Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid‐dynamics model of the pulmonary circulation

Paun, L. M. and Husmeier, D. (2021) Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid‐dynamics model of the pulmonary circulation. International Journal for Numerical Methods in Biomedical Engineering, 37(2), e3421. (doi: 10.1002/cnm.3421) (PMID:33249755) (PMCID:PMC7901000)

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Abstract

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Item Type:Articles
Additional Information:This work is part of the research programme of the Centre for Multiscale Soft Tissue Mechanics with Application to Heart & Cancer (SofTMech), funded by the Engineering and Physical Sciences Research Council (EPSRC) of the UK, grant reference number EP/N014642/1. Dirk Husmeier is supported by a grant from the Royal Society of Edinburgh, award number 62335.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Paun, Miss Mihaela and Husmeier, Professor Dirk
Authors: Paun, L. M., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:International Journal for Numerical Methods in Biomedical Engineering
Publisher:Wiley
ISSN:2040-7939
ISSN (Online):2040-7947
Published Online:28 November 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in International Journal for Numerical Methods in Biomedical Engineering 37(2): e3421
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics