Biophysical basis for inner ear decompression sickness.

Isolated inner ear decompression sickness (DCS) is recognized in deep diving involving breathing of helium-oxygen mixtures, particularly when breathing gas is switched to a nitrogen-rich mixture during decompression. The biophysical basis for this selective vulnerability of the inner ear to DCS has not been established. A compartmental model of inert gas kinetics in the human inner ear was constructed from anatomical and physiological parameters described in the literature and used to simulate inert gas tensions in the inner ear during deep dives and breathing-gas substitutions that have been reported to cause inner ear DCS. The model predicts considerable supersaturation, and therefore possible bubble formation, during the initial phase of a conventional decompression. Counterdiffusion of helium and nitrogen from the perilymph may produce supersaturation in the membranous labyrinth and endolymph after switching to a nitrogen-rich breathing mixture even without decompression. Conventional decompression algorithms may result in inadequate decompression for the inner ear for deep dives. Breathing-gas switches should be scheduled deep or shallow to avoid the period of maximum supersaturation resulting from decompression.     

Decompression outcome following saturation dives with multiple inert gases in rats

This investigation examined the question of whether gas mixtures containing multiple inert gases provide a decompression advantage over mixtures containing a single inert gas. Unanesthetized male albino rats, Rattus norvegicus, were subjected to 2-h simulated dives at depths ranging from 145 to 220 fsw. At pressure, the rats breathed various He-N2-Ar-O2 mixtures (79.1% inert gas-20.9% O2); they were then decompressed rapidly (within 10 s) to surface pressures. The probability of decompression sickness (DCS), measured either as severe bends symptoms or death, was related to the experimental variables in a Hill equation model incorporating parameters that account for differences in the potencies of the three gases and the weight of the animal. The relative potencies of the three gases, which affect the total dose of decompression stress, were determined as significantly different in the following ascending order of potency: He less than N2 less than Ar; some of these differences were small in magnitude. With mixtures, the degree of decompression stress diminished as either N2 or Ar was replaced by He. No obvious advantage or disadvantage of mixtures over the least potent pure inert gas (He) was evident, although limits to the expectation of possible advantage or disadvantage of mixtures were defined. Also, model analysis did not support the hypothesis that the outcome of decompression with multiple inert gases in rats under these experimental conditions can be explained totally by the volume of gas accumulated in the body during a dive.     

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.     

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.     

Effect of inert gas switching at depth on decompression outcome in rats

The present investigation was performed to determine whether inert gas sequencing at depth would affect decompression outcome in rats via the phenomenon of counterdiffusion. Unanesthetized rats (Rattus norvegicus) were subjected to simulated dives in either air, 79% He-21% O2, or 79% Ar-21% O2; depths ranged from 125 to 175 feet of seawater (4.8-6.3 atmospheres absolute). After 1 h at depth, the dive chamber was vented (with depth held constant) over a 5-min period with the same gas as in the chamber (controls) or one of the other two inert gas-O2 mixtures. After the gas switch, a 5- to 35-min period was allowed for gas exchange between the animals and chamber atmosphere before rapid decompression to the surface. Substantial changes in the risk of decompression sickness (DCS) were observed after the gas switch because of differences in potencies (He less than N2 less than Ar) for causing DCS and gas exchange rates (He greater than Ar greater than N2) among the three gases. Based on the predicted gas exchange rates, transient increases or decreases in total inert gas pressure would be expected to occur during these experimental conditions. Because of differences in gas potencies, DCS risk may not directly follow the changes in total inert gas pressure. In fact, a decline in predicted DCS risk may occur even as total inert gas pressure in increasing.     

The interaction of diffusion and perfusion in homogeneous tissue

A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.     

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.     

Factors determining temporal pattern of isobaric supersaturation

It is possible to produce a transient supersaturation or undersaturation in tissues and blood by sequentially breathing gases with different equilibration rates. If the ambient gas pressure is sufficiently high, the induced supersaturation can produce vascular bubbles. By means of the classical perfusion-dependent model of inert gas elimination, which assumes that the effects of diffusion are minimal, the magnitude of the total inert gas pressure can be predicted. If, however, the effects of diffusion cannot be ignored, the supersaturation could be substantially larger. This paper estimates the effects of diffusion in a Krogh cylinder on the supersaturation produced by suddenly changing the inert gas partial pressure in the blood. The results of these estimates indicate that diffusion plays a role in this transient supersaturation only in long Krogh cylinders with high blood flows. The effects of diffusion are further reduced by the finite time necessary to switch the inert gases in arterial blood. The conclusions are supported by experiments that measure vascular bubble production after a switch of the inert portion of the inspired gas. These experiments further show that the formation of vascular bubbles after such a switch cannot be entirely explained by the different diffusion constants of the gases used.     

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.     

A model of extravascular bubble evolution: effect of changes in breathing gas composition.

Observations of bubble evolution in rats after decompression from air dives (O. Hyldegaard and J. Madsen. Undersea Biomed. Res. 16: 185-193, 1989; O. Hyldegaard and J. Madsen. Undersea Hyperbaric Med. 21: 413-424, 1994; O. Hyldegaard, M. Moller, and J. Madsen. Undersea Biomed. Res. 18: 361-371, 1991) suggest that bubbles may resolve more safely when the breathing gas is a heliox mixture than when it is pure O(2). This is due to a transient period of bubble growth seen during switches to O(2) breathing. In an attempt to understand these experimental results, we have developed a multigas-multipressure mathematical model of bubble evolution, which consists of a bubble in a well-stirred liquid. The liquid exchanges gas with the bubble via diffusion, and the exchange between liquid and blood is described by a single-exponential time constant for each inert gas. The model indicates that bubbles resolve most rapidly in spinal tissue, in adipose tissue, and in aqueous tissues when the breathing gas is switched to O(2) after surfacing. In addition, the model suggests that switching to heliox breathing may prolong the existence of the bubble relative to breathing air for bubbles in spinal and adipose tissues. Some possible explanations for the discrepancy between model and experiment are discussed.     

Mathematical approaches to decompression

A flexible mathematical treatment of diver decompression has been developed by modifying the classical Haldanian model of inert gas transport. It is based on the assumption that inert gases will remain in solution in the tissues of a diver as long as a particular metastable limit is not exceeded,and that this limit varies with depth, nature of the inert gas,and the specific time constant of its transport in the body. Proposed metastable limits (M-values)of dissolved helium partial pressure have been developed empirically by the Experimental Diving Unit of the United States Navy. These limits permit the design by digital computer of decompression procedures expected to be safer than contemporary decompression tables for extended deep dives.

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Zusammenfassung Ein flexibles mathematisches Verfahren zur Überwachung der Dekompression bei Tauchern wurde entwickelt, durch Modifikation des klassischen Modells von Haldane für den Transport träger Gase.Es beruht auf der Annahme,dass träge Gase so lange in den Geweben eines Tauchers in Lösung bleiben, als eine bestimmte metastabile Grenze nicht überschritten wird. Diese Grenze ändert sich mit der Tiefe,der Natur des trägen Gases und der spezifischen Zeitkonstante seines Transports im Körper. Die vorgeschlagenen metastabilen Grenzen (M-Werte) des Partialdruckes von gelöstem Helium wurden empirisch entwickelt in der Experimental Diving Unit der Marine der Vereinigten Staaten.Diese Grenzen erlauben die Erfassung der Dekompressionsvorgänge durch Digital Computer und es wird angenommen, dass sie sicherer sind als die gebräuchlichen Dekompressions-Tabellen für langes Tieftauchen.

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Resume On a établi un procédé mathématique fléxible pour suivre les phénomènes de décompression chez les plongeurs.Pour ce faire, on a modifié le modèle classique de Haldane concernant le transport d'un gaz inerte. Comme base, on admet que les gaz inertes resteront en solution dans les tissues des plongeurs aussi longtemps qu'une limite métastatique n'est pas franchie.Cette limite varie avec la profondeur,la nature du gaz inerte et la constante de temps spécifique de son transport dans le corps. Les limites métastatiques proposées (valeurs-M)de la pression partielle de l'hélium dissous ont été déterminées empiriquement à l' "Expérimental Diving Unit"de la marine des Etats-Unis. Ces limites permettent de calculer les processus de décompression au moyen d'ordinateurs.On admet en outre que ce procédé est plus sûr que les tables de décompression usuelles, surtout dans le cas de plongées profondes et de longue durée.

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Based on a paper presented at the Forth International Biometeorological Congress, New Brunswick, N.J., 26 August – 2 September 1966.     

Short oxygen prebreathing and intravenous perfluorocarbon emulsion reduces morbidity and mortality in a swine saturation model of decompression sickness.

Disabled submarine (DISSUB) survivors will achieve inert gas tissue saturation within 24 h. Direct ascent to the surface when saturated carries a high risk of decompression sickness (DCS) and death, yet may be necessary during rescue or escape. O(2) has demonstrated benefits in decreasing morbidity and mortality resulting from DCS by enhancing inert gas elimination. Perfluorocarbons (PFCs) also mitigate the effects of DCS by decreasing bubble formation and increasing O(2) delivery. Our hypothesis is that combining O(2) prebreathing (OPB) and PFC administration will reduce the incidence of DCS and death following saturation in an established 20-kg swine model. Yorkshire swine (20 +/- 6.5 kg) were compressed to 5 atmospheres (ATA) in a dry chamber for 22 h before randomization into one of four groups: 1) air and saline, 2) OPB and saline, 3) OPB with PFC given at depth, 4) OPB with PFC given after surfacing. OPB animals received >90% O(2) for 9 min at depth. All animals were returned to the surface (1 ATA) without decompression stops. The incidence of severe DCS < 2 h after surfacing was 96%, 63%, 82%, and 29% for groups 1, 2, 3, and 4, respectively. The incidence of death was 88%, 41%, 54%, and 5% for groups 1, 2, 3, and 4, respectively. OPB combined with PFC administration after surfacing provided the greatest reduction in DCS morbidity and mortality in a saturation swine model. O(2)-related seizure activity before reaching surface did not negatively affect outcome, but further safety studies are warranted.     

Kinetics of isobaric counterdiffusion

Isobaric inert gas counterdiffusion has been demonstrated to produce gas lesions in man (Lambertsen and Idicula, 1975) and lethal gas embolism in animals (Lambertsen, Cunnington and Cowley, 1975). Equations have been derived for the stable-state supersaturation pressures developing at interfaces during inert gas counterdiffusion (Graveset al., 1973). The present analysis is a mathematical treatment of the kinetics of the isobaric counterdiffusion of a pair of gases through a membrane consisting of two layers composed of substances with different diffusion coefficients and solubilities for each of the gases involved. The time to reach the stable supersaturation state due to isobaric counterdiffusion, even when circulatory transport and pulmonary washout times are included, is found to be at least an order of magnitude smaller than the time required for visible bubble formation and tissue distortion.     

Conducting airway gas exchange: diffusion-related differences in inert gas elimination.

We studied CO2 and inert gas elimination in the isolated in situ trachea as a model of conducting airway gas exchange. Six inert gases with various solubilities and molecular weights (MW) were infused into the left atria of six pentobarbital-anesthetized dogs (group 1). The unidirectionally ventilated trachea behaved as a high ventilation-perfusion unit (ratio = 60) with no appreciable dead space. Excretion of higher-MW gases appeared to be depressed, suggesting a MW dependence to inert gas exchange. This was further explored in another six dogs (group 2) with three gases of nearly equal solubility but widely divergent MWs (acetylene, 26; Freon-22, 86.5; isoflurane, 184.5). Isoflurane and Freon-22 excretions were depressed 47 and 30%, respectively, relative to acetylene. In a theoretical model of airway gas exchange, neither a tissue nor a gas phase diffusion resistance predicted our results better than the standard equation for steady-state alveolar inert gas elimination. However, addition of a simple ln (MW) term reduced the remaining residual sum of squares by 40% in group 1 and by 83% in group 2. Despite this significant MW influence on tracheal gas exchange, we calculate that the quantitative gas exchange capacity of the conducting airways in total can account for less than or equal to 16% of any MW-dependent differences observed in pulmonary inert gas elimination.     

The variation in susceptibility to decompression sickness

The Weibull function is shown to provide a particularly good fit for published data demonstrating the variation between individuals with respect to their susceptibility to decompression sickness. These data include the distributions of minimum bends depths for men and for goats breathing air,and that of resting pilots for aerial decompression.The correlations are shown to hold only if the vital parameter for estimating the imminence of symptoms is taken as the volume fraction of gas predicted to have separated from solution in unit volume of tissue.

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Zusammenfassung Es wird gezeigt, dass die nach der Weibull-Gleichung berechneten Werte für die Variation der Empfindlichkeit von Individuen auf Caissonkrankheit besonders gut übereinstimmen mit gemessenen Werten. Diese Werte umfassen die Verteilung der minimalen Anzahl "bends" bei Menschen und Ziegen unter Luftatmung in verschiedenen Tiefen und von ruhenden Piloten bei Luftdekompression. Es wird gezeigt, dass die Korrelationen nur gültig sind,wenn als Parameter zur Bestimmung der drohenden Symptome das Gasvolumen verwendet wird,dessen Abtrennung von der Lösung in einer Volumeneinheit Gewebe vorausgesagt wird.

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Resume On démontre que les valeurs des variations de la sensibilité à la décompression calculées selon la formule de Weibull correspondent très bien aux valeurs mesurées. Ces valeurs comprennent la répartition du nombre minimum de "bends" chez des hommes ou des chèvres respirant de l'air à différentes profondeurs ainsi quepour des pilotes au repos subissant une décompression.Les corrélations ne sont toutefois valables que si le paramètre principal d'estimation de l'imminence des symptômes est exprimé par le rapport entre le volume des gaz devant se séparer de la solution et le volume des tissus.

     

The secretion of inert gas into the swim-bladder of fish

The composition of the gas mixture secreted into the swim-bladders of several species of fish has been determined in the mass spectrometer. The secreted gas differed greatly from the gas mixture breathed by the fish in the relative proportions of the chemically inert gases, argon, neon, helium, and nitrogen. Relative to nitrogen the proportion of the very soluble argon was increased and the proportions of the much less soluble neon and helium decreased. The composition of the secreted gas approaches the composition of the gas mixture dissolved in the tissue fluid. A theory of inert gas secretion is proposed. It is suggested that oxygen gas is actively secreted and evolved in the form of minute bubbles, that inert gases diffuse into these bubbles, and that the bubbles are passed into the swim-bladder carrying with them inert gases. Coupled to a preferential reabsorption of oxygen from the swim-bladder this mechanism can achieve high tensions of inert gas in the swim-bladder. The accumulation of nearly pure nitrogen in the swim-bladder of goldfish (Carassius auratus) is accomplished by the secretion of an oxygen-rich gas mixture followed by the reabsorption of oxygen.     

The Extended Oxygen Window Concept for Programming Saturation Decompressions Using Air and Nitrox

Saturation decompression is a physiological process of transition from one steady state, full saturation with inert gas at pressure, to another one: standard conditions at surface. It is defined by the borderline condition for time spent at a particular depth (pressure) and inert gas in the breathing mixture (nitrogen, helium). It is a delicate and long lasting process during which single milliliters of inert gas are eliminated every minute, and any disturbance can lead to the creation of gas bubbles leading to decompression sickness (DCS). Most operational procedures rely on experimentally found parameters describing a continuous slow decompression rate. In Poland, the system for programming of continuous decompression after saturation with compressed air and nitrox has been developed as based on the concept of the Extended Oxygen Window (EOW). EOW mainly depends on the physiology of the metabolic oxygen window—also called inherent unsaturation or partial pressure vacancy—but also on metabolism of carbon dioxide, the existence of water vapor, as well as tissue tension. Initially, ambient pressure can be reduced at a higher rate allowing the elimination of inert gas from faster compartments using the EOW concept, and maximum outflow of nitrogen. Then, keeping a driving force for long decompression not exceeding the EOW allows optimal elimination of nitrogen from the limiting compartment with half-time of 360 min. The model has been theoretically verified through its application for estimation of risk of decompression sickness in published systems of air and nitrox saturation decompressions, where DCS cases were observed. Clear dose-reaction relation exists, and this confirms that any supersaturation over the EOW creates a risk for DCS. Using the concept of the EOW, 76 man-decompressions were conducted after air and nitrox saturations in depth range between 18 and 45 meters with no single case of DCS. In summary, the EOW concept describes physiology of decompression after saturation with nitrogen-based breathing mixtures.     

Formation of gas bubbles in biological tissues in decompression (a mathematical model)

A mathematical model simulating transport of gases between a bubble resulted from decompression and tissue around is presented. With the help of the model the influence of gas mixture and density of the bubble forming centres upon the growth rate was studied. An important part of CO2 in the bubble forming was found out. The bubbles with He have been shown to grow faster than those with N2. At a 5-10-fold decrease of the outer pressure during 1-2 seconds the bubbles can reach sizes which violate hemodynamics in the system of microcirculation.     

Influence of blood flow on cutaneous permeability to inert gas

A thermally regulated Plexiglas chamber was designed for investigation of transcutaneous diffusion of N2 and helium (He) in the human hand. Influence of cutaneous blood flow in this process was studied simultaneously with gas diffusion measurements. Changes in cutaneous blood flow (Q, in ml X min-1 X 100 ml tissue-1) were effected by altering ambient temperature (T) from 20 to 40 degrees C (Q = 0.08 X 100.07T). We found that the rate of inert gas diffusion through human skin, expressed as conductance (G, in ml STPD X h-1 X m-2 X atm-1), increases exponentially as a function of blood flow, and was indistinguishable between He and N2 (G = 21.19 X 100.0124Q). The permeability, diffusion coefficient per unit diffusion distance (D/h, in cm/h), also rose exponentially as a function of blood flow. But permeability for He (D/h = 0.1748 X 100.0203Q) was greater than that for N2 (D/h = 0.1678 X 100.0114Q). As cutaneous blood flow rises, because of increased temperature, the apparent diffusion distance falls linearly for both N2 and He. The change is more prominent for He than for N2 diffusion. Estimated replacement time for the body stores of N2 by transcutaneous diffusion alone was shortened from 26.8 h at 31 degrees C to 15.1 h at 37 degrees C. It is suggested from this study that beneficial results may be derived during decompression procedure 1) by maintaining an appropriate transcutaneous pressure gradient of inert gases, and 2) by elevating ambient temperature.     

Modeling diffusion limitation of gas exchange in lungs containing perfluorocarbon

We reportedchanges in alveolar-arterial PO₂ gradient,ventilation-perfusion heterogeneity, and arterial-alveolarPCO₂ gradient during partial liquid ventilation(PLV) in healthy piglets (E. A. Mates, P. Tarczy-Hornoch, J. Hildebrandt, J. C. Jackson, and M. P. Hlastala. In: OxygenTransport to Tissue XVII, edited by C. Ince. New York: Plenum,1996, vol. 388, p. 585-597). Here we develop two mathematicalmodels to predict transient and steady-state (SS) gas exchangeconditions during PLV and to estimate the contribution of diffusionlimitation to SS arterial-alveolar differences. In the simplest model,perfluorocarbon is represented as a uniform flat stirred layer and, ina more complex model, as an unstirred spherical layer in a ventilatedterminal alveolar sac. Time-dependent solutions of both models showthat SS is established for various inert and respiratory gases within5-150 s. In fluid-filled unventilated terminal units, all times toSS increased sometimes by hours, e.g., SF₆ exceeded 4 h. SSsolutions for the ventilated spherical model predicted minorend-capillary disequilibrium of inert gases and significantdisequilibrium of respiratory gases, which could explain a largeportion of the arterial-alveolar PCO₂ gradient measured during PLV (14). We conclude that, during PLV, diffusion gradients for gases are generally small, except for CO₂.