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 some 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 per 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 stimulus intensity is related to the P(DCS); it may be related to the intensity of the stimulus to a power (alpha). Our stimuli are defined as pressure ratio [PR = (phi P1N2/ P2)-11] or pressure difference [delta P = phi P1N2-P2], where phi P1N2 is the N2 partial pressure calculated in the 360 min half-time (t1/2) compartment or t1/2 is estimated with other parameters and P2 is ambient pressure after the ascent. Both stimuli represent a potential released volume of gas. We tested the null hypothesis that alpha > 1 was no better than alpha = 1 in PR alpha and delta P alpha in a log logistic survival analysis of 1085 exposures in hypobaric chambers. The log likelihood number increased from -1198 for alpha = 0 for the null model to -724 for PR alpha 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 expressions for decompression dose with alpha > 1 is not by random chance and that alpha may link the physics of gas evolution to the biology of pain perception. Because of our empirical approach, we do not exclude other possible interpretations.