## Decompression Models and Phase Mechanics by B.R. Wienke

.Decompression Models and Phase Mechanics by B.R. Wienke Advanced Computing Laboratory Los Alamos National Laboratory Los Alamos, N.M. 87545

**INTRODUCTION**

Modeling of decompression pheneomena in the human body is, at times, more of an art form than a science. Some take the view that deterministic modeling can only be fortuitous. technological advance, elucidation of competing mechanisms, and resolution of model issues over the past 80 years has not been rapid. Model applications tend to be ad hoc, tied to data fits, and difficult to quantify on first principles. Almost any description of decompression processes in tissue and blood can be disputed, and turned around on itself. The fact the decompression takes place in metabolic and perfused matter makes it difficult to design and analyze experiments outside living matter. Yet, for application to safe diving, we need models to build tables and meters. And deterministic models, not discounting shortcomings, are the subject of this discourse.

**MODERN DIVING**

A concensus of opinions, and for a variety of reasons, suggests that modern diving began in the early 1960s. Technological achievements, laboratory programs, military priorities, safety concerns, commercial diving requirements, and international business spurred diving activity and scope of operation. Diving bells, hot water heating, mixed gases, saturation, deep diving, expanded wet testing, computers, and efficient decompression algorithms signaled the modern diving era. Equipment advances in open and closed circuit breathing devices, wet and dry suits, gear weight, mask and fin design, high pressure compressors, flotation and buoyancy control vests, communications links, gauges and meters, lights, underwater tools (cutting, welding, drilling, explosives), surface supplied air, and photographic systems paced technological advances. Training and certification requirements for divers, in military, commercial, sport, and scientific sectors, took definition with growing concern for underwater safety and well being. In the conquest and exploration of the oceans, saturation diving gained prominence in the 1960s, permitting exploitation of the continental shelf impossible with the short exposure times allowed by conventional diving. Spurred by both industrial and military interests in the ability of men to work underwater for long periods of time, notable habitat experiments, such as Sealab, Conshelf, Man In Sea, Gulf Task, Tektite, and Diogene, demonstrated the feasibility of living and working underwater for long periods of time. These efforts followed proof of principle validation, by Bond and coworkers (USN) in 1958, of saturation diving. Saturation exposure programs and tests have been conducted from 35 fsw to 2,000 fsw.

The development and use of underwater support platforms, such as habitats, bell diving systems, lockout and free flooded submersibles, and diver propulsion units also accelerated in the 1960s and 1970s, for reasons of science and economics. Support platforms extended both diver usefulness and bottom time, by permitting him to live underwater, reducing descent and ascent time, expanding mobility, and lessing physical activity. Today, themselves operating from underwater platforms, remotely operated vehicles (ROVs) scan the ocean depths at 6,000 fsw for minerals and oil.

Around 1972, strategies for diving in excess of 1,000 fsw received serious scrutiny, driven by a commercial quest for oil and petroleum products, and the needs of the commercial diving industry to service that quest. Questions concerning pharmacological additives, absolute pressure limits, thermal exchange, therapy, compression-decompression procedures, effective combinations of mixed breathing gases, and equipment functionality addressed many fundamental issues, unknown or only partially understood. By the early 1980s, it became clear that open sea water work in the 1,000 to 2,000 fsw range was entirely practical, and many of the problems, at least from an operational point of view, could be solved. Today, the need for continued deep diving remains, with demands that cannot be answered with remote, or 1 atm, diver systems. Heliox and trimix have become standards for deep excursion breathing gases, with heliox the choice for shallower exposures, and trimix the choice for deeper exposures in the field.

Yet, despite tremendous advances in deep diving technology, most of the ocean floor is outside human reach. Breathing mixtures that are compressible are limiting. Breathing mixtures that are not compressible offer interesting alternatives. In the 1960s, serious attention was given to liquid breathing mixtures, physiological saline solutions. Acting as inert respiratory gas diluents, oxygenated fluids have been used as breathing mixtures, thereby eliminating decompression requirements. Some synthetic fluids, such as

**Models**

Most believe that the pathophysiology of decompression sickness syndrome follows formation of a gas phase after decompression. Yet, the physiological evolution of the gas phase is poorly understood. Bubble detection technology has established that moving and stationary bubbles do occur following decompression, that the risk of decompression sickness increases with the magnitude of detected bubbles, that symptomless, or silent, bubbles are also common following decompression, and that the variability in gas phase formation is likely less than the variability in symptom generation. Taken together, gas phase formation is not only important to the understanding of decompression sickness, but is also a crucial model element in theory and computation.

Bubbles can form in tissue and blood when ambient pressure drops below tissue tensions, according to dissolved-free phase mechanics. Trying to track free and dissolved gas buildup and elimination in tissue and blood, especially their interplay, is extremely complex, beyond the capabilities of even supercomputers. But safe computational prescriptions are necessary in the formulation of dive tables and digital meter algorithms. The simplest way to stage decompression, following extended exposures to high pressure with commensurate dissolved gas buildup, is to limit tissue tensions. Historically, Haldane first employed the approach, and it persists today in modified form.

**History**

Tables and schedules for diving at sea level can be traced to a model proposed in 1908 by the eminent English physiologist, John Scott Haldane. He observed that goats, saturated to depths of 165 feet of sea water (fsw), did not develop decompression sickness (DCS) if subsequent decompression was limited limited to half the ambient pressure. Extrapolating to humans, researchers reckoned that tissues tolerate elevated dissolved gas pressures (tensions), greater than ambient by factors of two, before the onset of symptoms. Haldane then constructed schedules which limited the critical supersaturation ratio to two in hypothetical tissue compartments. Tissue compartments were characterized by their halftime, tau . Halftime is also termed halflife when linked to exponential processes, such as radioactive decay. Five compartments (5, 10, 20, 40, 75 minutes) were employed in decompression calculations and staged procedures for fifty years. Some years following, in performing deep diving and expanding existing table ranges in the 1930s, US Navy investigators assigned separate limiting tensions (M-values) to each tissue compartment. Later in the 1950s and early 1960s, other US Navy investigators, in addressing repetitive exposures for the first time, advocated the use of six tissues (5, 10, 20, 40, 80, 120 minutes) in constructing decompression schedules, with each tissue compartment again possessing its own limiting tension. Temporal uptake and elimination of inert gas was based on mechanics addressing only the macroscopic aspects of gas exchange between blood and tissue. Exact bubble production mechanisms, interplay of free and dissolved gas phases, and related transport phenomena were not quantified, since they were neither known nor understood. Today, we know much more about dissolved and free phase dynamics, bubbles, and transport mechanisms, but still rely heavily on the Haldane model. Inertia and simplicity tend to sustain its popularity and use, and it has been a workhorse.

To maximize the rate of uptake or elimination of dissolved gases, the gradient, simply the difference between arterial and tissue tension, is maximized by pulling the diver as close to the surface as possible. Exposures are limited by requiring that the tissue tensions, never exceed limits (called M-values), for instance, written for each compartment in the US Navy approach (5, 10, 20, 40, 80, and 120 minute tissue halftimes, tau , as M = M sub 0 + DELTA M d, with, M sub 0 = 152.7 tau sup -1/4 , and, DELTA M = 3.25 tau sup -1/4 , as a function of depth, d, for DELTA M the change per unit depth. Obviously, M, is largest for fast tissue compartments ( tau small), and smallest for slow tissue compartments ( tau large). Fast compartments control short deep excursions, while slow compartments control long shallow excursions. Surfacing values, M sub 0 , are principal concerns in nonstop diving, while values at depth, DELTA M d , concern decompression diving. In both cases, the staging regimen tries to pull the diver as close to the surface as possible, in as short a time as possible. By contrast, free phase (bubble) elimination gradients, as seen, increase with depth, directly opposite to dissolved gas elimination gradients which decrease with depth. In actuality, decompression is a playoff between dissolved gas buildup and free phase growth, tempered by body ability to eliminate both. But dissolved gas models cannot handle both, so there are problems when extrapolating outside tested ranges.

In absolute pressure units, the corresponding critical gradient, G = Q – P, is related to ambient pressure, P, and critical nitrogen pressure, M, with, Q = 1.27 M. In bubble theories, supersaturation is limited by the critical gradient, G. In decompressed gel experiments, Strauss suggested that G approx 20 fsw at ambient pressures less than a few atmospheres. Other studies suggest, 14 <= G <=”30″ fsw, as a range of critical gradients (G-values). In diffusion-dominated approaches, the tissue tension can be limited by a single, pressure criterion, such as, M=”709″ P / P + 404 .

Blood rich, well-perfused, aqueous tissues are usually thought to be fast (small tau ), while blood poor, scarcely-perfused, lipid tissues are thought to be slow (large tau ), though the spectrum of halftimes is not correlated with actual perfusion rates in critical tissues. As reflected in relationship above, critical parameters are obviously larger for faster tissues. The range of variation with compartment and depth is not insignificant. Fast compartments control short deep exposures, while slow compartments control long shallow, decompression, and saturation exposures.

**Bulk Diffusion Model**

Diffusion limited gas exchange is modeled in time by a sum of exponential response functions, bounded by arterial and initial tissue tensions. However, instead of many tissue compartments, a single bulk tissue is assumed for calculations, characterized by a gas diffusion constant, D. Tissue is separated into intravascular (blood) and extravascular (cells) regions. Blood containing dissolved inert and metabolic gases passes through the intravascular zone, providing initial and boundary conditions for subsequent gas diffusion into the extravascular zone. Diffusion is driven by the difference between arterial and tissue tensions, according to the strength of a single diffusion coefficient, D, appropriate to the media. Diffusion solutions, averaged over the tissue domain, resemble a weighted sum over effective tissue compartments with time constants, alpha sub 2n-1 sup 2 D, determined by diffusivity and boundary conditions, with alpha sub 2n-1 = (2n – 1) pi / l for tissue thickness, l.

Applications fit the time constant, K = pi sup 2 D / l sup 2 , to exposure data, with a typical value employed by the Royal Navy given by, K = 0.007928 min sup -1 , approximating the US Navy 120 minute compartment used to control saturation, decompression, and repetitive diving. Corresponding critical tensions in the bulk model, M = 709 P / P + 404 , fall somewhere between fixed gradient and multitissue values. At the surface, M = 53 fsw, while at 200 fsw, M = 259 fsw. A critical gradient, G = P ( 493 – P ) / ( P + 404 ), also derives from the above. Originally, a critical gradient, G, near 30 fsw was used to limit exposures. Such value is too conservative for deep and bounce exposures, and not conservative enough for shallow exposures. Hempleman introduced the above relationship, providing the means to parameterize bounce and saturation diving.

Bulk models are attractive because they permit the whole dive profile to be modeled with one equation, and because they predict a t sup 1/2 behavior of gas uptake and elimination. Nonstop time limits, t sub n , are related to depth, d, by the bulk diffusion relationship, d t sub n sup 1/2 = C, with approximate range, 400 <= C <=”500″ fsw min sup 1/2 , linking nonstop time and depth simply through the value of C. For the US Navy nonstop limits, C approx 500 fsw min sup 1/2 , while for the Spencer reduced limits, C approx 465 fsw min sup 1/2 . In the Wienke-Yount model, C approx 400 fsw min sup 1/2 .

**Multitissue Model**

Multitissue models, variations of the original Haldane model, assume that dissolved gas exchange, controlled by blood flow across regions of varying concentration, is driven by the local gradient, that is, the difference between the arterial blood tension and the instantaneous tissue tension. Tissue response is modeled by exponential functions, bounded by arterial and initial tensions, and perfusion constants, lambda , linked to the tissue halftimes, tau , for instance, 1, 2, 5, 10, 20, 40, 80, 120, 180, 240, 360, 480, and 720 minute compartments assumed to be independent of pressure.

In a series of dives or multiple stages, initial and arterial tensions represent extremes for each stage, or more precisely, the initial tension and the arterial tension at the beginning of the next stage. Stages are treated sequentially, with finishing tensions at one step representing initial tensions for the next step, and so on. To maximize the rate of uptake or elimination of dissolved gases the gradient, simply the difference between arterial and tissue tensions is maximized by pulling the diver as close to the surface as possible. Exposures are limited by requiring that the tissue tensions never exceed M = M sub 0 + DELTA M d, as a function of depth, d, for DELTA M the change per unit depth. A set of M sub 0 and DELTA M are listed in Table 1.

At altitude, some critical tensions have been correlated with actual testing, in which case, an effective depth, d = P – 33, is referenced to the absolute pressure, P, with surface pressure, P sub h = 33 exp ( -0.0381 h ), at elevation, h, and h in multiples of 1,000 ft. However, in those cases where critical tensions have not been tested, nor extended, to altitude, an exponentially decreasing extrapolation scheme, called similarity, has been employed. Extrapolations of critical tensions, below P = 33 fsw, then fall off more rapidly then in the linear case. A similarity extrapolation holds the ratio, R = M/P, constant at altitude. Estimating minimum surface tension pressure of bubbles near 10 fsw, as a limit point, the similarity extrapolation might be limited to 10,000 ft in elevation, and neither for decompression nor heavy repetitive diving.

Models of dissolved gas transport and coupled bubble formation are not complete, and all need correlation with experiment and wet testing. Extensions of basic (perfusion and diffusion) models can redress some of the difficulties and deficiencies, both in theory and application. Concerns about microbubbles in the blood impacting gas elimination, geometry of the tissue region with respect to gas exchange, penetration depths for gas diffusion, nerve deformation trigger points for pain, gas uptake and elimination asymmetry, effective gas exchange with flowing blood, and perfusion versus diffusion limited gas exchange, to name but a few, motivate a number of extensions of dissolved gas models.

The multitissue model addresses dissolved gas transport with saturation gradients driving the elimination. In the presence of free phases, free-dissolved and free-blood elimination gradients can compete with dissolved-blood gradients. One suggestion is that the gradient be split into two weighted parts, the free- blood and dissolved-blood gradients, with the weighting fraction proportional to the amount of separated gas per unit tissue volume. Use of a split gradient is consistent with multiphase flow partitioning, and implies that only a portion of tissue gas has separated, with the remainder dissolved. Such a split representation can replace any of the gradient terms in tissue response functions.

If gas nuclei are entrained in the circulatory system, blood perfusion rates are effectively lowered, an impairment with impact on all gas exchange processes. This suggests a possible lengthening of tissue halftimes for elimination over those for uptake, for instance, a 10 minute compartment for uptake becomes a 12 minute compartment on elimination. Such lengthening procedure and the split elimination gradient obviously render gas uptake and elimination processes asymmetric. Instead of both exponential uptake and elimination, exponential uptake and linear elimination response functions can be used. Such modifications can again be employed in any perfusion model easily, and tuned to the data.

**Thermodynamic Model**

The thermodynamic approach suggested by Hills, and extended by others, is more comprehensive than earlier models, addressing a number of issues simultaneously, such as tissue gas exchange, phase separation, and phase volume trigger points. This model is based on phase equilibration of dissolved and separated gas phases, with temporal uptake and elimination of inert gas controlled by perfusion and diffusion. From a boundary (vascular) zone of thickness, a, gases diffuse into the cellular region. Radial, one dimensional, cylindrical geometry is assumed as a starting point, though the extension to higher dimensionality is straightforward. As with all dissolved gas transfer, diffusion is controlled by the difference between the instantaneous tissue tension and the venous tension, and perfusion is controlled by the difference beween the arterial and venous tension. A mass balance for gas flow at the vascular cellular interface, a, enforces the perfusion limit when appropriate, linking the diffusion and perfusion equations directly. Blood and tissue tensions are joined in a complex feedback loop. The trigger point in the thermodynamic model is the separated phase volume, related to a set of mechanical pain thresholds for fluid injected into connective tissue.

The full thermodynamic model is complex, though Hills has performed massive computations correlating with the data, underscoring basic model validity. One of its more significant features can be seen in Figure 3. Considerations of free phase dynamics (phase volume trigger point) require deeper decompression staging formats, compared to considerations of critical tensions, and are characteristic of phase models. Full blown bubble models require the same, simply to minimize bubble excitation and growth.

**Reduced Gradient Bubble Model**

The reduced gradient bubble model (RGBM), developed by Wienke, treats both dissolved and free phase transfer mechanisms, postulating the existence of gas seeds (micronuclei) with permeable skins of surface active molecules, small enough to remain in solution and strong enough to resist collapse. The model is based upon laboratory studies of bubble growth and nucleation, and grew from a similar model, the varying permeability model (VPM), treating bubble seeds as gas micropockets contained by pressure permeable elastic skins

Inert gas exchange is driven by the local gradient, the difference between the arterial blood tension and the instantaneous tissue tension. Compartments with 1, 2, 5, 10, 20, 40, 80, 120, 240, 480, and 720 halftimes, tau , are again employed. While, classical (Haldane) models limit exposures by requiring that the tissue tensions never exceed the critical tensions, fitted to the US Navy nonstop limits, for example. The reduced gradient bubble model, however, limits the supersaturation gradient, through the phase volume constraint. An exponential distribution of bubble seeds, falling off with increasing bubble size is assumed to be excited into growth by compression-decompression. A critical radius, r sub c , separates growing from contracting micronuclei for given ambient pressure, P sub c . At sea level, P sub c = 33 fsw , r sub c = .8 microns, and DELTA P = d. Deeper decompressions excite smaller, more stable, nuclei.

Within a phase volume constraint for exposures, a set of nonstop limits, t sub n , at depth, d, satisfy a modified law, d t sub n sup 1/2 = 400 fsw min sup 1/2 , with gradient, G, extracted for each compartment, tau , using the nonstop limits and excitation radius, at generalized depth, d = P – 33 fsw. Tables 2 and 3 summarize t sub n , G sub 0 , DELTA G , and delta , the depth at which the compartment begins to control exposures.

Table 2.

Critical Phase Volume Time Limits.

______________________________________________

depth nonstop limit depth nonstop limit

d(fsw) t sub n (min) d (fsw) t sub n (min)

30 250 130 9.

40 130. 140 8.

50 73. 150 7.

60 52. 1606 5

70 39. 1705 8

80 27. 1805 3

90 22. 1904 6

100 18. 2004 1

110 15. 2103 7

120 12. 2203 1

Gas filled crevices can also facilitate nucleation by cavitation. The mechanism is responsible for bubble formation occuring on solid surfaces and container walls. In gel experiments, though, solid particles and ragged surfaces were seldom seen, suggesting other nucleation mechanisms. The existence of stable gas nuclei is paradoxical. Gas bubbles larger than 1 micron should float to the surafce of a standing liquid or gel, while smaller ones should dissolve in a few seconds. In a liquid supersaturated with gas, only bubbles at the critical radius, r sub c , would be in equilibrium (and very unstable equilibrium at best). Bubbles larger than the critical radius should grow larger, and bubbles smaller than the critical radius should collapse. Yet, the Yount gel experiments confirm the existence of stable gas phases, so no matter what the mechanism, effective surface tension must be zero.

Table 3.

Critical Phase Volume Gradients.

__________________________________________________________________________

halftime threshold depth surface gradient gradient change

tau (min) delta (fsw) G sub 0 (fsw) DELTA G

________________________ ____________ ____________

2 190 151.0 .518

5 135 95.0 .515

10 95 67.0 .511

20 65 49.0 .506

40 40 36.0 .468

80 30 27.0 .417

120 28 24.0 .379

Although the actual size distribution of gas nuclei in humans is unknown, these experiments in gels have been correlated with a decaying exponential (radial) distribution function. For a stabilized distribution accommodated by the body at fixed pressure, P sub c , the excess number of nuclei excited by compression-decompression must be removed from the body. The rate at which gas inflates in tissue depends upon both the excess bubble number, and the supersaturation gradient, G. The critical volume hypothesis requires that the integral of the product of the two must always remain less than some volume limit point, alpha V , with alpha a proportionality constant. A conservative set of bounce gradients, G bar , can be also be extracted for multiday and repetitive diving, provided they are multiplicatively reduced by a set of bubble factors, eta sup rep, eta sup reg , eta sup exc , all less than one, such that G bar = eta sup rep eta sup reg eta sup exc G.

These three bubble factors reduce the driving gradients to maintain the phases volume constraint. The first bubble factor reduces G to account for creation of new stabilized micronuclei over time scales of days. The second factor accounts for additional micronuclei excitation on deeper-than-previous dives. The third bubble factor accounts for bubble growth over repetitive exposures on time scales of hours. Clearly, the repetitive factors, eta sup rep , relax to one after about 2 hours, while the multiday factors, eta sup reg , continue to decrease with increasing repetitive activity, though at very slow rate. Increases in bubble elimination halftime and nuclei regeneration halftime will tend to decrease eta sup rep and increase eta sup reg . The repetitive fractions, eta sup rep , restrict back to back repetitive activity considerably for short surface intervals. The multiday fractions get small as multiday activities increase continuously beyond 2 weeks. Deeper-than-previous excursions incur the greatest reductions in permissible gradients (smallest eta sup exc ) as the depth of the exposure exceeds previous maximum depth.

**Tissue Bubble Diffusion Model**

The tissue bubble diffusion model (TBDM), according to Gernhardt and Vann, considers the diffusive growth of an extravascular bubble under arbitrary hyperbaric and hypobaric loadings. The approach incorporates inert gas diffusion across the tissue-bubble interface, tissue elasticity, gas solubility and diffusivity, bubble surface tension, and perfusion limited transport to the tissues. Tracking bubble growth over a range of exposures, the model can be extended to oxygen breathing and inert gas switching. As a starting point, the TBDM assumes that, through some process, stable gas nuclei form in the tissues during decompression, and subsequently tracks bubble growth with dynamical equations. Diffusion limited exchange is invoked at the tissue-bubble interface, and perfusion limited exchange is assumed between tissue and blood, very similar to the thermodynamic model, but with free phase mechanics. Across the extravascular region, gas exchange is driven by the pressure difference between dissolved gas in tissue and free gas in the bubble, treating the free gas as ideal. Initial nuclei in the TBDM have assumed radii near 3 microns at sea level, to be compared with .8 microns in the RGBM.

As in any free phase model, bubble volume changes become more significant at lower ambient pressure, suggesting a mechanism for enhancement of hypobaric bends, where constricting surface tension pressures are smaller than those encountered in hyperbaric cases. For instance, a theoretical bubble dose of 5 ml correlates with a 20% risk of decompression sickness, while a 35 ml dose correlates with a 90% risk, with the bubble dose representing an unnormalized measure of the separated phase volume. Coupling bubble volume to risk represents yet another extension of the phase volume hypothesis, a viable trigger point mechanism for bends incidence.

SATURATION CURVE

The saturation curve, relating permissible gas tension, Q, as a function of ambient pressure, P, for air, sets a lower bound, so to speak, on decompression staging. All staging models and algorithms must collapse to the saturation curve as exposure times increase in duration. In short, the saturation curve represents one extreme for any staging model. Bounce curves represent the other extreme. Joining them together for diving activities in between is a model task, as well as joining the same sets of curves over varying ambient pressure ranges. In the latter case, extending bounce and saturation curves to altitude is just such an endeavor.

Models for controlling hypobaric and hyperbaric exposures have long differed over range of applicability. Recent analyses of very high altitude washout data question linear extrapolations of the hyperbaric saturation curve, to hypobaric exposures, pointing instead to correlation of data with constant decompression ratios in animals and humans. Correlations of hypobaric and hyperbaric data, however, can be effected with a more general form of the saturation curve, one exhibiting the proper behavior in both limits. Closure of hypobaric and hyperbaric diving data can be managed with one curve, exhibiting linear behavior in the hyperbaric regime, and bending through the origin in the hypobaric regime. Using the RGBM and a basic experimental fact that the number of bubble seeds in tissue increase exponentially with decreasing bubble radius, just such a single expression can be obtained. The limiting forms are exponential decrease with decreasing ambient pressure (actually through zero pressure), and linear behavior with increasing ambient pressure. Asymptotic forms are quite evident. Such general forms derive from the RGBM, depending on a coupled treatment of both dissolved and free gas phases. Coupled to the phase volume constraint, these models suggest a consistent means to closure of hypobaric and hyperbaric data.

**Abyss incorporates RGBM**

Dr. Bruce Wienke, Director of the Computation Testbed for Industry, Advanced Computing Laboratory at Los Alamos National Laboratory, and the creator of the RGBM (Reduced Gradient Bubble Model) has joined the Abysmal Diving team. Dr. Wienke will be assisting us in the implementation of his latest decompression model into Abyss.

This means that Abyss will be the first and only product in the world with a fully operational Bubble Mechanics model.

1. This will allow Abyss to more effectively handle Technical Repetitive decompression diving!!!(not a small issue in itself!!)

2. Dives in which the following dive is deeper than the first. (a real potential problem area).

3. This will also allow Abyss to run active tracking, in real time, of actual bubble growth based upon his published and proprietary unpublished research.

**RGBM/ABYSS Implementation**

The Reduced Gradient Bubble Model (RGBM) is a dual phase (dissolved and free gas) algorithm for diving calculations. Incorporating and coupling historical Haldaniean dissolved gas transport with bubble excitation and growth, the RGBM extends the range of computational applicability of traditional methods. The RGBM is correlated with diving and exposure data on more complete physical principles. Much is new in the RGBM algorithm, and troublesome multidiving profiles with higher incidence of DCS are a target here. Some highlighted extensions for the ABYSS implementation of the Buhlmann basic algorithm include:

1. Standard Buhlmainiann nonstop time limits;

2. Restricted repetitive exposures, particularly beyond 100 ft, based on reduction in permissible bubble diffusion gradients within 2 hr time spans;

3. Restricted yo-yo and spike (multiple ascents and descents) dives based on excitation of new bubble seeds;

4. Restricted deeper-than-previous divers based on excitation of very small bubble seeds over 2 hr time spans:

5. Restricted multiday diving based on adaptation and regrowth of new bubble seeds;

6. Smooth coalescence of bounce and saturation limit points using 32 tissue compartments;

7. Consistent treatment of altitude diving, with proper zero point extrapolation of limiting tensions and permissible bubble gradients (through zero as pressure approaches zero);

8. Algorithm linked to diving data (tests), Doppler bubble, and laboratory micronuclei experiments;

9. Overall, parameters in RGBM/ABYSS are conservative, but flexible and easy to change or fit to new data.

**What’s in store for the future?**

Quoting from Dr. Bruce Wienke…”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 such as CRAYS or their massively parallel cousins CMs for three dimensional modeling. Stochastic Monte Carlo methods and sampling techniques exist which could generate and stabilize nuclei from the thermodynamic functions, such as 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 geometrics.”

Such types of simulations of similarly complicated problems last for 16-32 hours at the Los Alimos Laboratories, on lightning fast supercomputers with near Gigaflop speed (1billion floating point operations per second)

DECOMPRESSION MODELS AND PHASE MECHANICS

B.R. Wienke

Advanced Computing Laboratory

Los Alamos National Laboratory

Los Alamos, N.M. 87545