INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS DATA RESULTS DISCUSSION REFERENCES APPENDIX

DECOMPRESSION SICKNESS (DCS) can affect divers, caisson workers, aviators, and astronauts after a change from a higher to a lower ambient pressure. Symptoms and signs can include painful joints, neurological dysfunction, skin rash, and, in some cases, cardiopulmonary collapse (4). The accepted cause of DCS is tissue injury resulting either directly or indirectly from the formation of bubbles of inert gas during decompression (5). Application of survival analysis to DCS incidence data of humans has led to successful risk prediction under decompression conditions that do not carry high DCS risk (12, 14, 16). The most successful of these models, USN93 (10), is an excellent predictor of DCS risk in a variety of dives that use air and other nitrogen-oxygen breathing gases. However, there are situations (such as escape from a disabled submarine) for which it is necessary to estimate the risk of a profile that is outside the range of known human data and for which human trials are prohibited.

Extrapolating DCS risk predictions to humans under severe decompression conditions by using models derived from low-risk data, such as USN93, has proven inadequate. For example, USN93 substantially underpredicts the DCS risk of deep no-decompression stop air dives not included in its calibration data, as shown in Fig. 1. An approach to solving this problem is to use animal decompression data, which can include high-DCS incidence exposures. In this paper, we introduce a method for combining animal data with human data under a common probabilistic model of DCS risk to predict human DCS incidence from high-risk profiles.

View larger version (10K): [in this window] [in a new window]   Fig. 1.   Model ability to predict decompression sickness (DCS) observed incidence () in validation data for 150-fsw no-decompression air dive. Model USN93 substantially underpredicts DCS occurrence (dashed line). Error bars are 95% confidence intervals on prediction for model and binomial 95% confidence interval for observed incidence. P, probability.

Initial work, by Boycott and colleagues (3), to predict decompression responses in humans from those in animals was conducted at the beginning of this century. Goats were used to develop a decompression model for application to human divers breathing compressed air. This work compared observed outcomes in goats after a dive simulated by hyperbaric exposure with the calculated partial pressures of inert gas in a parallel-compartment model of tissue inert-gas exchange. Safety thresholds for the theoretical tissue compartments were developed based on the maximum calculated "overpressure" that could be tolerated before the decompressed goats exhibited signs of DCS. On the basis of subsequent decompression experience in humans (6), this technique was extended to human divers by empirically adjusting the number of compartments, the compartment washout times, and threshold values of symptomatic DCS.

Rates of biological processes in animals are allometric if they are proportional to body mass raised to some power (18). Application of allometric scaling demonstrates that experimental DCS incidence in animals scales as a function of species body mass (2, 7). However, it remains to be shown that it is possible to use animal DCS outcomes from a particular dive profile to accurately predict the risk of DCS in humans from the same profile.

We hypothesized that, because the DCS risk models underlying survival analysis of DCS data incorporate information on the physiology of decompression, this method could be applied to predict the risk of DCS in humans from the risk observed in decompressed animals for specific dive profiles.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS DATA RESULTS DISCUSSION REFERENCES APPENDIX

Principles of combining human and animal data. Our goal is to demonstrate that the human dose-response relationship can be obtained from the animals through parameters used to adjust or "scale" the animal dose response to that of the human. We first define a probabilistic model of DCS risk that relates the decompression dose (i.e., the pressure history of the dive) to the probability of developing DCS, using methods that have been previously described (12, 14, 16). In these probabilistic models, model parameters are estimated from the outcome data (i.e., DCS or no DCS) by using the method of maximum likelihood rather than representing values obtained from physiological experiments. Our model differs from those that use a single species in that we add parameters that allow the model to "adjust" the response, depending on which species is represented. In developing this species "scalable" model, we consider three factors that may give rise to divergence of the interspecies dose-response relationships: species differences in tissue gas kinetics, in tissue sensitivity to the presence of bubbles, and in the accuracy of the diagnosis of DCS. Any probabilistic model of DCS risk used for interspecies scaling must be able to account for these differences.

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Modeling DCS risk. The DCS risk model selected for this approach is the model that best fits a large series of air and nitrogen-oxygen (N₂ and O₂ at hyperoxic concentrations) human dives (10, 12). This model is an extension of well-stirred multiple parallel-compartment models with single-exponential inert-gas pressure decay. The present model differs from earlier models developed by Haldane and modified by other investigators (6) in that it uses linear-exponential gas-elimination kinetics (12). The inert-gas washin phase is exponential, and the washout phase can be linear initially, followed by a return to exponential kinetics. Use of this kinetic flexibility has given rise to the name linear-exponential (LE) model. Instantaneous risk is defined as the weighted sum of compartmental inert-gas supersaturation divided by the ambient pressure. Up to four parameters are estimated from the data for each compartment: G_i is a weighting factor (referred to as the "gain" of the compartment), _i is the exponential washout time constant, PXO_i is the gauge pressure at which the switch from linear to exponential kinetics takes place, and Thr_i is the gauge pressure threshold above which inert-gas pressure contributes to DCS risk for the ith compartment. Any number of compartments can be included in the model, although USN93, which is the best-fitting model to a comprehensive set of 3,222 human air and nitrogen-oxygen exposures, required only three compartments (10). The best model is defined as the one with the minimum number of estimated parameters that gives the maximum LL (14, 16). Complete details of the parameter estimation process are given elsewhere (9, 12).

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	DATA

TOP ABSTRACT INTRODUCTION METHODS DATA RESULTS DISCUSSION REFERENCES APPENDIX

Although many animal species could be used, the sheep was selected as a human surrogate, because its body size and tissue blood flow are similar to those in humans (1, 7, 8). The sheep used in these studies were 22-124 kg, with an overall mean (±SD) weight of 78 ± 22 kg (8). Blood flow is thought to be a major determinant of inert-gas uptake and elimination and a major contributor to DCS risk. In mammals, metabolism and tissue blood flow rates scale to the three-fourths power of body mass (18). By having our comparison species' body size and blood flows similar to humans, we felt we would reduce the species differences between the animal and human decompression kinetics. As a result, we expected little difference in the kinetic-parameter estimates of the LE model, but the procedure we have outlined allowed us to test this hypothesis formally. Moreover, DCS is manifested in sheep by limb lifting and by neurological and cardiopulmonary abnormalities that are roughly analogous to the primary manifestations of DCS in humans. These similarities should increase the likelihood of successful scaling of DCS risk to the human diver.

Sheep underwent hyperbaric exposures in a high-pressure chamber at the University of Wisconsin Biotron to simulate dive profiles. Data of no-stop sheep air dives and DCS outcomes were obtained by review of logbooks and recorded in detail in a previous report (8). All dives were conducted dry with freestanding sheep in the hyperbaric chamber. The subjects were observed continuously, beginning with rapid decompression to ambient pressure until at least 4 h after surfacing and again at 24 h. The data comprise dive profile and outcome information, including whether DCS occurred, the type of DCS (limb, central nervous system, or cardiopulmonary), and information about the latency of DCS after decompression. The temporal information includes the times of first occurrence of possible DCS (T₁), probable DCS (T_1.5), and the earliest time that the sheep definitely displayed symptomatic DCS (T₂).

Human data represent a subset of dives, which were selected to match the sheep dive profiles, from the original primary decompression database maintained at the Naval Medical Research Institute (NMRI) (15, 17) and additional dive trials conducted at the Naval Submarine Medical Research Laboratory (NSMRL; Groton, CT), NMRI, and the Naval Experimental Diving Unit (NEDU; Panama City, FL) (11). (Note: NEDU, NMRI, and NSMRL reports are available from the National Technical Information Service, 5285 Port Royal Rd., Springfield, VA 22161, or on the internet at www.ntis.gov.) The dives were conducted under a variety of conditions and included both wet and dry exposures. Information contained in the human database consists of dive profile and outcome, including whether or not DCS occurred, and the time of DCS occurrence. The human temporal information differed somewhat from the sheep and included the latest time that the diver was definitely normal (T₁) and the earliest time the diver was definitely considered to have DCS (T₂). Divers were typically under direct medical observation for 2 h after surfacing and then again for a brief time between 18 and 24 h postdive. Both sheep and humans made multiple dives, usually with at least 48-h recovery between dives.

The time of DCS for sheep and humans is represented as an occurrence density function (ODF) (12) in Fig. 2. The ODF for a single DCS case is constructed by spreading the risk for that case uniformly over the time interval between T₁ and T₂ associated with the case. The ODF is zero until T₁, then rises to 1/(T₂  T₁), and then falls back to zero at T₂. The ODF for all cases is calculated by summing the vertical distances for all individual ODFs. The total area within each time interval is added up and divided by the length of the time interval (in the case of Fig. 2, the time interval is 1 h), and this average value is assigned to the entire interval.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Occurrence density function of time of DCS. A: human DCS; B: sheep DCS. Note all sheep DCS occur within 4 h of surfacing (B), whereas human DCS occurs as late as 24 h after return to the surface (A).

The ideal test of the hypothesis is under conditions in which the human and sheep are exposed to the identical pressure profile. This approach allows for a direct comparison of the dose-response curves. Any differences in parameter estimates between species (i.e., any nonzero scaling parameters) can be interpreted as being due to species differences and not from a bias introduced by the extrapolation between dose-response curves. To meet this criterion as closely as possible, we selected sheep and human dives with overlapping bottom times and matched those dives as closely as possible by depth. Sheep dives from dive duration groups of 30, 60, and 240 min (8) were found to match human dive profiles. For human data, the original data set name and the dive profiles extracted from those data sets (11, 15, 17) after being matched with a sheep dive profile are given in Table 1.

Many of the human dives were done on gas mixes containing 12-40% oxygen, with the balance nitrogen. In those cases, the equivalent air depth was used for matching. All sheep and human dives were no-stop dives, although ascent rates varied slightly (sheep: 17-40 feet of seawater (fsw)/min, human: 25-67 fsw/min). The distribution of sheep and human dives and DCS cases in 18 depth-time categories is shown in Table 2. Dives matched nearly exactly by bottom time and within 10 fsw of depth for most of the dives. The matching process resulted in the selection of a total of 463 human dives with 21 DCS cases (4.5%) and 20 marginal cases (4.3%), and 394 sheep dives with 57 DCS cases (14.5%) and 53 marginals (13.5%). For humans, a marginal case consisted of "transient aches or pains following a dive that seem related to the pressure exposure, but were not of a severity or persistence to warrant treatment" (12). A sheep that exhibited signs suggesting a diagnosis of probable DCS, but that did not progress to the stage of definite DCS, was given a marginal DCS classification. Each marginal case was weighted as one-tenth of a definite DCS case, because they cause a much lower level of concern for potential serious injury in human divers (12).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS DATA RESULTS DISCUSSION REFERENCES APPENDIX

Combined human and sheep decompression dose response. The sheep and human data were each individually fit best by an LE model with two compartments. The sheep and human models required six and seven parameters, respectively, as shown in Table 3 (2nd and 3rd columns). The model fit to the combined data required seven parameters (4th column). The LR statistic for testing whether the two separate models provide a better fit to the data than the combined model is given by Eq. 1

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The LR is > ²_(0.95, 6) = 12.59, so we conclude that the separate models provide a better fit to the data (P < 0.005). Not surprisingly, this suggests that human and sheep DCS dose responses are not identical and that some adjustment is required to obtain one from the other. To put this another way, the six "additional" estimated parameters required by the separate fits were statistically justified by the resulting improvement of the LL fit.

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	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS DATA RESULTS DISCUSSION REFERENCES APPENDIX

We conclude that the sheep and human data sets are combinable under the scalable LE model with jointly estimated kinetic parameters  and PXO. Predicting human responses from sheep only requires adjustment of the response parameters. Although it is tempting to place physiological interpretations on the parameters, they are best viewed as mathematical constructs that are quasiphysiological. We present an application of the model for predicting DCS risk on a dive not included in the calibration database that suggests the practical utility of this approach. Limitations of this study and directions for future research, including a direct test of the allometric scaling hypothesis, are discussed.

A precise physiological interpretation of the LE model parameters remains elusive. Differentiating the contribution of different physiological components, such as tissue blood flow, to the parameter values is not possible with the type of outcome data that we analyze in this work. However, the scaling parameters do tell us about differences in human and sheep DCS processes on a phenomenological level. The value of the change in gain (G) for compartment 1 (0.540) is less negative than the value for compartment 2 (1.76), suggesting that the processes modeled by compartment 2 are more important for modeling human DCS compared with sheep than are the processes represented by compartment 1. Similarly, the change in threshold (Thr) is negative in compartment 2 but does not change in compartment 1, supporting the notion that human DCS depends more on the processes in compartment 2 than on those in compartment 1. The emphasis on the processes represented by compartment 2 in modeling human DCS reflects the prolonged latency of human DCS compared with sheep (Fig. 2). Only the most obvious and early DCS signs are noticeable in sheep, because they cannot complain of symptoms as can human divers. Whether the difference in response latency represents a true physiological phenomenon or simply an artifact of DCS diagnosis in sheep remains unanswered. Regardless of the underlying mechanism, for purposes of estimating DCS risk we do not need to know the physiological basis of the observation.

An application of this model is shown in Fig. 3. In this application, we test the ability of several models to predict DCS incidence of relatively high-risk human air dives (13) not included in the human or sheep calibration data set. We show the observed DCS incidence for 150-fsw no-stop air dives and the response-scaled, separate human fit, and USN93 model predictions. The error bars on the observed points are 95% binomial confidence intervals, and those for model predictions are 95% confidence intervals from propagation of errors (14). A sample of the procedure used to calculate the DCS risk shown in Fig. 3 with the use of the response-scaled model is given in the APPENDIX. We compare the predictive ability of the models by conducting the Pearson ² goodness-of-fit test for the observed and model-predicted DCS outcomes. The best general model of human DCS response to date (USN93) substantially underpredicts DCS incidence in these deep no-stop dives [P < 1 × 10⁶, ²_(0.95, 6)]. The separate human and the response-scaled fits from this study both predict the DCS incidence in these dives quite well, and the predictions are both statistically indistinguishable from the observed incidence [both P > 0.4, ²_(0.95, 6)].

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Model ability to predict DCS observed incidence () in validation data for 150-fsw no-decompression air dive. Model USN93 substantially underpredicts DCS occurrence (short dashed line). Both human-only fit (long dashed line) and response-scaled fit (solid line) are good predictors of DCS incidence in these divers. Error bars are 95% confidence intervals on prediction for models and binomial 95% confidence interval for observed incidence.

This example illustrates the ability of the response-scaled model to predict outcome from high-risk human dives not included in the calibration data set. However, it begs the question, why should the response-scaled model be used if the model fit to the human-only data predicts at least as well? The answer lies in the application of this approach to predict the risk for human dive profiles that are far beyond the range of available human data. [It should be noted that the human dives, shown in Fig. 1, were conducted more than 50 years ago (13), are unusual in the magnitude of observed DCS incidence, and would not be attempted today.] One of the limitations of an approach based on parameter estimation is that predictions are likely to become inaccurate as they are extrapolated beyond the range of the calibration data. We propose that sheep could replace humans on the extreme profiles, and the resulting response (DCS or no DCS) would be entered into the combined data set. The response-scaled model parameters would be reestimated by using this updated data set. The resulting predictions should provide reasonable estimates of the risk in humans, because of the similarity in the underlying kinetics and the adjustment made by the model for differences in DCS response. The only assumption is that the difference in response between sheep and humans represented by the response-scaled parameters remains the same for the dives in the new region. If the goal is development of a new decompression procedure for use in humans, the scaled model could provide profiles that were of acceptable risk for validation by human divers. Such an approach should make decompression table development safer and less expensive, because it would no longer be necessary to rely on human divers during the exploratory phase when DCS risk is likely to be the highest.

A limitation of this work is that it involved constructing several models and making multiple comparisons of the ability of these models to predict the observed outcome. If an adjustment for the number of comparisons is not made, then the chance of finding a falsely significant result is greater than the nominal level of the critical value used for a single comparison (e.g.,  = 0.05). The P values obtained in our comparisons are generally much <0.05, making the likelihood of a false-positive study because of the multiple-comparison problem small. However, a prospective validation of this work should be conducted to fully account for the multiple-comparison issue and any other biases that may have been present, unknown to us, in the data of this study.

Ideally, prospective validation would involve both new human and sheep dives on the same profile. New human dives are costly and unlikely to be conducted simply to validate this method. A compromise is to select representative human dives already conducted and not included in this analysis and to carry out sheep dives on the same profiles. Completing the no-decompression-stop database in sheep to match the existing no-decompression dives in humans is a logical first step. This could be done by conducting air saturation dives in the 20- to 30-fsw region in which human, but not sheep data, exist. Selecting decompression stop dives that represent the full range of human data would be a next step to test whether or not these results can be reproduced with that type of dive. Dives on higher partial pressures of oxygen, dives that use helium-oxygen mixes, and dives that extend the depth and bottom time range outside of what is possible in humans might be a next step.

Additional efforts focused on extending these results to other species with smaller body mass may also prove to be useful. Our motivation to select sheep as the comparison species was based on allometric scaling of physiological rates, but we did not directly test the allometric scaling hypothesis in this study because body mass data were not available for all human subjects. The fact that human DCS risk can be accurately predicted without including body mass (12) and that human and sheep data can be combined under the response-scaled model suggests that the intraspecies variability of body mass for sheep and humans in these data is not a controlling factor.

A direct test of the allometric-scaling hypothesis with the use of the approach introduced in this report is possible with species with greater differences in body mass, e.g., rats, pigs, goats, and sheep. An allometric approach can be incorporated into the scalable LE model by replacing the parameters used in this report with the LE parameters multiplied by body mass raised to a power. The parameter itself and the power can be estimated from the data. For example, if one wishes to test the hypothesis that  scales allometrically, one would substitute  × (body mass) for ( + ) in the model and estimate  and  from the data. The procedure outlined in this manuscript for testing for combinability of different species under a scalable model by using the LR test could be followed. A better fit from a model with the use of allometrically scaled parameters would provide a means of combining data from animals without kinetic similarity. Moreover, it would provide a means of separating the role of kinetic processes from decompression responses in different species.

In conclusion, we have demonstrated the kinetic similarity of DCS after no-stop air dives in sheep and humans and have introduced a method for quantitatively adjusting for differences in decompression responses between two species. We believe this work provides a means to improve the safety and efficiency of developing new decompression procedures, to predict the risk of DCS for conditions that prohibit the use of human subjects, and to explore the differences in DCS among species of different body mass.