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

L. Mihaela Paun,Nicholas A. Hill,Mette S. Olufsen,Dirk Husmeier,Mitchel J. Colebank

doi:10.1098/rsif.2020.0886

L. Mihaela Paun, Nicholas A. Hill + Show 3 more

Open Access

https://doi.org/10.1098/rsif.2020.0886

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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.

Highlights

Computational haemodynamics models are emerging as powerful tools for analysing cardiovascular disease progression and the effects of treatments [1] by providing essential haemodynamic metrics which could not be obtained from in vivo experiments [2]
We compare inference results based on Markov chain Monte Carlo (MCMC) between the conventional method ignoring model mismatch and our proposed approach, which explicitly incorporates the model mismatch, defined in equation (4.7), with Gaussian processes (GPs)
Parameter estimates obtained from these two simulations are compared to the ground truth parameter values in table 3 using the relative sum of squared errors (SSE), Xk i1⁄41 ui

Summary

Introduction

Computational haemodynamics models are emerging as powerful tools for analysing cardiovascular disease progression and the effects of treatments [1] by providing essential haemodynamic metrics which could not be obtained from in vivo experiments [2]. Before using the models for decision-making in the clinic, they must be calibrated and fitted to data, and their credibility rigorously tested by modelling all sources of uncertainty using statistical analysis. The current study assesses the health of the pulmonary system by integrating imaging data (obtained with micro-computed tomography (CT)), blood pressure data (measured invasively via catheterization) and blood flow data (measured with ultrasound), using a one-dimensional (1D) fluid-dynamics model combined with statistical inference. Predictions of blood pressure, blood flow and vessel area are computed in an arterial network model constructed from micro-CT images from a control mouse, and the pressure predictions are compared to dynamic data in the main pulmonary artery (MPA). Our analysis includes the uncertainty in the model parameters (which are naturally variable), in the model form/structure (the discrepancy between the model and the reality), in the measurements (the noise model), and in the simulator output (e.g. the errors from numerically integrating the model equations)

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