The SAUL Dive Planner is Here

The SAUL dive planner is the first probabilistic dive planner available.  Deciding how to structure it took some time but, in the end, after considering more complex set-ups, I decided to keep the dive planner relatively simple.  There is a choice of breathing gas – air or 32 nitrox.   The dive profiles available are all square profile with specified descent and ascent rates (60 fsw/min) and include a mandatory 3 minute safety stop at 15 fsw.  There is a further choice of doing a “forward” or a “reverse” calculation.

In the “forward” calculation, you will input the maximum depth, and the maximum time you want to spend there.  The planner will output the probability of incurring decompression sickness for that dive (unlike currently available planners, which would either permit or not permit that dive).   In the dive planner’s forward calculation, if you should, in some instance, see the probability of decompression sickness shown as 0%, remember that this does not, of course, represent an absolute zero probability but 0% when the calculated probability is rounded to a finite number of figures.

In the “reverse” calculation, you will input your maximum acceptable P(DCS) along with the maximum depth, and the planner will provide you with the maximum bottom time to keep within your chosen P(DCS).  (So, the “reverse” calculation, after you choose your maximum acceptable P(DCS),  will give results in a style similar to currently available planners.)

Just a few reminders before we start:  There is always some possibility (even when very minimal) of decompression sickness when you dive.  You might want to reread the previous blog post on probability.   Because all the dive profiles included are square profiles with a stop, this is what they would look like in diagram form.



You may already know that, by definition, bottom time begins when you enter the water and ends when you begin your ascent.   Please realize as well that, with SAUL, the safety stop is an essential part of the calculations, as are the descent and ascent rates.  Any changes to these could affect the probabilities given.   In addition, these probabilities are for single dives only. Repetitive dives are not included in this version of the planner.

As you should be aware, a dive planner is only that.  It is not an adequate substitute for a dive computer.  This is true in general for all algorithms.  Because of SAUL’s greater accuracy and complexity, it is particularly true for SAUL.


To use the SAUL Dive Planner:

Probability in Relation to “The Bends” – Changing the Way We Think About Dive Safety

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

On Planning a SAUL Dive Planner

Okay, I’m finally ready to start working on the long-delayed SAUL dive planner.

As I mentioned briefly in an earlier post, I had been working on a book with two other authors – one of them a math/physics/chemistry type like myself, and the other an anaesthesiologist/hyperbaric medicine physician. Perhaps not surprisingly, writing the book took much more of my time, and lasted longer than I had anticipated.  The book, “Gas Bubble Dynamics in the Human Body”, by Saul Goldman, Juan Manuel Solano-Altamirano, and Kenneth M. LeDez is published by Elsevier/Academic Press, and you can find it by clicking on the book title, or by entering ISBN 9780128105191 on your web browser. It’s aimed primarily at researchers and graduate students in the sciences, and medical doctors (anesthesiologists, hyperbaric medicine and emergency medicine physicians).  But there is a long chapter on decompression models which details the scientific underpinnings of SAUL that will be of interest to SCUBA divers, and another chapter on arterial gas emboli (AGEs) in breath-hold diving that will be of particular interest to breath-hold divers.


On Planning a SAUL Dive Planner:

Complete details have not been finalized yet, but some initial decisions were made.  Two things it will not be – It won’t be in the form of dive tables, and it won’t be downloadable for use.  Two things it will be – It will be useable online.  And it will be, at least initially, free.

Figuring out the best way to set up a SAUL dive planner is more complicated than for currently used deterministic algorithms, because it’s probability-based.  This means that there are many more questions you could ask.

For example, let’s consider a simple square-profile, such as is done on a wreck dive. Let’s assume the wreck is level, and you know its depth, so the question is about how much time you may have to explore it. Other algorithms will give you a definite maximum time (the “NDL”) for that depth. With SAUL, however, there are (at least) two ways to approach the question. You could first decide on a personal acceptable level of DCS risk (e.g. P(DCS) < 0.001 ), and from that point, using it like any other dive planner, ask how long you can stay at that depth without exceeding that risk. But another approach would be to think about a range of possible bottom times spent at the depth of the wreck, and ask what your risk of DCS would be if you were to stay for different lengths of time at the wreck’s depth.

True, that’s only two different ways – rather than “many” – of asking the question in that simple example. But dives being planned are often not that simple.  When you consider repetitive and/or multilevel dives, forward and reverse dive profiles, multi-day diving, and breathing gas choices (air/nitrox), the number of ways you can approach the dive planning process, as well as the numbers of questions you can ask, increases considerably.

Ideally, it should be possible to use the SAUL dive planner for any type of question or approach in dive planning.    I will try to make its overall use as simple as I can, but, for this to happen, it would help if I had some input from potential users as to how they might want to use it. I’m not going to ask you to fill out a survey, but if any of you would like to comment on how likely you might be to use the SAUL dive planner in specific different diving situations, I’d appreciate it. As a starting point I’m listing a number of obvious scenarios, but I welcome your suggested additions and elaborations.

  1. a) a single recreational low-risk profile – either square or multi-level – with a safety stop, on air or nitrox.
  2. b) repetitive recreational low-risk square profiles with a safety stop, on air or nitrox.
  3. c) forward and reverse multilevel dive profiles with a safety stop, on air or nitrox.
  4. d) multi-day diving based on the above profiles, on air or nitrox.
  5. e) a single high-risk decompression dive on air – at most one dive per the day.


While I’m working on getting the SAUL dive planner ready, I will also try to start posting again on a somewhat regular basis. If you’re familiar with this blog, you’ll know that, for me, a regular basis is still not very frequent, but the most recent very long gap has been largely because of the book.

More About The SAUL Decompression Algorithm

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.

SAUL and Decompression Dives

How does Saul handle decompression dives or dives that overstay the allowable no-decompression limit (for the chosen level of probability of DCS) ?  I haven’t previously been discussing decompression because I’ve been focussing on recreational diving.  Recreational diving and decompression diving are handled somewhat separately by SAUL, for reasons outlined below.  When SAUL goes into dive computers, it will handle both recreational and decompression diving  (unless a manufacturer wishes to limit it to recreational).  The reason they are handled separately, is that the algorithm was calibrated separately for each type.

Before the dive, along with choosing the probability level for DCS, the diver will select “recreational” or “decompression”.   Neither of these choices can be changed during the dive.


SAUL’s recreational algorithm does not specifically allow for decompression diving.  On the other hand, unlike other recreational dive computers, SAUL will not lock you out even if you exceed your chosen probability level.  It will continue to update and show you your probability of DCS.  You will see some improvement in  probability with a longer safety stop.   At all stops, whether safety or decompression, the greatest benefit is achieved in the earliest part of the stop.  While benefit continues to accrue throughout the duration of the stop, it does so at an increasingly slower pace.  Obviously, the real problem with trying to significantly decompress on dives planned as  recreational is that you wouldn’t have sufficient air remaining to manage it.


Decompression dives work much the same way as recreational dives except for the stop.  Thus, before starting the decompression dive, the diver would input their maximum acceptable risk, and would input the fact that the dive is to be a decompression dive. (The latter tells the computer to use a decompression diving-based calibration for the underlying model). Then during the dive, the dive computer, every few seconds, tells the diver how much time is left at the depth the diver is at, so as to ultimately ascend with a total risk (ascent risk + risk at the surface) that doesn’t exceed the allowed risk (again, exactly as in no-decompression diving). When its time to come up, the dive computer tells the diver how much time to spend at specified stop depths, so as to surface within the acceptable inputted risk.

Generally, the stop depths for decompression diving start at a deeper 1st stop (e.g. 25 or 30 fsw, rather than 15 fsw), relative to no-decompression diving.  Obviously, less time is needed when on nitrox than when on air, for the same level of risk. Also, of course, the total time spent at all the decompression stops will, in decompression diving,  be considerably greater than the 2-5 minutes typical for no-decompression diving.


SAUL has been calibrated for use in air decompression diving, assuming a maximum of 1 dive per 24 hour period. It will also become available, hopefully in the not too distant future, for use in trimix decompression diving using rebreathers.


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.

Decompression Sickness in Breath-Hold Diving

Decompression sickness is not just a worry for scuba divers – some “free” or “breath-hold” divers also suffer from it occasionally.  This could come as a surprise to you, if you had previously taken for granted that you have to breathe pressurized gas containing nitrogen to get “bent”.

Many of you are aware, at least vaguely, of divers in the South Pacific who free-dive to harvest pearls commercially.  You may also be aware of the competitive sport called breath-hold diving. Possibly, you even participate, or know people who do.   Interestingly, both these types of diving, very different from each other as well as from scuba diving, can sometimes lead to decompression sickness.

First, how are they different?  The most obvious difference between both types of free-diving and scuba is: no scuba, i.e., no underwater breathing gas. This leads to other differences.  With less internal gas pressure in the lungs, the lung volume decreases under the pressure of increased depth. With immersion, and increasing depth, a number of other physiological changes occur, collectively known as the “diving reflex” that makes breath-hold diving feasible. These include a slowing down of the heart rate and decreased peripheral circulation, which allows near normal circulation and perfusion to the heart and brain to be maintained.

The differences between the pearl divers and competitive breath-hold divers, while in one sense quite pronounced, are essentially differences in the nature of the dive profiles.  The pearl divers would dive to a range of depths, sometimes to over 100 fsw, with a bottom time of 30 to 60 seconds for a total underwater time of about one and a half minutes per dive. With approximately one minute of surface interval between dives, they would then repeat the process for perhaps 6 hours daily.   By contrast, competitive breath hold divers generally do a single very deep dive, the actual depth and bottom time achieved being specific to the particular competition, but, with the aid of specialized sleds and buoyancy devices, depths of 150 – 250 meters can be – and are – achieved.

It has long been known that the pearl divers of the Tuamato archipelago (near Tahiti) do suffer some ill effects from their diving practices, a sickness known locally as Taravana which translates – very roughly – as “falling crazily”.  More recently, cases of probable inner ear decompression sickness and probable cerebral decompression sickness have been diagnosed. The number of cases of Taravana or DCS decreased dramatically when the surface intervals were increased from 1 minute to 15 minutes.

In the case of competitive “breath-hold” divers, it used to be thought that decompression sickness could not occur, the idea being that the small amount of nitrogen present in a single free dive was not enough to lead to DCS.  Two reported cases, one of cerebral DCS, one with both cerebral and inner-ear DCS symptoms, have shown that DCS can and does occur, even in single free dives. There also have been relatively frequent descriptions by breath-hold divers, after certain types of dives, of symptoms consistent with inner-ear DCS.

From my research group’s 2014 paper, “The lifetimes of small arterial gas emboli, and their possible connection to Inner Ear Decompression Sickness”, which was based on arterial gas emboli in scuba diving, we were able to extend the calculations to both types of breath-hold diving. In the resulting paper, “Decompression Sickness in Breath-hold diving, and its probable connection to the growth and dissolution of small arterial gas emboli”, Mathematical Biosciences, 2015,  the calculated predictions, were consistent with the observed occurrence of DCS in both types of breath-hold diving.

(Copies of both the 2014 and 2015 papers can be read in the Articles section of this blog.)



Unfortunately, some divers are confused or irritated by the fact that SAUL is a probabilistic algorithm, particularly those looking to compare it directly with other existing algorithms in terms of what dive profiles are permitted.   The comparisons they would like to see are, essentially, between NDLs.  SAUL doesn’t have a set of NDLs to compare with.  Here’s why not.

First, a clarification:  It’s not that SAUL doesn’t use NDLs at all, just that they’re not pre-set ones.   In effect, the diver calls up an individualized set of NDLs by setting an acceptable degree of risk (of  decompression sickness).  One “size” does not fit all NDL needs.  Reasonable people can – and do – differ on how much risk they are prepared to take, both in general, and in specific situations. SAUL is sufficiently accurate that it can viably use a probabilistic algorithm, and it chooses to do so for the following reasons.

1.   In diving – as in other aspects of life – adults with access to adequate information are presumed responsible enough to make decisions for themselves (and for any children under their supervision).

2.  One important piece of the information divers need to keep in mind is that there is always some degree of risk in diving.  Over-reliance on fixed NDLs may mislead some divers into forgetting that fact.   An NDL does not mean that divers are always safe under that limit, always in danger above it.  Actively choosing an acceptable level of risk helps divers keep that in mind.

3.  The most important reason, though, is that a probabilistic algorithm is the most realistic way to deal with the occurrence of decompression sickness in diving.  This is true even just considering the general reasons outlined in an earlier posting   (NDLs, etc.). But it is the chaotic behaviour of bubbles themselves that makes a probabilistic algorithm particularly appropriate for any serious attempt to deal with the risks in diving.

Bubble behaviour can vary drastically depending on exactly where, and under what circumstances, the bubble arose, its size, whether it has entered the bloodstream and, if so, where it’s carried from there.  Most of these factors are matters of chance and unpredictable in advance.

I mention “where the bubble arose” as a factor because my research found that bubbles embedded in a soft elastic solid (i.e., muscle or cartilage tissue) will behave very differently from bubbles in a more liquid environment like blood.  In some cases, a bubble in a soft elastic solid may persist for long times, or grow, even when the tissue it’s in is undersaturated.

Luckily, predicting the behaviour of individual bubbles is not necessary in order to manage the danger of decompression sickness.  In general, algorithms try to do this by  calculating, in accordance with their particular underlying models, the accumulation and dispersal of excess nitrogen in the body.  Most algorithms then set NDLs based on the calculated nitrogen load.  It’s obvious that the frequency of decompression sickness is strongly correlated with the presence of excess nitrogen in the body.  And it’s also true that the presence of excess nitrogen in the body is correlated with an increase in the number and size of bubbles and, therefore, an increase in the cumulative  probability that one or more individual bubbles will cause problems.  This cumulative effect of bubbles on decompression sickness is already taken into account by calibrating algorithms with known data.  A more accurate algorithm (like SAUL) will do it better.

But it’s equally obvious that decompression sickness can, and sometimes does, occur when it seems to be “undeserved”.   Since bubbles are believed to be the initiating cause of decompression sickness, certain algorithms have purported to account for bubble behaviour in their calculations.  For reasons described above, this does not, and cannot work.  In my view the only proper way to take into account individual bubble behaviour is to recognize and work with its chaotic and therefore probabilistic nature.

(For anyone interested, my latest paper, Gas bubble dynamics in soft materials, has just been published by The Royal Society of Chemistry and has now been posted here under Articles.)

Once the degree of nitrogen saturation is accounted for, the additional effect caused by bubbles is effectively summarized by the bit of verse below.

on probability


Halloween is almost upon us, so it seems like a good time to talk about some seriously scary stuff:  Neurological DCS and inner ear DCS – the really bad cases of the “bends”- that can sometimes result in permanent  paralysis, deafness, even death.

You may be aware that many cases of neurological DCS are the result of a PFO (Patent Foramen Ovale) which is, essentially, a hole in the septum of the heart that divides the right side (which receives blood from the veins) from the left side (which pumps out oxygenated blood to the body).   Venous blood passing through a PFO into the arterial system is not in itself a problem, except in the case of “medically significant” ( i.e. large) PFOs.   PFOs are not uncommon in otherwise healthy individuals and usually go unnoticed.   These individuals may also naturally develop small bubbles in their circulatory system, some of which may occasionally pass through even small PFO’s.

Even when bubbles do pass through the PFO, these AGEs, or Arterial Gas Emboli (which is what they are known as once they reach the arterial system) are usually harmless – until we consider diving.   This is because  AGEs coming through PFOs are generally small, which makes them thermodynamically unstable.  Larger AGEs, if they were to occur, would be more stable, as both they and arterial blood would be pretty much equally saturated with gas.  But with a small AGE, the surface tension increases the pressure on the gas within it, which causes it to dissolve rapidly.  No more bubble, no problem.

By changing just a few features of an essentially harmless situation, compression and decompression during diving turn it into a  potentially dangerous one.  These are the changes that matter:  1) During compression, body tissues accumulate increasing amounts of nitrogen so that, during decompression, they become super-saturated with nitrogen; 2)  During decompression, the number and size of bubbles in the veins increase;  3)  The size of bubbles decreases during compression.

Here’s what happens then.

The first result of these changes during a dive is a much greater probability that a bubble will pass through the PFO, simply because there are so many more of them.  (While the increase in number of bubbles occurs during decompression, remember that decompression includes, roughly speaking, all time spent after ascending from the deepest point of the dive.)

The second result is that a bubble with more gas in it could get in at depth than could happen when not diving.  How can this be, when the size of the PFO hasn’t changed?   When the size of bubbles decreases during compression, there are actually two separate things happening: One is that gas is escaping from bubbles under pressure – less gas in the bubble makes it smaller and some bubbles will disappear.  The other thing that happens is that bubbles under pressure become smaller even without losing any gas.  The radius of the bubble gets smaller, but it contains the same amount of gas.  The effect of this is that a bubble small enough to pass through a small PFO will contain more gas at depth than will be in a bubble with the same radius at the surface.  Or, to put it another way, a bubble that might be too big to pass through a PFO under normal (surface) conditions might be compressed enough at, for example, 100 fsw. to pass through.

So, we’re more likely to have a bubble pass through a PFO, and that bubble, now an AGE,  will be slower to dissolve than an AGE of the same radius formed at the surface.  This makes it more likely that the AGE will survive long enough to exit the artery into the capillaries of tissues that are supersaturated.

If the AGE does reach supersaturated tissues, it will grow, taking on nitrogen from the supersaturated tissues, and, if it gets large enough, can damage the tissues by blocking blood from reaching them (producing what’s known as ischemia) and/or by directly damaging some very sensitive tissues, like those in the inner ear, as just the pressure exerted by the growing bubble may be enough to cause them to tear.   When this damage takes place in brain, spinal column or inner ear, the damage is often permanent.

While PFOs are the most common route for bubbles to become AGEs, they can also access the arteries through AVAs (Arterio-Venous Anastomoses, which are remnants of fetal pulmonary shunts bypassing the lungs that didn’t fully close at birth), or through the lungs themselves, when alveoli of the lungs fail to completely filter out the bubbles from the venous blood.

I have a scientific interest in AGEs, and have recently published a paper on “The lifetimes of small arterial gas emboli, and their possible connection to Inner Ear Decompression Sickness” which looks at the time required for an AGE of a particular size to dissolve and the time required for it to reach the inner ear.  (I used the inner ear, because the arterial route to it is more amenable to calculation.)  I’ve posted it under Articles, just in case anyone is interested.

But, like all of you, I have a personal interest, as a diver, in avoiding DCS in general and these particularly nasty manifestations of it in particular.  Here are some precautions you may want to consider:

1.  If you have a specific reason to suspect an PFO, you definitely should see a doctor, preferably one experienced in diving medicine, for further investigation.   One example: you should suspect a PFO if you have had undeserved skin bends on more than one occasion. (And, by “undeserved” I mean, not just that you were technically within the limits set out by whatever NDL or dive computer you were using, but that you were far away from any such limits.)    In some cases where a PFO is found to exist but is not “medically significant” a doctor may suggest that, if you continue to dive you should dive “conservatively”.

2.  Unless you know otherwise, it’s safest to assume that you do have a PFO, an AVA or that the alveoli in your lungs miss filtering some bubbles.

Let’s suppose, then, that either you’ve been diagnosed with a PFO (but still permitted to dive), or that you’re being prudent by assuming you may have one.  What does diving “conservatively” mean in this context?

To start with, it means doing essentially the same things you already do to avoid any form of DCS.   (Once SAUL is available in computers, I would also suggest setting it for a lower acceptable probability of DCS than you might otherwise be inclined to do.)    Beyond, this, to dive conservatively, you might particularly want to:

a)  Allow a long surface interval between dives.  Never do a second dive less than an hour after the first.  Waiting more than an hour, if feasible, is even better.

b)  If you’re a smoker, consider stopping.  Smoking damages the lungs, which means it may increase the likelihood of the alveoli letting more and/or larger bubbles into arterial circulation.

c)  Where feasible, do all your diving on Nitrox.  If you aren’t already certified for Nitrox, get certified.

d)  Wait at least 24 hours after diving before flying (or sightseeing, etc. that involves altitudes over 6,000 ft.)

e)  Remain well hydrated.

Update – October 2014

It’s time for an update on when SAUL will be out in a dive computer.

The bad news is – there’s nothing definite yet.

On the plus side, I have contacted some computer manufacturers and am continuing to identify and contact others whose computers would benefit from incorporating SAUL.  Still on the plus side, SAUL is completely dive-computer-ready, lacking only the specific software connection between it and any given computer (a user interface that will work with SAUL).  For this reason, I haven’t given up on a potential 2015 release of SAUL.  It’s a bit of a long-shot at this point, but not out of the question.

If you have a favourite mid-range dive computer in mind that you’d like to see SAUL in, feel free to suggest it to the manufacturer.  I’d welcome inquiries, whether or not it’s from one I have already contacted.

On to other matters.  Part of the reason I haven’t posted for a while (aside from efforts re SAUL) is an active research program.  I have a very capable young researcher from Mexico in my lab who’s now approaching the end of his 3 year term.  Together, we’ve produced a sizeable body of interesting research.  The downside to that is the somewhat tedious and time-consuming process of transforming that research into published papers.  With one substantial paper published this summer, there are still another 4 or 5 papers at various stages of their evolution towards a published state.

The focus of the research was on the fundamentals of bubble behaviour.  Along the way, some of what we’ve found has interesting implications for diving, including PFO’s, inner-ear DCS, muscle and joint DCS, and DCS in breath-hold diving.  I will be discussing some of this in future posts, as each relevant paper is published.  (The reason for waiting is so I can post the published paper in the Articles section at the same time.)