Human dose-response relationship for decompression and endogenous bubble formation

The dose-response relationship for decompression magnitude and venous gas emboli (VGE) formation in humans was examined. Pressure exposures of 138, 150, and 164 kPa (12, 16, and 20.5 ft of seawater gauge pressure) were conducted in an underwater habitat for 48 h. The 111 human male volunteer subjects then ascended directly to the surface in less than 5 min and were monitored for VGE with a continuous-wave Doppler ultrasound device over the precordium or the subclavian veins at regular intervals for a 24-h period. No signs or symptoms consistent with decompression sickness occurred. However, a large incidence of VGE detection was noted. These data were combined with those from our previously reported experiments at higher pressures, and the data were fit to a Hill dose-response equation with nonlinear least-squares or maximum likelihood routines. Highly significant fits of precordial VGE incidences were obtained with the Hill equation (saturation depth pressure at which there is a 50% probability of detectable VGE [D(VGE)50] = 150 +/- 1.2 kPa). Subclavian monitoring increased the sensitivity of VGE detection and resulted in a leftward shift [D(VGE)50 = 135 +/- 2 kPa] of the best-fit curve. We conclude that the reduction in pressure necessary to produce bubbles in humans is much less than was previously thought; 50% of humans can be expected to generate endogenous bubbles after decompression from a steady-state pressure exposure of only 135 kPa (11 ft of seawater). This may have significant implications for decompression schedule formulation and for altitude exposures that are currently considered benign. These results also imply that endogenous bubbles arise from preexisting gas collections.     

On the likelihood of decompression sickness

The occurrence of decompression sickness in animals and humans is characterized by the extreme variability of individual response. Nevertheless, models and analyses of decompression results have generally used a critical value approach to separate safe and unsafe decompression procedures. Application of the principle of maximum likelihood provides a formal and consistent way to quantify decompression risk and to apply models to data on decompression outcome. By use of the maximum likelihood principle, a number of models were fit to data from dose-response and maximum pressure-reduction experiments with both rats and men. Several different formulations of two- and three-parameter models described the data well. In addition to summarizing data sets, the analyses provide a way to maximize the value of experimental observations, test theoretical predictions, estimate uncertainty in conclusions, and recommend safe practices.     

Cerebral gas embolism absorption during hyperbaric therapy: theory.

Cerebral gas embolism is a serious consequence of diving. It is associated with decompression sickness and is assumed to cause severe neurological dysfunction. A mathematical model previously developed to calculate embolism absorption time based on in vivo bubble geometry is used in which various conditions of hyperbaric therapy are considered. Effects of varying external pressure and inert gas concentrations in the breathing mixtures, according to US Navy and Royal Navy diving treatment tables, are predicted. Recompression alone is calculated to reduce absorption times of a 50-nl bubble by up to 98% over the untreated case. Lowering the inhaled inert gas concentration from 67.5% to 50% reduces absorption time by 37% at a given pressure. Bubbles formed after diving and decompression with He are calculated to absorb up to 73% faster than bubbles created after diving and decompression with air, regardless of the recompression gas breathed. This model is a useful alternative to impractical clinical trials in assessing which initial step in hyperbaric therapy is most effective in eliminating cerebral gas embolisms should they occur.     

Predicting risk of decompression sickness in humans from outcomes in sheep.

In animals, the response to decompression scales as a power of species body mass. Consequently, decompression sickness (DCS) risk in humans should be well predicted from an animal model with a body mass comparable to humans. No-stop decompression outcomes in compressed air and nitrogen-oxygen dives with sheep (n = 394 dives, 14.5% DCS) and humans (n = 463 dives, 4.5% DCS) were used with linear-exponential, probabilistic modeling to test this hypothesis. Scaling the response parameters of this model between species (without accounting for body mass), while estimating tissue-compartment kinetic parameters from combined human and sheep data, predicts combined risk better, based on log likelihood, than do separate sheep and human models, a combined model without scaling, and a kinetic-scaled model. These findings provide a practical tool for estimating DCS risk in humans from outcomes in sheep, especially in decompression profiles too risky to test with humans. This model supports the hypothesis that species of similar body mass have similar DCS risk.     

Mixed-gas model for predicting decompression sickness in rats.

A mixed-gas model for rats was developed to further explore the role of different gases in decompression and to provide a global model for possible future evaluation of its usefulness for human prediction. A Hill-equation dose-response model was fitted to over 5,000 rat dives by using the technique of maximum likelihood. These dives used various mixtures of He, N(2), Ar, and O(2) and had times at depth up to 2 h and varied decompression profiles. Results supported past findings, including 1) differences among the gases in decompression risk (He < N(2) < Ar) and exchange rate (He > Ar approximately N(2)), 2) significant decompression risk of O(2), and 3) increased risk of decompression sickness with heavier animals. New findings included asymmetrical gas exchange with gas washout often unexpectedly faster than uptake. Model success was demonstrated by the relatively small errors (and their random scatter) between model predictions and actual incidences. This mixed-gas model for prediction of decompression sickness in rats is the first such model for any animal species that covers such a broad range of gas mixtures and dive profiles.     

Effect of N2-He-O2 on decompression outcome in rats after variable time-at-depth dives

No study of decompression sickness has examined both variable gas mixtures and variable time at depth to the point of statistical significance. This investigation examined the effect of N2-He-O2 on decompression outcome in rats after variable time-at-depth dives. Unanesthetized male albino rats were subjected to one of two series of simulated dives: 1) N2-He-O2 dives (20.9% O2) at 175 feet of seawater fsw) and 2) N2-O2 dives (variable percentage of O2; depths from 141 to 207 fsw). Time at depth ranged from 10 to 120 min; rats were then decompressed within 10 s to surface pressure. The probability of decompression sickness (severe bends symptoms or death) was analyzed with a Hill equation model, with parameters for gas potency and equilibrium time for the three gases and weight of the animal. Relative potencies for the three gases were of similar magnitude for bends and statistically different for death in ascending order: O2 less than He less than N2. Estimated gas uptake rates were different. N2 took three to four times as long as He to reach full effect; the rate of O2 appeared to be considerably shorter than that of N2 or He. The large influence of O2 on decompression outcome questions the simplistic view that O2 cannot contribute to the decompression requirement.     

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.     

A multicompartment model of carboxyhemoglobin and carboxymyoglobin responses to inhalation of carbon monoxide.

We have developed a model that predicts the distribution of carbon monoxide (CO) in the body resulting from acute inhalation exposures to CO. The model includes a lung compartment, arterial and venous blood compartments, and muscle and nonmuscle soft tissues with both vascular and nonvascular subcompartments. In the model, CO is allowed to diffuse between the vascular and nonvascular subcompartments of the tissues and to combine with myoglobin in the nonvascular subcompartment of muscle tissue. The oxyhemoglobin dissociation curve is represented by a modified Hill equation whose parameters are functions of the carboxyhemoglobin (HbCO) level. Values for skeletal muscle mass and cardiac output are calculated from prediction formulas based on age, weight, and height of individual subjects. We demonstrate that the model fits data from CO rebreathing studies when diffusion of CO into the muscle compartment is considered. The model also fits responses of HbCO to single or multiple exposures to CO lasting for a few minutes each. In addition, the model reproduces reported differences between arterial and venous HbCO levels and replicates predictions from the Coburn-Forster-Kane equation for CO exposures of a 1- to 83-h duration. In contrast to approaches based on the Coburn-Forster-Kane equation, the present model predicts uptake and distribution of CO in both vascular and tissue compartments during inhalation of either constant or variable levels of CO.     

Risk Assessment as a Decision-Making Tool for Treatment of Emissions at a New Aluminum Smelter in Iceland: 1. Background and Introduction

Protection of human health and ecosystems is gaining importance in corporate decision- making regarding industrial development. During the design phase for an aluminum smelter in East Iceland, it became necessary to determine whether a wet scrubber system should be installed to reduce sulfur dioxide emissions. Predictive risk assessment was used to determine whether there would be a consequential difference in the level of risk to human and ecological receptors from constituents in air emissions from the aluminum smelter, either with or without wet scrubbers. Benchmark exposure concentrations were established for avian, mammalian, and plant receptors and were compared to air modeling predictions to develop risk estimates. Benchmark concentrations were derived using plant uptake models for fluoride and polycyclic aromatic hydrocarbons (PAHs), and food-web modeling for birds and mammals. Exposure models were developed for all receptors, and population-level effects were modeled for plant, bird, and mammal receptors. Results indicated that exposures under both scenarios are lower than risk thresholds, and overall risk was lower for a smelter without wet scrubbers. Thus, although mass loading of sulfur dioxide (and other constituents) would be reduced using wet scrubbers, the corresponding risk to ecological receptors would actually be higher because of higher exposure-point concentrations in air.     

Modeling the dynamics of risk of altitude decompression sickness

A probabilistic model of decompression sickness is modified by introducing corrections that determine more precisely the risk of tissue injury by gas bubbles as a function of blood supply and bubble nucleation intensity. Parameters of the “worst” virtual tissues and theoretical curves corresponding to empirical data on the cumulative probability of decompression sickness symptoms for some altitude decompression procedures are determined. The parameters are shown to depend on final pressure, physical load, and duration of preoxygenation.     

Review of Information Resources to Support Human Exposure Assessment Models

Efforts to model human exposures to chemicals are growing more sophisticated and encompass increasingly complex exposure scenarios. The scope of such analyses has increased, growing from assessments of single exposure pathways to complex evaluations of aggregate or cumulative chemical exposures occurring within a variety of settings and scenarios. In addition, quantitative modeling techniques have evolved from simple deterministic analyses using single point estimates for each necessary input parameter to more detailed probabilistic analyses that can accommodate distributions of input parameters and assessment results. As part of an overall effort to guide development of a comprehensive framework for modeling human exposures to chemicals, available information resources needed to derive input parameters for human exposure assessment models were compiled and critically reviewed. Ongoing research in the area of exposure assessment parameters was also identified. The results of these efforts are summarized and other relevant information that will be needed to apply the available data in a comprehensive exposure model is discussed. Critical data gaps in the available information are also identified. Exposure assessment modeling and associated research would benefit from the collection of additional data as well as by enhancing the accessibility of existing and evolving information resources.     

On the Hill plot of NMR data for titration of protein residues

The Hill plots of NMR titration data for protein residues disclose more clearly than the usual titration curves the presence of multiple weak perturbations originating from other titratable groups, and should be used whenever the conventional curve fitting is poor. For a quantitative interpretation, we derive here expressions for the Hill equation and the Hill coefficient when the titration of the observed group is perturbed by more than one titratable group. When the generalized Hill equation is fitted to the data, values of the interaction parameters between the observed group and the others are extracted provided that there are no mutual interactions between the latter groups. The method is applied to the titration data of two histidyl residues of l-arginine phosphotransferase (E.C. 2.7.3.3.) in the transition state analogue complex (enzyme-Mg²⁺-ADP-NOsk3/–l-Arg). From the Hill plots, interactions with three titratable groups are disclosed for both residues, and the fitting with the Hill equation reveals that they experience perturbations from the same three groups. Microscopic pK values are obtained for all the involved groups, indicating large changes (up to 3 pH units) upon protonation of the interacting groups. As compared to the conventional fitting procedure, the use and fitting of Hill plots yields from NMR data more information on the neighbourhood of enzyme residues and on the changes intervening therein through the steps involved in the catalysis.     

A new class of biophysical models for predicting the probability of decompression sickness in scuba diving.

Interconnected compartmental models have been used for decades in physiology and medicine to account for the observed multi-exponential washout kinetics of a variety of solutes (including inert gases) both from single tissues and from the body as a whole. They are used here as the basis for a new class of biophysical probabilistic decompression models. These models are characterized by a relatively well-perfused, risk-bearing, central compartment and one or two non-risk-bearing, relatively poorly perfused, peripheral compartment(s). The peripheral compartments affect risk indirectly by diffusive exchange of dissolved inert gas with the central compartment. On the basis of the accuracy of their respective predictions beyond the calibration regime, the three-compartment interconnected models were found to be significantly better than the two-compartment interconnected models. The former, on the basis of a number of criteria, was also better than a two-compartment parallel model used for comparative purposes. In these latter comparisons, the models all had the same number of fitted parameters (four), were based on linear kinetics, had the same risk function, and were calibrated against the same dataset. The interconnected models predict that inert gas washout during decompression is relatively fast, initially, but slows rapidly with time compared with the more uniform washout rate predicted by an independent parallel compartment model. If empirically verified, this may have important implications for diving practice.     

Validation of species–climate impact models under climate change

Increasing concern over the implications of climate change for biodiversity has led to the use of species–climate envelope models to project species extinction risk under climate‐change scenarios. However, recent studies have demonstrated significant variability in model predictions and there remains a pressing need to validate models and to reduce uncertainties. Model validation is problematic as predictions are made for events that have not yet occurred. Resubstituition and data partitioning of present‐day data sets are, therefore, commonly used to test the predictive performance of models. However, these approaches suffer from the problems of spatial and temporal autocorrelation in the calibration and validation sets. Using observed distribution shifts among 116 British breeding‐bird species over the past ～20 years, we are able to provide a first independent validation of four envelope modelling techniques under climate change. Results showed good to fair predictive performance on independent validation, although rules used to assess model performance are difficult to interpret in a decision‐planning context. We also showed that measures of performance on nonindependent data provided optimistic estimates of models' predictive ability on independent data. Artificial neural networks and generalized additive models provided generally more accurate predictions of species range shifts than generalized linear models or classification tree analysis. Data for independent model validation and replication of this study are rare and we argue that perfect validation may not in fact be conceptually possible. We also note that usefulness of models is contingent on both the questions being asked and the techniques used. Implementations of species–climate envelope models for testing hypotheses and predicting future events may prove wrong, while being potentially useful if put into appropriate context.     

Species distribution models in climate change scenarios are still not useful for informing policy planning: an uncertainty assessment using fuzzy logic

We compared the effect of general circulation models and greenhouse gas emission scenarios on the uncertainty associated with models predicting changes in areas favourable to animal species. Given that mountain species are particularly at risk due to climate warming, we selected one amphibian (Baetic midwife toad), one reptile (Lataste's viper), one bird (Bonelli's eagle), and one mammal (Iberian wild goat) present in Spanish mountains to model their distributional response to climate change during this century. Climate forecasts for the whole century were provided by the Agencia Estatal de Meteorología (AEMET; National Meteorological Agency) of Spain, which adapted the general circulation models CGCM2 and ECHAM4 and produced expected temperature and precipitation values for Spain according to the A2 and B2 emission scenarios. We constructed separate models of the species response to spatial, topographic, human, and climate variables using current values of the corresponding variables. We predicted future areas favourable to the species by replacing the current climate values with those expected according to each climate change scenario, while keeping spatial, topographic and human variables constant. Fuzzy logic was used to compute the coincidence between predictions for different emission scenarios in the same global circulation model, and the consistency between predictions for the same emission scenario applying different general circulation models. In general, coincidences were higher than consistencies and, thus, discrepancies between predictions were more attributable to uncertainty in global circulation models, i.e. our insufficient knowledge concerning the effect of the oceans and atmosphere on climate, than to the putative effect of different emission scenarios on future climates. Our conclusion is that species distribution models in climate warming scenarios are still not useful for informing emission policy planning, although they have great potential as tools once consistencies become higher than coincidences.     

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.     

A two-mutation model of radiation-induced acute myeloid leukemia using historical mouse data

From studies of the atomic bomb survivors, it is well known that ionizing radiation causes several forms of leukemia. However, since the specific mechanism behind this process remains largely unknown, it is difficult to extrapolate carcinogenic effects at acute high-dose exposures to risk estimates for the chronic low-dose exposures that are important for radiation protection purposes. Recently, it has become clear that the induction of acute myeloid leukemia (AML) in CBA/H mice takes place through two key steps, both involving the Sfpi1 gene. A similar mechanism may play a role in human radiation-induced AML. In the present paper, a two-mutation carcinogenesis model is applied to model AML in several data sets of X-ray- and neutron-exposed CBA/H mice. The models obtained provide good fits to the data. A comparison between the predictions for neutron-induced and X-ray-induced AML yields an RBE for neutrons of approximately 3. The model used is considered to be a first step toward a model for human radiation-induced AML, which could be used to estimate risks of exposure to low doses.     

Delayed Recompression for Decompression Sickness: Retrospective Analysis

Introduction

Most cases of decompression sickness (DCS) occur soon after surfacing, with 98% within 24 hours. Recompression using hyperbaric chamber should be administrated as soon as feasible in order to decrease bubble size and avoid further tissue injury. Unfortunately, there may be a significant time delay from surfacing to recompression. The time beyond which hyperbaric treatment is non effective is unclear. The aims of the study were first to evaluate the effect of delayed hyperbaric treatment, initiated more than 48h after surfacing for DCS and second, to evaluate the different treatment protocols.

Methods

From January 2000 to February 2014, 76 divers had delayed hyperbaric treatment (≥48h) for DCS in the Sagol center for Hyperbaric medicine and Research, Assaf-Harofeh Medical Center, Israel. Data were collected from their medical records and compared to data of 128 patients treated earlier than 48h after surfacing at the same hyperbaric institute.

Results

There was no significant difference, as to any of the baseline characteristics, between the delayed and early treatment groups. With respect to treatment results, at the delayed treatment divers, complete recovery was achieved in 76% of the divers, partial recovery in 17.1% and no improvement in 6.6%. Similar results were achieved when treatment started early, where 78% of the divers had complete recovery, 15.6% partial recovery and 6.2% no recovery. Delayed hyperbaric treatment using US Navy Table 6 protocol trended toward a better clinical outcome yet not statistically significant (OR=2.786, CI95%[0.896-8.66], p=0.07) compared to standard hyperbaric oxygen therapy of 90 minutes at 2 ATA, irrespective of the symptoms severity at presentation.

Conclusions

Late recompression for DCS, 48 hours or more after surfacing, has clinical value and when applied can achieve complete recovery in 76% of the divers. It seems that the preferred hyperbaric treatment protocol should be based on US Navy Table 6.     

Sources of Variability in Net Primary Production Predictions at a Regional Scale: A Comparison Using PnET-II and TEM 4.0 in Northeastern US Forests

Because model predictions at continental and global scales are necessarily based on broad characterizations of vegetation, soils, and climate, estimates of carbon stocks and fluxes made by global terrestrial biosphere models may not be accurate for every region. At the regional scale, we suggest that attention can be focused more clearly on understanding the relative strengths of predicted net primary productivity (NPP) limitation by energy, water, and nutrients. We evaluate the sources of variability among model predictions of NPP with a regional-scale comparison between estimates made by PnET-II (a forest ecosystem process model previously applied to the northeastern region) and TEM 4.0 (a terrestrial biosphere model typically applied to the globe) for the northeastern US. When the same climate, vegetation, and soil data sets were used to drive both models, regional average NPP predictions made by PnET-II and TEM were remarkably similar, and at the biome level, model predictions agreed fairly well with NPP estimates developed from field measurements. However, TEM 4.0 predictions were more sensitive to regional variations in temperature as a result of feedbacks between temperature and belowground N availability. In PnET-II, the direct link between transpiration and photosynthesis caused substantial water stress in hardwood and pine forest types with increases in solar radiation; predicted water stress was relieved substantially when soil water holding capacity (WHC) was increased. Increasing soil WHC had little effect on TEM 4.0 predictions because soil water storage was already sufficient to meet plant demand with baseline WHC values, and because predicted N availability under baseline conditions in this region was not limited by water. Because NPP predictions were closely keyed to forest cover type, the relative coverage of low- versus high-productivity forests at both fine and coarse resolutions was an important determinant of regional NPP predictions. Therefore, changes in grid cell size and differences in the methods used to aggregate from fine to coarse resolution were important to NPP predictions insofar as they changed the relative proportions of forest cover. We suggest that because the small patches of high-elevation spruce-fir forest in this region are substantially less productive than forests in the remainder of the region, more accurate NPP predictions will result if models applied to this region use land cover input data sets that retain as much fine-resolution forest type variability as possible. The differences among model responses to variations in climate and soil WHC data sets suggest that the models will respond quite differently to scenarios of future climate. A better understanding of the dynamic interactions between water stress, N availability, and forest productivity in this region will enable models to make more accurate predictions of future carbon stocks and fluxes. Received 19 June 1998; accepted 25 June 1999.