Modern Decompression

I thought about calling this post “The Pros and Cons of Diving with Nitrox”, but there aren’t really a lot of “cons” other than the ones you’re already familiar with, cost and convenience:  The time and cost associated with getting certified for Nitrox diving, the extra cost of Nitrox, and the inconvenience of Nitrox being unavailable in some locations.  On the “pro” side, you’re already aware of the increased bottom times Nitrox allows, compared to air.

What You Don’t Know About Diving With Nitrox

In getting certified for Nitrox diving, you learned that the Nitrox dive tables were developed by extending air dive tables using the “Equivalent Air Depth” (EAD) rule, the intent being to develop NDL’s for Nitrox that were equivalent in decompression risk to the NDL’s for air.  In that respect, the EAD rule earns a big “FAIL”.

The EAD rule results in Nitrox tables whose NDL’s are vastly different in decompression risk from the NDL’s for air.  (More about that below)

The EAD Rule – What it Does and Doesn’t Do

It’s tempting to say “There’s nothing equivalent about the Equivalent Depth Rule”, but that would be incorrect.  In your certification classes, you learned to calculate equivalent air depths for Nitrox (in case you happen to have your air tables, but not your Nitrox tables handy).  Some of you may even still remember how to do those calculations.  What the calculations actually do is produce equivalence for the nitrogen partial pressure being breathed in from air and Nitrox at their “equivalent” depths. Or, to put it in less technical terms, you’re breathing in the same amount of nitrogen from Nitrox as you would be from air at their equivalent depths.  So, in that respect alone – the amount of nitrogen being inhaled – the depths are in fact equivalent.

The problem with the application of the EAD Rule comes from the idea that, since DCS risk stems from excess nitrogen in the blood and tissues, if the nitrogen partial pressure being breathed is the same for two gases (e.g. air and Nitrox) at two different depths, then the risk is the same for these gases at these two depths, provided the same time is spent at these depths.  Unfortunately, this idea is overly simplistic.  While the rule equalizes the nitrogen entering the system through the lungs at the equivalent depths, the amount of excess nitrogen that builds up in tissues depends additionally on all parts of the dive profile, not just the deepest portion.  As just one example, if both dives include (as they should) a safety stop at 15′ for 3 minutes, less nitrogen is entering the system from breathing Nitrox than from breathing air during the safety stop.

The great advantage of probabilistic decompression theory is that it elevates the discussion of decompression risk to a quantitative level.  By using it, “risk” becomes calculable, with actual numerical values assigned to it for specific profiles.  But, even thinking in terms of whatever model of decompression you are currently most familiar with, you can see that, by focusing solely on the pressure of gas breathed in at depth, and ignoring the full on- and off-gassing of the tissues, the EAD Rule is unlikely to actually result in equivalent DCS risks for profiles at the “equivalent” depths.

Comparing DCS Risks for Air and Nitrox at “Equivalent” Depths

“Equivalent” depths for Air and Nitrox will, of course have identical NDL’s (i.e., allowing the same bottom times at their respective actual depths).  So, for example, a 32 Nitrox dive to 75 fsw is treated the same as an air dive to 60 fsw.  They share the same maximum bottom time of 55 minutes.  What they don’t share is the same risk of DCS.  As shown in the table below, the air dive for 55 minutes will have a risk of .32 percent (or, roughly, almost a 1 in 300 chance) of DCS.  The Nitrox dive for 55 minutes will have a risk of .089 percent (less than a 1 in 1000 chance) of DCS.  On these two “equivalent” dives, the DCS risk on air is more than 3 times the DCS risk on Nitrox.

The table below illustrates the differences in DCS risk between supposedly equivalent dives on air and 32 Nitrox.   All the dives include a stop at 15′ for 3 minutes.  The probability calculations are based on SAUL.  (A link to the SAUL Dive Planner is in the header of this page.)  The Nitrox dives shown in red print (the three deepest) are included solely for the DCS risk comparison.  NEVER DIVE THOSE DEPTHS ON NITROX.  The risk there is not of DCS – which, as you can see, is minimal – but of oxygen toxicity.  Not much is known about the degree of risk for oxygen toxicity or what other factors may affect it.  But two things are clear.  First, in the recreational dive range, the risk is very much greater with Nitrox than with air, where it is almost negligible.  And, second – but more important – the result of oxygen toxicity at depth is almost invariably fatal (by way of convulsions and loss of consciousness, leading to drowning).  For this reason, I would recommend an even more cautious approach of using 32 Nitrox only under 120 fsw.

COMPARISON OF DCS RISK FOR AIR AND 32 NITROX AT THEIR EAD RULE EQUIVALENT DEPTHS

(DCS risks calculated using SAUL and all dives assume 60 fsw/min ascent and descent rates and include a stop at 15′ for 3 min.)

“equivalent” Depths(fsw)             PADI (NDL)                             Risk of DCS (%)

Air              32 Nitrox                  BT (min)                              Air              32 Nitrox

50                  63                               80                               .21                .028

60                  75                               55                               .32                .089

70                  86                               40                               .40                .124

80                  98                               30                               .41                .133

90                 110                              25                               .47                .173

100                121                             20                               .41                .118

110                133                             16                               .30                .060

120                144                             13                               .20                .016

130                156                             10                               .080             0.0 

As you can see from the above table, the “equivalent” depths for air and Nitrox are far from equivalent in terms of DCS risk.   The good news is that Nitrox is a lot safer in terms of DCS risk than current practices assume.

A comment by Craig on the Saul dive planner raised issues that may be of general interest, and merit a somewhat detailed answer, so here it is.

Thanks for posting the planner, interesting to try out. I could not get 130 feet for 32% to do any calculations.

With 32% O2, out of an abundance of caution (in order to avoid Oxygen toxicity), the depth is often limited to less than 120 feet, which is what I have done here.

 Many algorithms have a slower ascent rate of 30 feet/min, or that rate when at 60 ft or less.

During free ascents, i.e. in the absence of an ascent/descent or anchor line, it is actually pretty difficult to maintain an ascent rate of 30 feet/min (or less). 60 feet/min is more common and easier to do, so the ascent rate calculations in the dive planner are for 60 feet/min.  Planning for an ascent rate of 30 feet/min when you’re unlikely to achieve that slow an ascent would be underestimating your actual level of risk.  A dive computer using Saul would, of course, be able to take actual ascent rates into account.

It is difficult for me to interpret the probability of DCS. I ran all the DSAT NDLs between 60-120 feet for 32%. All probabilities ran between 0.27 and 0.46% 

The result you just found, that the DSAT NDLs are not “iso-risk” (i.e. they don’t all entail the same degree of risk), is something that many people have wondered about, but – in the absence of a probabilistic model – didn’t have a handle on. This is one of the many advantages that a probabilistic model provides.  But I presume that your immediate concern is with what those differences in probabilities mean in real life.

Firstly, the probabilities shown in the planner are stated as percentages, so that a 0.27 risk of decompression sickness means a .27 percent risk (or 2.7 chances in 1000, 27 chances in 10,000, or just a bit above 1 chance in 400).   Similarly, a .46 percent risk means 4.6 chances in 1000, 46 chances in 10,000, or  about 1 chance in 218.

With respect to interpreting the probabilities, it may be helpful to appreciate more fully what these numbers mean or imply, by seeing what they predict for large numbers of dives.  We’ve already looked at that a bit in a previous blog post (Probability in Relation to “The Bends”) where we showed that, for a probability of 1 in 400, over a series of 400 dives, the probability of getting no instance of decompression sickness in any of the dives was .367 while the probability of having one or multiple instances of sickness during the series was .633.  (So – very roughly – the probability of being hit at least once in 400 dives at that level of risk was almost double the probability of completing 400 dives unscathed.)   We looked at a series of 1000 dives at that same risk level, and found the probability of being hit at least once in the series works out to .918, while the probability of completing 1000 dives unscathed has decreased to a measly .082 (or less than 1 in 10).

How do the two P(DCS) extremities of 0.27 % and 0.46 %, obtained for the DSAT NDLs on 32 % O2 (above) compare?   If we do similar calculations on those probabilities, we find that – skipping right to a series of 1000 dives –

For a risk level of .27%,  the probabilities of no hits and at least one hit in a 1000 dive series are, respectively, .067 and .933.  (The chances of completing the series of 1000 dives unscathed is not looking too good – just under 7%.)

For a risk level of .46%, the probabilities of no hits and at least one hit in a 1000 dive series are, respectively, .010 and .990.  (The chances of completing the series of 1000 dives unscathed is highly unlikely – 1% .)

So the probability of getting at least one hit over the series of 1000 dives rises from about 93 % to about 99 %, depending on whether one dives the profile corresponding to the low or the high extremity for the range of  DSAT NDL’s for single-dive profiles.  Even the seemingly negligible difference between the 1 in 400 (.25%) level of risk in the initial example and the .27% risk level, when carried over 1000 dives, moves the probability of getting hit at least once from less than 92% to over 93%.

These and related calculations are described more fully at the end of Chapter 8 of the book I recently co-authored:

Saul Goldman, J.Manuel Solano-Altamirano, and Kenneth M. LeDez: “Gas Bubble Dynamics in the Human Body”. Elsevier/Academic Press (2017).

Hope this helps.

One of the features I’ve been emphasizing about the SAUL algorithm (besides its greater accuracy), is that it allows the diver to choose a level of risk that he/she feels is appropriate.   Since this is quite different from the way we initially learned to think about dive safety, now is a good time to review the differences and to go over some basic ideas and facts about probability.

When you were first learning to dive, you would have been told that, in diving, there is always some small probability of decompression sickness (DCS), but that you can minimize your risk by diving safely – all of which is true.   But, once you were introduced to dive tables and/or dive computers, there was no further discussion of probability in relation to DCS.  Instead, you went on to look at dive tables to work out no-decompression limits (NDL’s), and then proceeded to dive computers which, in effect, automated the working out of  NDL’s.

The problem with NDL’s  (and with current dive computers) is that they are deterministic.   That is, they have an absolute dividing line: below it you’re okay, above it you’re in trouble.  As with speed limits on highways, there may be a tendency to continually push the limit – until you get caught or “bent”.  (Although, to be fair, PADI dive tables, do have a disclaimer of sorts on them advising that you shouldn’t actually plan to dive to the limits, that the limits are something of an absolute maximum.  But, then, you’re left wondering – “How close to the limits is too close?”)

While some current dive computers offer riskier or less risky options, how can anyone make a sensible choice without a clear idea of how much risk each option involves?

So let’s look at the probability of DCS in diving.  In the higher ranges, if you were to dive each of the listed profiles on the PADI recreational diving tables, right at their no-decompression limits (on air, including a 3 minute safety stop at 15 fsw), your risk of DCS would average out to .00264, which is 264 chances in 100 thousand or, roughly, just over a 1 in 400 chance of getting bent.  (I averaged over all the listed profiles because the risks at the limits of the different profiles are not equal.)  To see the comparative risks of PADI’s NDL’s for different profiles, check out my post on How Saul Relates to the PADI Dive Tables.

On the other hand, most recreational diving typically involves much lower risks.  Project Dive Exploration, which solicits and collects actual  dive data from large numbers of divers found (in one subset of their data, that roughly corresponds to typical recreational diving) a DCS rate in the neighbourhood of .0007, which is about 70 chances in 100 thousand.  Or, to put it another way, only about 1 chance in 1,400 of getting bent.

What factors should you consider when choosing an acceptable level of risk?  Obviously, less risk is preferable to greater risk.  No one wants to get bent.  (On the other hand, the least risk of all is to stay out of the water.  Not a serious option.)   But less risk generally does mean less bottom time.  So what do you do?

Regardless of the level of risk you choose, there is some possibility (even if very small) of getting DCS on any single dive.   As you increase the number of dives, you’re more likely to experience the consequences of a higher level of risk.  Using the (not recommended) 1 in 400 level of risk mentioned above, if you were to dive 400 times at that level of risk you’re quite likely to get bent.

It’s probably unnecessary to remind you (but I’ll do it anyhow) that a 1 in 400  risk doesn’t mean exactly 1 incident of DCS in every 400 dives, but that, over a large enough number of dives, or a large enough number of divers, the number of cases of DCS will average out to 1 in 400.   Meaning that, while you might manage those 400 dives without getting bent at all, you’re about twice as likely to get bent one or more times.  And, if you were to continue at that same level of risk through 1000 dives….  Well, just don’t. (To see the probability calculations, click here. Continue reading →

As some of you may be aware, the Inter-connected Compartment Model (ICM) described in my published journal article now goes by the name of “SAUL”.  This is not entirely, or even primarily, an ego trip.  Rather, it’s an attempt to avoid the unnecessary use of jargon – particularly when it results in unpronounceable acronyms.  While ICM is an appropriate and relevant way to describe the model’s properties in a scientific context,   in the context of diving,   it becomes less meaningful, less directly relevant and, of course, less easily remembered.

“SAUL” – for Safe Advanced Underwater algorithm – is a more relevant description from a diver’s perspective.

As I’ve mentioned before in this blog, “SAUL” is completely different from current algorithms, being probability-based rather than based on the Haldane model.  This may raise two different questions in the minds of divers: 1. Is “SAUL” tested to the same extent as other models?  and  2. Would I have to learn a whole new way of interacting with my dive computer with “SAUL”?

Is “SAUL” tested to the same extent as other models?                       

The short answer to this question is “yes”.  The most extensive body of research on dive profiles and decompression sickness was done and compiled by the U.S Navy, together with the (British) Royal Navy and the Canadian Navy (currently “DRDC”).  All diving algorithms have (in a rough sense) been “tested”, either directly or indirectly, against the Navy data. This is because they are usually tested against the PADI recreational dive planner data, which is a more conservative form of the US Navy tables. While new dive computers do undergo testing, this is not a test of the accuracy of the algorithm, but a check primarily of being not too inconsistent with other popular algorithms in current use.  I have access to the Navy data and believe that “SAUL”, for both decompression and no-decompression diving on air or nitrox, for both single and repetitive dives,  provides a better fit to the Navy data than does any other algorithm. This is why SAUL, but not any other algorithm, can account for the beneficial effect of safety stops and slow ascents. This, in turn, explains why SAUL accounts for DAN’s Project Dive Exploration (PDE) data for air and nitrox, far better than any other algorithm.

Would I have to learn a whole new way of interacting with my dive computer with “SAUL”?

The short answer here is “no”.  Even though “SAUL” is probability-based, during a dive, you would still have the familiar “time remaining” to go by and your ascent would include a 3-minute safety stop at 15 feet (for recreational dives).  What would be different would be how that function is calculated, and what additional information you would have.   Before the dive, you would select the maximum probability of decompression sickness that you are prepared to accept.  (Of course, we would all prefer a zero probability of DCS  –  except, unfortunately,  a) zero probability of DCS is not really feasible in diving, and b) the lower the probability of DCS, the more limited your dive will be in length and/or depth.)   The “time remaining” that you see during the dive would be calculated to correspond to your chosen probability of DCS, together with the dive profile you have done so far.  In addition to “time remaining”, you would also see two other functions: the probability of DCS if you were to begin your ascent right then, including a safety stop , and the probability of DCS if you were to begin your ascent right then but omit the safety stop.  These three functions would be continually recalculated during the course of the dive.

The above description is what you would see during recreational diving.  (Before the dive you would have selected either recreational diving or decompression diving.)  During decompression diving, what you would see would be very similar, except that, instead of only one safety stop, you would have one or more decompression stops.  You may be wondering why recreational diving and decompression diving are calculated separately instead of being merged as one.  It is because the model parameters (i.e. the constants in the equations of the model) for the two are different, and can’t be switched on the fly.  In any event, if you’re on a recreational dive but have seriously overstayed your maximum time remaining (a seriously bad idea), there’s no point in directing you to do a proper decompression stop if you don’t have enough air left to do it.  If you do overstay your maximum remaining time, the “time remaining” function will, of course, tell you to ascend immediately, but, unlike with other computers, it will not shut you out.  The functions indicating your probability of DCS on an immediate ascent, with and without a safety stop, will continue to provide you that information.

Dive Planner

I do intend to put a dive planner online, but can’t say exactly when that will happen.   It may take some time because I have a number of other professional commitments that I am working on at this time.

A recent comment on my The Doctor is In Part IV blog post, followed by a more detailed letter to me raised some issues that need to be addressed.  The comment read as follows:

SAUL sounds like a giant leap forward in dive safety and one that will always be attributed to the brain work of Dr Saul Goldman. As far as I understand however a route has been chosen to make the invention a proprietary solution, which is an unbelievable shame. Have you considered to make this algorithm available to the public domain so that *every* dive computer manufacturer can implement it, including those that do not want to be involved in the proprietary IP madness of this world. What if Einstein had taken a patent on all his inventions? What’s more important: A bank account or saving lives?

The writer refers to my making SAUL “a proprietary solution”.  This is not exactly the case.  SAUL – or, more accurately, the model upon which it is based – is patented.  What’s the difference?  A proprietary solution is generally kept secret, because, not being patented, secrecy is often the only way to protect it from being “stolen” by others.  A patent provides its own legal protection, is not secret, and, in fact, is published online by the U.S. Patent Office.  In addition to that, my article in Journal of Physiology (which can be downloaded from the Articles section) contains details of my model.

The two main objections the writer seems to have to what he calls a “proprietary solution” are: first, that he would like every dive computer manufacturer to be able to implement it, and, secondly, some apparent distaste for my wanting to make money from it.

I have no problem with the first objection.  In fact, it is my goal and my expectation that  every dive computer manufacturer will eventually implement it.  I have no intention of selling exclusive rights to a single manufacturer, nor have I ever considered doing so.  SAUL was, and is, my way of giving something back to the diving community for all the enjoyment I have had, and continue to have from diving.

So, why do I not overcome the second objection by putting it in the public domain (or, as one computer manufacture I approached put it, “make it open source, like Buhlman”.)?   Perhaps I would – if computer manufacturers offered their products for free, mechanics repaired cars for free, airlines gave free flights, etc. – but I don’t really see that happening.

I spent years of my life, and a fair amount of my own money, developing SAUL and, while I’m not looking to get rich from it, there’s no way I will allow computer manufacturers to profit from it without my profiting as well.

There’s also a secondary reason I won’t make it open source:  The model underlying SAUL is different from, and more complex mathematically than, Haldane-based models (which includes all the others out there, including so-called “bubble-based” ones).  I have some concerns about the potential for people with insufficient mathematical and scientific skills trying to “adapt” or change the algorithm.

In his longer letter to me, the writer mentions some objections he has heard from dive computer manufacturers he queried: specifically, that they were either “unaware of” SAUL or that it was “untested”.  I can’t speak to whether any of them are actually unaware of SAUL (although I have my doubts).   SAUL is also no less “tested” – in a formal sense – than are any of the algorithms in use today.  While dive computer manufacturers do  test their computers before their release, they do not test the accuracy of the algorithm.  What they test is, essentially, the functioning of the hardware and the software environment – in other words, that the computer is actually doing what the algorithm tells it to do.

As far as being tested, the largest body of test data in existence was amassed in an extensive series of experiments conducted by the U.S. Navy, in conjunction with the Canadian Navy and the (British) Royal Navy.  Real-life testing to that same degree can’t  be done by anyone nowadays –  not even by the Navy  (some of it would never pass an ethics committee).  These provide the data that all algorithms use, either directly or indirectly, as they calibrate their equations to fit, as best they can, the known facts.  (In the case of SAUL, I had access to that entire data set and used it extensively.)   To the best of my knowledge and belief, SAUL’s predictions fit the Navy data better than any other algorithm.  I have also been given access to a large portion of the recreational dive data collected by DAN in their Project Dive Exploration.  SAUL predicted the actual incidence of decompression sickness in those dives very accurately, much more so than typical Haldane based algorithms whose predictions were too high by a factor of 10 or more.  SAUL is also the only model to account for the beneficial effect of safety stops and slow ascents.

It’s also worth mentioning, that I have given about 20 invited talks about on my model and related subjects to audiences composed variously of physicians, scientists, and divers.  I have spoken at meetings of the Undersea Hyperbaric Medicine Society (UHMS), American Academy of Underwater Sciences (AAUS), Canadian Association of Underwater Sciences (CAUS), South Pacific Underwater Medicine Society (SPUMS), and the International Congress on Hyperbaric Medicine (ICHM).   Of all the questions I was asked following these talks, the single most common one was “When will this be available in a dive computer?”  So far, I haven’t been able to provide a definitive answer to that question, but I’m still trying.