Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

Paun, L. M., Colebank, M. J., Olufsen, M. S., Hill, N. A. and Husmeier, D. (2020) Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation. Journal of the Royal Society: Interface, 17(173), 20200886. (doi: 10.1098/rsif.2020.0886) (PMID:33353505)

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Abstract

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Paun, Miss Luiza Mihaela and Hill, Professor Nicholas and Husmeier, Professor Dirk
Authors: Paun, L. M., Colebank, M. J., Olufsen, M. S., Hill, N. A., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Journal of the Royal Society: Interface
Publisher:The Royal Society
ISSN:1742-5689
ISSN (Online):1742-5662
Published Online:23 December 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Journal of the Royal Society: Interface 2020
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
305655Inference of cardio-mechanical parameters in real time: moving mathematical modelling into the clinicDirk HusmeierThe Royal Society of Edinburgh (ROYSOCED)62335M&S - Statistics