Uncertainty Quantification of a Multiscale Model for In-Stent Restenosis

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

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

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

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

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

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

Uncertainty quantification patterns for multiscale models

Uncertainty quantification (UQ) is a key component when using computational models that involve uncertainties, e.g. in decision-making scenarios. In this work, we present uncertainty quantification patterns (UQPs) that are designed to support the analysis of uncertainty in coupled multi-scale and multi-domain applications. UQPs provide the basic building blocks to create tailored UQ for multiscale models. The UQPs are implemented as generic templates, which can then be customized and aggregated to create a dedicated UQ procedure for multiscale applications. We present the implementation of the UQPs with multiscale coupling toolkit Multiscale Coupling Library and Environment 3. Potential speed-up for UQPs has been derived as well. As a proof of concept, two examples of multiscale applications using UQPs are presented. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

VECMAtk: a scalable verification, validation and uncertainty quantification toolkit for scientific simulations

We present the VECMA toolkit (VECMAtk), a flexible software environment for single and multiscale simulations that introduces directly applicable and reusable procedures for verification, validation (V&V), sensitivity analysis (SA) and uncertainty quantication (UQ). It enables users to verify key aspects of their applications, systematically compare and validate the simulation outputs against observational or benchmark data, and run simulations conveniently on any platform from the desktop to current multi-petascale computers. In this sequel to our paper on VECMAtk which we presented last year [1] we focus on a range of functional and performance improvements that we have introduced, cover newly introduced components, and applications examples from seven different domains such as conflict modelling and environmental sciences. We also present several implemented patterns for UQ/SA and V&V, and guide the reader through one example concerning COVID-19 modelling in detail. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

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.

[Review of studies on the biomechanical modelling of the coupling effect between stent degradation and blood vessel remodeling]

The dynamic coupling of stent degradation and vessel remodeling can influence not only the structural morphology and material property of stent and vessel, but also the development of in-stent restenosis. The research achievements of biomechanical modelling and analysis of stent degradation and vessel remodeling were reviewed; several noteworthy research perspectives were addressed, a stent-vessel coupling model was developed based on stent damage function and vessel growth function, and then concepts of matching ratio and risk factor were established so as to evaluate the treatment effect of stent intervention, which may lay the scientific foundation for the structure design, mechanical analysis and clinical application of biodegradable stent.

Easing Multiscale Model Design and Coupling with MUSCLE 3

Multiscale modelling and simulation typically entails coupling multiple simulation codes into a single program. Doing this in an ad-hoc fashion tends to result in a tightly coupled, difficult-to-change computer program. This makes it difficult to experiment with different submodels, or to implement advanced techniques such as surrogate modelling. Furthermore, building the coupling itself is time-consuming. The MUltiScale Coupling Library and Environment version 3 (MUSCLE 3) aims to alleviate these problems. It allows the coupling to be specified in a simple configuration file, which specifies the components of the simulation and how they should be connected together. At runtime a simulation manager takes care of coordination of submodels, while data is exchanged over the network in a peer-to-peer fashion via the MUSCLE library. Submodels need to be linked to this library, but this is minimally invasive and restructuring simulation codes is usually not needed. Once operational, the model may be rewired or augmented by changing the configuration, without further changes to the submodels. MUSCLE 3 is developed openly on GitHub, and is available as Open Source software under the Apache 2.0 license.

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

Background

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

Methods

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

Results

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

Conclusions

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

Electronic supplementary material

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

Multiscale modelling, simulation and computing: from the desktop to the exascale

This short contribution introduces a theme issue dedicated to 'Multiscale modelling, simulation and computing: from the desktop to the exascale'. It holds a collection of articles presenting cutting-edge research in generic multiscale modelling and multiscale computing, and applications thereof on high-performance computing systems. The special issue starts with a position paper to discuss the paradigm of multiscale computing in the face of the emerging exascale, followed by a review and critical assessment of existing multiscale computing environments. This theme issue provides a state-of-the-art account of generic multiscale computing, as well as exciting examples of applications of such concepts in domains ranging from astrophysics, via material science and fusion, to biomedical sciences. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

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'.

Multiscale computing for science and engineering in the era of exascale performance

In this position paper, we discuss two relevant topics: (i) generic multiscale computing on emerging exascale high-performing computing environments, and (ii) the scaling of such applications towards the exascale. We will introduce the different phases when developing a multiscale model and simulating it on available computing infrastructure, and argue that we could rely on it both on the conceptual modelling level and also when actually executing the multiscale simulation, and maybe should further develop generic frameworks and software tools to facilitate multiscale computing. Next, we focus on simulating multiscale models on high-end computing resources in the face of emerging exascale performance levels. We will argue that although applications could scale to exascale performance relying on weak scaling and maybe even on strong scaling, there are also clear arguments that such scaling may no longer apply for many applications on these emerging exascale machines and that we need to resort to what we would call multi-scaling. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.