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.

Deadly diving? Physiological and behavioural management of decompression stress in diving mammals.

Decompression sickness (DCS; 'the bends') is a disease associated with gas uptake at pressure. The basic pathology and cause are relatively well known to human divers. Breath-hold diving marine mammals were thought to be relatively immune to DCS owing to multiple anatomical, physiological and behavioural adaptations that reduce nitrogen gas (N(2)) loading during dives. However, recent observations have shown that gas bubbles may form and tissue injury may occur in marine mammals under certain circumstances. Gas kinetic models based on measured time-depth profiles further suggest the potential occurrence of high blood and tissue N(2) tensions. We review evidence for gas-bubble incidence in marine mammal tissues and discuss the theory behind gas loading and bubble formation. We suggest that diving mammals vary their physiological responses according to multiple stressors, and that the perspective on marine mammal diving physiology should change from simply minimizing N(2) loading to management of the N(2) load. This suggests several avenues for further study, ranging from the effects of gas bubbles at molecular, cellular and organ function levels, to comparative studies relating the presence/absence of gas bubbles to diving behaviour. Technological advances in imaging and remote instrumentation are likely to advance this field in coming years.

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.

On the likelihood of decompression sickness during H(2) biochemical decompression in pigs.

A probabilistic model was used to predict decompression sickness (DCS) outcome in pigs during exposures to hyperbaric H(2) to quantify the effects of H(2) biochemical decompression, a process in which metabolism of H(2) by intestinal microbes facilitates decompression. The data set included 109 exposures to 22-26 atm, ca. 88% H(2), 9% He, 2% O(2), 1% N(2), for 0.5-24 h. Single exponential kinetics described the tissue partial pressures (Ptis) of H(2) and He at time t: Ptis = integral (Pamb - Ptis). tau(-1) dt, where Pamb is ambient pressure and tau is a time constant. The probability of DCS [P(DCS)] was predicted from the risk function: P(DCS) = 1 - e(-r), where r = integral (Ptis(H(2)) + Ptis(He) - Thr - Pamb). Pamb(-1) dt, and Thr is a threshold parameter. Inclusion of a parameter (A) to estimate the effect of H(2) metabolism on P(DCS): Ptis(H(2)) = integral (Pamb - A - Ptis(H(2))). tau(-1) dt, significantly improved the prediction of P(DCS). Thus lower P(DCS) was predicted by microbial H(2) metabolism during H(2) biochemical decompression.

Natural history of severe decompression sickness after rapid ascent from air saturation in a porcine model.

We developed a swine model to describe the untreated natural history of severe decompression sickness (DCS) after direct ascent from saturation conditions. In a recompression chamber, neutered male Yorkshire swine were pressurized to a predetermined depth from 50-150 feet of seawater [fsw; 2.52-5.55 atmospheres absolute (ATA)]. After 22 h, they returned to the surface (1 ATA) at 30 fsw/min (0.91 ATA/min) without decompression stops and were observed. Depth was the primary predictor of DCS incidence (R = 0.52, P < 0.0001) and death (R = 0.54, P < 0.0001). Severe DCS, defined as neurological or cardiopulmonary impairment, occurred in 78 of 128 animals, and 42 of 51 animals with cardiopulmonary DCS died within 1 h after surfacing. Within 24 h, 29 of 30 survivors with neurological DCS completely resolved their deficits without intervention. Pretrial Monte Carlo analysis decreased subject requirement without sacrificing power. This model provides a useful platform for investigating the pathophysiology of severe DCS and testing therapeutic interventions. The results raise important questions about present models of human responses to similar decompressive insults.

Escape from a disabled submarine: decompression sickness risk estimation.

Individual crewmember escape from a disabled U.S. Navy nuclear submarine has never been necessary, but remains an important contingency. Decompression sickness (DCS) is one of the foreseeable risks and a robust mathematical model of DCS incidence has been used to estimate the magnitude of this risk under a variety of escape scenarios. The model was calibrated with over 3000 well-controlled human pressure exposures, less than 2% of which simulated pressure profiles of submarine escape. For disabled submarine depths < 300 ft of sea water (fsw) and internal submarine pressures of <11 fsw (arguably the most likely conditions), the DCS risks are comparable to those routinely undertaken by U.S. Navy divers--less than 5%. For progressively deeper depths and especially for higher submarine internal pressures, the risk of DCS becomes much greater, including unknown chances of permanent injury and death. Variations from the baseline escape procedure are explored, including equipment differences, delays in exiting the submarine and changes in the oxygen content of the breathing mix.

Probabilistic models of the role of oxygen in human decompression sickness.

Probabilistic models of human decompression sickness (DCS) have been successful in describing DCS risk observed across a wide variety of N2-O2 dives but have failed to account for the observed DCS incidence in dives with high PO2 during decompression. Our most successful previous model, calibrated with 3,322 N2-O2 dives, predicts only 40% of the observed incidence in dives with 100% O2 breathing during decompression. We added 1,013 O2 decompression dives to the calibration data. Fitting the prior model to this expanded data set resulted in only a modest improvement in DCS prediction of O2 data. Therefore, two O2-specific modifications were proposed: PO2-based alteration of inert gas kinetics (model 1) and PO2 contribution to total inert gas (model 2). Both modifications statistically significantly improved the fit, and each predicts 90% of the observed DCS incidence in O2 dives. The success of models 1 and 2 in improving prediction of DCS occurrence suggests that elevated PO2 levels contribute to DCS risk, although less than the equivalent amount of N2. Both models allow rational optimization of O2 use in accelerating decompression procedures.

Improved probabilistic decompression model risk predictions using linear-exponential kinetics.

Using a data base of 2,383 air and nitrogen-oxygen dives resulting in 131 cases of decompression sickness (DCS), risk functions were developed for a set of probabilistic decompression models according to survival analysis techniques. Parameters were optimized using the method of maximum likelihood Gas kinetics were either traditional exponential uptake and elimination, or an exponential uptake followed by linear elimination (LE kinetics) when calculated supersaturation was excessive. Risk functions either used the calculated relative gas supersaturation directly, or a delayed risk using a time integral of prior supersaturation. The most successful model (considering both incidence and time of onset of DCS) used supersaturation risk, and LE kinetics (in only 1 of 3 parallel compartments). Several methods of explicitly incorporating metabolic gases in physiologically plausible functions were usually found in lumped threshold terms and did not explicitly affect the overall data fit. The role of physiologic fidelity vs. empirical data fitting ability in accounting for model success is discussed.

Hydrogen bonding. 30. Solubility of gases and vapors in biological liquids and tissues.

The general solvation equation log L = c + rR2 + pi H2 + a alpha H2 + b beta H2 + l log L16 has been used to analyze the solubility of solute gases and vapors, as log L values, in water, blood, and a variety of other biological fluids and tissues. The explanatory variables are R2, the solute excess molar refraction; pi H2, the solute dipolarity/polarizability; alpha H2 and beta H2, the solut hydrogen-bond acidity and basicity; and log L16, where L16 is the solute Ostwald solubility coefficient of hexadecane. The obtained coefficients then serve to characterize the biological phase as follows: r + s is the phase dipolarity/polarizability, a is the phase hydrogen-bond basicity, b is the phase hydrogen-bond acidity, ald l is the phase lipophilicity. In addition to characterization of phases, the equation can be used to determine quantitatively solute/phase interactions and predict further log L values. A similar equation in which McGowan's characteristic volume, Vx, replaces the log L16 descriptor can be used to analyze partitions between phases. For example, water/phase and blood/phase partition coefficients are analyzed, and the analysis leads again to coefficients that characterize phases and to the prediction of partition coefficients.

Predicting the time of occurrence of decompression sickness.

Probabilistic models and maximum likelihood estimation have been used to predict the occurrence of decompression sickness (DCS). We indicate a means of extending the maximum likelihood parameter estimation procedure to make use of knowledge of the time at which DCS occurs. Two models were compared in fitting a data set of nearly 1,000 exposures, in which greater than 50 cases of DCS have known times of symptom onset. The additional information provided by the time at which DCS occurred gave us better estimates of model parameters. It was also possible to discriminate between good models, which predict both the occurrence of DCS and the time at which symptoms occur, and poorer models, which may predict only the overall occurrence. The refined models may be useful in new applications for customizing decompression strategies during complex dives involving various times at several different depths. Conditional probabilities of DCS for such dives may be reckoned as the dive is taking place and the decompression strategy adjusted to circumstance. Some of the mechanistic implications and the assumptions needed for safe application of decompression strategies on the basis of conditional probabilities are discussed.

Maximum likelihood analysis of air and HeO2 dives.

The method of maximum likelihood analysis was applied to data consisting of 1,949 man-dives, of which 1,041 were on air and 908 were on HeO2 mixtures. These dives represented a wide range of bottom time and depth combinations, and had an overall incidence of decompression sickness (DCS) of 4.64%. Several models, based on single exponential gas uptake in either one or two compartments, were tested for predicting the incidence of DCS. The criterion for defining the risk of DCS was based on the concept of potential gas volume (i.e., the volume of a bubble that could form and be in equilibrium with the remaining gas dissolved in solution). This criterion takes into account the solubilities of the gases in solution, but can be adjusted to account only for the partial pressures of the gases. The best model for the prediction of DCS was found for two compartments where the kinetics (time constants) and not the gas solubilities of nitrogen and helium were distinguished from each other. Results using the best prediction model with the present data suggests the following: 1) most of the risk of DCS occurs after surfacing; 2) most of the risk occurs in the "slow" compartment (approximately 420 min time constant); and 3) nitrogen contributes about twice as much as helium to the risk of DCS for HeO2 dives.

Relative decompression risk of dry and wet chamber air dives.

The difference in risk of decompression sickness (DCS) between dry chamber subjects and wet, working divers is unknown and a direct test of the difference would be large and expensive. We used probabilistic models and maximum likelihood estimation to examine 797 dry (and generally resting and comfortable) and 244 wet (and generally working and cold) chamber dives from the Defence and Civil Institute of Environmental Medicine, supplemented with 483 wet (working, cold) dives from the Navy Experimental Diving Unit. Several analyses considered whether dry and wet data were distinguishable using several models, whether models obtained from one set of exposure conditions would correctly predict the occurrence of DCS in the other condition, and whether a single wet-dry risk difference parameter was different from zero. Although the two conditions may not produce identical risks, immersion appears to change relative risk of DCS by less than 30% and certainly involves less than a doubling of DCS risk. Uncontrolled differences in exercise and temperature stresses unavoidably complicate interpretation. Several methods are presented to extrapolate results from dry-test subjects in decompression trials to expected at-sea performance.

How countercurrent blood flow and uneven perfusion affect the motion of inert gas.

Monte Carlo simulations of the passage of inert gas through muscle tissue reveal that countercurrent gas exchange is more important than heterogeneity of flow in determination of the shape of inert gas washout curves. Semilog plots of inert gas washout are usually curved rather than straight. Two explanations often offered are that countercurrent flow may distort the shape and that uneven perfusion of the tissue gives rise to nonuniform washout. The curvature of the semilog plot may be summarized by the relative dispersion (RD), which is the ratio of the standard deviation of transit times to the mean transit time. For straight semilog plots, RD is 1. Semilog plots of data showing xenon washout from dog tissues are curved and have and RD of approximately 2. We have simulated the transit of gas particles through a vascular bed composed of repeating units of 100 mg of tissue perfused by three small vessels 80 microns in diameter and several levels of branching that direct flow through 190,000 capillaries. Geometric distribution of flow is important. Similar degrees of flow heterogeneity affect the curvature of the washout curve more if regions of heterogeneous flow are widely spaced than if they are close together. Diffusion blunts the effects of heterogeneous flow by mixing particles in high-flow regions with particles in low-flow regions. Because of this mixing, alternating regions of high flow and low flow spaced at intervals of less than 0.5 cm are unlikely explanations for the curved semilog plots.(ABSTRACT TRUNCATED AT 250 WORDS)

Xenon kinetics in muscle are not explained by a model of parallel perfusion-limited compartments.

Experimental tissue gas kinetics do not follow the prediction for a single stirred perfusion-limited compartment. One hypothesis proposes that the kinetics might be explained by considering the tissue as a collection of parallel compartments, each with its own flow, reflecting the tissue microcirculatory flow heterogeneity. In this study, observed tissue gas kinetics were compared with the kinetics predicted by a model of multiple parallel compartments. Gas exchange curves were generated by recording the time course of tissue radioactivity in the intact calf muscles of anesthetized ventilated dogs exposed to step function changes of 133Xe in the inspired air for 5-h periods. Microcirculatory flow heterogeneity in the same tissue was determined by the radioactive microsphere method. Observed mean tissue transit times were on average longer than predicted by a factor of 6.7. Observed means averaged 52.1 min compared with 8.3 min predicted by the perfusion-limited model. Relative dispersions of tissue transit times were also uniformly larger than predicted. We conclude that Xe gas kinetics in intact canine skeletal muscle are not explained by a model of multiple parallel perfusion-limited compartments. Countercurrent exchange of gas between vessels is a possible explanation.

Use of the maximum likelihood method in the analysis of chamber air dives.

The method of maximum likelihood was used to evaluate the risk of decompression sickness (DCS) for selected chamber air dives. The parameters of two mathematical models for predicting DCS were optimized until the best agreement (as measured by maximum likelihood) corresponding to the observed DCS incidents from a series of dives was attained. The decompression data used consisted of 800 man-dives with 21 incidents of DCS and 6 occurrences of marginal symptoms. The first model investigated was based on a nonlinear gas exchange in a series arrangement of four compartments. The second model was based on a monoexponential gas exchange in a parallel arrangement of two compartments. The overall statistical success in describing the 800 man-dives was quite similar for the two models. Predictions of safety for dives not part of the original data differed for the models due to differences in gas kinetics. For short, no-decompression dives, the series arrangement of compartments predicted a lower incidence of DCS. These predictions were more consistent with the outcome of subsequent testing than were predictions of the parallel compartment model. Predictions of the series arrangement model were also similar to those of a single-compartment, two-exponential model that was evaluated with over 1700 man-dives by the U.S. Navy.

The modulation of oxygen toxicity by intermittent exposure.

Intermittent delivery of hyperbaric O2 protects animals from pulmonary and central nervous system toxicity: more total O2 time can be tolerated if interrupted by short periods of low O2. Little is known about the mechanisms or optimization of systematically varied intermittency. Survival time was recorded in groups of 16 awake guinea pigs (239 +/- 23(SD) g) exposed to continuous O2 at 2.8 ATA or to one of six different schedules of O2 delivered with periodic air (PO2 = 0.588 ATA) interruptions. The survival curves had a lag time (11-14 hr of O2 time depending on the intermittency schedule) with a rapid loss of animals thereafter. Data were analyzed with risk models linking the probability of death to the accumulation of a putative toxic substance, X1. A model in which X1 accumulated in proportion to the PO2 and disappeared by first-order decay during periods of low O2 exposure was modified to include an effective rate constant for changes in X1: dX1/dt = a.PO2 + K1.(PO2 - Os).X1. First-order kinetics operated when PO2 was below the oxygen set point (Os), but the rate constant reversed sign to become a self-amplifying system when PO2 was above Os. This model achieved an excellent fit as judged by goodness-of-fit statistics while a simpler one did not. Our analysis suggests that the accumulation of toxicity does not correspond to a stable linear toxic process, but requires one in which a toxic process grows autocatalytically.

Role of oxygen in the production of human decompression sickness.

In the calculation of decompression schedules, it is commonly assumed that only the inert gas needs to be considered; all inspired O2 is ignored. Animal experiments have shown that high O2 can increase risk of serious decompression sickness (DCS). A trial was performed to assess the relative risks of O2 and N2 in human no-decompression dives. Controlled dives (477) of 30- to 240-min duration were performed with subjects breathing mixtures with low (0.21-0.38 ATA) or high (1.0-1.5 ATA) Po2. Depths were chosen by a sequential dose-response format. Only 11 cases of DCS and 18 cases of marginal symptoms were recorded despite exceeding the presently accepted no-decompression limits by greater than 20%. Analysis by maximum likelihood showed a shallow dose-response curve for increasing depth. O2 was estimated to have zero influence on DCS risk, although data variability still allows a slight chance that O2 could be 40% as effective as N2 in producing a risk of DCS. Consideration of only inert gases is thus justified in calculating human decompression tables.

An analysis of decrements in vital capacity as an index of pulmonary oxygen toxicity.

Decrements in vital capacity (% delta VC) were proposed by the Pennsylvania group in the early 1970s as an index of O2-induced lung damage. These workers used the combined effects of PO2 and time of exposure to develop recommendations to limit expected % delta VC. Adopting this general approach, we fitted human pulmonary O2 toxicity data to the hyperbolic equation % delta VC = Bs.(PO2 - B1).(time)B3 using a nonlinear least squares analysis. In addition to the data considered in 1970, our analysis included new data available from the literature. The best fit was obtained when 1) an individual slope parameter, Bs, was estimated for each subject instead of an average slope; 2) PO2 asymptote B1 = 0.38 ATA; and 3) exponent B3 = 1.0. Wide individual variation imposed large uncertainty on any % delta VC prediction. A 12-h exposure to a PO2 of 1 ATA would be expected to yield a median VC decrement of 4%. The 80% confidence limits, however, included changes from +1.0 and -12% delta VC. Until an improved index of pulmonary O2 toxicity is developed, a simplified expression % delta VC = -0.011.(PO2 - 0.5).time (PO2 in ATA and time in min) can be used to predict a median response with little loss in predictability. The limitations of changes in VC as an index are discussed.

Nitrogen gas exchange in the human knee.

Human decompression sickness is presumed to result from excess inert gas in the body when ambient pressure is reduced. Although the most common symptom is pain in the skeletal joints, no direct study of nitrogen exchange in this region has been undertaken. For this study, nitrogen tagged with radioactive 13N was prepared in a linear accelerator. Nine human subjects rebreathed this gas from a closed circuit for 30 min, then completed a 40- to 100-min washout period breathing room air. The isotope 13N was monitored continuously in the subject's knee during the entire period using positron detectors. After correction for isotope decay (half-life = 9.96 min), the concentration in most knees continued to rise for at least 30 min into the washout period. Various causes of this unexpected result are discussed, the most likely of which is an extensive redistribution of gas within avascular knee tissues.

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.