A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Impact of geometric and hemodynamic changes on a mechanobiological model of atherosclerosis

BACKGROUND AND OBJECTIVE

In this work, the analysis of the importance of hemodynamic updates on a mechanobiological model of atheroma plaque formation is proposed.

METHODS

For that, we use an idealized and axisymmetric model of carotid artery. In addition, the behavior of endothelial cells depending on hemodynamical changes is analyzed too. A total of three computational simulations are carried out and their results are compared: an uncoupled model and two models that consider the opposite behavior of endothelial cells caused by hemodynamic changes. The model considers transient blood flow using the Navier-Stokes equation. Plasma flow across the endothelium is determined with Darcy's law and the Kedem-Katchalsky equations, considering the three-pore model, which is also employed for the flow of substances across the endothelium. The behavior of the considered substances in the arterial wall is modeled with convection-diffusion-reaction equations, and the arterial wall is modeled as a hyperelastic Yeoh's material.

RESULTS

Significant variations are noted in both the morphology and stenosis ratio of the plaques when comparing the uncoupled model to the two models incorporating updates for geometry and hemodynamic stimuli. Besides, the phenomenon of double-stenosis is naturally reproduced in the models that consider both geometric and hemodynamical changes due to plaque growth, whereas it cannot be predicted in the uncoupled model.

CONCLUSIONS

The findings indicate that integrating the plaque growth model with geometric and hemodynamic settings is essential in determining the ultimate shape and dimensions of the carotid plaque.

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.

A physics-informed deep learning framework for modeling of coronary in-stent restenosis

Machine learning (ML) techniques have shown great potential in cardiovascular surgery, including real-time stenosis recognition, detection of stented coronary anomalies, and prediction of in-stent restenosis (ISR). However, estimating neointima evolution poses challenges for ML models due to limitations in manual measurements, variations in image quality, low data availability, and the difficulty of acquiring biological quantities. An effective in silico model is necessary to accurately capture the mechanisms leading to neointimal hyperplasia. Physics-informed neural networks (PINNs), a novel deep learning (DL) method, have emerged as a promising approach that integrates physical laws and measurements into modeling. PINNs have demonstrated success in solving partial differential equations (PDEs) and have been applied in various biological systems. This paper aims to develop a robust multiphysics surrogate model for ISR estimation using the physics-informed DL approach, incorporating biological constraints and drug elution effects. The model seeks to enhance prediction accuracy, provide insights into disease progression factors, and promote ISR diagnosis and treatment planning. A set of coupled advection-reaction-diffusion type PDEs is constructed to track the evolution of the influential factors associated with ISR, such as platelet-derived growth factor (PDGF), the transforming growth factor- β (TGF- β ), the extracellular matrix (ECM), the density of smooth muscle cells (SMC), and the drug concentration. The nature of PINNs allows for the integration of patient-specific data (procedure-related, clinical and genetic, etc.) into the model, improving prediction accuracy and assisting in the optimization of stent implantation parameters to mitigate risks. This research addresses the existing gap in predictive models for ISR using DL and holds the potential to enhance patient outcomes through predictive risk assessment.

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.

Multilevel Assessment of Stent-Induced Inflammation in the Adjacent Vascular Tissue

A recent U.S. Food and Drug Administration report presented the currently available scientific information related to biological response to metal implants. In this work, a multilevel approach was employed to assess the implant-induced and biocorrosion-related inflammation in the adjacent vascular tissue using a mouse stent implantation model. The implications of biocorrosion on peri-implant tissue were assessed at the macroscopic level via in vivo imaging and histomorphology. Elevated matrix metalloproteinase activity, colocalized with the site of implantation, and histological staining indicated that stent surface condition and implantation time affect the inflammatory response and subsequent formation and extent of neointima. Hematological measurements also demonstrated that accumulated metal particle contamination in blood samples from corroded-stetted mice causes a stronger immune response. At the cellular level, the stent-induced alterations in the nanostructure, cytoskeleton, and mechanical properties of circulating lymphocytes were investigated. It was found that cells from corroded-stented samples exhibited higher stiffness, in terms of Young's modulus values, compared to noncorroded and sham-stented samples. Nanomechanical modifications were also accompanied by cellular remodeling, through alterations in cell morphology and stress (F-actin) fiber characteristics. Our analysis indicates that surface wear and elevated metal particle contamination, prompted by corroded stents, may contribute to the inflammatory response and the multifactorial process of in-stent restenosis. The results also suggest that circulating lymphocytes could be a novel nanomechanical biomarker for peri-implant tissue inflammation and possibly the early stage of in-stent restenosis. Large-scale studies are warranted to further investigate these findings.

Arterial tissues and their inflammatory response to collagen damage: A continuum in silico model coupling nonlinear mechanics, molecular pathways, and cell behavior

Damage in soft biological tissues causes an inflammatory reaction that initiates a chain of events to repair the tissue. This work presents a continuum model and its in silico implementation that describe the cascade of mechanisms leading to tissue healing, coupling mechanical as well as chemo-biological processes. The mechanics is described by means of a Lagrangian nonlinear continuum mechanics framework and follows the homogenized constrained mixtures theory. Plastic-like damage, growth and remodeling as well as homeostasis are taken into account. The chemo-biological pathways account for two molecular and four cellular species, and are activated by damage of collagen molecules in fibers. To consider proliferation, differentiation, diffusion and chemotaxis of species, diffusion-advection-reaction equations are employed. To the best of authors' knowledge, the proposed model combines for the first time such high number of chemo-mechano-biological mechanisms in a consistent continuum biomechanical framework. The resulting set of coupled differential equations describe balance of linear momentum, evolution of kinematic variables as well as mass balance equations. They are discretized in time according to a backward Euler finite difference scheme, and in space through a finite element Galerkin discretization. The features of the model are firstly demonstrated presenting the species dynamics and highlighting the influence of damage intensities on the growth outcome. In terms of a biaxial test, the chemo-mechano-biological coupling and the model's applicability to reproduce normal as well as pathological healing are shown. A last numerical example underlines the model's applicability to complex loading scenarios and inhomogeneous damage distributions. Concluding, the present work contributes towards comprehensive in silico models in biomechanics and mechanobiology.

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

Development of in silico models that capture progression of diseases in soft biological tissues are intrinsic in the validation of the hypothesized cellular and molecular mechanisms involved in the respective pathologies. In addition, they also aid in patient-specific adaptation of interventional procedures. In this regard, a fully-coupled high-fidelity Lagrangian finite element framework is proposed within this work which replicates the pathology of in-stent restenosis observed post stent implantation in a coronary artery. Advection-reaction-diffusion equations are set up to track the concentrations of the platelet-derived growth factor, the transforming growth factor-β, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of volumetric growth involved in the restenotic process, coupled to the evolution of the previously defined vessel wall constituents, is presented. Further, the finite element implementation of the model is discussed, and the behavior of the computational model is investigated via suitable numerical examples. Qualitative validation of the computational model is presented by emulating a stented artery. Patient-specific data are intended to be integrated into the model to predict the risk of in-stent restenosis, and thereby assist in the tuning of stent implantation parameters to mitigate the risk.

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.

Multiscale Modeling of Vascular Remodeling Induced by Wall Shear Stress

Objective

Hemodynamics-induced low wall shear stress (WSS) is one of the critical reasons leading to vascular remodeling. However, the coupling effects of WSS and cellular kinetics have not been clearly modeled. The aim of this study was to establish a multiscale modeling approach to reveal the vascular remodeling behavior under the interaction between the macroscale of WSS loading and the microscale of cell evolution.

Methods

Computational fluid dynamics (CFD) method and agent-based model (ABM), which have significantly different characteristics in temporal and spatial scales, were adopted to establish the multiscale model. The CFD method is for the second/organ scale, and the ABM is for the month/cell scale. The CFD method was used to simulate blood flow in a vessel and obtain the WSS in a vessel cross-section. The simulations of the smooth muscle cell (SMC) proliferation/apoptosis and extracellular matrix (ECM) generation/degradation in a vessel cross-section were performed by using ABM. During the simulation of the vascular remodeling procedure, the damage index of the SMC and ECM was defined as deviation from the obtained WSS. The damage index decreased gradually to mimic the recovery of WSS-induced vessel damage.

Results

(1) The significant wall thickening region was consistent with the low WSS region. (2) There was no evident change of wall thickness in the normal WSS region. (3) When the damage index approached to 0, the amount and distribution of SMCs and ECM achieved a stable state, and the vessel reached vascular homeostasis.

Conclusion

The established multiscale model can be used to simulate the vascular remodeling behavior over time under various WSS conditions.

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.

Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices

This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.

Effects of the Haemodynamic Stimulus on the Location of Carotid Plaques Based on a Patient-Specific Mechanobiological Plaque Atheroma Formation Model

In this work, we propose a mechanobiological atheroma growth model modulated by a new haemodynamic stimulus. To test this model, we analyse the development of atheroma plaques in patient-specific bifurcations of carotid arteries for a total time of 30 years. In particular, eight geometries (left or right carotid arteries) were segmented from clinical images and compared with the solutions obtained computationally to validate the model. The influence of some haemodynamical stimuli on the location and size of plaques is also studied. Plaques predicted by the mechanobiological models using the time average wall shear stress (TAWSS), the oscillatory shear index (OSI) and a new index proposed in this work are compared. The new index predicts the shape index of the endothelial cells as a combination of TAWSS and OSI values and was fitted using data from the literature. The mechanobiological model represents an evolution of the one previously proposed by the authors. This model uses Navier-Stokes equations to simulate blood flow along the lumen in the transient mode. It also employs Darcy's law and Kedem-Katchalsky equations for plasma and substance flow across the endothelium using the three-pore model. The mass balances of all the substances that have been considered in the model are implemented by convection-diffusion-reaction equations, and finally the growth of the plaques has been computed. The results show that by using the new mechanical stimulus proposed in this study, prediction of plaques is, in most cases, better than only using TAWSS or OSI with a minimal and maximal errors on stenosis ratio of 2.77 and 32.89 %, respectively. However, there are a few geometries in which haemodynamics cannot predict the location of plaques, and other biological or genetic factors would be more relevant than haemodynamics. In particular, the model predicts correctly eleven of the fourteen plaques presented in all the geometries considered. Additionally, a healthy geometry has been computed to check that plaque is not developed with the model in this case.

An in-silico Investigation Into the Role of Strain and Structure on Vascular Smooth Muscle Cell Growth

The orientation of vascular cells can greatly influence the in vivo mechanical properties and functionality of soft vascular tissues. How cell orientation mediates the growth response of cells is of critical importance in understanding the response of soft tissues to mechanical stimuli or injury. To date, considerable evidence has shown that cells align with structural cues such as collagen fibers. However, in the presence of uniaxial cyclic strain on unstructured substrates, cells generally align themselves perpendicularly to the mechanical stimulus, such as strain, a phenomenon known as “strain avoidance.” The cellular response to this interplay between structural cues and a mechanical stimulus is poorly understood. A recent in vitro experimental study in our lab has investigated both the individual and collective response of rat aortic smooth muscle cells (RASMC) to structural (collagenous aligned constructs) and mechanical (cyclic strain) cues. In this study, a 2D agent-based model (ABM) is developed to simulate the collective response of RASMC to varying amplitudes of cyclic strain (0–10%, 2–8%, 4–6%) when seeded on unstructured (PDMS) and structured (decellularized collagenous tissue) constructs. An ABM is presented that is fit to the experimental outcomes in terms of cellular alignment and cell growth on PDMS substrates, under cyclic strain amplitudes of (4–6%, 2–8%, 0–10%) at 24 and 72 h timepoints. Furthermore, the ABM can predict RASMC alignment and change in cell number on a structured construct at a cyclic strain amplitude of 0–10% after 10 days. The ABM suggests that strain avoidance behavior observed in cells is dominated by selective cell proliferation and apoptosis at these early time points, as opposed to cell re-orientation, i.e., cells perpendicular to the strain increase their rate of proliferation, whilst the rate of apoptosis simultaneously increases in cells parallel to the strain direction. The development of in-silico modeling platforms, such as that presented here, allow for further understanding of the response of cells to changes in their mechanical environment. Such models offer an efficient and robust means to design and optimize the compliance and topological structure of implantable devices and could be used to aid the design of next-generation vascular grafts and stents.

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.

Simulation of atherosclerotic plaque growth using computational biomechanics and patient-specific data

Atherosclerosis is the one of the major causes of mortality worldwide, urging the need for prevention strategies. In this work, a novel computational model is developed, which is used for simulation of plaque growth to 94 realistic 3D reconstructed coronary arteries. This model considers several factors of the atherosclerotic process even mechanical factors such as the effect of endothelial shear stress, responsible for the initiation of atherosclerosis, and biological factors such as the accumulation of low and high density lipoproteins (LDL and HDL), monocytes, macrophages, cytokines, nitric oxide and formation of foams cells or proliferation of contractile and synthetic smooth muscle cells (SMCs). The model is validated using the serial imaging of CTCA comparing the simulated geometries with the real follow-up arteries. Additionally, we examine the predictive capability of the model to identify regions prone of disease progression. The results presented good correlation between the simulated lumen area (P < 0.0001), plaque area (P < 0.0001) and plaque burden (P < 0.0001) with the realistic ones. Finally, disease progression is achieved with 80% accuracy with many of the computational results being independent predictors.

A multiphase model of growth factor-regulated atherosclerotic cap formation

Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why some caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to diffusible growth factor signals from the endothelium. Platelet-derived growth factor stimulates SMC migration, proliferation and collagen degradation, while transforming growth factor (TGF)-[Formula: see text] stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using in vivo and in vitro experimental data, reproduces several observations from plaque growth in mice. Numerical and analytical results demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF-[Formula: see text] in effective cap formation. These findings provide unique insight into the mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque model.

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.

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.

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.

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.

Mathematical Modelling and Simulation of Atherosclerosis Formation and Progress: A Review

Cardiovascular disease (CVD) is a major threat to human health since it is the leading cause of death in western countries. Atherosclerosis is a type of CVD related to hypertension, diabetes, high levels of cholesterol, smoking, oxidative stress, and age. Atherosclerosis primarily occurs in medium and large arteries, such as coronary and the carotid artery and, in particular, at bifurcations and curvatures. Atherosclerosis is compared to an inflammatory disease where a thick, porous material comprising cholesterol fat, saturated sterols, proteins, fatty acids, calcium etc., is covered by an endothelial membrane and a fragile fibrous tissue which makes atheromatic plaque prone to rupture that could lead to the blockage of the artery due to the released plaque material. Despite the great progress achieved, the nature of the disease is not fully understood. This paper reviews the current state of modelling of all levels of atherosclerosis formation and progress and discusses further challenges in atherosclerosis modelling. The objective is to pave a way towards more precise computational tools to predict and eventually reengineer the fate of atherosclerosis.

A fully coupled framework for in silico investigation of in-stent restenosis

Finite element analysis (FEA) can be implemented along with Agent-based model (ABM) to investigate the biomechanical and mechanobiological mechanisms of pathophysiological processes. However, traditional ABM-FEA approaches are often partially coupled and lack the feedback responses from biological analysis. To overcome this problem, a fully coupled ABM-FEA framework is developed in this paper by linking the macro-scale and cell-scale modules bi-directionally. Numerical studies of the in-stent restenosis process are conducted using the proposed approach and comparisons are made between the two types of frameworks. A reduction in lumen loss rate, which is possibly caused by the time-varying stresses, is observed in the fully coupled simulations. The re-endothelialisation process is also simulated under different frameworks and the simulation results show strong inhibition of endothelial cells to vascular restenosis. The proposed method is proved to be effective to explain the biomechanical-mechanobiological coupling characteristics of the restenosis problem and can be utilized for stent design and optimization.

Mechanobiological model of arterial growth and remodeling

A coupled agent-based model (ABM) and finite element analysis (FEA) computational framework is developed to study the interplay of bio-chemo-mechanical factors in blood vessels and their role in maintaining homeostasis. The agent-based model implements the power of REPAST Simphony libraries and adapts its environment for biological simulations. Coupling a continuum-level model (FEA) to a cellular-level model (ABM) has enabled this computational framework to capture the response of blood vessels to increased or decreased levels of growth factors, proteases and other signaling molecules (on the micro scale) as well as altered blood pressure. Performance of the model is assessed by simulating porcine left anterior descending artery under normotensive conditions and transient increases in blood pressure and by analyzing sensitivity of the model to variations in the rule parameters of the ABM. These simulations proved that the model is stable under normotensive conditions and can recover from transient increases in blood pressure. Sensitivity studies revealed that the model is most sensitive to variations in the concentration of growth factors that affect cellular proliferation and regulate extracellular matrix composition (mainly collagen).

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.

A Multiscale Computational Framework to Understand Vascular Adaptation

The failure rate for vascular interventions (vein bypass grafting, arterial angioplasty/stenting) remains unacceptably high. Over the past two decades, researchers have applied a wide variety of approaches to investigate the primary failure mechanisms, neointimal hyperplasia and aberrant remodeling of the wall, in an effort to identify novel therapeutic strategies. Despite incremental progress, specific cause/effect linkages among the primary drivers of the pathology, (hemodynamic factors, inflammatory biochemical mediators, cellular effectors) and vascular occlusive phenotype remain lacking. We propose a multiscale computational framework of vascular adaptation to develop a bridge between theory and experimental observation and to provide a method for the systematic testing of relevant clinical hypotheses. Cornerstone to our model is a feedback mechanism between environmental conditions and dynamic tissue plasticity described at the cellular level with an agent based model. Our implementation (i) is modular, (ii) starts from basic mechano-biology principle at the cell level and (iii) facilitates the agile development of the model.

Mathematical modelling of atheroma plaque formation and development in coronary arteries

Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modelling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.