A Physiological Approach to a New Decompression Algorithm Using Nonlinear Model Predictive Control

Abstract

Diving involves breathing of pressurized inert gas, which accumulates in body tissues during the dive. When the diver ascends towards the surface, the pressure is relieved and gas bubbles may form. These bubbles are the root cause of Decompression Sickness (DCS) and staged ascent schedules are used to prevent this event. Available procedures are shown to have shortcomings in terms of safety and efficiency, which is the motivation for the work behind the present thesis. The thesis presents a new decompression algorithm founded on a dynamic dual-phase model, named Copernicus, using Venous Gas Emboli (VGE) as a stress predictor. VGE is the occurrence of intra-vascular bubbles in the central venous pool, where the bubbles may be detected using ultrasonic Doppler or imaging. VGE is graded after a semi-quantitative scale, and is currently the only objective measure of decompression stress. Copernicus is calibrated against three different data sets of VGE measurements in human divers, counting 457 exposures in total. The data consist of complete time-sampled depth trajectories from computer logs combined with post-dive measurements of bubble grade. A selected set of model parameters is estimated using nonlinear optimization of a cost function based on least square error. Since the model fundamentals are derived from a physiological approach, many of the model coefficients are given from individual and physiological parameters. Individual settings, such as weight, age, and fitness level, will thus affect the model outcome. Workload estimates from heart-rate measurements are also incorporated in the model by modifying tissue gas dynamics in real time. With a comprehensive and observable model as foundation, optimal control theory is applied to calculate decompression procedures. It is hypothesized that if post-dive VGE peak is kept sufficiently low, the risk of DCS is at an acceptable level, which, in this thesis, is defined as a Low VGE (LVGE) dive. The methodology is based on nonlinear model predictive control (NMPC) to provide the fastest possible ascent schedule subject to the constraint of a model-predicted VGE peak. Implementation aspects for low-cost, embedded processors in dive computers are also discussed, using explicit solutions through multi-parametric nonlinear programming (mp-NLP).