlation is further used to predict the effect of a complex clinical procedure, such as stent overlapping, on the level of in-stent restenosis developed after percutaneous coronary intervention.

Computational modelling of magnesium stent mechanical performance in a remodelling artery: Effects of multiple remodelling stimuli

Significant research has been conducted in the area of coronary stents/scaffolds made from resorbable metallic and polymeric biomaterials. These next-generation bioabsorbable stents have the potential to completely revolutionise the treatment of coronary artery disease. The primary advantage of resorbable devices over permanent stents is their temporary presence which, from a theoretical point of view, means only a healed coronary artery will be left behind following degradation of the stent potentially eliminating long-term clinical problems associated with permanent stents. The healing of the artery following coronary stent/scaffold implantation is crucial for the long-term safety of these devices. Computational modelling can be used to evaluate the performance of complex stent devices in silico and assist in the design and development and understanding of the next-generation resorbable stents. What is lacking in computational modelling literature is the representation of the active response of the arterial tissue in the weeks and months following stent implantation, ie, neointimal remodelling, in particular for the case of biodegradable stents. In this paper, a computational modelling framework is developed, which accounts for two major physiological stimuli responsible for neointimal remodelling and combined with a magnesium corrosion model that is capable of simulating localised pitting (realistic) stent corrosion. The framework is used to simulate different neointimal growth patterns and to explore the effects the neointimal remodelling has on the mechanical performance (scaffolding support) of the bioabsorbable magnesium stent.

Location-Specific Comparison Between a 3D In-Stent Restenosis Model and Micro-CT and Histology Data from Porcine In Vivo Experiments

Background

Coronary artery restenosis is an important side effect of percutaneous coronary intervention. Computational models can be used to better understand this process. We report on an approach for validation of an in silico 3D model of in-stent restenosis in porcine coronary arteries and illustrate this approach by comparing the modelling results to in vivo data for 14 and 28 days post-stenting.

Methods

This multiscale model includes single-scale models for stent deployment, blood flow and tissue growth in the stented vessel, including smooth muscle cell (SMC) proliferation and extracellular matrix (ECM) production. The validation procedure uses data from porcine in vivo experiments, by simulating stent deployment using stent geometry obtained from micro computed tomography (micro-CT) of the stented vessel and directly comparing the simulation results of neointimal growth to histological sections taken at the same locations.

Results

Metrics for comparison are per-strut neointimal thickness and per-section neointimal area. The neointimal area predicted by the model demonstrates a good agreement with the detailed experimental data. For 14 days post-stenting the relative neointimal area, averaged over all vessel sections considered, was 20 ± 3% in vivo and 22 ± 4% in silico. For 28 days, the area was 42 ± 3% in vivo and 41 ± 3% in silico.

Conclusions

The approach presented here provides a very detailed, location-specific, validation methodology for in silico restenosis models. The model was able to closely match both histology datasets with a single set of parameters. Good agreement was obtained for both the overall amount of neointima produced and the local distribution. It should be noted that including vessel curvature and ECM production in the model was paramount to obtain a good agreement with the experimental data.

Electronic supplementary material

The online version of this article (10.1007/s13239-019-00431-4) contains supplementary material, which is available to authorized users.

Semi-intrusive multiscale metamodelling uncertainty quantification with application to a model of in-stent restenosis

We explore the efficiency of a semi-intrusive uncertainty quantification (UQ) method for multiscale models as proposed by us in an earlier publication. We applied the multiscale metamodelling UQ method to a two-dimensional multiscale model for the wound healing response in a coronary artery after stenting (in-stent restenosis). The results obtained by the semi-intrusive method show a good match to those obtained by a black-box quasi-Monte Carlo method. Moreover, we significantly reduce the computational cost of the UQ. We conclude that the semi-intrusive metamodelling method is reliable and efficient, and can be applied to such complex models as the in-stent restenosis ISR2D model. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

Uncertainty Quantification of a Multiscale Model for In-Stent Restenosis

Purpose

Coronary artery stenosis, or abnormal narrowing, is a widespread and potentially fatal cardiac disease. After treatment by balloon angioplasty and stenting, restenosis may occur inside the stent due to excessive neointima formation. Simulations of in-stent restenosis can provide new insight into this process. However, uncertainties due to variability in patient-specific parameters must be taken into account.

Methods

We performed an uncertainty quantification (UQ) study on a complex two-dimensional in-stent restenosis model. We used a quasi-Monte Carlo method for UQ of the neointimal area, and the Sobol sensitivity analysis (SA) to estimate the proportions of aleatory and epistemic uncertainties and to determine the most important input parameters.

Results

We observe approximately 30% uncertainty in the mean neointimal area as simulated by the model. Depending on whether a fast initial endothelium recovery occurs, the proportion of the model variance due to natural variability ranges from 15 to 35%. The endothelium regeneration time is identified as the most influential model parameter.

Conclusion

The model output contains a moderate quantity of uncertainty, and the model precision can be increased by obtaining a more certain value on the endothelium regeneration time. We conclude that the quasi-Monte Carlo UQ and the Sobol SA are reliable methods for estimating uncertainties in the response of complicated multiscale cardiovascular models.

A versatile hybrid agent-based, particle and partial differential equations method to analyze vascular adaptation

Peripheral arterial occlusive disease is a chronic pathology affecting at least 8–12 million people in the USA, typically treated with a vein graft bypass or through the deployment of a stent in order to restore the physiological circulation. Failure of peripheral endovascular interventions occurs at the intersection of vascular biology, biomechanics, and clinical decision making. It is our hypothesis that the majority of endovascular treatment approaches share the same driving mechanisms and that a deep understanding of the adaptation process is pivotal in order to improve the current outcome of the procedure. The postsurgical adaptation of vein graft bypasses offers the perfect example of how the balance between intimal hyperplasia and wall remodeling determines the failure or the success of the intervention. Accordingly, this work presents a versatile computational model able to capture the feedback loop that describes the interaction between events at cellular/tissue level and mechano-environmental conditions. The work here presented is a generalization and an improvement of a previous work by our group of investigators, where an agent-based model uses a cellular automata principle on a fixed hexagonal grid to reproduce the leading events of the graft’s restenosis. The new hybrid model here presented allows a more realistic simulation both of the biological laws that drive the cellular behavior and of the active role of the membranes that separate the various layers of the vein. The novel feature is to use an immersed boundary implementation of a highly viscous flow to represent SMC motility and matrix reorganization in response to graft adaptation. Our implementation is modular, and this makes us able to choose the right compromise between closeness to the physiological reality and complexity of the model. The focus of this paper is to offer a new modular implementation that combines the best features of an agent-based model, continuum mechanics, and particle-tracking methods to cope with the multiscale nature of the adaptation phenomena. This hybrid method allows us to quickly test various hypotheses with a particular attention to cellular motility, a process that we demonstrated should be driven by mechanical homeostasis in order to maintain the right balance between cells and extracellular matrix in order to reproduce a distribution similar to histological experimental data from vein grafts.

A cell-based mechanical model of coronary artery tunica media

A three-dimensional cell-based mechanical model of coronary artery tunica media is proposed. The model is composed of spherical cells forming a hexagonal close-packed lattice. Tissue anisotropy is taken into account by varying interaction forces with the direction of intercellular connection. Several cell-centre interaction potentials for repulsion and attraction are considered, including the Hertz contact model and its neo-Hookean extension, the Johnson-Kendall-Roberts model of adhesive contact, and a wormlike chain model. The model is validated against data from in vitro uni-axial tension tests performed on dissected strips of tunica media. The wormlike chain potential in combination with the neo-Hookean Hertz contact model produces stress-stretch curves which represent the experimental data very well.

Nanomatrix Coated Stent Enhances Endothelialization but Reduces Platelet, Smooth Muscle Cell, and Monocyte Adhesion under Physiologic Conditions

Cardiovascular disease is presently the number one cause of death worldwide. Current stents used to treat cardiovascular disease have a litany of unacceptable shortcomings: adverse clinical events including restenosis, neointimal hyperplasia, thrombosis, inflammation, and poor re-endothelialization. We have developed a biocompatible, multifunctional, peptide amphiphile-based nanomatrix coating for stents. In this study, we evaluated the ability of the nanomatrix coated stent to simultaneously address the issues facing current stents under physiological flow conditions in vitro. We found that the nanomatrix coated stent could increase endothelial cell migration, adhesion, and proliferation (potential for re-endothelialization), discourage smooth muscle cell migration and adhesion (potential to reduce neointimal hyperplasia and restenosis), and decrease both platelet activation and adhesion (potential to prevent thrombosis) as well as monocyte adhesion (potential to attenuate inflammatory responses) under physiological flow conditions in vitro. These promising results demonstrate the potential clinical utility of this nanomatrix stent coating, and highlight the importance of biocompatibility, multifunctionality, and bioactivity in cardiovascular device design.

Optimizing endothelial cell functionalization for cell therapy of vascular proliferative disease using a direct contact co-culture system

Increased susceptibility to thrombosis, neoatherosclerosis, and restenosis due to incomplete regrowth of the protective endothelial layer remains a critical limitation of the interventional strategies currently used clinically to relieve atherosclerotic obstruction. Rapid recovery of endothelium holds promise for both preventing the thrombotic events and reducing post-angioplasty restenosis, providing the rationale for developing cell delivery strategies for accelerating arterial reendothelialization. The successful translation of experimental cell therapies into clinically viable treatment modalities for restoring vascular endothelium critically depends on identifying strategies for enhancing the functionality of endothelial cells (EC) derived from high cardiovascular risk patients, the target group for the majority of angioplasty procedures. Enhancing EC-associated nitric oxide (NO) synthesis by inducing overexpression of NO synthase (NOS) has shown promise as a way of increasing paracrine activity and restoring function of EC. In the present study, we developed a direct contact co-culture approach compatible with highly labile effectors, such as NO, and applied it for determining the effect of EC functionalization via NOS gene transfer on the growth of co-cultured arterial smooth muscle cells (A10 cell line) exhibiting the defining characteristics of neointimal cells. Bovine aortic endothelial cells magnetically transduced with inducible NOS-encoding adenovirus (Ad) formulated in zinc oleate-based magnetic nanoparticles (MNP[_iNOSAd]) strongly suppressed growth of proliferating A10 and attenuated the stimulatory effect of a potent mitogen, platelet-derived growth factor (PDGF-BB), whereas EC functionalization with free _iNOSAd or MNP formulated with a different isoform of the enzyme, endothelial NOS, was associated with lower levels of NO synthesis and less pronounced antiproliferative activity toward co-cultured A10 cells. These results show feasibility of applying magnetically facilitated gene transfer to potentiate therapeutically relevant effects of EC for targeted cell therapy of restenosis. The direct contact co-culture methodology provides a sensitive and reliable tool with potential utility for a variety of biomedical applications.

A Comparison of Fully-Coupled 3D In-Stent Restenosis Simulations to In-vivo Data

We describe our fully-coupled 3D multiscale model of in-stent restenosis, with blood flow simulations coupled to smooth muscle cell proliferation, and report results of numerical simulations performed with this model. This novel model is based on several previously reported 2D models. We study the effects of various parameters on the process of restenosis and compare with in vivo porcine data where we observe good qualitative agreement. We study the effects of stent deployment depth (and related injury score), reendothelization speed, and simulate the effect of stent width. Also we demonstrate that we are now capable to simulate restenosis in real-sized (18 mm long, 2.8 mm wide) vessel geometries.

Computational Modeling of the Mechanical Performance of a Magnesium Stent Undergoing Uniform and Pitting Corrosion in a Remodeling Artery

Coronary stents made from degradable biomaterials such as magnesium alloy are an emerging technology in the treatment of coronary artery disease. Biodegradable stents provide mechanical support to the artery during the initial scaffolding period after which the artery will have remodeled. The subsequent resorption of the stent biomaterial by the body has potential to reduce the risk associated with long-term placement of these devices, such as in-stent restenosis, late stent thrombosis, and fatigue fracture. Computational modeling such as finite-element analysis has proven to be an extremely useful tool in the continued design and development of these medical devices. What is lacking in computational modeling literature is the representation of the active response of the arterial tissue in the weeks and months following stent implantation, i.e., neointimal remodeling. The phenomenon of neointimal remodeling is particularly interesting and significant in the case of biodegradable stents, when both stent degradation and neointimal remodeling can occur simultaneously, presenting the possibility of a mechanical interaction and transfer of load between the degrading stent and the remodeling artery. In this paper, a computational modeling framework is developed that combines magnesium alloy degradation and neointimal remodeling, which is capable of simulating both uniform (best case) and localized pitting (realistic) stent corrosion in a remodeling artery. The framework is used to evaluate the effects of the neointima on the mechanics of the stent, when the stent is undergoing uniform or pitting corrosion, and to assess the effects of the neointimal formation rate relative to the overall stent degradation rate (for both uniform and pitting conditions).

RNA-Eluting Surfaces for the Modulation of Gene Expression as A Novel Stent Concept

Presently, a new era of drug-eluting stents is continuing to improve late adverse effects such as thrombosis after coronary stent implantation in atherosclerotic vessels. The application of gene expression–modulating stents releasing specific small interfering RNAs (siRNAs) or messenger RNAs (mRNAs) to the vascular wall might have the potential to improve the regeneration of the vessel wall and to inhibit adverse effects as a new promising therapeutic strategy. Different poly (lactic-co-glycolic acid) (PLGA) resomers for their ability as an siRNA delivery carrier against intercellular adhesion molecule (ICAM)-1 with a depot effect were tested. Biodegradability, hemocompatibility, and high cell viability were found in all PLGAs. We generated PLGA coatings with incorporated siRNA that were able to transfect EA.hy926 and human vascular endothelial cells. Transfected EA.hy926 showed significant siICAM-1 knockdown. Furthermore, co-transfection of siRNA and enhanced green fluorescent protein (eGFP) mRNA led to the expression of eGFP as well as to the siRNA transfection. Using our PLGA and siRNA multilayers, we reached high transfection efficiencies in EA.hy926 cells until day six and long-lasting transfection until day 20. Our results indicate that siRNA and mRNA nanoparticles incorporated in PLGA films have the potential for the modulation of gene expression after stent implantation to achieve accelerated regeneration of endothelial cells and to reduce the risk of restenosis.

Towards the virtual artery: a multiscale model for vascular physiology at the physics-chemistry-biology interface

This discussion paper introduces the concept of the Virtual Artery as a multiscale model for arterial physiology and pathologies at the physics-chemistry-biology (PCB) interface. The cellular level is identified as the mesoscopic level, and we argue that by coupling cell-based models with other relevant models on the macro- and microscale, a versatile model of arterial health and disease can be composed. We review the necessary ingredients, both models of arteries at many different scales, as well as generic methods to compose multiscale models. Next, we discuss how this can be combined into the virtual artery. Finally, we argue that the concept of models at the PCB interface could or perhaps should become a powerful paradigm, not only as in our case for studying physiology, but also for many other systems that have such PCB interfaces.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

An in silico study on the role of smooth muscle cell migration in neointimal formation after coronary stenting

Excessive migration and proliferation of smooth muscle cells (SMCs) has been observed as a major factor contributing to the development of in-stent restenosis after coronary stenting. Building upon the results from in vivo experiments, we formulated a hypothesis that the speed of the initial tissue re-growth response is determined by the early migration of SMCs from the injured intima. To test this hypothesis, a cellular Potts model of the stented artery is developed where stent struts were deployed at different depths into the tissue. An extreme scenario with a ruptured internal elastic lamina was also considered to study the role of severe injury in tissue re-growth. Based on the outcomes, we hypothesize that a deeper stent deployment results in on average larger fenestrae in the elastic lamina, allowing easier migration of SMCs into the lumen. The data also suggest that growth of the neointimal lesions owing to SMC proliferation is strongly dependent on the initial number of migrated cells, which form an initial condition for the later phase of the vascular repair. This mechanism could explain the in vivo observation that the initial rate of neointima formation and injury score are strongly correlated.

Anatomy and Physiology of Multiscale Modeling and Simulation in Systems Medicine

Systems medicine is the application of systems biology concepts, methods, and tools to medical research and practice. It aims to integrate data and knowledge from different disciplines into biomedical models and simulations for the understanding, prevention, cure, and management of complex diseases. Complex diseases arise from the interactions among disease-influencing factors across multiple levels of biological organization from the environment to molecules. To tackle the enormous challenges posed by complex diseases, we need a modeling and simulation framework capable of capturing and integrating information originating from multiple spatiotemporal and organizational scales. Multiscale modeling and simulation in systems medicine is an emerging methodology and discipline that has already demonstrated its potential in becoming this framework. The aim of this chapter is to present some of the main concepts, requirements, and challenges of multiscale modeling and simulation in systems medicine.

Magnetically enhanced cell delivery for accelerating recovery of the endothelium in injured arteries

Arterial injury and disruption of the endothelial layer are an inevitable consequence of interventional procedures used for treating obstructive vascular disease. The slow and often incomplete endothelium regrowth after injury is the primary cause of serious short- and long-term complications, including thrombosis, restenosis and neoatherosclerosis. Rapid endothelium restoration has the potential to prevent these sequelae, providing a rationale for developing strategies aimed at accelerating the reendothelialization process. The present studies focused on magnetically guided delivery of endothelial cells (EC) functionalized with biodegradable magnetic nanoparticles (MNP) as an experimental approach for achieving rapid and stable cell homing and expansion in stented arteries. EC laden with polylactide-based MNP exhibited strong magnetic responsiveness, capacity for cryopreservation and rapid expansion, and the ability to disintegrate internalized MNP in both proliferating and contact-inhibited states. Intracellular decomposition of BODIPY558/568-labeled MNP monitored non-invasively based on assembly state-dependent changes in the emission spectrum demonstrated cell proliferation rate-dependent kinetics (average disassembly rates: 6.6±0.8% and 3.6±0.4% per day in dividing and contact-inhibited EC, respectively). With magnetic guidance using a transient exposure to a uniform 1-kOe field, stable localization and subsequent propagation of MNP-functionalized EC, markedly enhanced in comparison to non-magnetic delivery conditions, were observed in stented rat carotid arteries. In conclusion, magnetically guided delivery is a promising experimental strategy for accelerating endothelial cell repopulation of stented blood vessels after angioplasty.

A comprehensive study on different modelling approaches to predict platelet deposition rates in a perfusion chamber

Thrombus formation is a multiscale phenomenon triggered by platelet deposition over a protrombotic surface (eg. a ruptured atherosclerotic plaque). Despite the medical urgency for computational tools that aid in the early diagnosis of thrombotic events, the integration of computational models of thrombus formation at different scales requires a comprehensive understanding of the role and limitation of each modelling approach. We propose three different modelling approaches to predict platelet deposition. Specifically, we consider measurements of platelet deposition under blood flow conditions in a perfusion chamber for different time periods (3, 5, 10, 20 and 30 minutes) at shear rates of 212 s⁻¹, 1390 s⁻¹ and 1690 s⁻¹. Our modelling approaches are: i) a model based on the mass-transfer boundary layer theory; ii) a machine-learning approach; and iii) a phenomenological model. The results indicate that the three approaches on average have median errors of 21%, 20.7% and 14.2%, respectively. Our study demonstrates the feasibility of using an empirical data set as a proxy for a real-patient scenario in which practitioners have accumulated data on a given number of patients and want to obtain a diagnosis for a new patient about whom they only have the current observation of a certain number of variables.

1H-pyrrole-2,5-dione-based small molecule-induced generation of mesenchymal stem cell-derived functional endothelial cells that facilitate rapid endothelialization after vascular injury

Introduction

Despite the success of interventional processes such as drug-eluting stents, complete prevention of restenosis is still hindered by impaired or delayed endothelialization or both. Here, we report that 1H-pyrrole-2,5-dione-based small molecule-generated mesenchymal stem cell-derived functional endothelial cells (MDFECs) facilitated rapid transmural coverage of injured blood vessels.

Methods

Small molecules that induced CD31 expression were screened by principal component analysis (PCA). Rat mesenchymal stem cells (MSCs) were treated with selected small molecules for up to 16 days, and the expression levels of CD90 and CD31 were examined by immunocytochemistry. In vitro functional assays of MDFECs, including tube formation assays and nitric oxide production assays, were performed. After MDFECs (intravenous, 3×10⁶ cells per animal) were injected into balloon-injured rats, neointima formation was monitored for up to 21 days. The endothelial coverage of denuded blood vessels was evaluated by Evans Blue staining. The functionality of repaired blood vessels was evaluated by measuring vasorelaxation and hemodynamic changes. Additionally, derivatives of the selected small molecules were examined for their ability to induce endothelial markers.

Results

PCA indicated that 3-(2,4-dichlorophenyl)-4-(1-methyl-1H-indol-3-yl)-1H-pyrrole-2,5-dione effectively induced MDFECs. MDFECs inhibited the neointima formation of denuded blood vessels by facilitating more rapid endothelialization. Further examination indicated that derivatives with a 1H-pyrrole-2,5-dione moiety are important for initiating the endothelial cell differentiation of MSCs.

Conclusions

Small molecules with 1H-pyrrole-2,5-dione as a core structure have great potential to improve the efficacy of MSC-based cell therapy for vascular diseases, such as atherosclerosis and restenosis.

Electronic supplementary material

The online version of this article (doi:10.1186/s13287-015-0170-6) contains supplementary material, which is available to authorized users.

Bis (aspirinato) zinc (II) complex successfully inhibits carotid arterial neointima formation after balloon-injury in rats

PURPOSE

Neointima formation following angioplasty is a serious consequence of endothelial damage in arteries. Inflammatory mediators and lack of endothelial regulatory mechanisms lead to migration and proliferation of smooth-muscle cells and thus to restenosis. This study examines the effect of the novel bis (aspirinato) zinc (II) complex on neointima formation in a rat model of carotid balloon-injury.

METHODS

Rats underwent balloon-injury of the right common carotid artery, then received PEG400 vehicle (untreated-group), acetylsalicylic-acid (ASA-group), zinc-chloride (Zn-group) and bis (aspirinato) zinc (II) complex (Zn(ASA) 2-group) orally for 18 consecutive days. From harvested carotid arteries, histology, immunohistochemistry and mRNA expression analysis were performed.

RESULTS

Compared to the untreated-group, Zn (ASA) 2-treatment significantly lowered stenosis ratio (54.0 ± 5.8% to 25.5 ± 3.9%) and reduced neointima/media ratio (1.5 ± 0.2 to 0.5 ± 0.1). Significantly higher alpha smooth muscle actin mRNA and protein expression were measured after Zn (ASA)2 and Zn-treatment in comparison with the untreated and ASA-groups while the expression of matrix-metalloproteinase-9 was significantly higher in these groups compared to Zn (ASA)2. The presence of collagen in media was significantly decreased in all treated groups. mRNA expressions of nuclear factor kappa-b, transforming growth-factor-β and proliferating cell nuclear antigen were significantly down-regulated, whereas a20 was up-regulated by Zn (ASA)2 treatment compared to the untreated and ASA-groups.

CONCLUSION

This study proves the effectivity of the novel bis (aspirinato) zinc complex in reducing neointima formation and restenosis after balloon-injury and supports the hypothesis that inhibition of smooth-muscle transformation/proliferation plays a key role in the prevention of restenosis.

Noninvasive molecular ultrasound monitoring of vessel healing after intravascular surgical procedures in a preclinical setup

OBJECTIVE

Cardiovascular interventions induce damage to the vessel wall making antithrombotic therapy inevitable until complete endothelial recovery. Without a method to accurately determine the endothelial status, many patients undergo prolonged anticoagulation therapy, denying them any invasive medical procedures, such as surgical operations and dental interventions. Therefore, we aim to introduce molecular ultrasound imaging of the vascular cell adhesion molecule (VCAM)-1 using targeted poly-n-butylcyanoacrylate microbubbles (MB(VCAM-1)) as an easy accessible method to monitor accurately the reendothelialization of vessels.

APPROACH AND RESULTS

ApoE(-/-) mice were fed with an atherogenic diet for 1 and 12 weeks and subsequently, endothelial denudation was performed in the carotid arteries using a guidewire. Molecular ultrasound imaging was performed at different time points after denudation (1, 3, 7, and 14 days). An increased MB(VCAM-1) binding after 1 day, a peak after 3 days, and a decrease after 7 days was found. After 12 weeks of diet, MB(VCAM-1) binding also peaked after 3 days but remained high until 7 days, indicating a delay in endothelial recovery. Two-photon laser scanning microscopy imaging of double fluorescence staining confirmed the exposure of VCAM-1 on the superficial layer after arterial injury only during the healing phase. After complete reendothelialization, VCAM-1 expression persisted in the subendothelial layer but was not reachable for the MBV(CAM-1) anymore.

CONCLUSION

Molecular ultrasound imaging with MB(VCAM-1) is promising to assess vascular damage and to monitor endothelial recovery after arterial interventions. Thus, it may become an important diagnostic tool supporting the development of adequate therapeutic strategies to personalize anticoagulant and anti-inflammatory therapy after cardiovascular intervention.

Performance of distributed multiscale simulations

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption.

A framework for multi-scale modelling

We review a methodology to design, implement and execute multi-scale and multi-science numerical simulations. We identify important ingredients of multi-scale modelling and give a precise definition of them. Our framework assumes that a multi-scale model can be formulated in terms of a collection of coupled single-scale submodels. With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation. Our approach has been successfully applied to an increasing number of applications from different fields of science and technology.

Chemical activation and changes in surface morphology of poly(ε-caprolactone) modulate VEGF responsiveness of human endothelial cells

The high degree of clinical routine in percutaneous transluminal coronary angioplasty (PTCA) with and without stenting has not changed the fact that a large number of coronary heart disease patients are still affected by post-operative complications such as restenosis and thrombosis. Because re-endothelialization is the crucial aspect of wound healing after cardiovascular implant surgery, there is a need for modern biomaterials to aid endothelial cells in their adhesion and functional recovery post-stenting. This study systematically examines the potential of numerous chemical polymer modifications with regard to endothelialization. Poly(ε-caprolactone) (PCL) and its chemically activated forms are investigated in detail, as well as the impact of polymer surface morphology and precoating with matrix protein. Human umbilical vein endothelial cells (HUVECs) are used to characterize endothelial cell responses in terms of in vitro viability and adhesion. As a potential component in drug eluting implants, VEGF is applied as stimulus to boost endothelial cell proliferation on the polymer. In conclusion, plasma chemical activation of PCL combined with VEGF stimulation best enhances in vitro endothelialization. Examining the impact of morphological, chemical and biological modifications of PCL, this study makes an important new contribution towards the existing body of work on polymer endothelialization.

From Histology and Imaging Data to Models for In-Stent Restenosis

The implantation of stents has been used to treat coronary artery stenosis for several decades. Although stenting is successful in restoring the vessel lumen and is a minimally invasive approach, the long-term outcomes are often compromised by in-stent restenosis (ISR). Animal models have provided insights into the pathophysiology of ISR and are widely used to evaluate candidate drug inhibitors of ISR. Such biological models allow the response of the vessel to stent implantation to be studied without the variation of lesion characteristics encountered in patient studies.

This paper describes the development of complementary in silico models employed to improve the understanding of the biological response to stenting using a porcine model of restenosis. This includes experimental quantification using microCT imaging and histology and the use of this data to establish numerical models of restenosis. Comparison of in silico results with histology is used to examine the relationship between spatial localization of fluid and solid mechanics stimuli immediately post-stenting. Multi-scale simulation methods are employed to study the evolution of neointimal growth over time and the variation in the extent of neointimal hyperplasia within the stented region. Interpretation of model results through direct comparison with the biological response contributes to more detailed understanding of the pathophysiology of ISR, and suggests the focus for follow-up studies.

In conclusion we outline the challenges which remain to both complete our understanding of the mechanisms responsible for restenosis and translate these models to applications in stent design and treatment planning at both population-based and patient-specific levels.

Endothelial repair process and its relevance to longitudinal neointimal tissue patterns: comparing histology with in silico modelling

Re-establishing a functional endothelium following endovascular treatment is an important factor in arresting neointimal proliferation. In this study, both histology (in vivo) and computational simulations (in silico) are used to evaluate neointimal growth patterns within coronary arteries along the axial direction of the stent. Comparison of the growth configurations in vivo and in silico was undertaken to identify candidate mechanisms for endothelial repair. Stent, lumen and neointimal areas were measured from histological sections obtained from eight right coronary stented porcine arteries. Two re-endothelialization scenarios (endothelial cell (EC) random seeding and EC growth from proximal and distal ends) were implemented in silico to evaluate their influence on the morphology of the simulated lesions. Subject to the assumptions made in the current simulations, comparison between in vivo and in silico results suggests that endothelial growth does not occur from the proximal and distal ends alone, but is more consistent with the assumption of a random seeding process. This may occur either from the patches of endothelium which survive following stent implantation or from attachment of circulating endothelial progenitor cells.