Modelling and predicting decompression sickness: an investigation

Abstract

In this thesis, we shall consider the mathematical modelling of Decompression Sickness (DCS), more commonly known as 'the bends', and, in particular, we shall consider the probability of its occurrence on escaping from a damaged submarine.

We shall begin by outlining the history of DCS modelling, before choosing one particular model-type - that originally considered by Thalmann et al. (1997) - upon which to focus our attention. This model combines tissues in the body sharing similar characteristics, in particular the rate at which nitrogen is absorbed into or eliminated from the tissues in question, terming such combinations 'compartments'. We shall derive some previously unknown analytical results for the single compartment model, which we shall then use to assist us in using Markov Chain Monte Carlo (MCMC) methods to find estimates for the model's parameters using data provided by QinetiQ. These data concerned various tests on a range of subjects, who were exposed to various decompression conditions from a range of depths and at a range of breathing pressures. Next, we shall consider the multiple compartment model, making use of Reversible Jump MCMC to determine the 'best' number of compartments to use.

We shall then move on to a slightly different problem, concerning a second dataset from QinetiQ that consists of subjective measurements on an ordinal scale of the number of bubbles passing the subjects' hearts (known as the Kisman-Masurel bubble score), for a different set of subjects. This dataset contains quite a number of gaps, and we shall seek to impute these before making use of our imputed datasets to identify logistic regression models that provide an alternative DCS probability.

Finally, we shall combine these two approaches using a model averaging technique to improve upon previously generated predictions, thereby offering additional practical advice to submariners and those rescuing them following an incident.

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Identifiers

ORCID for Jon Forster: orcid.org/0000-0002-7867-3411

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