Decompression tables and dive-outcome data: graphical analysis.

We compare outcomes of experimental air dives with prescriptions for ascent given by various air decompression tables. Among experimental dives compiled in the U.S. Navy Decompression Database, many profiles that resulted in decompression sickness (DCS) have longer total decompression times (TDTs, defined as times spent at decompression stops plus time to travel from depth to the surface) than profiles prescribed by the U.S. Navy table; thus, the divers developed DCS despite spending more time at stops than the table requires. The same is true to a lesser extent for the table used by the Canadian forces. A few DCS cases occurred in profiles having longer TDTs than those of the VVal-18 table and a table prepared at the University of Pennsylvania. The TDTs for 2.2% risk according to the probabilistic NMRI'98 Model are often far longer than TDTs of experimental dives that resulted in DCS. This analysis dramatizes the large differences among alternative decompression instructions and illustrates how the U.S. Navy table provides too little time at stops when bottom times are long.

A simple probabilistic model for standard air dives that is focused on total decompression time.

A statistical fit of an algorithm to "calibration data" gives parameter values for a "probabilistic decompression model." Our objective is to prepare a simple model that will estimate risk of decompression sickness (DCS) in air dives. We develop a logistic regression model using calibration data from carefully controlled experimental dives recorded in the U.S. Navy Decompression Database. We exclude saturation dives, which can have very long decompression times. For most depths, our model's prescriptions for 2% probability of DCS avoid the experimental DCS cases without mandating excessive time at decompression stops. Our model indicates that the long decompression times prescribed by some previous probabilistic models are not necessary. Our model cannot be used operationally because it cannot calculate depths and times at decompression stops; however, there is general concurrence between our model and prescriptions of a deterministic model known as the VVal-18 Algorithm; this supports the adoption of theVVal-18 Algorithm for operational use on decompression dives.

Direct ascent from air and N2-O2 saturation dives in humans: DCS risk and evidence of a threshold.

To estimate the risk of decompression sickness (DCS) for direct ascents from depth to the sea surface for personnel who are saturated with hyperbaric nitrogen, we analyzed 586 experimental air or nitrogen-based saturation dives. No DCS occurred on shallow saturation dives between 12.0 and 20.5 feet of seawater, gauge (fswg) but incidence of DCS rose abruptly when depth was deeper than 20.5 fswg, reaching 27% at 30 fswg. This is evidence of a threshold for clinical DCS. A model based on a Hill function that provides for a threshold predicts the observations better than a model having no threshold provision; the no-threshold model overestimates risk shallower than 20.5 fswg and underestimates risk between 20.5 and 30 fswg. For situations such as submarine rescues, we recommend our threshold model when the exposure pressure is 33 fswg or less. We also discuss deeper dives where there are no human data; extrapolations can be quite different for models that provide for a threshold than for models that do not.

Probability of decompression sickness in no-stop air diving and subsaturation diving.

Probabilistic models allow estimation of the probability (Pdcs) that decompression sickness (DCS) will occur in any particular dive. Our objective is to provide Pdcs estimates for no-stop diving instructions used by the U.S. Navy and various other navies. To do so, we develop statistics-based (probabilistic) and intuition-based (deterministic) models using dive-outcome data from the U.S. Navy Decompression Database. We give special attention to subsaturation dives (defined as no-stop dives shallower than 40 fswg with bottom times between 4 hr and one day), for which experimental dives are scarce. According to our models, probability of DCS is 2% or less for current U.S. Navy no-stop air dive schedules and near 1% for the navies of Great Britain, Canada, and France; also the current U.S. Navy prescriptions for subsaturation dives seem to be appropriate. Our probabilistic models fail for deep dives; they do not avoid observed DCS cases in the calibration dataset and provide longer no-stop times than allowed by tables used operationally; we advocate prescriptions by our deterministic model for deep no-stop dives.

Stabilized bubbles in the body: pressure-radius relationships and the limits to stabilization.

We previously outlined the fundamental principles that govern behavior of stabilized bubbles, such as the microbubbles being put forward as ultrasound contrast agents. Our present goals are to develop the idea that there are limits to the stabilization and to provide a conceptual framework for comparison of bubbles stabilized by different mechanisms. Gases diffuse in or out of stabilized bubbles in a limited and reversible manner in response to changes in the environment, but strong growth influences will cause the bubbles to cross a threshold into uncontrolled growth. Also, bubbles stabilized by mechanical structures will be destroyed if outside influences bring them below a critical small size. The in vivo behavior of different kinds of stabilized bubbles can be compared by using plots of bubble radius as a function of forces that affect diffusion of gases in or out of the bubble. The two ends of the plot are the limits for unstabilized growth and destruction; these and the curve's slope predict the bubble's practical usefulness for ultrasonic imaging or O2 carriage to tissues.

Testing of hypotheses about altitude decompression sickness by statistical analyses.

This communication extends a statistical analysis of forced-descent decompression sickness at altitude in exercising subjects (J Appl Physiol 1994; 76:2726-2734) with a data subset having an additional explanatory variable, rate of ascent. The original explanatory variables for risk-function analysis were environmental pressure of the altitude, duration of exposure, and duration of pure-O2 breathing before exposure; the best fit was consistent with the idea that instantaneous risk increases linearly as altitude exposure continues. Use of the new explanatory variable improved the fit of the smaller data subset, as indicated by log likelihood. Also, with ascent rate accounted for, replacement of the term for linear accrual of instantaneous risk by a term for rise and then decay made a highly significant improvement upon the original model (log likelihood increased by 37 log units). The authors conclude that a more representative data set and removal of the variability attributable to ascent rate allowed the rise-and-decay mechanism, which is expected from theory and observations, to become manifest.

Relationship of oxygen content to PO2 for stabilized bubbles in the circulation: theory.

Stabilized bubbles can pass through capillary beds, recirculate for a few minutes or hours, and carry O2 from the lungs to the tissues. Here, we develop the theory for the O2 content-PO2 relationship of bubbles and the alterations of the bubbles that are coupled to the O2 transport. We provide examples for bubbles stabilized by a slowly permeating gas; bubbles stabilized by mechanical structures may behave similarly. Because there are two mechanisms for O2 unloading (lowering of PO2 and shrinkage), the bubbles release a large fraction of their O2 content at high PO2; when pure O2 is breathed, one-half of the content of a 3-microns-radius bubble is released before PO2 falls to 500 Torr. The possibility that stabilized bubbles could become a clinical tool for therapeutic transport of O2 raises many issues to be investigated. The highunloading PO2 offers opportunities for delivering O2 by diffusion to poorly perfused regions of the tissue but also presents a hazard of O2 toxicity to perfused tissue.

Breathing a mixture of inert gases: disproportionate diffusion into decompression bubbles.

To study the consequences of diving with gas mixtures, we simulated growth of decompression bubbles using an equation system that accounts for major determinants of bubble behavior. When breathing a mixture, bubbles are smaller than expected from linear interpolation between bubbles with either of the unmixed component gases because of disproportionate diffusion effects: a) When few bubbles form, the inert gas that permeates fastest becomes over-represented, relative to the breathing gas, inside bubbles during growth; this slows further entrance of the fast gas and enhances entrance of the slower gas. b) With N2-He mixtures and few bubbles, the over-represented gas is He in aqueous tissue, but is N2 in lipid tissue. c) When many bubbles form, the over-represented gas is the one with higher tissue solubility. Our simulations indicate that the smallest bubbles always occur with breathing of one of the component gases, but which gas that is depends on whether the tissue is lipid or aqueous and whether few or many bubbles form.

Effects of physical properties of the breathing gas on decompression-sickness bubbles.

To explore the relative dangers of different inert gases, we developed mathematical relationships concerned with bubble growth, using equations that separate gas properties from other variables. Predictions for saturation exposures were as follows. 1) Peak volume of a bubble is proportional to solubility in tissue when bubble density is high and to the 3/2 power of the ratio of the permeation coefficient to the partition coefficient when density is low. 2) Bubble duration is inversely proportional to the partition coefficient for the inert gas. 3). Sizes and durations of bubbles for one inert gas relative to another depend on whether the tissue is aqueous or lipid but are independent of the magnitude of the decompression and tissue half time. 4). He should give smaller bubbles than N2, except in aqueous tissue with low bubble density; our prediction correlates qualitatively with relative dangers observed with animals but seems to overestimate the safety afforded by He. Numerical simulations illustrate how nonsaturation dives are less predictable because more variables are involved.

Bubbles in circulating blood: stabilization and simulations of cyclic changes of size and content.

Surface tension, blood pressure, and inherent unsaturation due to O2 metabolism promote diffusion of gases out of bubbles in the bloodstream. We review the mechanisms that can overcome the absorptive tendencies so small spherical bubbles can persist. One general type of stabilizer is a mechanical structure at the gas-liquid interface that can support a negative pressure so that gases inside can be in diffusion equilibrium with their counterparts outside; one possibility for mechanical stabilizers are surfactant films. We show that a slowly permeating gas is analogous to a mechanical stabilizer; it allows equilibration of other gases inside-to-outside by diluting the gases inside. By using numerically solved equations based on physics of diffusion, we demonstrate how nonrigid stabilized bubbles change size as they move through the circulatory system. In small pulmonary vessels, the bubbles enlarge because blood pressure is low, there is no inherent unsaturation, and O2 and N2 diffuse from lung gas into the bubble; these gases diffuse out again in the systemic circulation.

Behavior of bubbles of slowly permeating gas used for ultrasonic imaging contrast.

RATIONALE AND OBJECTIVES: The authors predict behavior of blood cell-sized bubbles containing a foreign gas that slowly crosses a gas-liquid interface. Such bubbles are being developed for ultrasonic contrast. METHODS: Using appropriate coefficients for N2, O2, CO2, and foreign gases, the authors simulate diffusion between bubbles and blood with a numerically solved equation system. RESULTS: Within 30 seconds after intravenous injection of bubbles, entrance of endogenous gases more than doubles the radius. In vivo size and duration of the bubbles are quantitatively related to the amount of the foreign gas inside. Size and ultrasonic imaging effectiveness of the circulating bubbles become larger in lungs than in the rest of the circulation. As the foreign gas is lost, imaging effectiveness diminishes more rapidly than bubble radius. CONCLUSIONS: Bubbles of slowly permeating gas change size and composition after injection and also during their passage through different parts of the circulation.

Simulation of gas bubbles in hypobaric decompressions: roles of O2, CO2, and H2O.

UNLABELLED: To gain insight into the special features of bubbles that may form in aviators and astronauts, we simulated the growth and decay of bubbles in two hypobaric decompressions and a hyperbaric one, all with the same tissue ratio (TR), where TR is defined as tissue PN2 before decompression divided by barometric pressure after. We used an equation system which is solved by numerical methods and accounts for simultaneous diffusion of any number of gases as well as other major determinants of bubble growth and absorption. We also considered two extremes of the number of bubbles which form per unit of tissue. RESULTS: A) Because physiological mechanisms keep the partial pressures of the "metabolic" gases (O2, CO2, and H2O) nearly constant over a range of hypobaric pressures, their fractions in bubbles are inversely proportional to pressure and their large volumes at low pressure add to bubble size. B) In addition, the large fractions facilitate the entry of N2 into bubbles, and when bubble density is low, enhance an autocatalytic feedback on bubble growth due to increasing surface area. C) The TR is not closely related to bubble size; that is when two different decompressions have the same TR, metabolic gases cause bubbles to grow larger at lower hypobaric pressures. We conclude that the constancy of partial pressures of metabolic gases, unimportant in hyperbaric decompressions, affects bubble size in hypobaric decompressions in inverse relation to the exposure pressure.

Oxygen transport to tissue by persistent bubbles: theory and simulations.

Persistent gas bubbles able to traverse capillaries can be prepared from a slowly permeating gas or with a mechanical structure surrounding a gas phase. If they are permeable to gases, such bubbles will carry O2 from the lungs to the tissues via the blood stream. Using a mathematical model based on physical laws, we present simulations of the behavior of bubbles stabilized by a slowly permeating gas (gas X). We show that the bubble persists longer if the tissue and venous blood contain N2 to dilute gas X and slow its outward diffusion. A 6-microns -diam bubble carries 0.11 pl of O2 during the breathing of pure O2, so 4.6 x 10(8) bubbles/ml in the blood will supply a normal arteriovenous difference. In conditions used for hyperbaric O2 therapy, a bubble carries approximately 0.26 pl of O2. Stabilized bubbles have the potential to transport O2 efficiently; they release O2 to tissue at high PO2 and require injection of only small amounts of a foreign substance.

Probabilistic model of altitude decompression sickness based on mechanistic premises.

To develop a predictive equation and to test ideas about the mechanisms involved in hypobaric decompression sickness, we performed statistical analyses on published results of 7,023 exercising O2-breathing men subjected to one-step decompressions in altitude chambers. The dependent variable was signs or symptoms so severe that the person's trial was terminated (forced descent). The three independent variables were 1) duration of 100% O2 breathing at ground level (prebreathing), 2) atmospheric pressure after ascent, and 3) exposure duration. The best model, chosen from trial-and-error combinations of premises about bubble behavior, indicates that decompression sickness outcome depends on 1) prebreathing time, but with an unexpectedly long washout half time for N2; 2) time at altitude, as if bubbles grow; and 3) the estimated difference, raised to the fifth power, between the partial pressure of N2 in tissue before and that in bubbles after decompression, perhaps an index of the number of bubbles generated. We expect the model to provide accurate predictions for decompressions matching those of the bulk of the data; the mechanistic cues should be considered hypotheses for further investigation.

Simulation of exchanges of multiple gases in bubbles in the body.

This communication introduces a system of equations, for numerical solution, which simulates the generation, growth, and decay of bubbles. The system is an advance over previous works because it allows for simultaneous diffusion of any number of gases. Our purpose for developing the system is to gain insight into the bubbles that occur in the body in decompression sickness (DCS). We validate the calculation system by matching observed data of DCS bubbles and of large subcutaneous gas pockets in rats. We demonstrate how a temporary supersaturation and bubble formation can occur without change of ambient pressure when there is a change in the inert gas being breathed. With exposures to hypobaric environments, such as when astronauts work in space, simulations show that O2, CO2, and water vapor add appreciably to volume of bubbles and affect the diffusion of inert gas.

Density of decompression bubbles and competition for gas among bubbles, tissue, and blood.

We used numerical solutions of a system of equations to simulate gas exchanges of bubbles after a decompression, with particular attention to the effect of number of bubble formation sites per unit of tissue. If many bubbles grow, they deplete the excess dissolved gas in the tissue. The consequences are as follows: 1) the many individual bubbles do not become as large as they would if fewer were competing for gas; 2) more gas is evolved when there are many sites; 3) the bubbles are absorbed sooner than the bigger bubbles that grow with few sites; 4) after diffusion into many bubbles causes N2 partial pressure in the tissue to fall immediately to a low level, N2 partial pressure in the tissue and the exiting blood remain "clamped" to this low level because dissolved N2 removed by blood is replenished by diffusion out of the bubbles; and 5) as long as many bubbles persist, the long-term removal of inert gas from the total system (tissue plus bubbles) follows a straight-line time course rather than an exponential course.

The oxygen window and decompression bubbles: estimates and significance.

The "oxygen window" causes a partial pressure difference of inert gas between the inside and outside of decompression bubbles. Estimates of Po2 and Pco2 in tissue are necessary for O2 window calculations and any calculations about growth or decay of decompression sickness bubbles, but the estimates involve many uncertainties. Using simplifying assumptions, we estimated the O2 window over a broad range of environments for tissues having a wide range of O2 extractions. The results were as follows: a) the window increases with ambient pressure, but levels off at very high pressure; b) the window is only 1 or 2 kPa for air breathing at extreme altitudes, and 200 kPa or more in hyperbaric environments; c) when O2 is breathed instead of air, the window is as much as 50 times larger at altitude but only about 10 times larger in hyperbaric environments; d) changes in bubble size due to the window decrease as barometric pressure increases; and e) there are seven additional factors which may supplement or oppose the action of the oxygen window.

Failure of the straight-line DCS boundary when extrapolated to the hypobaric realm.

The lowest pressure (P2) to which a diver can ascend without developing decompression sickness (DCS) after becoming equilibrated at some higher pressure (P1) is described by a straight line with a negative y-intercept. We tested whether extrapolation of such a line also predicts safe decompression to altitude. We substituted tissue nitrogen pressure (P1N2) calculated for a compartment with a 360-min half-time for P1 values; this allows data from hypobaric exposures to be plotted on a P2 vs. P1N2 graph, even if the subject breathes oxygen before ascent. In literature sources, we found 40 reports of human exposures in hypobaric chambers that fell in the region of a P2 vs. P1N2 plot where the extrapolation from hyperbaric data predicted that the decompression should be free of DCS. Of 4,576 exposures, 785 persons suffered decompression sickness (17%), indicating that extrapolation of the diver line to altitude is not valid. Over the pressure range spanned by human hypobaric exposures and hyperbaric air exposures, the best separation between no DCS and DCS on a P2 vs. P1N2 plot seems to be a curve which approximates a straight line in the hyperbaric region but bends toward the origin in the hypobaric region.