Post-decompression bubble and inflammation interactions: a non-extensive dynamical system model

Inert gas bubbles in tissues and in blood have been historically considered as the only triggering factors for DCS, but now many other factors are considered to affect the final outcome of a decompression profile for a certain individual. In this sense, inflammation seems to play a relevant role, not only due to the physical damage of tissues by the bubbles, but as a potentiator of the process as a whole. The present study aims to put forward a mathematical model of bubble formation associated with an inflammatory process related to decompression. The model comprises four state-variables (inert gas pressure, inert gas bubbles, proinflammatory and inflammatory factors) in a set of non-linear differential equations. The model is non-extensive: inert gas transitions between liquid and gaseous phases do not change the concentration of the dissolved gas. The relationship between bubbles and inflammation is given through parameters that form a positive feedback loop. The results of the model were compared with the experimental results of echocardiography from volunteers in two dive/decompression profiles; the model shows a very good agreement with the empirical data and previews different inflammatory outcomes for different experimental profiles. We suggest that slight changes in the parameters' values might turn the simulations from a non-inflammatory to an inflammatory profile for a given individual. Therefore, the present model might help address the problem of DCS on a particular basis.