Parameter estimation in decompression sickness

A problem presented at the UK MMSG Southampton 2007.

Presented by:
Mr Geoff Loveman (Submarine Escape and Diving Systems, QinetiQ)
H Byrne, J Forster, OE Jensen, J King, G Loveman, B MacArthur, C Please, SL Waters

Problem Description

During exposure to raised pressure, nitrogen in a diver's breathing air is carried to their body tissues in the blood where it diffuses into the tissues. On rapid decompression to a lower pressure, some tissues will be supersaturated with nitrogen relative to the ambient pressure. This supersaturation can drive the formation of bubbles in the body which may cause numerous symptoms, including joint pain (the 'bends'), paralysis and death. Decompression sickness (DCS), as this collection of symptoms is known, is a limiting factor in escape from a disabled submarine.

Large sets of pressure exposure data are available where the occurrence of DCS is expressed as a binary outcome. Several investigators have estimated model parameter values using the method of maximum likelihood on selected data sets. The complexity of the models is limited by the relative sparseness of DCS events within the data sets.

It has been suggested to us that the application of Bayesian ideology might allow us to include this type of information in our models – are there methods that we should be following to achieve this? The data we employ comes from many different trials which were conducted with different aims – should we be applying Bayesian techniques when we use this data in our parameter estimation?

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Study Group Report

A number of approaches have been taken to this problem and the Study Group looked at a few of these as well as considering other ideas. One approach is a "black box" model where some suitable functional form is assumed for the probability of the bends occurring dependent on the saturation pressure and the escape depth; introducing free parameters in this function allows the model to be fitted to the data. A second approach is to exploit existing mechanistic models of the processes occurring during gas pressure changes in the submariner and to then incorporate a stochastic model of the bends occurring. By allowing some of the parameters in such models to be adjusted the data could then be fitted. In both cases the fitted model can then be used to predict a contour map of the probability of the bends occurring. We shall discuss both of these approaches, although most effort was directed to the second approach.

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