SOME DECOMPRESSION DILEMMAS

B.R. Wienke
Applied Theoretical Physics Division
Los Alamos National Laboratory
Los Alamos, N.M. 87545

"Introduction"
Biophysical models of inert gas transport and bubble formation all try to prevent decompression sickness. Developed over years of diving application, they differ on a number of basic issues, still mostly unresolved today:

1. the rate limiting process for inert gas exchange, blood flow rate (perfusion) or gas transfer rate across tissue (diffusion);
2. composition and location of critical tissues (bends sites);
3. the mechanistics of phase inception and separation (bubble formation and growth);
4. the critical trigger point best delimiting the onset of symptoms (dissolved gas buildup in tissues, volume of separated gas, number of bubbles per unit tissue volume, bubble growth rate to name a few);
5. the nature of the critical insult causing bends (nerve deformation, arterial blockage or occlusion, blood chemistry or density changes).

Such issues confront every modeler and table designer, perplexing and ambiguous in their correlations with experiment and nagging in their persistence. And here comments are confined just to Type I (limb) and II (central nervous system) bends, to say nothing of other types and factors. These concerns translate into a number of what decompression modelers call dilemmas that limit or qualify their best efforts to describe decompression phenomena. Ultimately, such concerns work their way into table and meter algorithms, with the same caveats. A closer look at these issues is illuminating. .uh "Perfusion And Diffusion" Perfusion and diffusion are two mechanisms by which inert and metabolic gases exchange between tissue and blood. Perfusion denotes the blood flow rate in simplest terms, while diffusion refers to the gas penetration rate in tissue, or across tissue-blood boundaries. Each mechanism has a characteristic rate constant for the process. The smallest rate constant limits the gas exchange process. When diffusion rate constants are smaller than perfusion rate constants, diffusion dominates the tissue-blood gas exchange process, and vice-versa. In the body, both processes play a role in real exchange process, especially considering the diversity of tissues and their geometries. The usual Haldane tissue half-lives are the inverses of perfusion rates, while the diffusivity of water, thought to make up the bulk of tissue, is a measure of the diffusion rate.

Clearly in the past, model distinctions were made on the basis of perfusion or diffusion limited gas exchange. The distinction is somewhat artificial, especially in light of recent analyses of coupled perfusion-diffusion gas transport by Hills and Hennessy, recovering limiting features of the exchange process in appropriate limits. The distinction is still of interest today, however, since perfusion and diffusion limited algorithms are used in mutually exclusive fashion in diving. The obvious mathematical rigors of a full blown perfusion-diffusion treatment of gas exchange mitigate against table and meter implementation, where model simplicity is a necessity. So one or another limiting models is adopted, with inertia and track record sustaining use. Certainly Haldane models fall into that categorization. Still, within the context of just perfusion or diffusion limited gas exchange, a number of interesting anomalies arise, discussed by Kety and Schmidt, Hills, Tepper and Lightfoot, Roughton, and Hempleman.

In multitissue (Haldane) models, a nagging question of interpretation of a spectrum of half-lives and critical tensions arises. If the hypothetical compartments represent local differences in circulation within the same anatomical tissue, they should have the same critical tension, as originally proposed by Haldane. But, if they represent different anatomical identities, then the same insult to to different tissues should produce different clinical signs and manifestations, yet, the same set of symptoms occurs independent of the compartment affected. Some would argue that it is better to introduce critical tensions as variables depending on depth, time, temperature, and so on, while holding them independent of half-life. In single tissue models, of course, this happens de facto.

While the spectrum of half-lives in perfusion models is reasonable from the perspective of inert gas washout times, diffusion coefficients assigned to model calculations, or extracted from data fits, are more ambiguous. In calculational models, gas diffusivities in tissue are five orders of magnitude smaller than in water, comprising the bulk of tissue matter. Typical water diffusivities are on the order of 10 sup -5 ~cm sup 2 ~sec sup -1 , while model tissue values are near 10 sup -10 cm sup 2 ~ sec sup -1 . In critical sites, anomalously reduced diffusion might be ascribed to geometry of the site, or composition of the tissue. Hills suggested cellular effects, while Hempleman was concerned about avascularity, both implying longer diffusion time scales.

Such questions, of course, suffer from the same problem common to other vital issues, namely identification of the critical tissue and site. Another way to look at the question of perfusion-versus-diffusion might be through the bounce data for different breathing mixtures. In bounce diving, selection of helium or nitrogen as the inert gas is a trade between the lower solubility of helium, less than nitrogen by a factor of 3-5, and the greater diffusivity, about 2.7 times greater than nitrogen by Graham's law. For long exposure times, solubility factors dominate and helium is a better breathing gas than nitrogen. The solubility advantage should also hold up for short exposures if gas exchange is perfusion limited, while if diffusion is rate limiting, the 2.7 diffusion advantage of helium might be expected to outdistance its 3-5 solubility advantage over nitrogen, and so air (nitrogen) would be better for bounce diving. Goat experiments clearly show that nitrogen is better for bounce exposures of less than 20 minutes duration, that is, longer nonstop time limits compared to helium. The implication is then simple, namely that some gas uptake in critical tissues is diffusion limited.

But the controversy does not end there. An obvious way to differentiate between blood perfusion and diffusion is to measure the time it takes for inert gas to diffuse into tissue. Kety and Roughton measured this transit time, and found that the mean extravascular tension attained 95-99% of the blood tension in 1-5 seconds. This is so very rapid that diffusion cannot play a rate limiting role, that is, values smaller than water diffusivities are precluded.

"Bubble Sites"
We do not really know where bubbles form nor lodge, their migration patterns, their birth and dissolution mechanisms, nor the exact chain of physico-chemical insults resulting in decompression sickness. Many possibilities exist, differing in the nature of the insult, the location, and the manifestation of symptoms. Bubbles might form directly (de novo) in supersaturated sites upon decompression, or possibly grow from preformed, existing seed nuclei excited by compression-decompression. Leaving their birth sites, bubbles may move to critical sites elsewhere. Or stuck at their birth sites, bubbles may grow locally to pain-provoking size. They might dissolve locally by gaseous diffusion to surrounding tissue or blood, or passing through screening filters, such as the lung complex, they might be broken down into smaller aggregates, or eliminated completely. Whatever the bubble history, it presently escapes complete elucidation.

Bubbles may hypothetically form in the blood (intravascular) or outside the blood (extravascular). Once formed, intravascularly or extravascularly, a number of critical insults are possible. Intravascular bubbles may stop in closed circulatory vessels and induce ischemia, blood sludging, chemistry degradations, or mechanical nerve deformation. Circulating gas emboli may occlude the arterial flow, clog the pulmonary filters, or leave the circulation to lodge in tissue sites as extravasular bubbles. Extravascular bubbles may remain locally in tissue sites, assimilating gas by diffusion from adjacent supersaturated tissue and growing until a nerve ending is deformed beyond its pain threshold. Or, extravascular bubbles might enter the arterial or venous flows, at which point they become intravascular bubbles.

Spontaneous bubble formation in fluids usually requires large decompressions, like hundreds of atmospheres, somewhere near fluid tensile limits. Many feel that such circumstance precludes direct bubble formation in blood following decompression. Explosive, or very rapid decompression, of course is a different case. But, while many doubt that bubbles form in the blood directly, intravascular bubbles have been seen in both the arterial and venous circulation, with vastly greater numbers detected in venous flows (venous gas emboli). Ischemia resulting from bubbles caught in the arterial network has long been implied as a cause of decompression sickness. Since the lungs are effective filters of venous bubbles, arterial bubbles would then most likely originate in the arteries or adjacent tissue beds. The more numerous venous bubbles, however, are suspected to first form in lipid tissues draining the veins. Lipid tissue sites also possess very few nerve endings, possibly masking critical insults. Veins, thinner than arteries, appear more susceptible to extravascular gas penetration.

Extravascular bubbles may form in aqueous (watery) or lipid (fatty) tissues in principle. For all but extreme or explosive decompression, bubbles are seldom observed in heart, liver, and skeletal muscle. Most gas is seen in fatty tissue, not unusual considering the five-fold higher solubility of nitrogen in lipid tissue versus aqueous tissue. Since fatty tissue has few nerve endings, tissue deformation by bubbles is unlikely to cause pain locally. On the other hand, formations or large volumes of extravascular gas could induce vascular hemorrhage, depositing both fat and bubbles into the circulation as noted in animal experiments. If mechanical pressure on nerves is a prime candidate for critical insult, then tissues with high concentrations of nerve endings are candidate structures, whether tendon or spinal cord. While such tissues are usually aqueous, they are invested with lipid cells whose propensity reflects total body fat. High nerve density and some lipid content supporting bubble formation and growth would appear a conducive environment for a mechanical insult.

On the question of preformed nuclei, their presence in human tissue and blood has not been demonstrated. The existence of preformed nuclei in serum and egg albumin has been reported by Yount and Strauss. Since performed nuclei are found virtually in every aqueous substance known, their preclusion from the body would come as a surprise to many. Hence, while most regard nucleation as a random process, its occurrence in tissue seems highly probable, seen for instance in the studies of Evans, Walder, Strauss, Yount, Kunkle, and co-workers. Model correlations with incidence statistics of decompression sickness in salmon, rats, and humans speak favorably for the nucleation concept. .uh "Computational Algorithms And Complexity" The establishment and evolution of gas phases, and possible bubble trouble, involves a number of distinct, yet overlapping, steps:

1. nucleation and stabilization (free phase inception);
2. supersaturation (dissolved gas buildup);
3. excitation and growth (free-dissolved phase interaction);
4. coalescence (bubble aggregation);
5. deformation and occlusion (tissue damage and ischemia).

Over the years, much attention has focused on supersaturation. Recent studies have shed much light on nucleation, excitation and bubble growth, even though in vitro. bubble aggregation, tissue damage, ischemia, and the whole question of decompression sickness trigger points are difficult to quantify in any model, and remain obscure. Complete elucidation of the interplay is presently asking too much. Yet, the development and implementation of better computational models is necessary to address problems raised in workshops, reports, publications, disclaimers, and as a means to safer diving.

The computational issues of bubble dynamics (formation, growth, and elimination) are mostly outside the traditional framework, but get folded into half-life specifications in a nontractable mode. The very slow tissue compartments (half-lives large, or diffusivities small) might be tracking both free and dissolved gas exchange in poorly perfused regions. Free and dissolved phases, however, do not behave the same way under decompression. Care must be exercised in applying model equations to each component. In the presence of increasing proportions of free phases, dissolved gas equations cannot track either species accurately.

Computational algorithms tracking both dissolved and free phases offer broader perspectives and expeditious alternatives, but with some changes from classical schemes. Free and dissolved gas dynamics differ. The driving force (gradient) for free phase elimination increases with depth, directly opposite to the dissolved phase elimination gradient which decreases with depth. Then, changes in operational procedures become necessary for optimality. Considerations of growth and growth invariably require deeper staging procedures than supersaturation methods. Though not as dramatic, similar constraints remain operative in multiexposures, that is, multilevel, repetitive, and multiday diving.

Other issues concerning time sequencing of symptoms impact computational algorithms. That bubble formation is a predisposing condition for decompression sickness is universally accepted. However, formation mechanisms and their ultimate physiological effect are two related, yet distinct, issues. On this point, most hypotheses makes little distinction between bubble formation and the onset of bends symptoms. Yet we know that silent bubbles have been detected in subjects not suffering from decompression sickness. So it would thus appear that bubble formation, per se, and bends symptoms do not map onto each other in a one-to-one manner. Other factors are truly operative, such as the amount of gas dumped from solution, the size of nucleation sites receiving the gas, permissible bubble growth rates, deformation of surrounding tissue medium, and coalescence mechanisms for small bubbles into large aggregates, to name a few. These issues are the pervue of bubble theories, but the complexity of mechanisms addressed does not lend itself easily to table, nor even meter, implementation.

The ultimate computational algorithm, coupling nucleation, dissolved gas uptake and elimination, bubble growth and collisional coalescence, and critical sites, would be very, very complicated, requiring supercomputers (like CRAYs, CYBERs, VPs, CONVEXs, and ESSEXs, or their massively parallel cousins, CMs, NCUBESs, IWARPs, and DAPs) for three dimensional modeling. Stochastic Monte Carlo methods and sampling techniques exist which could generate and stabilize nuclei from thermodynamic functions, such as the Gibbs or Helmholtz free energy, transport dissolved gas in flowing blood to appropriate sites, inflate, deflate, move, and collide bubbles and nuclei, and then tally statistics on tensions, bubble size and number, inflation and coalescence rate, free phase volume, and any other meaningful parameter, all in necessary geometries. Such type simulations of similarly complicated problems last for 16-32 hours at the Los Alamos and Livermore National Laboratories, on lightning fast supercomputers with near gigaflop speed (10 sup 9 floating point operations per second). While decompression meters have revolutionized diving and decompression calculations, it will be some time before the ultimate computational algorithm fits into a wrist computer. .uh "Slow Tissue Compartments" Based on concerns in multiday and heavy repetitive diving, with the hope of controlling staircasing gas buildup in exposures through critical tensions, slow tissue compartments (half-lives greater than 80 minutes) have been incorporated into some algorithms. Calculations, however, show that virtually impossible exposures are required of the diver before critical tensions are even approached, literally tens of hours of near continuous activity. As noted in many calculations, slow compartment cannot really control multidiving through critical tensions, unless critical tensions are reduced to absurd levels, inconsistent with nonstop time limits for shallow exposures. That is a model limitation, not necessarily a physical reality. The physical reality is that bubbles in slow tissues are eliminated over time scales of days, and the model limitation is that the arbitrary parameter space does not accommodate such phenomena.

And that is no surprise either, when one considers that dissolved gas models are not suppose to track bubbles and free phases. Repetitive exposures do provide fresh dissolved gas for excited nuclei and growing free phases, but it is not the dissolved gas which is the problem just by itself. When bubble growth is considered, the slow compartments appear very important, because, therein, growing free phases are mostly left undisturbed insofar as surrounding tissue tensions are concerned. Bubbles grow more gradually in slow compartments because the gradient there is typically small, yet grow over longer time scales. When coupled to free phase dynamics, slow compartments are necessary in multidiving calculations.

For additional perspective, it should be noted that slow compartments have always been important in decompression and saturation diving, and flying-after-diving protocols. It is not clear now to what extent slow compartments are important to multidiving. As testing continues, that should become clearer in the near future. But, based on inert gas washout experiments, some physiologists suggest that tissue compartments with half-lives near 720 minutes are to be found in bone, and possibly other sites. And bubbles have been found in subjects as long as three days after diving exposures. So, caution is the signal and models insensitive to slow compartments are limited at best.

In using tables and meters without slow compartments, care must be exercised to dive only within their recommended ranges. For sport diving activities, this usually implies nominal bounce and a few shallow repetitive exposures separated by an hour or more surface interval. Multi-day activities cannot be controlled through fixed critical tensions in compartments as slow as 6 hours anyway, and a suggestion is to take a day off after 3 days of light repetitive diving. Even more study and testing are necessary in cases of heavy multidiving.

"Venous Gas Emboli"
Sound reflected off a moving boundary undergoes a shift in acoustical frequency, the so-called Doppler shift. The shift is directly proportional to the speed of the moving surface (component in the direction of sound propagation) and the acoustical frequency of the wave, and inversely proportional to the sound speed. Acoustical signals in the megahertz range (10 sup 6 cycles per second), termed ultrasound, have been directed at moving blood in the pulmonary arteries, where blood flow rates are the highest (near 20 cm/sec) due to confluence of the systemic circulation, with resulting Doppler shifts, in the form of audible chirps, snaps, whistles, and pops, noted and recorded. Sounds heard in divers have been ascribed to venous gas emboli (VGE), and in vitro (gels) simulations and evaluations have established minimum bubble detection size as a function of blood velocity. Coalesced lipids, platelet aggregates, and agglutinated red blood cells formed during decompression also pass through the pulmonary circulation, but are less reflective than bubbles, and usually smaller. Bubbles with radii in the 20 micron (10 sup -6  m) range represent a cutoff for Doppler detection for signals of a few megahertz.

Ultrasonic techniques for monitoring moving gas emboli in the pulmonary circulation are popular today. Silent bubbles, as applied to the venous gas emboli detected in sheep undergoing bends-free USN table decompression by Spencer and Campbell, were a first indication that asymptomatic free phases were present in blood, even under bounce loadings. Similar results were reported by Walder and Evans. After observing and contrasting venous gas emboli counts for various nonstop exposures at depth, Spencer suggested that nonstop limits be reduced below the USN table limits. Enforcing a 20% drop in venous gas emboli counts compared to the USN limits, corresponding nonstop limits are roughly 15% shorter.

While the numbers of venous gas emboli detected with ultrasound Doppler techniques can be correlated with nonstop limits, and the limits then used to fine tune the critical tension matrix for select exposure ranges, fundamental issues are not necessarily resolved by venous gas emboli measurements. First of all, venous gas emboli are probably not the direct cause of bends per se, unless they block the pulmonary circulation, or pass through the pulmonary traps and enter the arterial system to lodge in critical sites. Intravascular bubbles might first form at extravascular sites. According to Hills, electron micrographs have highlighted bubbles breaking into capillary walls from adjacent lipid tissue beds in mice. Fatty tissue, draining the veins and possessing few nerve endings, is thought to be an extravascular site of venous gas emboli. Similarly, since blood constitutes no more than 8% of the total body capacity for dissolved gas, the bulk of circulating blood does not account for the amount of gas detected as venous gas emboli. Secondly, what has not been established is the link between venous gas emboli, possible micronuclei, and bubbles in critical tissues. Any such correlations of venous gas emboli with tissue micronuclei would unquestionably require considerable first-hand knowledge of nuclei size distributions, sites, and tissue thermodynamic properties. While some believe that venous gas emboli correlate with bubbles in extravascular sites, such as tendons and ligaments, and that venous gas emboli measurements can be reliably applied to bounce diving, the correlations with repetitive and saturation diving have not been made to work, nor important correlations with more severe forms of decompression sickness, such as chokes and central nervous system (CNS) hits.

Still, whatever the origin of venous gas emboli, procedures and protocols which reduce gas phases in the venous circulation deserve attention, for that matter, anywhere else in the body. The moving Doppler bubble may not be the bends bubble, but perhaps the difference may only be the present site. The propensity of venous gas emboli may reflect the state of critical tissues where decompression sickness does occur. Studies and tests based on Doppler detection of venous gas emboli are still the only viable means of monitoring free phases in the body.

"Phase Constraints And Multi-Diving"
Concerns with multidiving can be addressed through variable critical gradients, or equivalently tissue tensions, in bubble models. While variable gradients or tensions are difficult to codify in table frameworks, they are easy to implement in digital meters. Reductions in critical parameters result from what is called the phase volume constraint, a constraint employing the separated volume of gas in tissue as trigger point for the bends, not dissolved gas buildup alone in tissue compartments. The phase volume is proportional to the product of the dissolved-free gas gradient times a bubble number representing the number of gas nuclei excited into growth by the compression-decompression. And it replaces just slow tissue compartments in controlling multidiving.

In considering bubbles and free-dissolved gradients within critical phase hypotheses, repetitive criteria develop which require reductions in Haldane critical tensions or dissolved-free gas gradients. This reduction simply arises from lessened degree of bubble elimination over repetitive intervals, compared to long bounce intervals, and need to reduce bubble inflation rate through smaller driving gradients. Deep repetitive and spike exposures feel the greatest effects of gradient reduction, but shallower multiday activities are impacted. Bounce diving enjoys long surface intervals to eliminate bubbles while repetitive diving must contend with shorter intervals, and hypothetically reduced time for bubble elimination. Theoretically, a reduction in the bubble inflation driving term, namely, the tissue gradient or tension, holds the inflation rate down. Overall, concern is bubble excess driven by dissolved gas. And then both bubbles and dissolved gas are important. In such an approach, multidiving exposures experience reduced permissible tensions through lessened free phase elimination over time spans of two days. Parameters are consistent with bubble experiments, and both slow and fast tissue compartments must be considered.

"Adaptation"
Divers and caisson workers have long contended that tolerance to decompression sickness increases with daily diving, and decreases after a few weeks layoff. Paton and Walder, Golding and Griffiths have confirmed such suggestions, pointing out that in large groups of compressed air workers, new workers were at higher risk than those who were exposed to high pressure regularly. This acclimatization might result from either increased body tolerance to bubbles (physiological adaptation), or decreased number and volume of bubbles (physical adaptation). Walder advocated physical adaptation, resulting from systematic destruction or reduction in gas micronuclei, from which bubbles grow. Kunkle and Beckman monitored venous gas emboli in the pulmonary arteries of dogs, noting that the number of total emboli counted decreased as the repetitive frequency increased, but that the same bubble number precipitated decompression sickness in all cases. Repetitve spacings were on the order of a day or two in the experiments, and results are clearly consistent with physical adaptation.

"Acclimatization And Repetitive Exposures"
Yet, there is slight inconsistency here. Statistics point to slightly higher bends incidence in repetitive and multiday diving. Some hyperbaric specialists confirm the same, based on experience. The situation is not clear, but the resolution plausibly links to the kinds of first dives made and repetitive frequency in the sequence. If the first in a series of repetitive dives are kept short, deep, and conservative with respect to nonstop time limits, initial excitation and growth are minimized. Subsequent dives would witness minimal levels of initial phases. If surface intervals are also long enough to optimize both free and dissolved gas elimination, any nuclei excited into growth could be efficiently eliminated outside repetitive exposures, with adapatation occurring over day intervals as noted in experiments. But higher frequency, repetitive and multiday loading may not afford sufficient surface intervals to eliminate free phases excited by earlier exposures, with additional nuclei then possibly excited on top of existing phases. Physical adaptation seems less likely, and decompression sickness more likely, in the latter case. Daily regimens of a single bounce dive with slightly increasing exposure times are consistent with physical adaptation, and conservative practices. The regimens also require deepest dives first. In short, acclimatization is as much a question of eliminating any free phases formed as it it a question of crushing or reducing nuclei as potential bubbles in repetitive exposures. And then time scales on the order of a day might limit the adapatation process.

"Conservative Protocols"
Conclusions of adaptation experiments underscore reductions in physical disposition to bubble formation, seen in venous gas emboli counts, and not increases in physiological tolerance to bubbles. Acclimatization is principally a physical process, relating to free phases in the body. If bubbles grow from preformed, stable miconuclei that are destroyed when gross bubbles are excited, then controlled and conservative repetitive diving could reduce, by attrition, numbers of such bubble micronuclei. But, as discussed above, the important adjectives here are controlled and conservative.

Conservative repetitive protocols, recently proposed are consistent with such reasoning, as are bubble models employing growth and elimination time constants on the same time scale. Previous tables for humans were based upon unsupported assumptions because many of the underlying processes by which dissolved gas is liberated from blood and tissues were poorly understood. Some of those assumptions, as enumerated by Hills, Yount, and Wienke are known to be wrong. Recent developments in bubble nucleation models, linked to experiments, have made it possible to calculate diving tables from established principles. Both flexibilty and range of applicability are impressive, and they recover dissolved gas models in the proper limits. Bubble models more naturally incorporate protocols suggested for repetitive diving, speaking well for the models. These protocols include:

1. safety stops in the l0-20 foot zone for a few minutes;

2. ascent rates limited by 60 ft/min;

3. restricted repetitive and multiday exposures for deeper dives;

4. reduced nonstop time limits;

5. deeper-to-shallower repetitive schedules.

In terms of the above protocols, acclimatization becomes qualified within a regimen of reduced nonstop limits, slow ascent rates, safety stops, and most importantly, shallower-than-previous and low frequency repetitive activity. Outside of such framework, adaptation appears less favorably disposed. Certainly, more controlled study of multidiving diving and associated statistics is necessary to answer these questions conclusively. There is a paucity of repetitive and multiday data now, but that will probably change in time.

"References"

Boycott A.E., Damant G.C.C., and Haldane J.S., 1908, "The Prevention Of Compressed-Air Illness", J. Hyg. 8, 342-443.

Buhlmann A.A., 1984, "Decompresssion/Decompression Sickness", Berlin: Springer-Verlag. .np

Krogh A., 1918, "The Rate Of Invasion Of Gases Through Animal Tissue, With Some Remarks On The Coefficient Of Invasion", J. Physiol. 52, 391.

Hempleman H.V., 1957, "Further Basic Facts On Decompression Sickness", Investigation Into The Decompression Tables, Medical Research Council Report, UPS 168, London.

Kety S.S. and Schmidt C.F., 1945, "The Determination Of Cerebral Blood Flow In Man By Use Of Nitrous Oxide In Low Concentrations", Amer. J. Physiol. 143, 53-56.

Kety S.S., 1951, "The Theory And Applications Of The Exchange Of Inert Gases At The Lungs And Tissues", Pharm. Rev. 3, 1-41.

Tepper R.S., Lightfoot E.N., Baz A., and Lanphier E.H., 1979, "Inert Gas Transport In The Microcirculation: Risk Of Isobaric Supersaturation", J. Appl. Physiol. 46, 1157-1163.

Hennessy T.R., 1974, "The Interaction Of Diffusion And Perfusion In Homogeneous Tissue", Bull. Math. Biol. 36, 505-527.

Wienke B.R., 1987, "Computational Decompression Models", Int. J. Bio-Med. Comp. 21, 205-221.

Wienke B.R., 1986, "DECOMP: Computational Package For Nitrogen Transport Modeling In Tissues", Comp. Phys. Comm. 40, 327-336.

Spencer M.P. and Campbell S.D., 1968, "The Development Of Bubbles In The Venous And Arterial Blood During Hyperbaric Decompression", Bull. Mason

Cli. 22, 26-32.

Spencer M.P., 1976, "Decompression Limits For Compressed Air Determined By Ultrasonically Detected Blood Bubbles", J. Appl. Physiol. 40, 229-235

Bennett P.B. and Elliot D.H., 1969, "The Physiology And Medicine Of Diving And Compressed Air Work", London: Bailliere Tindall And Cassell.

Hills B.A., 1977, "Decompression Sickness", New York: John Wiley And Sons Inc. .np

Yount D.E. and Strauss R.H., 1976, "Bubble Formation In Gelatin: A Model For

Decompression Sickness", J. Appl. Phys. 47, 5081-5089.

Hennessy T.R. and Hempleman H.V., 1977, "An Examination Of The Critical Released Gas Concept In Decompression Sickness", Proc. Royal Soc. London B197, 299-313.

Wienke B.R., 1989, "Tissue Gas Exchange Models And Decompression Computations: A Review", Undersea Biomed. Res. 16, 53-89.

Wienke B.R. and Hills B.A., 1989, "Bubbles And Bends And Bio-Transport", New York: Marcel Dekker Inc.

Yount D.E. and Hoffman D.C., 1986, On The Use Of A Bubble Formation Model To Calculate Diving Tables", Aviat. Space Environ. Med. 57, 149-156.

Lang M.A. and Hamilton R.W., 1989, "Proceedings Of The American Academy Of Underwater Sciences Dive

Computer Workshop", University Of Southern California Sea Grant Publication, USCSG-TR-01-89, Los Angeles.

Vann R.D., Dovenbarger J., Wachholz C., and Bennett P.B., 1989, "Decompression Sickness In Dive Computer And Table Use", DAN Newsletter 3-6.

Sheffield P.J., 1990, "Flying After Diving", Undersea And Hyperbaric Medical Society Publication 77 (FLYDIV), Bethesda.

Yount D.E. and Strauss R.H., 1976, "Bubble Formation In Gelatin: A Model For Decompression Sickness", J. Appl. Phys. 47, 5081-5089.

Epstein P.S. and Plesset M.S., 1950, "On The Stability Of Gas Bubbles In Liquid-Gas Solutions", J. Chm. Phys. 18, 1505-1509.

Bateman J.B. and Lang J., 1945, "Formation And Growth Of Bubbles In Aqueous Solutions", Canad. J. Res. E23, 22-31.

Buckles R.G., 1968, "The Physics Of Bubble Formation And Growth", Aerospace Med. 39, 1062-1069.

Kunkle T.D. and Beckman E.L., 1983, "Bubble Dissolution Physics And The Treatment Of Decompression Sickness", Med. Phys. 10, 184-190.

Wienke B.R., 1990, "Modeling Dissolved And Free Phase Gas Dynamics Under Decompression", Int. J. Bio-Med. Comp. 25, 193-205.

Strauss R.H., 1974, "Bubble Formation In Gelatin: Implications For Prevention Of Decompression Sickness", Undersea Biomed. Res. 1, 169-174.

Farm F.P., Hayashi E.M., and Beckman E.L., 1986, "Diving And Decompression Sickness Treatment Practices Among Hawaii's Diving Fisherman", University of Hawaii

Sea Grant Report, UNIHI-SEAGRANT-TP-86-01, Honolulu.

Lang M.A. and Egstrom G.H., 1990, "Proceedings Of The American Academy Of Underwater Sciences Biomechanics Of Safe Ascents Workshop" American Academy Of Underwater Sciences Diving Safety Publication, AAUSDSP-BSA-01-90, Costa Mesa.

Evans A. and Walder D.N., 1969, "Significance Of Gas Macronuclei In The Aetiology Of Decompression Sickness", Nature London 222, 251-252.

Walder D.N., 1968, "Adaptation To Decompression Sickness In Caisson Work", Biometeor. 11, 350-359.

Pilmanis A.A., 1976, "Intravenous Gas Emboli In Man After Compressed Air Ocean Diving", Office Of Naval Research Contract Report, N00014-67-A-0269-0026, Washington,

D.C.

Vann R.D. and Clark H.G., 1975, "Bubble Growth And Mechanical Properties Of

Tissue In Decompression", Undersea Biomed. Res. 2, 185-194.

Powell R.P.and Rogers R.E., 1989, "Doppler Ultrasound Monitoring Of Gas Phase Formation And Resolution In Repetitive Diving", Undersea Biomed. Res. 16, 69.

Rogers R.E. and Powell M.R., 1989, "Controlled Hyperbaric Chamber Tests Of Multi-Day Repetitive Dives", Undersea Biomed. Res. 16, 68.

Walder D.N., Evans A., and Hempleman H.V., 1968, "Ultrasonic Monitoring Of Decompression", Lancet. 1, 897-898.

Paton W.D.M. and Walder D.N., 1954, "Compressed Air Illness", Medical Research Council Report, HMSO 281, London.

Golding F.C., Griffiths P.D., Paton W.D.M., Walder D.N., and Hempleman H.V., 1960, "Decompression Sickness During Construction Of The Dartford Tunnel",

Brit. J. Ind. Med. 17, 167-180.

Roughton F.J.W., 1952, "Diffusion And Chemical Reaction Velocity In Cylindrical And Spherical Systems Of Physiological Interest", Proc. Royal Soc. B140, 203-221.

Bruce Wienke is a Section Head For Computational Physics in the Applied Theoretical Physics Division

of the Los Alamos National Laboratory, located in New Mexico, with interests

in computational decompression and models, gas transport, and phase mechanics. He is an Instructor Trainer with the National Association Of Underwater Instructors (NAUI), serving on the Decompression Review Board, a Master Instructor with the Professional Association Of Diving Instructors (PADI), serving on the Instructor Review Committee, and an Institute Director with the YMCA. He also works as a ski racing coach and instructor, functioning as clinician with the United States Ski Coaches Association (USSCA) and the Professional Ski Instructors of America (PSIA). Bruce received a BS in physics and mathematics form Northern Michigan University, an MS in nuclear from Marquette University, and a PhD in particle physics from Northwestern University. He is a fellow of the American Physical Society, a technical committee member of the American Nuclear Society and the Society Of Industrial And Applied Mathematics, and a member of the Undersea And Hyperbaric Medical Society and the American Academy Of Underwater Sciences. He has just completed two diving monographs, High Altitude Diving and Basic Decompression Theory And Application, which will be released by the publishers shortly.