PAI may have a huge potential to motivate people to become and stay physically active, as it is an easily understandable and scientifically proven metric that could inform potential users of how much physical activity is needed to reduce the risk of premature cardiovascular disease death.

Accumulated inert gas during a dive and subsequent reduction of ambient pressure may lead to formation of gas bubbles, which is the initial cause of decompression sickness (DCS). Decompression procedures are used to get divers safely up from depth, and traditionally, the algorithms are evaluated against clinical symptoms of DCS. However, this approach has several weaknesses. The symptomatology of DCS is very diffuse and there are ethical concerns evaluating procedures through provoking DCS on the test subjects. In recent decades ultrasonic Doppler and imaging to detect venous gas emboli (VGE) have been used as additional tools to evaluate decompression procedures. A statistical correlation between VGE and DCS has been shown and the method is more sensitive than clinical manifestation. This paper suggests a dynamic mathematical model for VGE. We have used a physiological approach in the model derivation with VGE as a measurable endpoint. We propose that the underlying physiological and physical mechanisms of the model can be better validated with such an objective quantitative measurement method. Two simulation examples are given to illustrate the properties of the model and why there is a potential of improving the consistency of controlling bubble formation, and consequently, the risk of getting DCS.

Decompression Sickness (DCS) may occur when divers decompress from a hyperbaric environment. To prevent this, decompression procedures are used to get safely back to the surface. The models whose procedures are calculated from, are traditionally validated using clinical symptoms as an endpoint. However, DCS is an uncommon phenomenon and the wide variation in individual response to decompression stress is poorly understood. And generally, using clinical examination alone for validation is disadvantageous from a modeling perspective. Currently, the only objective and quantitative measure of decompression stress is Venous Gas Emboli (VGE), measured by either ultrasonic imaging or Doppler. VGE has been shown to be statistically correlated with DCS, and is now widely used in science to evaluate decompression stress from a dive. Until recently no mathematical model has existed to predict VGE from a dive, which motivated the development of the Copernicus model. The present article compiles a selection experimental dives and field data containing computer recorded depth profiles associated with ultrasound measurements of VGE. It describes a parameter estimation problem to fit the model with these data. A total of 185 square bounce dives from DCIEM, Canada, 188 recreational dives with a mix of single, repetitive and multi-day exposures from DAN USA and 84 experimentally designed decompression dives from Split Croatia were used, giving a total of 457 dives. Five selected parameters in the Copernicus bubble model were assigned for estimation and a non-linear optimization problem was formalized with a weighted least square cost function. A bias factor to the DCIEM chamber dives was also included. A Quasi-Newton algorithm (BFGS) from the TOMLAB numerical package solved the problem which was proved to be convex. With the parameter set presented in this article, Copernicus can be implemented in any programming language to estimate VGE from an air dive.

A key process in the pathophysiological steps leading to decompression sickness (DCS) is the formation of inert gas bubbles. The adverse effects of decompression are still not fully understood, but it seems reasonable to suggest that the formation of venous gas emboli (VGE) and their effects on the endothelium may be the central mechanism leading to central nervous system (CNS) damage. Hence, VGE might also have impact on the long-term health effects of diving. In the present review, we highlight the findings from our laboratory related to the hypothesis that VGE formation is the main mechanism behind serious decompression injuries. In recent studies, we have determined the impact of VGE on endothelial function in both laboratory animals and in humans. We observed that the damage to the endothelium due to VGE was dose dependent, and that the amount of VGE can be affected both by aerobic exercise and exogenous nitric oxide (NO) intervention prior to a dive. We observed that NO reduced VGE during decompression, and pharmacological blocking of NO production increased VGE formation following a dive. The importance of micro-nuclei for the formation of VGE and how it can be possible to manipulate the formation of VGE are discussed together with the effects of VGE on the organism. In the last part of the review we introduce our thoughts for the future, and how the enigma of DCS should be approached.

Abstract-This paper is based on a comprehensive dynamic mathematical model (Copernicus) of vascular bubble formation and growth during and after decompression from a dive. The model describes the underlying relationship between Venous Gas Emboli (VGE) and risk of severe Decompression Sickness (DCS). By using the Copernicus model the diving decompression problem can be formulated as a nonlinear optimal control problem, where the objective is to minimize the total ascend time subject to constraints on the maximum number of bubbles in the pulmonary artery (also referred to as the decompression stress). A recent study reveals that the optimal solution can be obtained by solving the optimization problem with some equality constraints. Inspired by which, a simpler approach using barrier function is proposed in this paper, through which we achieve a more efficient and robust numerical implementation. The paper also studies the effect of ascent profile parameterization.