EVOLVED GAS, PAIN, THE POWER-LAW, AND PROBABILITY OF HYPOBARIC DECOMPRESSION-SICKNESS

The intensity of a pain-only decompression sickness (DCS) symptom with respect to time at altitude increases, peaks, and then declines in so me cases. A similar pattern is also seen in a graph of the probability density function [f(t)] for DCS. The f(t) is the proportion of DCS pe r unit time with respect to time at altitude. The integration of f(t) with respect to time provides the cumulative probability of DCS [P(DCS )]. We suspect that the perceived intensity of pain with a given stimu lus intensity is related to the P(DCS); it may be related to the inten sity of the stimulus to a power (alpha). Our stimuli are defined as pr essure ratio [PR = (phi P1N(2)/P2) - 1] or pressure difference [Delta P = phi P1N(2) - P2], where phi P1N(2) is the N-2 partial pressure cal culated in the 360 min half-time (t1/2) compartment or t1/2 is estimat ed with other parameters and P2 is ambient pressure after the ascent. Both stimuli represent a potential released volume of gas. We tested t he null hypothesis that alpha > 1 was no better than alpha = 1 in PRal pha and Delta P-alpha in a log logistic survival analysis of 1085 expo sures in hypobaric chambers. The log likelihood number increased from -1198 for alpha = 0 for the null model to -724 for PRalpha when alpha = 3.52 with a 42 min t1/2 and -714 for Delta P-alpha when alpha = 8.44 with a 91 min t1/2. We conclude that the improvement in our expressio ns for decompression dose with alpha > 1 is not by random chance and t hat alpha may link the physics of gas evolution to the biology of pain perception. Because of our empirical approach, we do not exclude othe r possible interpretations.