Probabilistic gas and bubble dynamics models of decompression sickness occurrence in air and nitrogen-oxygen diving

Probabilistic models of the occurrence of decompression sickness (DCS) with instantaneous risk defined as the weighted sum of bubble volumes in each of three parallel-perfused gas exchange compartments were fit using likelihood maximization to the subset of the USN Primary Air and N2-O2 database [n = 2,383, mean P(DCS) = 5.8%] used in development of the USN LE1 probabilistic models. Bubble dynamics with one diffusible gas in each compartment were modeled using the Van Liew equations with the nucleonic bubble radius, compartmental volume, compartmental bulk N2 diffusivity, compartmental N2 solubility, and the N2 solubility in blood x compartmental blood flow as adjustable parameters. Models were also tested that included the effects of linear elastic resistance to bubble growth in one, two, or all three of the modeled compartments. Model performance about the training data and separate validation data was compared to results obtained about the same data using the LE1 probabilistic model, which was independently implemented from published descriptions. In the most successful bubble volume model, BVM(3), diffusion significantly slows bubble growth in one of the modeled compartments, whereas mechanical resistance to bubble growth substantially accelerates bubble resolution in all compartments. BVM(3) performed generally on a par with LE1, despite inclusion of 12 more adjustable parameters, and tended to provide more accurate incidence-only estimates of DCS probability than LE1, particularly for profiles in which high fractional O2 gas mixes are breathed. Values of many estimated BVM(3) parameters were outside of the physiologic range, indicating that the model emerged from optimization as a mathematical descriptor of processes beyond bubble formation and growth that also contribute to DCS outcomes. Although incomplete as a mechanistic description of DCS etiology, BVM(3) remains applicable to a wider variety of decompressions than LE1 and affords a conceptual framework for further refinements motivated by mechanistic principles.