Incorporating Model Mismatch in a Bayesian Uncertainty Quantification Analysis of a Fluid-Dynamics Model of Pulmonary Blood Circulation

• Activity Number: 265 - Stochastic Processes in Medicine and Medical Engineering: Theoretical Foundations and Applications
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Medical Devices and Diagnostics
• Author(s): Mihaela Paun* and Mitchel Colebank and Mette Olufsen and Nicholas Hill and Dirk Husmeier
• Companies: University of Glasgow and University of California and North Carolina State University and University of Glasgow and University of Glasgow
• Keywords: Bayesian uncertainty quantification; Model mismatch; MCMC; Gaussian Processes; Fluid dynamics; Pulmonary circulation

Abstract

This study employs Bayesian methods (MCMC) for uncertainty quantification of model parameters and haemodynamic predictions in a one-dimensional fluid-dynamics model of the pulmonary circulation based on mouse haemodynamic and micro-computed tomography imaging data. Our Bayesian analysis integrates an often ignored, yet essential source of uncertainty: in the model form, as the mathematical model may not faithfully capture the full flexibility of the unknown real processes, and in the measurements, as the error (noise) model may not adequately match the data (jointly called `model mismatch'). Our results demonstrate that in the presence of model mismatch the conventional method based on minimisation of the mean squared error between the measurements and predictions results in biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method based on Gaussian Processes allows for model mismatch, thus corrects the bias.