MCMC methods for inference in a mathematical model of pulmonary circulation

TL;DR

This paper develops a Bayesian inference framework using MCMC methods to estimate parameters in a complex pulmonary circulation model, aiding understanding of pulmonary hypertension progression.

Contribution

It introduces a reduced-dimensional fluid dynamics model and an improved parameter scaling technique for efficient MCMC inference in pulmonary circulation modeling.

Findings

Successful parameter estimation with uncertainty quantification

Model reduction from 55D to 5D improves tractability

Effective use of DRAM algorithm with convergence diagnostics

Abstract

This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis (DRAM) algorithm, coupled with constraint nonlinear optimization is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates. To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the DRAM algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.