The approach

The b-values, as compiled by Bühlmann in his 1983 book “Decompression Sickness”, that govern decompression need to vary smoothly throughout the range of depths. These values were modelled using a hyperbolic tanh function. Trial and error is then used to determine the coefficients that allow the user to adjust how aggressive they want their dive to be. The old algorithm was used as a benchmark in the range for which tables are well documented, i.e. 0-80m.

In parallel, the company also wanted a method for validating their algorithms based on a more scientific approach to decompression modelling. Since it is hypothesised that microbubbles in the body formed from gas coming out of solution contribute to DCS, a tissue model containing stable nuclei from which microbubbles can grow was developed to calculate gas absorption and subsequent bubble dynamics. The aim was to monitor and limit microbubble size in order to reduce the chances of DCS for a given decompression profile.

“The internship with VR Technology has allowed me to be part of the development of a new decompression algorithm that could positively impact the experience of divers all over the world. The valuable insights into the use of mathematics in industry and the skills acquired during the project will be useful in my PhD research and career.” said intern Jean-Pierre O'Brian, PhD student, University College London.

Outcomes and benefits

The project enabled VR Technology to improve upon their existing VGM algorithm incorporating aspects of Bühlmann models with microbubble theories, essentially extending the range of depths over which their model can be used whilst maintaining substantial customisability for both the company and the user.

Furthermore, work on tissue models underline the complicated nature of decompression theory. This part of the project has enabled the company to feel confident with their current algorithms and given them a foundation on which to base future decompression models containing microbubble physics.

The project allowed the student to gain an understanding of the nature of decompression modelling in the human body. The skills gained by the student included tailoring mathematical concepts for commercial use and numerical methods such as finite difference solutions of diffusion equations employed in the tissue model. Involvement with the company enabled the student to interact with different departments particularly when explaining his ideas, in addition to appreciating the effort involved in running a medium sized company.

“This project has been our first use of the internship system with KTN. The results and progress have exceeded our expectations. We will continue to keep working with the KTN and the members of the team to continue this project and start others.” said Nick Bushell, Industrial Supervisor, VR Technology.