Decompression sickness predictive models for unsafe human exposure.

Decompression sickness (DCS) incidence prediction models have achieved useful predictive success under conditions of routine Navy diving. However, extrapolation into higher-risk exposures, e.g., emergency conditions, has been a problem. We have assembled a calibration data set of 3,300 single exposures with 200 DCS cases emphasizing high-incidence data from the U.S. Navy compilation of manned diving trials. We also evaluated a variant of the older linear-exponential risk model family where the instantaneous risk is defined as the relative supersaturation squared. Goodness of fit was assessed by maximum likelihood, by comparison of categories of observed and predicted cases in three ways (component data set, depth-time group, and risk level), and by reproduction of data dose-response trends. Four models fit the data well. Two had the old risk definition, and two had the new. With each risk definition, a satisfactory set of parameters was found differing mainly in treatment of gas kinetics in the fastest compartment. Multimodel inferences were made with a combination of the four models weighted using the Akaike Information Criterion. The combined model is recommended for use in emergency preparations where compressed-air exposures may lead to a 40% or higher incidence of DCS.

Using animal data to improve prediction of human decompression risk following air-saturation dives.

To plan for any future rescue of personnel in a disabled and pressurized submarine, the US Navy needs a method for predicting risk of decompression sickness under possible scenarios for crew recovery. Such scenarios include direct ascent from compressed air exposures with risks too high for ethical human experiments. Animal data, however, with their extensive range of exposure pressures and incidence of decompression sickness, could improve prediction of high-risk human exposures. Hill equation dose-response models were fit, by using maximum likelihood, to 898 air-saturation, direct-ascent dives from humans, pigs, and rats, both individually and combined. Combining the species allowed estimation of one, more precise Hill equation exponent (steepness parameter), thus increasing the precision associated with human risk predictions. These predictions agreed more closely with the observed data at 2 ATA, compared with a current, more general, US Navy model, although the confidence limits of both models overlapped those of the data. However, the greatest benefit of adding animal data was observed after removal of the highest risk human exposures, requiring the models to extrapolate.

Calibration of a bubble evolution model to observed bubble incidence in divers.

The method of maximum likelihood was used to calibrate a probabilistic bubble evolution model against data of bubbles detected in divers. These data were obtained from a diverse set of 2,064 chamber man-dives involving air and heliox with and without oxygen decompression. Bubbles were measured with Doppler ultrasound and graded according to the Kisman-Masurel code from which a single maximum bubble grade (BG) per diver was compared to the maximum bubble radius (Rmax) predicted by the model. This comparison was accomplished using multinomial statistics by relating BG to Rmax through a series of probability functions. The model predicted the formation of the bubble according to the critical radius concept and its evolution was predicted by assuming a linear rate of inert gas exchange across the bubble boundary. Gas exchange between the model compartment and blood was assumed to be perfusion-limited. The most successful calibration of the model was found using a trinomial grouping of BG according to no bubbles, low, and high bubble activity, and by assuming a single tissue compartment. Parameter estimations converge to a tissue volume of 0.00036 cm3, a surface tension of 5.0 dyne.cm-1, respective time constants of 27.9 and 9.3 min for nitrogen and helium, and respective Ostwald tissue solubilities of 0.0438 and 0.0096. Although not part of the calibration algorithm, the predicted evolution of bubble size compares reasonably well with the temporal recordings of BGs.

Prediction of decompression illness using bubble models.

The method of maximum likelihood was applied to models of bubble formation and evolution against data involving decompression illness (DCI). Equilibrium and non-equilibrium gas kinetic models were tested under the constraint of a finite tissue volume. The equilibrium model (leq), where the internal gas of a bubble is in partial pressure and mechanical equilibrium with the gas dissolved in tissue, assumed formation of a bubble upon any gas supersaturation. The non-equilibrium model (neq), where mechanical equilibrium is maintained but the exchange of gas between the bubble and the tissue is governed by a rate constant, assumed formation of a bubble at the metastable equilibrium state which requires a specific degree of gas supersaturation. In addition, another version of bubble evolution based on the diffusivity of gas in tissue (vl) was tested under similar finite volume constraints. Model parameters included liquid surface tension, the gas exchange rate constant, gas solubility, and the tissue time constant. The risk of DCI was based on the bubble radius (R) raised to powers ranging from 0 to 6. The data included 2,023 man-dives in 630 different dive profiles of air and nitrox gas mixtures with depth ranging from 1.75 to 7.09 bar and bottom time ranging from 2.8 to 300.2 min. There were 97 occurrences of DCI and 27 occurrences of marginal symptoms. Predictions of the neq and vl models were quite similar and suggested that the tissue primarily responsible for bubble formation leading to DCI in the present analysis has a perfusion rate of about 4.0 ml blood.100 ml-1.min-1. The best fit of the data for a single compartment of 10(-4) ml vol was obtained with the leq model and a risk based on R4, and an estimated time constant of 95.6 +/- 9.8 min.