INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

PROBABILISTIC MODELS HAVE been used during the last 15 yr to predict decompression sickness (DCS) in humans (22, 23) as well as animals (15). Unfortunately, because of uncertainties about risk factors associated with DCS, such efforts have usually involved empirically fitting functions to dive data, resulting in models that allow risk prediction but lack a sound physiological basis. As a result, these models often do not extrapolate reliably to dive profiles much different from the original data. This can be especially problematic when making predictions about human dives for which there is little or no available human data. These include relevant but high-risk profiles that cannot be performed experimentally because of ethical concerns.

Presently, the US Navy needs the ability to estimate the risk of DCS in a disabled submarine (DISSUB) scenario, which would involve rapid surfacing from air-saturation exposures at pressures up to 5 atmospheres absolute (ATA). Such a scenario would be expected to result in a high incidence of severe DCS. Unfortunately, present decompression models are based on little data directly relevant to this type of exposure and, therefore, should not be expected to produce the most reliable predictions. Previous best estimates of DCS risk for human dive profiles that use mixtures of N₂ and nonelevated O₂ (<1 ATA PO₂) have been generated from a decompression model called USN93 (20, 22). However, its intended application was for the depth-time range used in regular Navy diving, not the long, severe exposures of the DISSUB scenario. This model was calibrated with 3,322 human exposures, but only 467 were long enough to be categorized as saturation. Only a subset of these (149 dives) consisted of saturation dives with direct ascent, the type relevant to the DISSUB scenario. As raw data, those human dives demonstrated that direct ascent from ~1.8 ATA would result in perhaps 10% DCS but with nonalarming symptoms, generally slow onset, and good response to standard recompression therapy. However, with the exception of 15 dives at 1.9 ATA, all dives were done between 1.6 and 1.8 ATA. Consequently, human predictions beyond ~1.8 ATA with USN93 should be considered an extrapolation. Nevertheless, this model has been used recently for DISSUB predictions (24), although the model has been shown to substantially underpredict some other types of high-risk human dives (1).

Fortunately, the use of animal data offers the potential to improve prediction of DCS in humans, particularly for high-risk DISSUB profiles. The abundance of high-incidence data, available from a number of animal species and based on a much larger range of pressure, may be more suitable for modeling a range in DCS risk compared with human data containing relatively few cases of DCS. Consequently, the dose-response curves for animals are usually steeper than human curves that are derived from low-incidence data (15). However, although a great deal of animal DCS research has been done, there have been only limited attempts to use animal outcome to estimate quantitative human risk of DCS. One reason for this may be the long-standing concern that the much more severe DCS often observed in animals after experimental dives may not be directly relevant to the normally mild cases of joint pain in humans. Although these severe animal cases are often purposely produced by using profiles with inadequate decompression to facilitate the research, differences in symptoms will be an issue with any multispecies approach.

The few attempts to translate from animal to human provide background for the present work. Boycott et al. (4) were among the first to use decompression data from a large-animal model to predict decompression parameters in humans. Through a comparison of respiratory exchange rates in humans and goats, they estimated the saturation time for a goat to be about three-fifths of that of humans. More recently, Berghage et al. (2), building on the work of Flynn and Lambertsen (7), analyzed data from seven species, including humans and rat, from air-saturation exposures with direct ascent. They found that the N₂ "dose" required to produce a 50% incidence of DCS for each species was highly correlated with the average body weight of the species. Lin et al. (17) applied interspecies relationships to calculate decompression schedules for saturation dives at 30 ATA, assuming that saturation half times in four species (human, rat, rabbit, and dog) were related to body weight. They proposed shorter human decompression schedules, although very little animal data were used in their analysis. However, it is not known whether any of these schedules were ever tested on humans. More recently, using maximum-likelihood techniques, Ball et al. (1) fitted linear exponential models to a set of human and sheep air dives (none saturated) with direct ascent. A model that estimated the N₂ kinetics from the combined human and sheep data was found to fit the decompression outcome data better than totally separate human and sheep models. However, this model required species-dependent factors of "gain" (a weighting factor) and "threshold" (the pressure above which the inert-gas pressure begins to contribute to DCS risk).

This report describes the development and evaluation of multispecies (human, pig, rat) models for prediction of DCS after air-saturation dives with direct ascent. The hypothesis being tested is that combining animal data with human data significantly improves the model predictions of human DCS. The differences that we are introducing include differences in models, data, and purpose. We emphasize that this was an ad hoc approach specifically designed to improve the ability to predict risk associated with these types of dives and not to replace other more general models, such as USN93, that are used for a much wider range of profiles. The relatively simple profiles that we are dealing with allowed our use of very simplistic empirical models that are not suitable for more complex situations. By combining three species with differences in severity of DCS, we assume that the decompression responses of these species share a common underlying mechanism(s) that can help to better define the human decompression response. Although these findings may suggest directions for future work, the limited scope of this project prevented the addressing of broader issues, such as general techniques and best types of models for using animal data in this manner.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Summary. Hill equation dose-response models were fit, by using the technique of maximum likelihood, to three species (humans, pigs, and rats), individually and in combination. For the main models, a total of 898 air-saturation, direct-ascent dives were used: 245 human dives, 128 pig dives, and 525 rat dives. The predictions of these models were compared 1) among themselves to judge the benefit of combining species and 2) to USN93, presently the most used probabilistic decompression model for predicting human outcome, to provide a baseline reference for judging their performance.

Animal use. The experimental protocols for all animal experiments used in this work were reviewed and approved by the Animal Care and Use Committee at the Naval Medical Research Institute [now the Naval Medical Research Center (NMRC)]. The committee used the animal use guidance required at the time of review by the Department of the Navy, which was the current version of the "Guide for the Care and Use of Laboratory Animals" [Institute of Laboratory Animal Resources, National Research Council, DHHS Publication Nos. (NIH) 78-23, 85-23, 86-23].

Intraspecies data used for modeling. All exposures were air-saturation dives, with minimal decompression, from existing published databases and are summarized in Table 1. The models that we developed deliberately did not incorporate gas uptake and washout but assumed saturation before decompression and no important loss of gas during ascent. Saturation was defined as a total bottom time of a minimum of 24 h (1,440 min) for humans, 22 h (1,320 min) for pigs, and 1 h (60 min) for rats. Direct ascent is defined as employing no stops and having a total ascent time after leaving the bottom of 20 min for humans, 11 min for pigs, and 0.2 min for rats.

Human data. The primary source of human data was the comprehensive NMRC technical report describing the manifestations of DCS after air and N₂-O₂ diving (21). The human data meeting the present selection criteria consisted of 245 dives to depths ranging from 1.61 to 2.00 ATA, with bottom times from 1,440 to 6,181 min. For 65 dives that used an N₂-O₂ mixture containing 0.4 ATA O₂ at depth, equivalent air depths (3) were used to replace the actual depths. Other dives were included that had excursions to other depths, as long as a final 24 h were spent at a constant depth. The 245 dives included 1) all of the 149 air-saturation dives with direct ascent that were part of the much larger set of dives used to produce the human USN93 model and 2) an additional 96 human saturation dives. These additional dives included 22 extra dives at 1.91 or 2.00 ATA, representing a substantial increase in higher risk dives over the 15 dives at 1.91 ATA used in the calibration of USN93.

Pig data. The 128 air-saturation pig dives were done at Naval Medical Research Institute/NMRC from 1997 to 2000 and are described in Ref. 5. Dives ranged in depth from 2.52 to 5.55 ATA. Overall DCS incidence was 60.9%; incidence of death was 33.6%. Pig weights before diving ranged from 17.1 to 24.8 kg with a mean of 20.0 ± 1.7 (SD) kg.

Rat data. The 525 air-saturation rat dives were selected from three dive sets analyzed in previous reports (11, 12, 14). Depths ranged from 5.39 to 7.67 ATA with times at depth from 60 to 120 min. For the gas-switching experiments (14), only the control air dives were used. Overall DCS incidence was 64.6%; death incidence was 46.7%. Rat weights after diving ranged from 206 to 316 g, with an overall mean of 245 ± 18 (SD) g.

Scoring criteria for modeling. In the main analysis, we chose to exclude human marginal symptoms as less relevant for our main concern. In the animals, we chose to use all occurrences of DCS (which includes death) as the response to the model. Other possibilities are presented in the APPENDIX.

Data analysis: the model. Hill equation dose-response models predicting the probability of DCS were fit to the data of all three species, both individually and combined, by using maximum likelihood (6). Models also evaluated the feasibility of replacing the highest risk portions of human data with animal data. The Hill function is adapted from models previously fit to our rat data (15). These models appear to fit animal decompression well, but we emphasize that they are not based on any known or presumed physiology of DCS.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Model parameters for single and combined species fits are reported in Table 2 for the main model and Table 3 for the models evaluating replacement of high-risk human data with animal data. Additional analyses examining changes in scoring criteria are presented in the APPENDIX. Only parameters found to be significant at the 0.05 level are presented. As rat weight is shown to have an effect on DCS risk (as discussed below), we emphasize that the plotted curves presented in Figs. 1-6, unless otherwise indicated, are based on a rat weight of 245 g, the average weight of all of the rats.

View larger version (28K): [in this window] [in a new window]   Fig. 1.   Predictive curves (solid lines) [and 95% confidence limits (dashed lines)] for single-species (A) and multispecies models (B) relating decompression risk to saturation depth for direct-ascent air dives are shown for the 3 species. Symbols represent actual data with mean incidence rate of decompression sickness (DCS) calculated for each depth. Rat predictions were based on body weight set at 245 g, the mean weight of all rats.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Effect of rat weight on decompression risk. A: dramatic shift to the left of the predictive curves as rat weight is increased in 10-g increments, demonstrating that, for heavier rats, a shallower range of depths is required to produce the same range of DCS incidence. B: predictive probabilities with increasing rat weight at 3 depths: 5.55, 6.30, and 7.06 ATA. The average slope for each of these curves over the 225- to 265-g range was +1% DCS/g.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Replacing high-risk human data (A) with animal data. Much of the predictive precision that is lost, after the 37 human dives at the 2 deepest depths 1.91 ATA (symbols circled) were removed (B), is restored after adding back all of the pig and rat data (C). Predictive curves (solid lines) [and 95% confidence limits (dashed lines)] are based on data that exclude human marginals and use animal DCS. Symbols represent human data with mean incidence rate of DCS calculated for each depth.

View larger version (19K): [in this window] [in a new window]   Fig. 4.   Error for single-species (A) and multispecies models (B) are shown by plotting the difference between model prediction and observed incidence vs. saturation depth. Observed values are the mean incidence rates at each depth. Rat predictions were based on body weight set at 245 g, the mean weight of all rats. Both types of models predict DCS for a given species without significant bias and generally equally well, regardless of depth. Multispecies model also predicts across species without distortion.

View larger version (27K): [in this window] [in a new window]   Fig. 5.   Alternative scoring criteria for DCS: human marginals included, all animal DCS (including death). Predictive curves (solid lines) [and 95% confidence belts (dashed lines)] for single-species (A) and multispecies models (B) relating decompression risk to saturation depth for direct-ascent air dives are shown for the 3 species. Symbols represent actual data with mean incidence rate of DCS calculated for each depth. Rat predictions were based on body weight set at 245 g, the mean weight of all rats.

View larger version (25K): [in this window] [in a new window]   Fig. 6.   Alternative scoring criteria for DCS: human marginals excluded, animal death only. Predictive curves (solid lines) [and 95% confidence belts (dashed lines)] for single-species (A) and combined species models (B) relating decompression risk to saturation depth for direct-ascent air dives are shown for the 3 species. Symbols represent actual data with mean incidence rate of DCS calculated for each depth. Rat predictions were based on body weight set at 245 g, the mean weight of all rats.

Single-species models. Models fit separately to the three species showed substantial differences in their P₅₀ values, reflecting increasing tolerance (human < pig < rat) to decompression with decreasing species size, as well as differences in scoring criteria. This is graphically shown by the shift to the right, from human to pig to rat, of the predictive curves relating probability of DCS to saturation depth (Fig. 1A). In other words, a deeper saturation dive was required to produce the same incidence of DCS in rats compared with pigs, and a deeper dive in pigs than in humans, emphasizing again that the scoring criteria were very different for the three species.

Multispecies models. Models fit to the combined three species produced separate P₅₀ values for each species that were shown to be significant (P < 0.01) by applying the likelihood ratio test with the use of Eqs. 4 and 5. As expected, these P₅₀ values were very similar in magnitude and precision (i.e., standard error) to those from the single-species fits. On the other hand, exponents for the three multispecies models could not be resolved: P > 0.05 for both n_human and n_pig in Eqs. 6 and 7. Admittedly, this finding must be partly attributed to the large estimation error associated with the individual exponents. However, based on these results, a common exponent was estimated for all three species, producing a value with considerably less error than for the single-species estimates. This would be expected, as all the data were now used to estimate one common exponent vs. the previous three, demonstrating one of the major benefits of combining data. However, the value of the common exponent was now a compromise among the three species.

Deletion of highest risk human dives. Results showed that exponent error increased dramatically for the human-only model fit to the abridged human data set (depths <1.91 ATA), producing a much wider confidence belt surrounding the predictive curve, compared with that fit to all of the original human data (Fig. 3, A and B, Table 3). Consequently, the ability to make meaningful predictions was lost, especially at the greater depths. One disturbing result of the data removal was the failure of the model to resolve risk predictions for 1.91 and 2.00 ATA from zero (Fig. 3B, Table 3), although the 95% confidence limits of the actual data at these depths do not overlap zero. This provided little credibility to the poorly defined predictions in this region. However, much of the lost precision was restored to the human predictions after adding the pig and rat dives to the reduced human data set and refitting with multispecies models (Fig. 3C, Table 3). This improvement occurred primarily via a reduction in the exponent error. However, the main Hill multispecies model was the best predictor of high-risk human dives in terms of precision. This was expected as this model had the advantage of both the animal data and the most human dives at 1.91-2.00 ATA.

Effectiveness of the models (single species vs. multispecies). The ability of the single species and multispecies models to describe the dive profiles for all three species was compared by plotting the difference between the model prediction and the observed incidence vs. the saturation depth (Fig. 4). All data were used with the observed DCS values defined as the mean incidence at each depth.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Multispecies models were developed in this study that allowed the sharing of common parameters among the three species. By employing one, more precise Hill equation exponent, the multispecies models allowed human risk predictions with smaller confidence limits compared with our human-only models. The predictions of the multispecies model agreed more closely with the observed data at 2 ATA, compared with the present US Navy model (USN93), although the confidence limits of both models overlapped those of the data. Thus it was impossible to declare one model better than the other at this depth, a situation that is very common in the field of risk prediction of DCS. However, it would not have been surprising if our relatively simplistic models, which were fit to data only from air-saturation, direct-ascent dives, improved prediction over more complex models such as USN93 that were fit to, and used to predict risk for, a wide variety of profiles.

The benefit of combining species, in terms of reducing the confidence limits of model predictions for human prediction, was relatively modest within the region in which human data are available. The real value of our approach becomes evident when extrapolation is necessary, and the addition of animal data is essential to make predictions without huge uncertainties. This was demonstrated when animal data were added to the abridged human data set, which was missing the dives at the two deepest depths. The addition restored the ability to resolve risk predictions for these two depths from zero. Unfortunately, we cannot presently determine the reliability of our predictions for depths greater than these. Consequently, the accuracy of our approach for human prediction awaits further experience and testing with other types of data, as has often been the case with the introduction of other new predictive models for DCS. However, it is this unique ability to predict human outcome, where no data are available, that is the primary goal of animal-to-human modeling. Certainly, any future work should focus on whether our conclusions regarding combining data hold true for other species and other types of dive profiles, such as those involving nonsaturation exposures or decompression stops.

The use of a common exponent in our multispecies models was based on the inability to resolve exponents among the individual species at least partly because of their large confidence limits, rather than very close agreement in their actual values. In a sense, by combining species, we have "merely" increased the number of observations used to calibrate a model for subsequent predictions of a human response. More observations lead to better predictive precision by well-established statistical principles. However, the additional subjects were "small" laboratory animals, not humans, illustrating one way that animal data might be of value in developing human decompression procedures. Such an approach translating animal models to human prediction could conceivably allow initial development of human procedures by using limited animal dives, while eliminating many human trials.

With the multispecies models, we are able to adjust the dose-response curve of any one of the three species to derive the curves of the other two by changing a single parameter, P₅₀. Because of the nature of the Hill equation, the steepness of any plotted dose-response curve depends on both the exponent and the dose range selected for the plot. Thus the multispecies curves show decreasing steepness going from human to pig to rat, despite having the same exponent, reflecting the larger magnitudes of dose at the greater saturation depths. A more detailed evaluation of the contribution of the P₅₀ and exponent to these combined-species models would, in our opinion, push the interpretation of the parameters beyond what appears warranted, in view of the relative imprecision associated with these (e.g., Fig. 4) and other decompression models.

The simple profiles used in this study allowed any differences in gas kinetics to be ignored. However, a previous study defining risk of DCS in humans and sheep needed to include parameters explicitly defining gas kinetics, because bottom times were 3 h (1). That study reported that separate gas-exchange parameters for humans and sheep were not statistically warranted, allowing common parameters to be estimated from the combined data with reduced error, as was the case here. Those adjustments for species are analogous to the adjustments in P₅₀ required in the present work and provide precedent for our work, although their risk-based models are very different from our Hill equation models.

The elevated risk of DCS with increasing weight within a species was confirmed in rats, although not in pigs in this study. Thus an intraspecies weight correction for DCS risk can be very important and potentially large. In the illustration presented earlier (Fig. 2), a remarkable increase of ~1% in DCS risk was estimated for each gram increase of rat weight, which agrees with observations made for rats over 15 yr ago, subjected to saturation dives with multiple inert gases (12). Unfortunately, there was no attempt to incorporate sheep weight into the previously reported combined human and sheep model of decompression risk, despite a fivefold range in weight of the animals (1).

As expected, the additional analyses in the APPENDIX show that the parameter estimates were affected by the specific scoring criteria for DCS selected for the model. Thus the adjustment in P₅₀ for interspecies predictions reflects differences not only in tolerance to decompression, but also in scoring criteria. However, regardless of which of the three sets of definitions of DCS was used, the multispecies models agreed in terms of 1) a common Hill equation exponent for all three species and 2) the relative magnitude of the precision associated with the parameter estimates. This occurred despite the fact that the degree of overlap of incidence levels among species varied with how DCS was defined. Indeed, the multispecies models did not seem to be affected by whether there was little data overlap among species (as with humans and rats in Fig. 1) or considerable overlap (as in Fig. 6). These findings are encouraging to any future efforts where there may be differences in symptoms and incidence levels of DCS among species.

We would caution against immediate rejection of our approach of combining animal and human data simply because animal DCS in many cases is more severe than that in humans and, therefore, appears "different" from the average human case. Within any human data set, there is normally also a range in symptoms and severity among DCS cases, particularly when working with a variety of different types of profiles (21). Among species, there certainly are differences in tolerance to decompression, with relative susceptibility to DCS tending to increase with species size (2, 7). One common explanation for these differences is that higher metabolism, with accompanying faster circulation, hastens gas elimination in smaller animals. However, others have suggested that small animals may also be better able to cope with an excess amount of gas and avoid DCS (9). On the basis of the strong relationship between body weight and DCS susceptibility, Flynn and Lambertsen (7) suggested that species differences probably reflect differences in susceptibility to DCS rather than a fundamental difference in the nature of DCS among animals. Interestingly, Lin (16) concluded from Doppler experiments that the maximum change in pressure without forming intravascular bubbles was the same in rats, cats, and dogs with the use of rapid decompression rates designed to minimize any gas off-loading. These observations suggest that response differences among species to the insult of decompression may reflect a combination of factors, including differences in gas exchange and tolerance to excess gas in the body.