Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation. Issue 173 (23rd December 2020)

• Record Type: Journal Article
• Authors: Paun, L. Mihaela; Colebank, Mitchel J.; Olufsen, Mette S.; Hill, Nicholas A.; Husmeier, Dirk
• Is Part Of: Journal of the Royal Society interface. Volume 17:Issue 173(2020)
• Publication Date: 2020-12-23
• Subjects: uncertainty quantification -- model mismatch -- model selection -- MCMC -- Gaussian processes -- pulmonary circulation; Physical sciences -- Research -- Periodicals; Life sciences -- Research -- Periodicals; Interdisciplinary research -- Periodicals; 570.5
• DOI: 10.1098/rsif.2020.0886
• Languages: English
• ISSNs: 1742-5689

Abstract

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.