The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on the inverse problem, more specifically on the parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The particular application is pulmonary hypertension, requiring an analysis of the blood pressure, whose measurement in the pulmonary system can only be obtained invasively for patients. The ultimate goal is to develop a non-invasive disease diagnostication method. This could be accomplished by combining non-invasively obtained haemodynamic data (blood flow measured with MRI) with imaging data (CT scans of the lung structure), to be used in conjunction with mathematical and statistical modelling. This will provide a decision-making support mechanism in the clinic, ultimately aiding in personalised medicine.
This thesis adopts a Bayesian approach to uncertainty quantification in physiological models, allowing to assess the credibility of these models. The danger with using overly confident models is that they could produce biased predictions, ultimately leading to the wrong disease diagnosis and treatment. Inference of unknown and immeasurable parameters of several 1D fluid-dynamics models, expressed through partial differential equations, is performed with Markov Chain Monte Carlo. These parameters act as bio-indicators for the disease, e.g. vessel wall stiffness, which is high in pulmonary hypertension patients. In addition, the uncertainty in the model form and the data measurement process (jointly called model mismatch) is captured, and the model mismatch is represented with Gaussian Processes. Given that the mathematical model is not a perfect representation of the reality, and that the data measurement process is prone to errors, this introduces an extra layer of uncertainty. If unaccounted for, the result is biased and overly confident parameter estimates and model predictions. Yet another source of uncertainty modelled in this study is the variability in the vessel network geometry, connectivity and size, which is shown to introduce variability in the model predictions, and must be accounted for. The uncertainty in the model parameters, model form, data measurement process and vessel network propagates through to the model predictions, which is also quantified.
Lastly, this thesis is concerned with accelerating the computational efficiency of the statistical inference procedure, aiming to make the methods suitable for use in the clinic. Statistical emulation is used in conjunction with a series of efficient Hamiltonian Monte Carlo
algorithms, particularly adapted to computationally expensive models. A comparative evaluation study is carried out to identify the algorithm giving the best trade-off between accuracy and efficiency on a set of representative benchmark differential equation models
