Probabilistic model of decompression sickness based on stochastic models of bubbling in tissues

BACKGROUND: Decompression sickness (DCS) is caused by gas bubbles formed from pre-existing and new microscopic gas nuclei in blood and tissues. Assuming a random pattern of bubbling processes in living tissues, we developed a probabilistic model of DCS. We hypothesized that symptoms of DCS in an individual exposed to decompression appear when the total volume of bubbles in a unit volume of any tissue, w(t), exceeds the critical specific volume of a free gas phase, wcr. Therefore, one may consider the expectation of w(t)/wcr as a measure of the dynamic risk of gas bubble lesion of a given tissue segment. METHODS: Using the standard approach to estimation of various risks and the sum rule of probabilities of joint events, we defined the cumulative probability of DCS onset by the equation Pcum(t) = 1 - exp[Fcum(t)], where Fcum(t) = sigmaVnQnMnc(t), Qn = 1/wncr, where Vn is the volume of a tissue n. The function Mnc(t) coincides with the function Mn(t), defining a time history of the expectation of wn(t) until it achieves its maximum and then becomes a constant. Evaluating Pcum(t) for particular altitude decompressions, we identified the additive cumulative risk function of development of any DCS symptoms, Fcum-tot(t), with the function defining the cumulative risk of any bubble lesion of the "worst" virtual tissue (WVT) of Type A. On the other hand, we identified the additive cumulative risk function of development of intolerable DCS symptoms, Fcum-int(t), with the function defining the cumulative risk of acute bubble lesion of the WVT of Type phi. RESULTS: We found parameters of the curves Pcum-tot(t) and Pcum-int(t) that fit the known empirical curves for the cumulative probability of DCS onset. For men performing mild exercise at 30 kPa after preoxygenation, our estimated parameters for curves Pcum-tot(t) indicate that the WVTs of Type A have nitrogen washout half-times of 260 and 290 min for preoxygenation times of 75 and 135 min, respectively. On the other hand, the parameters of curves Pcum-int(t) show that the WVTs of Type phi in men performing mild exercise at 20-40 kPa after preoxygenation during 0-6 h are virtual tissues with nitrogen washout half-times of 400 to 615 min. CONCLUSION: Our model provides a new approach to predicting DCS risk for various decompression profiles. By demonstrating the dependence of DCS risk on body tissue parameters, the model explains why resistance to DCS in mammals increases with a lower body mass and greater specific blood flow in tissues.