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

arXiv: https://arxiv.org/abs/2111.06173 · HTML: https://mlsanity.com/paper/2111.06173/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 69 references that are in the map.
- First posted on arXiv 11 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation](https://mlsanity.com/paper/2007.12167/) (2020)

## Built on by (most cited first, 6 of 6)

- [Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots](https://mlsanity.com/paper/2302.11006/) (2023)
- [Gaussian process learning of nonlinear dynamics](https://mlsanity.com/paper/2312.12193/) (2023)
- [RONOM: Reduced-Order Neural Operator Modeling](https://mlsanity.com/paper/2507.12814/) (2025)
- [PDE-constrained Gaussian process surrogate modeling with uncertain data locations](https://mlsanity.com/paper/2305.11586/) (2023)
- [Physics-based Reduced Order Modeling for Uncertainty Quantification of Guided Wave Propagation using Bayesian Optimization](https://mlsanity.com/paper/2307.09661/) (2023)
- [Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression](https://mlsanity.com/paper/2403.09758/) (2024)

## Abstract (arXiv)

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 cells 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. Due to the computational intensity of the model and the number of evaluations required in the uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed which subsequently replaced the original In-Stent Restenosis model in the uncertainty quantification. A detailed analysis of the uncertainty propagation and sensitivity analysis is presented. Around 11% and 16% of uncertainty are observed on the average cross-sectional area and maximum relative area loss respectively, and the uncertainty estimates show that a higher fenestration mainly determines uncertainty in the neointimal growth at the initial stage of the process. On the other hand, the uncertainty 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. The uncertainty in the threshold strain is relatively small compared to the other uncertain parameters.