Bayesian uncertainty quantification and propagation for personalized cardiac modelling

Lead Supervisor
Dr Marina Riabiz
Lecturer in Statistics
Department of Mathematics, Faculty of Natural, Mathematical & Engineering Sciences
King’s College London
marina.riabiz@kcl.ac.uk

Co-supervisor
Prof Steven Niederer, Prof Chris Oates

Project Details

Personalization of cardiac models is fundamental for increasing our understanding of cardiovascular diseases and tailoring patient specific treatments.
Cardiac models can be formed at different scales (cell, tissue, whole organ) and they correspond to the solution to differential equations that represent the electro-mechanical coupling responsible for a heartbeat. In such computational setting, models can be personalized by calibrating the parameters governing the differential equations to data representing an individual. The Bayesian framework offers a natural way for parameter inference at a given scale, and uncertainty propagation across scales, by handling sets of samples representing the probability distributions of the parameters. However, Bayesian inference involves running numerical solvers in outer-loops, which becomes prohibitively expensive as the scale of focus increases and makes it difficult to assess the quality of the scientific conclusions because of the large variance of the estimates.
This PhD project will implement and study novel Bayesian computational tools, aimed at reducing the variance of the estimates at a given scale and help to effectively propagate uncertainty across scales. In particular, the PhD candidate will work on effective implementation of Stein thinning [1], an algorithm designed to retain an optimal subset of parameter samples, and whose performance is determined by the choice of a kernel function. Uncertainty propagation based on Stein thinning will be compared in accuracy and computing time to multi-fidelity methods for uncertainty propagation [2], including the combination of high and low-fidelity solvers aimed at variance reduction.

[1] Riabiz, M., Chen, W., Cockayne, J., Swietach, P., Niederer, S.A., Mackey, L. and Oates, C., 2020. Optimal thinning of MCMC output. Journal of the Royal Statistical Society Series B (Statistical Methodology). Forthcoming.
[2] Peherstorfer, B., Willcox, K., Gunzburger, M. Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Siam Review. 2018;60(3):550-91.

Keywords

Cardiac modelling, Bayesian inference, Uncertainty propagation