Multi-scale simulations of the dynamics of in-stent restenosis: impact of stent deployment and design

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.

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.

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.

Effects of stent shape on focal hemodynamics in intracranial atherosclerotic stenosis: A simulation study with computational fluid dynamics modeling

Background and aims

The shape of a stent could influence focal hemodynamics and subsequently plaque growth or in-stent restenosis in intracranial atherosclerotic stenosis (ICAS). In this preliminary study, we aim to investigate the associations between stent shapes and focal hemodynamics in ICAS, using computational fluid dynamics (CFD) simulations with manually manipulated stents of different shapes.

Methods

We built an idealized artery model, and reconstructed four patient-specific models of ICAS. In each model, three variations of stent geometry (i.e., enlarged, inner-narrowed, and outer-narrowed) were developed. We performed static CFD simulation on the idealized model and three patient-specific models, and transient CFD simulation of three cardiac cycles on one patient-specific model. Pressure, wall shear stress (WSS), and low-density lipoprotein (LDL) filtration rate were quantified in the CFD models, and compared between models with an inner- or outer-narrowed stent vs. an enlarged stent. The absolute difference in each hemodynamic parameter was obtained by subtracting values from two models; a normalized difference (ND) was calculated as the ratio of the absolute difference and the value in the enlarged stent model, both area-averaged throughout the arterial wall.

Results

The differences in focal pressure in models with different stent geometry were negligible (ND<1% for all cases). However, there were significant differences in the WSS and LDL filtration rate with different stent geometry, with ND >20% in a static model. Observable differences in WSS and LDL filtration rate mainly appeared in area adjacent to and immediately distal to the stent. In the transient simulation, the LDL filtration rate had milder temporal fluctuations than WSS.

Conclusions

The stent geometry might influence the focal WSS and LDL filtration rate in ICAS, with negligible effect on pressure. Future studies are warranted to verify the relevance of the changes in these hemodynamic parameters in governing plaque growth and possibly in-stent restenosis in ICAS.

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.

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.

M. P. Integrating particle tracking with computational fluid dynamics to assess haemodynamic perturbation by coronary artery stents

AIMS

Coronary artery stents have profound effects on arterial function by altering fluid flow mass transport and wall shear stress. We developed a new integrated methodology to analyse the effects of stents on mass transport and shear stress to inform the design of haemodynamically-favourable stents.

METHODS AND RESULTS

Stents were deployed in model vessels followed by tracking of fluorescent particles under flow. Parallel analyses involved high-resolution micro-computed tomography scanning followed by computational fluid dynamics simulations to assess wall shear stress distribution. Several stent designs were analysed to assess whether the workflow was robust for diverse strut geometries. Stents had striking effects on fluid flow streamlines, flow separation or funnelling, and the accumulation of particles at areas of complex geometry that were tightly coupled to stent shape. CFD analysis revealed that stents had a major influence on wall shear stress magnitude, direction and distribution and this was highly sensitive to geometry.

CONCLUSIONS

Integration of particle tracking with CFD allows assessment of fluid flow and shear stress in stented arteries in unprecedented detail. Deleterious flow perturbations, such as accumulation of particles at struts and non-physiological shear stress, were highly sensitive to individual stent geometry. Novel designs for stents should be tested for mass transport and shear stress which are important effectors of vascular health and repair.

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.

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.

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.

Preliminary outcomes of single antiplatelet therapy for surface-modified flow diverters in an animal model: analysis of neointimal development and thrombus formation using OCT

Objective

To evaluate the rate of neointimal development and thrombus formation of surface-modified flow diverters in single antiplatelet therapy (SAPT) using optical coherence tomography (OCT) in a porcine model.

Methods

We divided 10 experimental pigs into two groups. One group (n=6) received dual antiplatelet therapy (DAPT) and the other group (n=4) received SAPT. Four stents (two per carotid artery) were implanted in both groups. The stents used were the Pipeline Flex embolization device (PED Flex), Pipeline Flex with Shield technology (PED Shield), and the Solitaire AB stent. All animals underwent weekly angiography and OCT. The OCT data were analyzed using the following measurements: neointimal ratio ((stent – lumen area)/stent area), stent-coverage ratio (number of stent struts covered by neointima/total stent struts), and the presence or absence of thrombus formation per 1 mm cross-section.

Results

PED Flex and Shield in the SAPT group had higher neointimal ratios than in the DAPT group (P<0.001, respectively). In the DAPT group, the speed of endothelial growth on day 7 in the PED Shield group was higher than that in the PED Flex group (P<0.001). In the SAPT group, PED Flex demonstrated significantly more thrombus formation on day 7 than PED Shield (P<0.001).

Conclusions

The PED Shield stent showed faster endothelial growth than the other devices and comparable neointimal volume. There was significantly less thrombus formation on PED Shield than PED Flex when using SAPT in a porcine model.

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.

Predictive Physiological Modeling of Percutaneous Coronary Intervention - Is Virtual Treatment Planning the Future?

Computational modeling has been used routinely in the pre-clinical development of medical devices such as coronary artery stents. The ability to simulate and predict physiological and structural parameters such as flow disturbance, wall shear-stress, and mechanical strain patterns is beneficial to stent manufacturers. These methods are now emerging as useful clinical tools, used by physicians in the assessment and management of patients. Computational models, which can predict the physiological response to intervention, offer clinicians the ability to evaluate a number of different treatment strategies in silico prior to treating the patient in the cardiac catheter laboratory. For the first time clinicians can perform a patient-specific assessment prior to making treatment decisions. This could be advantageous in patients with complex disease patterns where the optimal treatment strategy is not clear. This article reviews the key advances and the potential barriers to clinical adoption and translation of these virtual treatment planning models.

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.

ASSESSMENT OF CORONARY STENT DEPLOYMENT IN TAPERED ARTERIES: IMPACT OF ARTERIAL TAPERING

Coronary stents are used to prop open blocked arteries in order to restore normal blood flow. A major setback in this technology is in-stent restenosis (ISR), which gravely limits the clinical success of stents, especially in tapered vessels. The present study used the finite element method to study the effects of arterial tapering on the biomechanical behavior of both stents and vessels during stent deployment inside tapered arteries. The effect of arterial tapering was demonstrated by a combination of corresponding tapered arteries with various tapering angles, including a straight artery case for comparison. Results indicated that an increase of vessel tapering led to an increase in stent radial recoil, stent tapering following expansion, and von Mises stresses on vessels. However, an increase of vessel tapering also led to a decrease in stent foreshortening. The analysis provides suggestions for clinical application in tapered vessels. The finite element method evaluated mechanical stent behavior in tapered vessels, and can help designers to optimize the design of stents for tapered vessels.

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.

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.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.

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.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

Where do the platelets go? A simulation study of fully resolved blood flow through aneurysmal vessels

Despite the importance of platelets in the formation of a thrombus, their transport in complex flows has not yet been studied in detail. In this paper we simulated red blood cells and platelets to explore their transport behaviour in aneurysmal geometries. We considered two aneurysms with different aspect ratios (AR = 1.0, 2.0) in the presence of fast and slow blood flows (Re = 10, 100), and examined the distributions of the cells. Low velocities in the parent vessel resulted in a large stagnation zone inside the cavity, leaving the initial distribution almost unchanged. In fast flows, an influx of platelets into the aneurysm was observed, leading to an elevated concentration. The connection of the platelet-rich cell-free layer (CFL) with the outer regions of the recirculation zones leads to their increased platelet concentration. These platelet-enhanced recirculation zones produced a diverse distribution of cells inside the aneurysm, for the different aspect ratios. A thin red blood CFL that was occupied by platelets was observed on the top of the wide-necked aneurysm, whereas a high-haematocrit region very close to the vessel wall was present in the narrow-necked case. The simulations revealed that non-trivial distributions of red blood cells and platelets are possible inside aneurysmal geometries, giving rise to several hypotheses on the formation of a thrombus, as well as to the wall weakening and the possible rupture of an aneurysm.

Flexible composition and execution of high performance, high fidelity multiscale biomedical simulations

Multiscale simulations are essential in the biomedical domain to accurately model human physiology. We present a modular approach for designing, constructing and executing multiscale simulations on a wide range of resources, from laptops to petascale supercomputers, including combinations of these. Our work features two multiscale applications, in-stent restenosis and cerebrovascular bloodflow, which combine multiple existing single-scale applications to create a multiscale simulation. These applications can be efficiently coupled, deployed and executed on computers up to the largest (peta) scale, incurring a coupling overhead of 1-10% of the total execution time.

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

Treatment of stenosed coronary arteries by balloon angioplasty and stenting results in arterial injury including severe damage to the endothelium at the site of treatment and initiates a complex cascade of inflammatory processes that may lead to the development of in-stent restenosis (ISR). Many clinical and biological factors involved in the progression of restenotic lesions have been studied in detail over the past few years but the mystery behind the pathophysiological mechanisms of this disease is still unresolved. In the present work, the effects of re-endothelialization and nitric oxide release on neointimal growth are investigated in-silico using a two dimensional multi-scale model of ISR. The effect of stent deployment depths on the development of ISR is studied as a function of time after stenting. Two dimensional domains were prepared by deploying bare metal stent struts at three different deployment depths into the tissue. Shear stress distribution on endothelial cells, obtained by blood flow simulations, was translated into nitric oxide production that keeps the smooth muscle cells in quiescent state. The cellular growth trends were plotted as a function of time and the data indicate a positive correlation between the neointimal growths and strut deployment depths in the presence of a functional endothelium, in qualitative agreement with in-vivo data. Additionally, no ISR is observed if a functional endothelium appears much earlier.

The effects of stenting on shear stress: relevance to endothelial injury and repair

Stent deployment following balloon angioplasty is used routinely to treat coronary artery disease. These interventions cause damage and loss of endothelial cells (EC), and thus promote in-stent thrombosis and restenosis. Injured arteries are repaired (intrinsically) by locally derived EC and by circulating endothelial progenitor cells which migrate and proliferate to re-populate denuded regions. However, re-endothelialization is not always complete and often dysfunctional. Moreover, the molecular and biomechanical mechanisms that control EC repair and function in stented segments are poorly understood. Here, we propose that stents modify endothelial repair processes, in part, by altering fluid shear stress, a mechanical force that influences EC migration and proliferation. A more detailed understanding of the biomechanical processes that control endothelial healing would provide a platform for the development of novel therapeutic approaches to minimize damage and promote vascular repair in stented arteries.

Bridging paradigms: hybrid mechanistic-discriminative predictive models

Many disease processes are extremely complex and characterized by multiple stochastic processes interacting simultaneously. Current analytical approaches have included mechanistic models and machine learning (ML), which are often treated as orthogonal viewpoints. However, to facilitate truly personalized medicine, new perspectives may be required. This paper reviews the use of both mechanistic models and ML in healthcare as well as emerging hybrid methods, which are an exciting and promising approach for biologically based, yet data-driven advanced intelligent systems.

Modeling stented coronary arteries: where we are, where to go

In the last two decades, numerical models have become well-recognized and widely adopted tools to investigate stenting procedures. Due to limited computational resources and modeling capabilities, early numerical studies only involved simplified cases and idealized stented arteries. Nowadays, increased computational power allows for numerical models to meet clinical needs and include more complex cases such as the implantation of multiple stents in bifurcations or curved vessels. Interesting progresses have been made in the numerical modeling of stenting procedures both from a structural and a fluid dynamics points of view. Moreover, in the drug eluting stents era, new insights on drug elution capabilities are becoming essential in the stent development. Lastly, image-based methods able to reconstruct realistic geometries from medical images have been proposed in the recent literature aiming to better describe the peculiar anatomical features of coronary vessels and increase the accuracy of the numerical models. In this light, this review provides a comprehensive analysis of the current state-of-the-art in this research area, discussing the main methodological advances and remarkable results drawn from a number of significant studies.

The Virtual Physiological Human

The Virtual Physiological Human is synonymous with a programme in computational biomedicine that aims to develop a framework of methods and technologies to investigate the human body as a whole. It is predicated on the transformational character of information technology, brought to bear on that most crucial of human concerns, our own health and well-being.