Article from COMEX Scientific Director on rebreathers, decompression and Penny Glover

RAL

Thank you sir for the time & effort you have put in to these posts.

Regards RAL

__________________
The sea does not care about you.

SFM

Here's some tentative answers for some of the questions on this thread:

"Where does he get his information on Penny & Jacques?"
He's the top decompression expert in the country where the deaths occured, he likely has been contacted as part of the formal inquiry and his company was mandated for the search.


"Its a very interesting piece but if you research the deaths there have been on CCR there are very few related to long deep exposure dives. Most have been shallow limited or no deco dives so is this really relevant?"
1) How many trimix CCR divers in the general world population today? A few hundreds? A couple thousands? I'm feeling very generous, so let's say 3000. Dr Gardette mentions 30 deaths. That's a 1% mortality rate and its a very conservative estimate. To offer a striking comparison point, it's much higher than the casualty rate of coalition troops in Iraq.
But let's just say we don't have enough data yet for the statistics to be significant. In that case, what could be more relevant than the informed opinion of one of the top civilian experts on decompression (who is likely aware of many more accidents and their circumstances than we are)?
2) Part of what he says (think like a pro) is relevant for all CCR divers, trimix or not, IMHO.


"I went way beyond the recommended limits/know people who did it/I am (they) are still alive with no accidents."
"Am I the only one who read the article and thought my profile should have killed me too?"
That's very good news. It means you and your acquaintances are very professional (and maybe somewhat lucky, who knows?). Hopefully the article will help you enhance your professionalism and alleviate even more the risks you take. That would be very good news too, wouldn't it?


"Literally there would be extremely bent people everywhere based on the sort of dives being done out there."
Actually no, at least not yet. But on this trend in a few years, no doubt it will happen (I'll spare you the computation). Today, it's a very small population of very good divers. But with democratization...


"With regard to the main article, I feel (but this is just a feeling nothing more)the Comex data is based on task loaded divers working hard at depth. The data is relevant in some ways but I don't feel it compares with the sort of dive we generally do."
Unfortunately today the choice is between their data (maybe there are other validated tables out there) or unvalidated tables with a very high and unspecified theoretical risk.


"Comex is like every other professional diving company they have total control of their divers on umbilical with coms this is fine for commercial diving but impractical in the type of diving we do."
That's funny. You perfectly inverted his reasoning which is that if you don't have professional means, don't dive at professional depths.


"Thank you sir for the time & effort you have put into these posts."
I wish my daily work would be as rewarding as this. Not only do I have the feeling I may have saved a few lives (how presomptuous... but very gratifying), but hopefully I honored the memory of a great lady. Now that I'm done, thank you for reading my prose!



Enjoy your dives!

MHD

A little bit of education for you

People don't get bent descending,

people don't get bent on the bottom

people don't get bent on the initial phase of ascent(although the damage can be done here)

And a lot of the Rebreather deaths in the 30 he mentions occurred in those phases, ie the deco schedule played no role. So the implied impact of deco schedules on the death rates in RBs is grossely overstated. It really is a red herring in relation to ths rest of his subsequent discussion of the short coming of commerically available deco profiles

While I thank for bringing this to at least my attention, it is a very thought provoking article, please, don't think you are an expert based on reading one piece of paper. There are more sides to this story than you think. I'll leave you with a quote from the article so you can ponder what the qentleman's true objective was in giving this interview

BG

divetheworld

Sorry, but I havnt heard any comments that reflect an understanding of the different approaches to decompression.
The crux of the article was that the Haldanian models (presume Buhlman) are not adequate for saturation exposures at depth. The use of tissue compartments which are individually calculated is different to the tissue gas exchange model that the French are using.
This is where it all gets a bit woolly for me. The haldane models are all very similar and validate each other. The mathamatical models are relatively easy to follow, but the MT92 tables are not so for me. I found some anecdotal notes which piqued my interest when I was researching for use of other gases, but any further information was difficult to surface.
So I am hoping that the conversation rolls slowly towards the differences and of what benefit we can draw from those models.
It's not enough to have the table, its understanding the theory behind it and I am of the opinion that there is something to learn here.

Brent.

__________________

Drmike

When I look at the people who I have know that died on Rbs none died during deco or as a result of deco.

When I look at the MANY near death experiences I have had they were all my fault, me screwing up, breaking rules, and had nothing generally to do with the rebreather (could have happened on OC) and certainly nothing to do with deco.

I agree we dont know enough about deco. I dont agree with the hypothesis that Rebreather divers are dieing due to deco.

__________________
Cave diving is a sport
Wreck diving is a sport
Diving in general is a sport

'Rebreather diving' is not a sport
its the delusional obsession with a highly dangerous and often inappropriate piece of equipment

Drmike

I am trying to understand the post.

Its always been my understanding that we knew a lot about saturation diving (commercial) deco requirements but knew little about bounce (sports) diving deco.

I had assumed traditional deco algos had better validation against saturation dives than 'bounce' dives

If I understand this guy what hes saying is newer deco models such as VPM/RGBM etc are less suitable for longer deeper dives that are more like saturation dives.

If that is what hes saying I would tend to say that it wouldnt surprise me if it was true seeing as these models were developed and more in use more for sport bounce diving.

When I looked at a deco model for our 200m dive I compared the deco profile as given by VPMBE/RGBM to that given by traditional models and in all cases the shallow stops were considerably longer. I note that since its inception VPMB has evolved with increasingly longer shallow stops to something now which more refelcts the traditional algos.....


Some very interesting reading with comparison with Comex/vpm etc here :-

Attached Images

Assessing dive profile safety using a combined decompression model V1_6.pdf (249.2 KB, 112 views)

__________________
Cave diving is a sport
Wreck diving is a sport
Diving in general is a sport

'Rebreather diving' is not a sport
its the delusional obsession with a highly dangerous and often inappropriate piece of equipment

divetheworld

Your right, its hard to get your head round what he is saying and he drops in a lot of exagerated comparisons. There is basis in fact of what he is saying from what I can understand.
There are two distinct decompression groups based on different methodologies. I dont think the MT92 models are as far different as he suggests.

While I read the ME article you posted, here is something else of interest which seems to relate a great deal with the article - Complete copy/paste below.

Brent.

Article by JP Imbert - Divetech, France
Our decompression tradition is based on the principles set by Haldane in 1908 (1). The classic or "Haldanian" models used for the calculation of present military, commercial and recreational diving tables all have the same mathematical expression: a) they figure inert gas exchanges with a series of exponential compartments, b) they specify the safe ascent criteria as a linear relation between the ambient pressure and the maximum permitted compartment tension. As a consequence, these models have produced similar decompression profiles, characterized by a rapid initial ascent on a relatively high distance. However, the drive for table development is operational pressure. Aside these traditional tables, marginal diver communities have empirically developed original decompression procedures for their needs. Refreshing experiences come from technical and cave divers who keep pushing their explorations supported by a new Internet culture. Surprising procedures come from coral or shell divers who keep diving deeper and deeper to make their livings. Apparently, all share the same strategy and use slower rates of ascent and deeper stops than would be predicted by the Haldanian models (2). An attempt is made to introduce new assumptions in the present models to obtain the typical profile of these successful decompressions.

Identifying the risk of decompression
The safety performances of decompression tables can be first defined in terms of the risk of decompression sickness (DCS) occurrence per dive exposure (3). This risk was difficult to assess until the development of diving databases in the 80's provided the volume of information required for the statistical analysis (4,5,6). DCS symptoms include a wide span of problems ranging from skin rash to articular pain and neurological symptoms which for operational reasons have for long been classified into two categories, Type I DCS and Type II DCS, according to the US Navy Diving Manual. Thus, the risk can further be defined in terms of symptoms.

Type I DCS includes simple symptoms like skin rash, articular or muscle pain. Because the symptoms are obvious, they are reported early and the treatment is initiated without hesitation. In most cases, administration of hyperbaric oxygen at 12m will rapidly resolve the symptoms. Safety wise, a Type I DCS is a "good" decompression accident because the diagnosis is easy, the onset is usually rapid, the treatment is applied rapidly, and the symptoms are treated efficiently in 95 % of the cases (7).

Type II DCS is always serious because it affects either the respiratory or the neurological systems. The symptoms which often include fatigue, headache or feeling unwell are vague and the diagnosis may be difficult at an early stage or for mild cases. The treatment is complex and requires a deep recompression, significant periods of hyperbaric oxygen breathing, fluid intake and sometimes steroids administration (7). Safety wise, a Type II DCS is a "bad" decompression accident because the diagnosis may not be easy, the treatment is often delayed, and the consequences can be dramatic.

It is interesting to note that in an earlier time, medical doctors tended to distinct more types of DCS symptoms. In the 1974 edition of the Comex Medical Book, Dr. X Fructus differentiated between vestibular hits and other neurological symptoms. At the time, he suspected that different dive profiles yield to different neurological symptoms. This came after he developed some early bounce decompression tables, called the "Cx70" tables, that were designed both for heliox surface supplied and bell diving.

The Cx70 tables were intensively used in the early North Sea developments before saturation diving finally took over bounce diving. The analysis of the safety records of the Cx70 tables (unpublished) stored in the Comex Data Base (8) showed that the risk was uneven over the exposures. The long bottom times (90 to 120 minutes) tended to induce Type I DCS in the last part of the decompression, which follows the logic of large amounts of dissolved gas to be eliminated. The intermediate bottom times (30 to 60 minutes) preferably produced neurological symptoms, either central or spinal, a common outcome with heliox bounce diving. Surprisingly, short bottom times (10 to 30 minutes) exclusively produced vestibular symptoms. Typical of their time, the Cx70 tables were characterized by a high distance between the bottom and the first stop and a rapid initial ascent. This was particularly significant for short bottom times. For instance, a particular concern was the 66m/20min table with a first stop at 12m, leading to an initial ascent of 54m done in 3 minutes (18m/min). The safety analysis of these early deep bounce tables already indicated that the dive profile controls the bubble scenario and decides on the safety outcome of the decompression and the initial phase was slowed down in the later revisions of the tables.

The lesson learnt after the Cx70 tables is that the main risk for technical divers, who usually dive 15 to 20 minutes bottom time, is a vestibular hit. It is already a serious accident when symptoms occur at the surface, with strong nausea and vertigo. As technical diving gets deeper, it will become dramatic the day the symptoms occur in the water. With bell diving, such accidents were kept under control: the diver was recompressed in the bell or the chamber and put on mask. Unfortunately, if a technical diver got bent in the water, he would not be able to take any therapeutic action, and when trying to ascend, would likely vomit in his regulator: a critical situation. Because of the threat of symptoms occurring in the water, technical divers must use very safe tables.

Strategies for successful decompressions
Divers have known the criticality of the initial ascent in decompression for long. In fact, each divers group has generated its own strategy to increase their decompression safety. The very first adaptation is the reduction of the ascent rate. In commercial diving, most of the diving supervisors admitted they used slower rates of ascent than the 60 ft/min recommendation of the US Navy. The French Navy reduced the ascent rate from 18 to 12 m/min in the 1990 revision of their air tables.

Another common modification is the introduction of a deep stop. One of the earlier accounts I heard came from two old divers who worked for red coral in the 50's. They told they used to stop at mid-depth during their ascent from deep dives and sang a gospel. They added with a smile that of course they would adapt the number of verses to how comfortable they felt with the decompression. Obviously these two old timers knew things I ignore for I have never been able to neither imagine how physically feels the decompression stress nor conceive any physiological mechanism for it. Deep stops appeared in the early edition of the Royal Navy diving manual. The manual included a set of deep air tables to 90 meters, the particularity of which was the presence of a mid-depth decompression stop (up to now, I have been unable to identify who introduced such stops and for what reasons). Deep stops were later advertised by Richard Pyle in articles published in the "AquaCorps" and "Deep Tech" magazines (2) and supported by other influent authors (9). Today's, deep stops are so popular that most decompression software's propose one or two arbitrary deep stops during the ascent. However, other diving strategies can be identified.

Mediterranean coral diving


Figure 1 : a typical dive profile of a coral diverRed coral jewels are a tradition around the Mediterranean and coral has been fished for centuries using an assembly of beams and nets, called "the cross", drag along the underwater walls. Since the introduction of SCUBA diving, there has been a small population of coral divers in France, mainly along the C?d'Azur and in Corsica. Diving for coral is a tough job as divers during the season usually dive twice a day for 20 minutes, to 80-90m on air. Recently, because coral is getting scarce, divers have moved to trimix and work at around 100-130m. Coral divers use a variety of decompression procedures that they have developed empirically and are very reluctant to give away. Over the years, I have been able to collect and document several of these original procedures. It appears that coral divers normally use one set of decompression stops that they learn by heart and apply to varying exposures, such as 25 minutes at 80m, 20 minutes at 90m and so on. They usually carry their bottom mix on a twin set or tri-cylinders backpack and rely on the boat to deploy an umbilical for the rest of their ascent. They all use oxygen aggressively, usually starting at 12m in the water, sometimes at 15m for few minutes. Some of them also have a chamber on board in which they finish their ascent after surface decompression.

Coral diver tables appeared dramatically short when compared to commercial or recreational references. The reason why coral divers survive such severe decompressions must be their specific operational procedures. Coral divers have explained that at the end of the bottom time, they ascend rapidly 10-15 meters above the bottom to get read of the narcosis. Then they slow down (9-6 m/min) until they reach 40 meters where they wait for the boat to spot their bubbles. When the boat is positioned above them, they send a lift bag to the surface with the basket attached to one end. The crew sends an umbilical down using the same line. When the basket is secured, the divers proceed with the rest of their decompression. This way, the dive profile is lengthened by some 8-10 minutes spent at mid-depth, apparently essential to their decompression safety (figure 1).

Comex deep decompression studies

Figure 2 : Semilog plot of the 180m/120 min test dive carried at Comex Hyperbaric Center in 1977. The decompression mixtures and depth of change are indicated during the ascent.In 1977, Comex, a commercial diving company, planned to conduct deep diving operations on a large scale and wanted to select a pool of deep divers based on their individual susceptibility to the High Pressure Nervous Syndrome. A test protocol was set up where divers were pressurized in 15 minutes to 180m, run a battery of tests for two hours at bottom and then were decompressed. The person calculating the decompression at the time had difficulties to define a mathematical model for such a severe exposure. He finally gave up the idea of any mathematical support and simply started drawing the decompression profiles on paper. After some trials, he discovered that by plotting the rate of ascent in a logarithm scale versus depth in a linear scale, decompressions roughly appear as a straight line (figure 2). He further used this property to design a set of decompression tables. His method produced decompressions with varying rates of ascent and very deep stops. After some adjustments, he designed a schedule for the 180m/120min dive that required 48 hours of decompression and which appeared extremely safe. A total of 49 divers went through the selection tests without any symptom (10). The characteristic of the "semi log plot" is that it expands the deeper portion of the decompression and makes it possible to define rates of ascent in an area where traditional models fail to control the ascent (figure 2). Although the method was deliberately empirical, it gave varying initial ascent rates that progressively turned into short deep stops. The result was outstanding when considering similar deep bounce dive trials at the Duke University (11). The French Navy, who attempted to design deep bounce tables in 150-180 meters range at the same time (unpublished) only succeeded in bringing the divers safely back to surface by using a near saturation decompression profile.

Possible ascent strategies
The classic approach of decompression is based on Haldanian models and involves assumptions that are summarized below:

Figure 3: Basic assumptions in classic decompression models.
1) Diving requires compressed air breathing and causes nitrogen to dissolve in the diver's tissues.
2) The critical issue is the amount of nitrogen stored in the tissues (dose) prior to the ascent.
3) The primary insult is the volume of the gas phase formed during the ascent.
4) Limb bends and neurological symptoms are not differentiated and are considered as different levels of severity of a same problem.
5) The sites for bubble formation are the tissue or the venous side of the blood circulation but no tissue is specifically identified and a series of "compartments" is considered instead.
6) The decompression strategy consists in managing the amount of gas dissolved in each compartment to control a gas phase formation and avoid DCS during the ascent (figure 3).

These assumptions are the basis of present table calculations although a large variety exists in the gas exchange models or in the criteria used to control bubbles formation. These models cannot be denied to have a certain efficiency since the present commercial air diving tables have an overall safety record around 0.5% DCS incidence (12). However, their initial ascent strategy can be questioned from the above accounts. These models work on tissue gas load. Their logic is to rapidly ascent to a stop close to the surface to create an off-gassing gradient. However, thinking in terms of bubbles instead of tissue gas load, the logic would rather be to slow down the ascent to the control bubble growth (13). Doppler detection studies with air diving up to 40m have already documented differences in ascent rate procedures (14, 15, 16). Effectively, we have noted that successful bounce decompressions tend to slow the initial ascent down by using (figure 4):
* simply slower rates of ascent to the first stop,
* varying rates of ascent, from 15 m/min to as slow as 6 m/min,
* deeper decompression stops
* mid-depth stops
* a combination of the above.


Figure 4 : strategies identified for the initial ascent in successful decompressions.It is difficult to document the efficiency of such strategies. Most of the cases reported are uncontrolled information that constitutes more anecdotes than scientific data. However, one can consider that for deep bounce tables, the criticality of the exposure replaces statistical significance. Then, there is an obvious influence of the depth. An advanced ascent strategies will not change much the safety performances of an air dive to 21 meters and data from traditional air diving are not expected to provide evidences on the matter. Finally, one can suppose that the nature of the inert gas also play a role, as helium bubbles seems to have a different behavior than the nitrogen ones. In that respect, trimix dives become difficult to analyze. To the best, one can accept the above information as a trend that could be scientifically documented in near future. This leads to reject the classic models and search for new assumptions. The arterial bubble assumption was used to propose an explanation.

The Arterial Bubble Assumption



The very idea of arterial bubbles can be tracked to page 352 of Haldane's 1908 publication where he wrote:

"If small bubbles are carried through the lung capillaries and pass, for instance, to a slowly de-saturating part of the spinal cord, they will there increase in size and may produce serious blockage of the circulation or direct mechanical damage".

Closer to our time, in paper a published in 1971, Hills (17) was able to show, using an animal model, that DCS symptoms could change from Type I to Type II by changing from continuous decompression to surface decompression. This elegant experiment demonstrated the existence of a different mechanism for the onset of Type II DCS which was later accounted for by arterial bubbles. The arterial bubbles were first detected and their possible role discussed by the scientists running Doppler detection studies (18, 19). The model was then proposed by James for the onset of CNS and spinal symptoms (20, 21). It was used to discuss the cerebral perfusion deficit in divers who had symptoms mainly referable to the spinal chord (22) and the role of a Patent Foramen Ovale in the diver's susceptibility to Type II DCS (23, 24). Finally, Hennessy published in 1989 all the physical aspects of the arterial bubbles scenario in a remarkable paper (25) that became the foundation of the Arterial Bubble assumption

The critical issue in the Arterial Bubble assumption is the filtering capacity of the lung (figure 5). The threshold radius is suspected to be the size of a blood cell. Publications on intra-vascular ultrasound techniques using a contrast agent called "Levovist" confirmed this assumption. The agent contains stable gas bubbles trapped in galactose that have a calibrated size distribution from 3 to 8 microns. The contrast agent is injected intra-venously and measurements are made few minutes later in the cerebral, renal and lower limb arteries (26). If Levovist bubbles up to 8 ? can freely cross trough the lungs, it means that decompression bubbles can pass to the arterial side, especially during the initial phase when bubbles are small. Later in the ascent, bubbles that are detected by ultrasound Doppler on the venous side have a much larger size (20-30 microns). They obviously are trapped at the lung as conventional Doppler measurements have not permitted to detect any bubbles on the arterial side.

The first merit of the Arterial Bubble assumption is to introduce variability in the decompression outcome through the lung function. The first variable is individual susceptibility. It is reasonable to accept that the filtering capacity of the lung may vary from persons to persons, and for one individual, from one day to the other. It thus accounts for the inter-individual variability (age, fat content, smoking, etc.) and intra-individual variability (fatigue, hang over, etc.) which have been observed for long in DCS susceptibility. Basically, a good diver is a good bubble filter. It is a justification for divers who claim top physical fitness for severe decompressions.

The second variable is related to dive conditions. It is reasonable to speculate a possible role of CO2 on the lung filter. CO2 could decrease its filtration capacity and cause bubbles to pass to the arterial side of the circulation. Thus diving situations that produce CO2 retention or hypercapnia should be associated to a higher risk of Type II DCS. It could explain why the following situations, which are all related to high levels of CO2, have been identified as contributing factors to DCS:
* anxiety and stress, either because of the dive conditions or of insufficient training,
* exhaustion or hyperventilation due to intense activity or work at the bottom,
* cold at bottom or during decompression,
* breathing resistance due to the poor performances of the regulator (bad maintenance or adjustment, insufficient flow).
*
The second advantage of the Arterial Bubble assumption is that is also consistent with accidental production of arterial bubbles.

Figure 5 : the Arterial Bubble Assumption

1. Diving requires breathing a compressed inert gas that dissolves in the various tissues during the bottom exposure. When the ascent is initiated, the compartments off-load the inert gas as soon as a gradient is created.
2. Bubbles are normally produced in the vascular bed and transported by the venous system to the lung.
3. The lung works as a filter and stops the bubbles in the capillaries by an effect of diameter. Gas transfer into the alveoli further eliminates the bubbles.
4. The critical issue is the filtering capacity of the lung system. Small bubbles may cross the lung and passes into the arterial system.
5. At the level of aorta cross, the distribution of blood is such that the bubble is likely to reach a neurological tissue such as the brain or the spinal cord.
6. The brain is a fast tissue and might be in supersaturated state in the early phase of the decompression. It acts as a gas reservoir and feeds the bubble that starts growing. The bubble may just proceed to the venous side for another cycle. It may also grow on place causing major alteration of the blood supply and finally ischemia. The consequence will soon be central neurological symptoms.
7. Similarly, arterial bubbles may also reach the spinal cord and grow on site from local gas and produce spinal neurological symptoms.
8. Much later in the decompression, bubbles may reach a significant size and exert a local pressure, specifically in dense tissues such as tendons and ligaments that excites nerve terminations and produces pain.

One scenario is a shunt at the heart or lung level that accidentally passes bubbles from the venous to the arterial side. A vast literature is now available on the subject but the latest conclusion is that a permeable patent foramen ovale (PFO) only opens in certain conditions (27, 28). A permeable PFO conveniently explains neurological accidents after recreational air diving without procedures violation. However, it does not fit the scheme for vestibular hits in deep diving. A first reason is that a deep diver generally has a long diving career and a diver with a permeable PFO would not be expected to follow it without any warning. The second is that vestibular symptoms can appear very early in the decompression, long before the massive bubble production required to overload the system.

A second scenario corresponds to pressure variations during decompression that reduce bubble diameters. Bubble trapped in the lung during a normal decompression process can suddenly pass through the capillaries and become responsible for Type II DCS symptoms. This scenario has been proposed to explain the difference in safety performances of in-water decompression versus surface decompression. Data collected in the North Sea have shown that if the overall incidence rate of the two diving methods is about the same, but that surface decompression tends to produce ten times more type II DCS than in-water decompression. The assumption is that at the moment the diver ascends to the surface, bubbles are produced that are stopped at the lung level. Upon recompression of the diver in the deck chamber, these bubbles reduce their diameter due to the Boyle's law and pass to the arterial side, later causing neurological symptoms. A similar scenario has been proposed for type II DCS recorded after yoyo diving or multiple repetitive diving (29).

The last advantage of the Arterial Bubble assumption is that it provides an explanation for the criticality of the initial ascent phase. Bubbles associated to symptoms are not necessarily generated on site. There is an amplification process at the beginning of the ascent that may last for several cycles. Once the bubbles have reached a critical size, they are either filtered in the lung or stopped at the tissue level. It is believed that the showering process of small arterial bubbles during the first minutes of the initial ascent prepares the prognostic for further DSC symptoms. An attempt was made to turn this scenario into a decompression model.

Definition of the critical case
Setting the scene for a decompression model, simplifications and restrictions must be specified:
* The divers' population targeted must correspond to "standard divers". Although such persons do not exist, it is assumed that they have a normal lung filtering function and that they have no physiological dysfunctions such as a cardiac or pulmonary shunt to accidentally pass bubbles through.
* The dive considered should also have "a standard condition" because our level of understanding does allow us to quantify the effect of fatigue, hyperventilation, cold, anxiety, etc. These conditions should be taken into account by applying the usual safety margins.
* Finally, the dive procedures must correspond to one "single square dive". Variations in the dive procedures such as yoyo diving, repetitive diving, multi-level diving introduce disturbances in the normal bubbles distribution that requires further assumptions.


Figure 6 : definition of the critical case.From the above analysis, the critical case is defined as the arrival of an arterial bubble passing by a tissue compartment. Again, a series of simplifying assumptions is introduced (figure 6):
* The bubble was formed elsewhere. Its growth did not modify the local tissue gas load.
* The bubble is reputed to be small when compared to the tissue gas capacity, at least at the beginning of the decompression process. It does not change the tissue perfusion time response.
* Stuck in place, the bubble exchanges gases with both blood and the adjacent tissue.
* However, the bubble is stable and keeps a critical volume.

Complementary assumptions could be added that will generate a family of solutions. However, as the validation of these models is done by data fitting, the mathematical expression should remain simple and the number of parameters should be kept minimum.

See the derivation of the AB Model in Appendix.

Validation of the model
Validation of a model should follow the recommendations of the UHMS Workshop on Validation of Decompression Tables (39). The validation should range from laboratory testing to operational evaluation. Scientists refer to the convention of Helsinki for human experiment and proceed with informed consent forms. However, nowadays, ethical committees will exclude manned trails from almost any decompression study. Commercial diving, that was the main driving force during the 70's and 80's, has been ruled by laws, industry recommendations and social pressure. This normal maturation process of an industry has proved very limiting too. The last time a decompression problem was identified in the North Sea, it was solved by forbidden diving in the area of concern (40). Since then, the collapse of the offshore diving has reduced money available for diving research in many countries. The precious diving databases were lost along with any hope of official support for the validation of decompression tables. The lack of manned experiments or documented operational experience makes new models difficult to validate. The only remaining possibility for tables design is to analyze old data with new models.

AB Model-1: validation of the 1992 French air tables
Comex had used on its worksites the first version French official air decompression tables, called "MT74 Tables", that were published in 1974 by the "Minist貥 du Travail" (41). In 1982, the French government supported a research project for the evaluation of their safety performances using the computer treatment of the dive reports. The database analysis showed that the MT74 tables had limitations for severe exposures (12). The French government then supported a second research project to edit and validate new tables. A complete set of air tables, offering pure oxygen breathing at 6m (surface supplied), at 12m (wet bell), surface decompression, split level diving, repetitive diving, etc. was developed in 1983.

The model used to compute the tables implemented the concept of continuous compartment half-times. For the safe ascent criteria, the formulation of equation E11 was suspected but not established mathematically. An approximation was defined empirically by fitting mathematical expressions to selected exposures stored in the Comex database. At the time, the best fit was obtained by the expression E12 below, now called "AB model-1". It is similar to the equation E11 when the last term is neglected.

E12

The values obtained by data fitting for the coefficients were A= 8 min and B= 0.4 bar. The AB model-1 was used to compute a set of decompression tables that was sent offshore for evaluation on selected Comex worksites. In 1986, after some minor adjustments, the tables were finally included in the Comex diving manuals and used as standard procedures (42). Later in 1992, the tables were included in the new French diving regulations under the name of "Tables du Minist貥 du Travail 1992" or "MT92" tables (43). The safety performances of the new AB model-1 are documented in table 1 after their offshore validation with air diving.

Table 2.
Comparison of the safety performances of the MT74 and the MT92 French air tables. The dives are classified in moderate, standard and severe exposures according to the Prt Index (5). The exposures correspond to in-water decompressions and exclude any surface decompressions. The data permit to quantify the safety performance improvement that is especially significant for type I DCS and severe exposures. Results on type II DCS are inconclusive as the general level of incidence is very low.

ExposuresModerate
(Prt<=25)Standard
(25<Prt<=35)Severe
(Prt>35)TablesMT74MT92MT74MY92MT74MT92Dives17,6837 ,1299,5908,3842,4262,055Number of Type I DCS
Percentage of cases 18
0.10%1
0.001%55
0.57%12
0.14%49
2.2%17
0.82%Number of Type II DCS
Percentage of cases 1
0.006%0
0.00%1
0.01%1
0.01%1
0.04%2
0.09%
AB Model-2: calibration with Comex deep experimental dives
The name "AB model-2" was given to the full expression of equation E11. Used in its full extend, the expression can be compared to a normal M-value associated to a corrective factor that tends to reduce the permitted gradient for small values of T. Its role is similar to the "Reduce gradient factor" method of calculation presented by Backer (44) or the reduction factor of the rgbm model (45). These compartments correspond to fast tissues that effectively direct the initial phase of the ascent. The overall consequence is much deeper stops. The initial rate of ascent to the first stop is not part of the model control and was set arbitrarily to 9-6 m/min. The combination of the deep stops and slow ascent rates gives decompression profiles with features identified above for successful decompressions. The AB model-2 was calibrated by data fitting on a series of Comex offshore and experimental dives using both air, nitrox and heliox gas mixtures. As an example, the fit obtained for the test dive to 180m/120min already mentioned in the above paragraph is presented in figure 10. The AB model-2 succeeded in introducing the deep stop at least to 153 m that is very close to the actual one at 162m.

Discussion and conclusion
* It is admitted that the shape of the decompression generated has prevailed over the theoretical basis in the derivation of the AB model-1 and 2.

However, a few points must be recognized in favor of the AB models:
* The concept of the arterial bubbles seems to be a way of designing tables with deep stops as we nowadays believe they should have.
* The model in its simplified form (AB model-1) has been effectively validated in controlled conditions with air diving at the time it was still possible to do so with diving data-bases.
* The mathematical formulation, based on a continuously varying compartment half-time, requires a minimum of parameters, and somehow proves the relevance of the assumptions.
* As such, the AB models have a surprising prediction capacity as they were successfully calibrated with air and heliox from 0 to 180m.

Appendix : Derivation of the AB Model
Decompression models are all based on the same structure (figure 7). The assumptions in the various boxes may vary from one author to another but the logic remains the same. The input parameters correspond to the operational conditions: bottom depth, bottom time, and gas protocol. They set the initial and boundary conditions for the various equations. The gas exchange model serves to evaluate the amount of available gas at the site. A second model is used to describe the gas exchanges between the bubble and its surrounding environment. Both models may interact depending on the assumptions. The safe ascent criteria is a decision on the critical phenomena to be controlled during the ascent. It could be super-saturation as in the Haldane's model, the volume of the gas phase in the critical volume hypothesis (30), or the bubble size, the rate of growth, etc.

Tissue gas exchanges model
Models require parameters to be defined. The number of parameters, or degrees of freedom, increases with the complexity of the model. It is currently admitted that models with a large number of parameters are purely descriptive models and that models with a limited number parameters, corresponding to more pertinent assumptions, are more predictive.

Figure 7 : structure of a decompression calculation model.
The consequence is that when the number of parameters increases, the domain of validity of the model shrinks. Classic models used in table calculations are obviously over dimensioned in terms of parameters. Typically, the Buhlman model (31) uses 16 compartments to calculate air tables. Considering the half-time and the two "a" and "b" coefficients for the safe ascent criteria of the various compartments, the model uses a total of 36 parameters to run. Although these tables are among of the best air tables available, it took Dr. Buhlman a lifetime to adjust these parameters. In addition, the model is fine as long it is used in its domain of validation that is mainly recreational diving. It could not be extrapolated for instance for very long bottom times as used in commercial diving.

The tissue gas exchange model is generally the main source of parameter proliferation because of the concept of tissue compartments. Tissue compartments are just an historical approach and their identification is not important. A series of compartments avoids the difficulty of accurately defining the process of the gas exchanges, would it be perfusion, diffusion or combined perfusion and diffusion. The exponential compartments are considered as harmonics of a complex mathematical solution that are controlling the decompression one after the other. For this reason, we used the general classic expression:

E1

Where T is the compartment half-time as defined in the perfusion equation, Pa and Ptis are the arterial and tissue inert gas tensions.

The modern trend in table computation is to consider all the possible compartments and treat their half-time as a continuous variable. The difficulty then is to express the safe ascent criteria in terms of the compartment half-time, an exercise that was solved only in simple cases (32). Because modern computers are fast, the solution adopted was to keep treating tissue compartments individually but express them with a geometrical series to remove any subjectivity in their selection. We used the Renard's series, named after a French admiral who faced the standardization of ropes, sails, planks, etc. in navy arsenals, and elegantly solved the problem with a progression based on a square root of 10. For instance, with 10 values per decade (), the series gives the following values:

10 - 12.5 - 16 - 20 - 25 - 32 - 40 - 50 - 63 - 80 - 100

Experimentally, we found that the computations become stable when the number of compartment is set between 15 to 20 values per decade. This way, the description of the tissue gas exchange model only requires defining the boundaries. The fastest compartment obviously corresponds to instant equilibration and does need to be specified. The slowest compartment is defined as the one used in saturation decompressions. Based on Comex saturation experience, these values were set to 270 minutes for heliox and 360 minutes for nitrox saturation (33). Finally, the tissue gas exchange model only requires one parameter to be defined, corresponding to the half-time of the slowest compartment.

Bubble gas exchanges model
All gases present in the surrounding of the bubble participate to the gas exchanges. Metabolic gases play an important role and especially CO2 (34), the presence of which has been reported in bubbles as soon as Paul Bert. However, Van Liew demonstrated in his the experiments that the permeations of O2 and CO2 are very rapid (35). If local tension of CO2 and water vapor are well documented in the surrounding tissue, the local values of the oxygen tension might become a problem, especially if various decompression mixtures are use during the ascent. As a first approximation we took the bubble oxygen pressure equal to the tissue oxygen tension and constant. However, when the decompression gas protocol is aggressive, or if pure oxygen is breathed in the last stops, this simple approach gives rapid changes of ascent rates that are incompatible with our operational experience. In an improved version of the model, the bubble oxygen partial pressure was computed as a function of the ambient pressure and the metabolic oxygen extraction (36, 37) and using the mathematical derivation of the oxygen window proposed by Egi (38).


Figure 8 : possible bubble gas exchange situationsTo cope with the complexity of the inert gas exchanges in the bubble, we decided to simplify the process by considering two extreme situations (figure 8). In one case, the bubble is purely vascular and remains on place. The blood flows around it and exchanges gas by convection so efficiently that there is no laminar layer and no diffusion delay at the bubble interface. In these conditions, we adopted for the bubble gas exchanges a formulation similar to the classic tissue perfusion equation. We further assumed that the blood flow draining the bubble is a small fraction of the tissue perfusion and that the blood leaves the bubble equilibrated with its gas pressure. This permitted to arbitrary express the quantity of inert gas molecules transiting through the bubble interface into the blood as:

E2

Where dn,bloodgas is the number of molecules of inert gas passed from the bubble into the blood, Pagas the arterial inert gas tension, Pbgas the bubble inert gas pressure, T the compartment half-time and C a coefficient that accounts for the fraction of the tissue blood perfusion that governs these exchanges, the relative capacity of the bubble to the surrounding tissue, etc.

In the second case, the bubble is purely extravascular. The bubble exchanges gas with the surrounding tissue by diffusion. We used the classic assumption of a linear gradient in a surrounding shell and obtain a second general expression for the number of inert gas molecules diffusing through the bubble interface into the tissue.

E3

Where dn,tisgas is the number of molecules of inert gas diffusing from the tissue into the bubble, Ptisgas the tissue inert gas tension, Pbgas the bubble inert gas pressure, K a coefficient that accounts the diffusibility of the gas, the thickness of the layer, the surface of the bubble, etc.

Finally, we imagined an intermediate situation where the bubble is at the interface between the blood and the tissue and exchanges gas through the two above mechanisms. The importance of the exchange varies with the relative area of the bubble exposed to each media. The ratio between the two exposed areas of the bubble is called ( and varies from 0 to 1. The inert gas mass balance of the bubble becomes:

E4

Where R is the gas constant, ( the absolute temperature and Vb the volume of the bubble.
Safe ascent criteria
The ascent criteria simply seeks the stability of an arterial bubble, with a critical size, stuck at the interface of the blood vessel and exchanging gas with both the blood and the tissue. We translated this statement by specifying that the overall mass balance of the arterial bubble remains unchanged in these conditions:

E5

At a constant ambient pressure, corresponding to the situation of a decompression stop, the stability of the bubble requires two conditions. The first one is that the bubble volume remains constant and the second that the various pressures are balanced at the surface of the bubble .
This last condition means that the sum of all the internal gas pressures equals the external ambient pressure plus the stabilization pressures (surface tension, skin elasticity, tissue compliance). This is written as:

E6


Figure 9 : pressure involved in the stabilization of the bubble surface.Where Pbgas, PbO2, PbH2O, PbCO2 are respectively the pressures of the inert gas, oxygen, water vapor and CO2 inside the bubble, Pamb the ambient pressure and Pstab the sum of the various stabilization pressures. Assuming PbO2 is constant and equal to the tissue oxygen tension and introducing B, a coefficient of obvious definition, we obtained a simpler form:

E7

In these conditions, the overall of gas transfers between the bubble and its surrounding is balanced. The same amount of molecules of inert gas must enter and leave the bubble during a unit of time. There is no gas accumulation inside the bubble. Equations E5 and E4 become:

E8 , and yields:
E9

Finally, equation E10 and E8 are combined to eliminate Pbgas. After defining a coefficient A as:

E10

The final expression of the safe ascent criteria becomes:

E11

Equation E11 sets the condition for a safe ascent to the next stop according to the initial hypothesis: an arterial bubble, exchanging gas with blood and tissue that keeps a critical size during the ascent. It is a function similar to an M-value. With the tissue compartment tension evolution defined in E1, it permits the classic computation of a decompression stop time. This computation model is later referred as the Arterial Bubble model or "AB" model.

The primary interest of the ascent criteria in E11 is that it is expressed as a function of T and thus can be defined continuously for each compartment. This definition is also extremely efficient in terms of parameters, as it only requires determining (when PbO2 is taken as a constant) the values of the A and B coefficients. The total number of model parameters reduces to three coefficients that are the longest tissue half-time and the two A and B coefficients.

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Sutty

Brent, Thanks for posting it - but where is your copy/paste from?

Neil

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Never forget that life is a finite resource.

RichClark

Neil,

I've read this before, I found the arictle here.... http://www.bsac.org/techserv/ndc/doc...04jpimbert.htm

Cheers

Rich

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