We spent a solid 90 minutes practising multiple skills and emergency drills; a most productive and valuable dive which will certainly be repeated in the near future!

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A staple of discussion amongst divers is the question of which decompression algorithm they use. From Haldanean to RGBM, to Bühlmann + Gradient Factors (GFs) and VPM-B (and any proprietary combination you care to throw in between), the options are considerable.

One of the pertinent questions on the topic is the issue of whether to adopt:

(1) **A bubble modelling approach** (e.g. VPM-B) that inserts deep stops into one’s dive profile (‘Deep Stops Profile’ hereafter), or

(2) **A dissolved-gas model** (e.g. a Bühlmann algorithm) that cuts down on deep stops in favour of longer shallower stops (‘Shallow Stops Profile’ hereafter).

In this article I assume that the reader has some basic familiarity with the two classes of model in question, so I will not dwell on that here. I will only say that from a theoretical standpoint, there are arguments that would favour either approach. So how could we decide between these two options? In science, such a decision can only be taken on the basis of empiricism, i.e. experiment. In other words, carry out a survey of an appropriate sample of dives on profiles dictated by both approaches, and pick the one that results in a smaller probability of decompression sickness (DCS) cases following the choice of an appropriate statistical test. This was the motivation of a 2008 study by the U.S. Navy Experimental Diving Unit (NEDU), authored by David Doolette, Wayne A. Gerth and Keith A. Gault and made public in 2011.

Much has been discussed already about this study, particularly on online fora, sometimes leading to very heated back-and-forths. Part of the discussion revolved around the question of equivalence (or, as the opponents argued, lack thereof) between the deep stop profiles adopted in the NEDU study and the actual deep stops profiles followed by divers in real-world situations; the arguments raised were answered there. **This article has nothing to do with that matter.**

**In this post, I wish to focus on** a different question altogether, namely **the interpretation of aspects of the NEDU study, specifically the statistical significance of the probability of DCS (for the two approaches) presented by the study**. I am referring in particular to Figure 2 of that report, which is being reproduced below, and which shows the DCS incidence for the two approaches:

Subsequent sections of the NEDU report include an investigation of Venous Gas Emboli (VGE) grades and a theoretical discussion of the reported results on DCS and VGE outcomes, but the main thrust of this study is the incidence of DCS as presented in the above figure (which is also the most often referred to result by divers who are aware of this study), at least in my experience.

Let me clarify an important point at the outset: my aim with this article is neither to support nor dismiss this report. The NEDU investigation is a careful study and the authors’ effort should be commended. The reason for this article is that I have time and again encountered arguments amongst divers that misinterpret the findings, very often because they’ve either not read the study itself, or because of a misunderstanding of the subtleties of statistical analysis. What I intend to achieve with this post is to elucidate what that plot is actually telling us, and the statistical significance associated with it.

Without further ado, let us dive in.

The authors are interested in finding out whether deep stops profiles dictated by a bubble model are more efficient than shallow stops profiles dictated by a gas content model. The gas-content model in use was VVAL 18 Thalmann, whereas the bubble model was BVM(3).

There are many different kinds of statistical analysis you can employ, and oftentimes the choice is dictated by the type of the experiment being carried out. The statistical analysis used in the NEDU study involves what is known as an **exact test**. More specifically, the test in use is known as **Fisher’s exact test**, named after its inventor, biologist and statistician Ronald Fisher.

What an exact test allows you to do in practice is the following: Suppose you want to find out whether there is a relationship between two given phenomena. You begin by assuming what is known as the ** null hypothesis**. The null hypothesis declares: “There is no relationship between the two phenomena.” Next, you try to reject this null hypothesis (i.e. nullify it, hence the name). If you manage to reject/nullify it, in effect you can say that there *is* a relationship between the two phenomena in question; in other words, you’ve found support for your **alternative hypothesis** that there *is* a relationship.

An exact test gives you the ability to be specific about your claim. First, before anything else, you choose what we call a **significance level**. Let us say you choose a significance level of 5%. That means that the study will have a 5% probability that it rejects the null hypothesis *even if it were true*. So in other words, **at a significance level of 5%, you can expect your study to mistakenly reject the null hypothesis 5% of the time in the long run**.

Now, let us say you are ready to accept this 5% “risk” of mistakenly rejecting the null hypothesis. You next carry out your experiment. Following this, you run your test statistic (e.g. Fisher’s exact test) on your result, and you get out **a number that represents the probability of obtaining your result IF the null hypothesis (which you want to reject) is actually true**. This number is known as the **p-value**. As you can infer, you don’t want this to be a large number.

**If the p-value you get is small, specifically smaller than the 5% significance level** you’ve adopted, then there’s too small a probability that you would obtain your result if the null hypothesis were true.

Therefore, the null hypothesis must be false, and therefore **you reject the null hypothesis**. On the other hand, **if the p-value is higher than your adopted significance level, you cannot reject the null hypothesis**.

Many research papers, including this study, employ this 5% threshold. This is merely an accepted convention, not some deeply revered number. Mathematically, this threshold is denoted by the Greek symbol α (alpha), such that a confidence level of 5% is written as α=0.05 (because 5% = 5/100 = 0.05). If the result of your test statistic yields an outcome (p-value) smaller than 0.05, then your result is statistically significant. Say you get a p-value of 0.02. 0.02 is less than 0.05, so you’re good.

So in summary: **the p-value obtained by your test statistic has to be less than the adopted significance level, α, if your result is to be deemed statistically significant. **

Now, one last word. If you’re not happy with a 5% threshold, i.e. if you feel that the chance of mistakenly rejecting the null hypothesis 5% of the time is too high for your comfort, then you can choose to adopt a smaller number (e.g. 1% or 0.01) for your study. That means that your p-value has to be less than 0.01 in order for your result to be statistically significant. The choice of threshold boils down to the following question: **what level of risk of wrongly rejecting the null hypothesis am I happy with?** 5%? 3% 1%?” Many papers use 5%. Some choose a more stringent threshold.

In physics, and in particular particle physics, the convention is that we use a p-value less than 0.003 (what we call a 3-sigma event) to say that a given result constitutes evidence for a phenomenon (e.g. evidence for a new particle), and a p-value less than 0.0000003 (a 5-sigma event) to call the result a discovery. This is much more stringent than most scientific papers.

Now, the way you proceed with this article from this point onwards depends on you. **If you feel like going into the details** of what a Fisher’s exact test is, and in particular would like to see some numbers, **then the green box below is for you**. If not, I am giving you the option to close the box (upper right corner) and proceed with the rest of this article.

Right, we are ready to move on to the NEDU study and apply our newfound knowledge of statistical testing.

Putting the NEDU study within the statistical framework we detailed above, this is what it’s saying:

In such a case, we will be using the same statistical test chosen by the authors, a * one-sided* Fisher’s exact test, with the alternative hypothesis being “greater” (i.e. we expect a larger probability of cases with a good outcome). If we do NOT find a statistically significant result according to this test, we do not have strong support (alternatively, our evidence is weak) that a deep stops profile is better. And we would say: “OK, we’ve tried to find evidence that a deep stops profile is better, but

If, on the other hand, while testing in this direction (that a deep stops profile is more efficient than a shallow stops profile) we indeed find support that a deep stops profile might be more efficient than a shallow stops profile, we say we have a statistically significant result. Now, we might be tempted to shout “hey, clearly a deep stops profile is better”. However, really, we should be careful. We have tested only in one direction. We decided a priori that our null hypothesis was going to be that “a deep stops profile is AS efficient as, or LESS efficient than, a shallow stops profile”, and are interested only in the result that a deep stops profile is more efficient than a shallow stops profile.

However, we really ought to entertain the possibility that a shallow stops profile might be better than a deep stops profile, given that our departure point should be that we do not know. Accounting for this possibility by adopting a two-sided (or two-tailed) test, reduces the statistical significance of a positive result in the first direction we were testing. The takeaway here is the following:

(1)** Testing in the same direction as the result you expect and obtaining a p-value larger than your significance level (a “negative” result) **constitutes a lack of statistical significance; you are “free” to stick to the “old” approach you have been using until now (pending a larger study perhaps). You cannot reject the null hypothesis because you don’t have a statistically significant result.

(2) **Testing in the same direction as the result you expect and obtaining a p-value less than your significance level (a “positive” result)** constitutes statistical significance, but does not provide enough justification to deem the supported approach conclusively better than the other UNLESS you also test in the opposite direction.

In summary, **ideally we should carry out what is known as a two-sided test, testing in both directions of possibility**.

As it turns out, and for a good reason which will be described in the next section, the authors of the study did not proceed with the hypothesis framework described in the “NEDU Original Framework” box above.

Given that the end-result of this study was DCS, the authors rightly tried to minimise unnecessary injury to test subjects. Therefore, they decided in advance that once they would reach the midway point (i.e. once they would reach 188 test dives out of the envisaged total of 375), they would “pause” and analyse the results, and if a significantly greater incidence of DCS was found for the deep stops profile than for the shallow stops profile, the trial would be put to a stop right there and then.

Putting their midpoint analysis in a statistical framework:

In this case, we shall again be using the one-sided Fisher’s exact test (chosen by the authors), with the alternative hypothesis being “less” (i.e. fewer cases of good outcome). If we test in this direction and indeed find that there are fewer good outcomes, then we might say, “hey, we tested in this direction (fewer cases of good outcomes) and we find support for that. We don’t want to take further risk and possibly injure our subjects. So we’ll stop our experiment here”.

However, as we saw above (in the orange box), finding support **in the direction you are testing** is NOT sufficient to conclude that this is necessarily the better approach.

Basically, we have excluded testing in the other direction (alternative hypothesis being “greater”). We have not tested the possibility that a deep stops profile might be better (i.e. gives a larger probability of good outcomes) than a shallow stops profile. Not testing in this other direction **as well** means that **we cannot decisively choose which is the best out of the two options of dive profile**.

Let me be clear: from an ethical point of view, in terms of protecting the test subjects of the study, the approach of stopping the trial if you found one-sided statistical significance that the new approach (a deep stops profile) yields a smaller probability of good outcomes is justifiable. **Given the context within which the study was carried out, namely the fact that the U.S. Navy would depart from continuing to use shallow-stop profiles ONLY in case of the “finding of significantly lower P _{DCS} [probability of DCS] for the bubble model schedule [deep-stops profiles] than the gas content model schedule [shallow-stops profile]” the choice of a one-sided test is appropriate**, as the authors point out.

What the above approach does NOT inform us about, is which of the two approaches (deep stops or shallow stops) is “the best”. In order to come to solid conclusions, we need to carry out a two-sided test that entertains both possibilities, because we simply do not know a priori which is the best of the two. **When trying to decide between two possible approaches, with the point of departure being that we do not yet know if there is any difference between the two and are equally interested in either outcome, then we carry out a two-tailed test. **

Let us say we are trying to establish whether there is any difference between two approaches, let’s call them A and B. Is the incidence of successes (good outcomes) equal for both? We would like to show that it is not. Our null hypothesis is that there is no difference between the two approaches, and that both yield the same result. (A “neutral” null hypothesis.)

So next we carry out the experiment. Let us say, for the purpose of this example, that we find A seems to be giving us a greater number of successes than B. We then run our two-sided test statistic, say a two-tailed Fisher exact test, and get a low p-value, smaller than our adopted significance level. In such a case, we can say that there is a difference between the outcomes of A and B at a statistically significant level. (If our p-value is found to be higher than the significance level, all we can say is that we do not have a statistically significant result. Full stop.)

In other words, within a statistical framework, we would like to pose our question about the two decompression approaches as:

However, as we’ve mentioned before, the authors carried out a ** one-sided** Fisher’s exact test (with α=0.05) at the midpoint analysis. What they are interested in here is the question of whether the deep stops profile is less efficient than a shallow stops profile (that’s the alternative hypothesis), lest they continue with the experiment and end up hurting the test subjects. They want to reject (the null hypothesis) that the deep stops profile is equally efficient to, or more efficient than, a shallow stops profile. Indeed, when the problem is framed this way, there is statistically significant support for their alternative hypothesis (smaller probability of DCS-free outcomes in a deep stops profile than in a shallow stops profile), and that justified the ending of their trial on ethical grounds. However, as we have seen, this result does not conclusively tell us which approach (deep stops profile or shallow stops profile) is more efficient. It merely tells us that up to the number of cases they tested, they found a result that supports their expected result

To make this as clear as possible, let me remind you what we said earlier on: just like many research papers, this report adopts the conventional significance level of 0.05 (i.e. it has a 5% chance of mistakenly rejecting the null hypothesis); that means that **the test result is deemed as statistically significant if the associated p-value is less than 0.05**. If it’s more than 0.05, it is deemed NOT to constitute a statistically significant finding. One could argue that 0.0489 is fairly close to 0.05, but strictly speaking, it passes this test because it’s below the adopted threshold. (The nature of p-values is such that the reader should then decide for themselves whether they find the adopted cutoff and the test result acceptable or not.)

In all this, it is important to keep in mind the context of the original question, and remember that a **one-sided** test is being used.

**If we were to frame our question as in the two-sided framework box above, adopting a two-sided test (i.e. testing in both directions of possibility), ****we would find a p-value of 0.087**, i.e. there is an 8.7% probability you would find a difference between the two algorithms *even if* the null hypothesis is true, i.e. even if the deep stops profile is, after all, as efficient as a shallow stops profile. 8.7% falls outside our acceptable 5% threshold. This means that **the result of a two-sided test applied to the hypothesis as stated in the two-sided framework box is not statistically significant**.

*(In the above, I have run the math and coded it up myself, but in the interest of space I have only presented the results.)*

Purely for purposes of illustration, let us take this analysis a bit further. Given the numbers of this study:

(1) **Had there been one more DCS case amongst the deep-stop profiles, i.e. a result of 11/198 DCS cases** (instead of 10/198), a two-sided Fisher exact test would have yielded a p-value of 0.054, i.e. **still NOT a statistically significant result** (adopting the p=0.05 cutoff).

(2) **Had there been one less DCS case amongst the shallow-stop profiles, i.e. a result of 2/192 DCS cases** (instead of 3/192), a two-sided Fisher exact test would have yielded a p-value of 0.036, i.e. **a statistically significant result**.

In case (2), we would have some certainty that there is a significant difference between the two approaches, because testing in both directions yields only a 3.6% chance of obtaining such a result even if the null hypothesis (that there was no difference) were true.

However, there’s a lesson to be learnt here. As you can see, **a tiny change in numbers (essentially just one datapoint) can shift the significance of the result. This is why the ideal way forward would be to collect more data, i.e. test more subjects.** The problem is that more data comes at the risk of harming more test divers. And that’s where ethical considerations come into play. This, I hope, helps you appreciate that indeed, the authors had to face quite a difficult decision. The options are:

(1) Carry out a larger study (i.e. collect more data) and carry out a two-sided test, potentially getting a statistically significant result that would help us learn more about difference in efficiency between the two profiles, or

(2) Place more importance on the safety of our subjects, and as soon as we suspect that there might be a risk of injury if we were to continue with our test, we stop.

Given that, as the authors themselves state in the introduction, “whether one approach is more efficient than the other is unknown”, a two-sided statistical test is desirable. Indeed, here I point the reader to Ruxton & Neuhäuser (2010, with whom I wholeheartedly agree) who point out that “we very rarely find ourselves in a position where we are comfortable with using a one-tailed test”. The nature of the NEDU study, however, entailed a real possibility of further injury to test subjects, and so the study foregoes two-sided statistical significance in favour of protecting the divers under study, utilising a one-sided test that delivers a statistically significant result with less data than a more demanding two-sided test would.

As a complete aside which you can skip (hence the fainter font colour), moving away from this study to speak more generally, it seems that a problem in biology literature is that authors often opt to use a one-sided test inappropriately. Lombardi & Hurlbert (2009) carried out a survey of every study published in 2005 in the two journals “Oecologia” and “Animal Behaviour” and found that 17% of the quoted p-values were derived from a one-sided test, whilst in 22% of cases the reader would not be able to tell whether a one- or two-sided test had been carried out. Ruxton & Neuhäuser (2010) also report that from their survey of a total of 359 papers in the journal “Ecology”, 17 (i.e. 5%) employed a one-sided test, and with the exception of one study, Ruxton & Neuhäuser (2010) find that this choice of one-sided testing was not appropriate.

There is one final aspect about Fig. 2 of the NEDU study that we haven’t yet mentioned. You might notice that each bar has a vertical line running through it. This is what is known as a **confidence interval**. Specifically, the authors tell us in the caption that they are using a “Binomial 95% CI” (CI=Confidence Interval). What does this mean?

Let’s say you wanted to present the result of some study you’ve carried out. You could show the mean of your data, for example. That’s a result encapsulated in a single point estimate. However, your readers would also be interested in having an estimate about other plausible values that the parameter in question might take in the population you’re sampling. That’s where the confidence interval comes in.

The confidence interval is giving us a range of plausible values that is likely to encompass the value of the population parameter we are interested in (the DCS incidence in the case of the NEDU study). This will become clearer by means of an example. But before we do that, let me just formally define the level, *C*, of the confidence interval. The level *C* of the confidence interval tells us the probability that the interval we produced contains the true value of the parameter of interest. Here’s an example. **Suppose the level C of the confidence interval is 95%. That means that the probability that the interval (drawn on the figure) contains the true value of DCS incidence is 95%.** As you can appreciate, the smaller the interval is, the better, because the narrower the range of plausible values would be.

Whilst going through the data and analysis of this study, I coded up the math and reproduced Fig. 2 myself. (I am not privy to the precise calculation the authors employed to compute the confidence interval in question.) For the mathematically interested reader, in my case I used the Wilson method to compute the CI. This gives me a slightly wider confidence interval for both cases, most appreciably for the Deep Stops case.

In scientific experiments it is of paramount importance that if a human decision is involved, the person taking that decision and logging the data is blind as to which trial the data came from to eliminate unconscious bias. The authors properly admit that for reasons of practicality, this study was not blind*: “*This large man-trial had unique potential for response or diagnosis bias because it was not practical to conceal the diverging DCS incidence on the two schedules, not possible to blind diver-subjects to the schedules, and some DCS presented as subjective symptoms only.*“

Appendix D opens by saying that “*the tables below give the case narratives written by the attending Diving medical Officer*”. Reading through the narratives, one encounters phrases such as the below three examples (bold font is my own):

- “
*34 year old active duty Navy diver presenting with right shoulder pain beginning 2 hours after surfacing from <gap> dive*“**under profile A1**. - “
*37 year old, active duty, male diver with 14 year history of Navy diving and no previous history of DCS injury completed a 170/30*”**experimental dive****(profile A2)**… - “
*A 37 year old active duty male diver completed*”**experimental**170/30 “deep stops” decompression dive… - “
*The test diver surfaced from a 170/30*”**(A-2 profile)****research profile**at 1223 hrs.

As is clear from the above, the DMO knew which dive profile was being followed on a given dive. And despite the best and purest of intentions, it is possible that if a DMO feels that they are assessing an “experimental” dive profile, then they would be more wary than usual, a situation that can lead to subconscious bias. If, on the other hand, the DMO had more faith in the “experimental” profile, this could lead to bias in the opposite direction. So we have a situation where neither the test subject nor the assessor (DMO) is blind to the category in which the dive falls (shallow stops or deep stops). Of course, for added safety reasons, whoever gets to treat the diver should know the case history, so the need for a DMO who is fully aware of the dive history is perfectly understandable. However, this does nothing to prevent potential bias from creeping in the study.

A possible way to mitigate this could be to have 2 DMOs: DMO 1 is blind about the study and case history, and simply writes down their assessment which is in turn used for the study. DMO 2 is fully aware of the case history and is given authority in the sense that, for extra safety, if DMO 2 feels the diver should undergo recompression treatment, it is *this* decision that is followed (while DMO 1 is kept blind). This is still not a perfect solution, but it helps to mitigate subconscious bias; DMO 1 is deciding basing ONLY upon the symptoms presented, and not any concern they might have about the fact that the dive was “experimental”.

Bias can go *both* ways, and trying to predict all possible factors of bias is mostly a hypothetical exercise and not a secure way of preventing it. The only way to be sure it’s eliminated is by designing (ideally double) blindness into an experiment.

**The authors comment, however, that the deep stops also generated higher VGE grades than shallow stops, and these are not subject to bias (e.g. a diver cannot increase their VGE grade just by thinking they might be bent).*

I wanted to mention one last thing about the kind of statistical analysis we’ve discussed in this article. The methodology we’ve talked about can be referred to as “classical hypothesis testing”. As we have seen, it is an approach that strives to reject a hypothesis (the null hypothesis) in the process giving us confidence in the alternative hypothesis. It does NOT, however, prove the alternative hypothesis. It is somewhat in our nature to be inclined to think that rejecting the null hypothesis automatically means proving the alternative hypothesis. However, our alternative hypothesis is just that: an alternative. It is not necessarily the only one; there could very well be others.

So where do we go from here? What is the whole point of this lengthy analysis and discussion of Figure 2 of the NEDU study? What should one take from all this?

First off, on the basis of these numbers, specifically, the aspect of this study dealing with incidence of clinical DCS, **we should be careful about claiming that we know for sure which is the best decompression modelling approach**.** The data does not really provide a definitive conclusion about this.** I would not be comfortable to claim otherwise; **I would very much like to see a statistically significant result from a two-sided test**. Moreover, the study has some shortcomings, such as the issue of blindness which, admittedly, can be hard to implement in a study of this kind. The study also had strengths; the subjects being Navy divers means that there’s a degree of commonality in their fitness that helps to make the sample somewhat more uniform.

There might very well be other studies in progress right now the results of which might eventually help us gain a better idea, but until such studies are completed and published, we cannot tell for sure. They might end up confirming the suggestions of this study, or not.

If I were to summarise the points going for and against this experiment, this would be it:

**FOR:**

(1) The **sample is probably fairly uniform**, in that it consists of experienced Navy divers with a degree of commonality in their fitness. (This reduces dependence on variables such as poor cardiovascular health, being overweight, etc.)

(2) A **one-sided test**** yields a statistically significant result**.

(3) **VGE counts seem to agree** (although VGE counts are not tantamount to DCS; the endpoint is clinical DCS).

**AGAINST:**

(1) **If we apply a two-sided test, we do not get a statistically significant result**. The study did not use a two-sided test (which test makes it harder to achieve statistical significance). Carrying out a two-sided test effectively means that we wouldn’t be focusing on just one direction. Our starting point is that we do not know if there is a difference between the two decompression approaches, and if there is, in which direction. If we take this approach, the experiment does not yield a statistically significant result.** **More data would be desirable, as can also be appreciated from the fairly wide confidence intervals.

(2) **The study is not a blind experiment**. Neither the subject nor the assessor (of whether a diver has suffered DCS or not) was blind as to which dive profile was followed.

(3) The combination of (1) and (2), i.e. the **combination of** **being a non-blind experiment making use of a one-sided test**, decreases the robustness of the study.

For my diving, **I do take into account the findings of the NEDU study**. Given the support – on the basis of

Specifically, I am diving on a Bühlmann ZHL-16C + GF algorithm, with a GF selection of 30/70. However, for added conservatism, once I’m in the shallows I usually try to clear the subsequent (shallower) stop while still holding the stop below. Moreover, I tend to pad my last (shallowest) stop by a few minutes as a further precaution. In this regard, my usual dive profile ends up looking more like a 30/65 than a 30/70. As for the low GF of 30, I am comfortable bringing that up to 40 or 45 (in effect moving further away from deep stops), but that’s as high as I’m happy to increase it for now.

Pending further studies, I do not have evidence that deep stops are more efficient, so overly stressing their importance is not a sensible approach. There are also other reasons for my choice, such as the seemingly higher median VGE grade described in the second section of this study (although, admittedly, a higher VGE grade is not tantamount to DCS) as well as *theoretical* considerations, but this article is long enough as it is, so I will not go into these topics here. Perhaps a post for another time. In the meantime, **despite my current choice, I’m keeping my mind open**.

Always remember that no set of gradient factors is universal in its ability to protect one from DCS. Each person’s physiology is different, and each of us can tolerate a different amount of decompression stress. Also, no two dives are exactly the same. The above simply seems to be working fine for me. Whichever dive algorithm you follow, you cannot guarantee you will not get bent. Your computer does not know how fit you are, what your weight and age are, whether you’re well-hydrated, cold, well-rested or stressed out. What you should do is take as many precautions as you can. I like to joke that diving is the sole activity in my life where I wholly embrace conservatism.

I dive because I enjoy this activity. I simply do not understand people who try to get out of the water as quickly as possible towards the end of a dive. Unless you’re freezing cold or otherwise uncomfortable, what could possibly be so annoying about staying a few extra minutes in the water beyond what your computer prescribes? Aren’t those few additional minutes a worthy precaution against landing for a few hours in a hyperbaric chamber? **Cutting down on deco time just to be the first one out of the water is nothing to be proud of.**

I hope this post will help clear any misunderstandings and misinterpretation (one way or another) of the NEDU data.

**Always strive to stay informed, and if you ever hear anyone claiming loudly with an air of certainty the superiority of their approach, be sceptical… VERY sceptical**.

*Joseph is an astrophysicist by profession who divides his time between thinking & teaching about space, breathing underwater, and taking pictures of both (and anything in between).*

For this post, I’ve collected a few pictures of the dives I’ve been doing over the past few weeks, whilst very much enjoying the silent diving that the JJ-CCR has opened up. Hope you enjoy them! Safe & happy diving!

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I’ve been on an anniversary dive to take some pictures for comparison, starting off from the Inland Sea and swimming out all the way to the Blue Hole and back. Here are some pictures from the dive.

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The most exciting development that’s happened during this time is given away by the title of this post. I have finally made the switch to rebreather diving. For too long had I been eyeing the world of silent diving. No bubbles, an optimised gas mix for any given depth, vastly extended bottom times with reduced decompression stop obligations, a totally different way of diving, reduced gas bills for eventual trimix dives, and the prospect of a new challenge, were all key factors in my decision to take the plunge (forgive the pun) into the world of rebreathers. And therefore, I recently trained with the fantastic Dave Gration from Rebreatherpro-Training.

However, before venturing any further, allow me to spare a few words for the uninitiated. “What is a rebreather?”, you might be asking. Well, let’s take this step by step.

As a primer, recall that air contains 21% Oxygen and 79% Nitrogen. (Actually, if we were going for precision, it’s 20.95% Oxygen and 78.09% Nitrogen, with the remaining ~1% consisting of other inert gases, mostly Argon [0.93%] and Carbon Dioxide [0.04%] However, for the purpose of this discussion, we can round up the numbers to 21% Oxygen and 79% Nitrogen).

With every breath you take at sea level, your body metabolises (i.e. uses up for respiration) about one-fifth of the Oxygen content. In other words, it metabolises just 20% of the Oxygen. That effectively means that your body is really making use of just 4% of the total volume of the air around you (0.2 multiplied by 0.21 = 0.04). That small volume of oxygen is converted to carbon dioxide in the process of respiration which is keeping you alive and kicking. The remaining 96% of the volume of air that you breathe in (17% unused oxygen and 79% nitrogen) is simply breathed out again into the atmosphere when you exhale. (Nitrogen and the other inert gases are not metabolised by our bodies.)

Now consider what this means for scuba diving. You take down with you a cylinder of compressed air, and for every breath you take in, you use up just 4% of that volume, with the rest wasted in the form of bubbles when you exhale. And the waste is larger the deeper you go. Why is that? The deeper you dive, the larger the pressure on your lungs from the surrounding water. Therefore, you need to breathe in a larger volume of air from your cylinder, otherwise your lungs would collapse under the mounting pressure. However, we said that 96% of the air volume goes to waste upon breathing out. Now, 96% of a large volume is certainly a larger number than than 96% of a small volume. So there you go, the deeper you go, the larger the waste.

Rebreathers

Wouldn’t it be great if we could somehow capture the exhaled gas from our lungs and reuse it? After all, we only use up a small fraction of the oxygen. Well, the matter is not quite as simple as breathing out into a sealed container and then breathing back in from said container. If I gave you a plastic bag and asked you to seal it over your mouth and keep breathing from it, at some point you’d suffocate. There are two points to consider here:

(1) Some of the oxygen is being used up by our bodies for respiration during each breath cycle, so left unchecked, the oxygen would eventually become depleted. We need to add oxygen as required to keep up the oxygen supply over time.

(2) As we mentioned above, the oxygen that our body uses up in respiration produces carbon dioxide – and carbon dioxide is toxic. We need a way to somehow capture/absorb the produced carbon dioxide and not allow it to go back to our lungs upon breathing back in.

Performing these two functions is the primary purpose of closed-circuit rebreathers. An electronic closed-circuit rebreather monitors the partial fraction of Oxygen in the gas mixture breathed by the diver, adds oxygen as required, and absorbs the carbon dioxide gas so that the diver does not breathe it back in. Let us look at both functions in a bit more detail.

The first function, that of monitoring the oxygen in the breathing loop, is achieved via galvanic oxygen cells. These cells produce a voltage that is proportional to the partial pressure of oxygen (PPO2). That voltage is in turn read in by a computer that determines whether it has to feed more oxygen into the loop or not in order to maintain a given PPO2 (as selected by the diver).

The diver is also relayed a reading of the PPO2 through a computer on the wrist and a heads-up display that displays/projects readings directly into the diver’s field of view. You might have noticed I said “cells” not “cell”. In fact, it is common for a rebreather to be fitted with three oxygen cells. Why not just one? Well, galvanic cells can act up for a number of reasons (moisture and ageing being just two). So we don’t rely on the reading of just one cell but at least three, so that we can make a well-informed decision should one cell (or more) deviate or misbehave.

Carbon dioxide scrubbing, on the other hand, is performed by means of a chemical known as sofnolime. This chemical comes in the form of small granules and is tightly packed by the diver inside a canister. Every breath the diver exhales goes through this canister where the carbon dioxide is trapped by the sofnolime. For those interested in the chemistry behind this, the following reaction takes place:

CO_{2(g)} + Ca(OH)_{2(s)} = CaCO_{3(s)}+H_{2}O_{(l)}

The end products of this exothermic (i.e. heat giving) reaction are Calcium Carbonate and Water. A scrubber canister will feel warm to the touch after a dive due to this reaction that’s taking place._{
}

OK, so we’ve seen how rebreathers help you save gas. That alone results in a number of advantages, along with a number of others. Let’s mention a few here:

(1) Since with rebreathers you can be efficient and recycle and reuse the air you breathe out, you don’t have to carry as many bulky cylinders with you underwater for a given dive (we’re talking technical dives here; for simple recreational dives, the picture is a bit different – more on this later).

(2) This much smaller volume of gas nonetheless lets you achieve vastly longer dives.

(3) An advantage related to gas economy is that when doing deep dives and using trimix instead of air (i.e. a mixture of oxygen, nitrogen and helium that mitigates narcosis at depth resulting from breathing Nitrogen at a high partial pressure), gas bills are vastly reduced. Helium is a very expensive gas, and if you reuse it you end up saving loads of money in the long run.

(4) Since the rebreather is able to monitor the amount of oxygen in the loop, we can ask it to supply us with a fixed partial pressure to our liking. Let us say we were scuba diving on regular open circuit instead of a rebreather, breathing normal air (21% Oxygen). Then we’d be breathing oxygen at a partial pressure of 0.21 at the surface (i.e. PPO2 = 0.21). At a depth of 10 metres, where the ambient pressure is twice that at the surface, the PPO2 would be 0.21 × 2 = 0.42. At 20 metres (3× surface pressure), 0.21×3=0.63, and so on. With a rebreather, on the other hand, we can choose to have a fixed setpoint of, say, 1.3, and breathe O_{2} at this partial pressure throughout our dive. The rebreather takes care of adding the right amount of oxygen for a given depth to ensure that the desired PPO2 is maintained. That means that we have an optimised breathing mix for any depth, which in turns means that upon our ascent, we’ll have less residual Nitrogen in our bodies that we have to off-gas (i.e. get rid off) during our decompression stops. That, in turn, means less time decompressing and more time having fun at the bottom phase of our dive.

(5) The rate of oxygen consumption by the diver is independent of depth (which is not the case in open-circuit scuba), and is determined solely by the basal metabolic rate of the diver and their work-rate (the higher the work-rate, the higher the consumption).

(6) At a given depth, buoyancy does not change throughout the diver’s breathing cycle. In open-circuit scuba, when the diver exhales the lungs contract. As a result, the diver is now displacing a smaller volume of water than when their lungs were full of air, and therefore they start to sink. (On breathing in, the opposite happens.) However, with a rebreather, the exhaled air simply moves into a bag called a counter-lung, which expands to accommodate it. Therefore, the overall volume remains constant all the time and the diver’s buoyancy does not change.

(7) If you take a quick look at the equation above describing the reaction that goes on between the exhaled carbon dioxide and sofnolime, you’ll notice that one of the end products is water (H_{2}O). Moreover, as was mentioned earlier, this reaction gives off heat. The combined result of these two points is that the recycled air is both warm and moist (as opposed to cold and dry). Consequently, one’s breathing can be more comfortable (less dry mouth) and the diver is also kept warmer.

Given the above advantages, you’d think everyone would be diving rebreathers by now. How come this is not the case? Here are a few reasons:

(1) Well, for starters, rebreathers are expensive machines. The combined cost of a unit and the required training can easily set one back 10,000Eur. Yes, you read that right – there are no typos there. Unless you’re really set on diving, and in particular envisage doing the kind of diving that benefits the most from using a rebreather, the cost outlay can be downright prohibitive.

(2) They require significantly more pre- and post-dive care and maintenance than regular open-circuit equipment. Before a dive, you have to pack the scrubber with sofnolime, assemble the unit, carefully check o-rings for damage and re-grease if necessary, calibrate the oxygen cells, and carry out an extensive pre-dive checklist. The latter in particular is crucial for one’s safety. Skip or overlook one step, and the rebreather could easily end up killing you without warning. After a dive, you need to disassemble the unit, clean and disinfect the hoses, clean and disinfect the canister, throw away the used-up sofnolime, and refill if doing a second dive. Clearly, rebreathers aren’t for you if rinsing out your regulator after a dive already feels like a chore too many!

(3) You need to be very disciplined with yourself. Compared to rebreathers, open-circuit scuba equipment is very straightforward, easy to use, and maintenance-free. Moreover, a mistake on open-circuit can be much more forgiving than on a rebreather. On open-circuit, you’re virtually OK as long as you have a gas to breathe. On a rebreather, if you fail to monitor your PPO2, you could end up breathing a hypoxic (too little oxygen) or hyperoxic (too much oxygen) mix, both of which can kill you without warning. In addition, an elevated work of breathing or a scrubber breakthrough can make your carbon dioxide level creep up until you get what is known as a CO2 hit – an insidious killer that can incapacitate the diver without much prior warning. A high level of alertness and attention to detail is a must with rebreathers. A cowboy attitude will most likely get you injured or killed.

(4) Annual maintenance costs can be higher than regular open-circuit equipment. In addition to the usual regulator service, the galvanic oxygen cells need to be replaced on a regular basis (they have a finite lifetime), together with o-rings and (occasionally) other components (e.g. the solenoid that controls the flow of oxygen into the unit). You also have to factor in the cost of sofnolime and oxygen fills.

(5) Depending on your perspective, training is long and complex. Before you can proceed to do 60m-range decompression dives, you have to do between one and two previous courses (rebreather diver and rebreather decompression diver, depending on previous experience) and accumulate a significant amount of hours and dives on a given unit. It should be said, however, that this in itself is not too dissimilar to open-circuit scuba, in that prior to moving up the ladder you are rightfully expected to have attained a certain amount of experience and comfort at the previous level of training.

(6) While diving to gain experience for subsequent higher levels of training, you’ll be carrying much more equipment (i.e. kilograms on your back!) with you than with an open-circuit setup. You can do a recreational dive on a single 12L cylinder. If you’re doing a simple recreational dive on a rebreather, apart from the significant weight of the unit itself (which varies amongst units), you also have to carry a bailout cylinder that’s used in case of emergencies. You can easily be carrying upwards of 50kg with you for each and every dive you make. You won’t feel the difference underwater, but you certainly will on the ground!

(7) The diver has to have a sound knowledge of diving physics and physiology. To a rebreather diver, this, I would argue, is even more important than prior open-circuit experience. And whilst every diver should strive to have a good knowledge base, it has to be accepted that not everyone is ready to commit to the same level of reading material and classroom work.

(8) Diving a rebreather is akin to learning how to dive from scratch again. You’re either happy with that or you’re not. In my limited experience so far, I would say that your past open-circuit experience is useful in terms of your being comfortable in the water but not much else. Deeply-ingrained open-circuit habits, such as fine-tweaking your buoyancy via control of your breathing, have to be eradicated the moment you dive a rebreather.

(8) Whilst the inception of a rebreather is even older than that of scuba, dating back to the 19th century, its use has mostly been the province of commercial and military diving. Development of the technology for the recreational diver market has not been as wide and fast as one would like. For many years, rebreathers have remained amateur garage projects. Recently, however, as rebreathers started gaining popularity, their market grew, as did investment in more reliable technology. Nevertheless, one could argue that they are still far from being truly “commercial devices”, and some would go as far as to say that they’re either still in test-pilot phase, or are just emerging from that.

The growth of the rebreather market has meant that a number of unit options have now become available. I will not dare enter the discussion of which rebreather is “the best out there”. Suffice to say that the usual remark that there is no perfect rebreather is a very valid one. In my case I proceeded as follows.

Firstly, I set out with a list of personal requirements and expectations, the most important amongst which were:

(1) Robust build.

(2) CAN bus-based communication protocol.

(3) Shearwater electronics due to their dependability. (I’ve been using their products for a while and apart from being already used to them, I’ve always found them to be outstanding, as is their exceptional customer service.)

(4) Simple minimalist design adhering to the KISS (Keep-It-Simple-Stupid) philosophy. No frivolous and distracting “bells and whistles”, and no more complications than really required.

(5) Solid reputation and “proof-of-use” for a number of years by demanding divers.

(6) CE certification.

(7) Reasonable possibility to carry out field-repairs (rather than having to send the unit back for every problem that crops up).

(8) Good work of breathing (WOB).

(9) Good trim characteristics. (A lot of this boils down to the diver, of course, but some units do trim out better than others.)

(10) Slim, streamlined design.

(11) Access to efficient repair/service if required.

(12) Access to a good, reputable instructor teaching given unit.

Secondly, I asked lots and lots of questions of a number of great exploration/expedition divers out there. These are people whom I knew to be active divers – people who dive, explore, push boundaries, and teach on a regular basis. (You all know who you are – and I thank each and every one of you again!)

The JJ-CCR fit my criteria perfectly, and the answers I sought agreed with my expectations. So after long deliberation, my choice was decisively made. Some of your criteria and requirements might be different than mine, so your choice can end up being a different one for good reason.

If I may mention a couple of things you should NOT do:

(1) Relying on just a single opinion. Some things are objectively true, and can be said to be brute facts. However, many others are personal opinions that carry with them the baggage of bias. That’s human nature. Accept it and watch out for it.

(2) Taking opinions on online forums and social media as the gospel truth. Quite often, they’re quite the opposite of that. In my own experience, I’ve found so much information relayed on these platforms by so-called “armchair divers” to be downright wrong and misguiding. In certain instances it was immediately clear that the information was wrong. In others, it only became apparent upon my asking further questions to the people I alluded to above, most especially my brilliant instructor, Dave.

The short answer: It’s been great and there is no going back. CCR diving has completely won me over.

If you’ve read all of the above, you’ll be seeking more than just the short answer. So here are a few thoughts.

The training can be intense. The aim is to be in the water with the unit as much as possible, so expect a minimum of two dives per day. When we did our course, the weather was as bad as it gets in Malta, and the entire week was graced with near gale-force winds of variable and unpredictable direction. On the last day, it was so bad that there was just a single diveable site on the entire archipelago that suited our purpose. This also meant that we spent way more time than one normally would in travelling. Immediately after each diving day came equipment cleaning and scrubber packing, followed by theory class. They were long days characterised by early starts, late bedtimes, and a lot of sore muscles – many of which I barely knew I even had! But it was huge fun and immensely rewarding – and having as brilliant, knowledgeable, patient, dedicated and gentlemanly a teacher and mentor as Dave Gration made a world of difference. (No, I’m not being paid to say that. Yes, I paid the full price for the course. No, I haven’t even told Dave I’ve said this about him. I’m just that pleased with his instruction is all.)

Emergency drills are easily forgotten if not practised regularly. Even more important than memorising the order in which to perform a drill is the actual ingraining of muscle memory such that you instinctively perform that drill without deliberating when presented with an emergency underwater. One of my hurdles to overcome has been overthinking, i.e. pausing to question (and flog to death the reasoning of) every step of a drill. With the continued practice of important drills, you can keep them fresh in your mind, the repetition turning them into automatic responses. To this end, I am making it a point to practise at least one emergency drill at the end of each dive I carry out. It’s not a matter of whether I will ever need it but when. At some point, the rebreather WILL probably fail. The diver’s timely reaction to that failure is all that matters.

Unit preparation takes time, as does proper cleaning and disinfecting. I went in already prepared for this, so this did not come as a surprise to me, but it’s worth stressing.

As for the experience itself of diving a CCR, which I have purposefully left for last, all I can say is that it’s been exhilarating. With the noise of bubbles all but gone, I can listen to the sounds of the reef and enjoy the true muffled silence of the underwater world. I’ve had fish coming right up to my face, unfazed by my presence now that I am another silent being in the sea. It’s as if they now consider me to be one of their kin. The sensation of true hovering is pure bliss. At the moment, I am still during that phase where I catch myself smiling each time I pin down neutral buoyancy at a given depth and then, irrespective of my breathing cycle, I just find myself staying perfectly fixed in the water column, effortlessly levitating in the deep, calming blue.

Quite frankly, I would say that diving a rebreather feels more “natural” to me than diving on open circuit (which is somewhat ironic given the increase in technological contraptions involved!). My bottom times have, of course, increased significantly – and after a dive I’m warmer than usual. Recently, I did a 70min dive in Dwejra, starting at the Inland Sea, finning all the way to the remains of the Azure Window and back. A good amount of the dive (~20mins) was spent around the 30m mark. I never approached my NDL time, not to mention the vast amount of scrubber time left had I wanted to dive for longer. Rebreather diving has opened a completely new world. The title of this post referred to rebreather diving as the “dark side”, but it has actually thrown a new light upon my diving experience, and I am looking forward to each and every dive I have yet to make on the JJ-CCR. So much more to learn, so much fun to be had! To many more dives!

I take the occasion to wish you all happy & safe diving, and a wonderful start to the new year!

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Following this first check-out dive, we were ready to do a normal, deeper dive. Charles Paul hadn’t yet dived the Inland Sea Tunnel, so our choice of site was an easy decision. The sight of the deep blue ahead with a touch of iridescence never fails to arrest my breath. I think I have said this before on this blog, but the Inland Sea tunnel truly is one of my top favourite dives on the island.

The dive profile for the second dive (33m max depth) is found below. Until the next one, happy and safe diving!

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The second picture comes from a separate dive that took place at one of my top favourite sites in Gozo, namely *Cathedral Cave*. Few places I have seen come close to the peace and beauty of this underwater cavern. I particularly cherish the silence that usually ensues when when divers surface inside this cave, stunned as they are by the sight of dazzling blue coming from below and the humbling quietness of the dry chamber.

I’ll close off this one here. Until the next one, I wish you all happy & safe diving!

]]>Unfortunately time is a bit lacking at the moment, so this post will be a very short one and I will leave you with the pictures, which I hope you’ll enjoy! I am also including a short video clip that gives an overall impression of the dive.

Happy & safe diving!

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We planned to stay for 30 minutes at 40m, switching to 52% O2 to accelerate our decompression.

After going around the stern, we proceeded to slightly shallower waters, making our way to the ship’s deck.

We finned along the deck and went for a quick excursion inside.

Just before leaving, we came upon a little scorpion fish by one of the windows.

The end of our bottom time quickly approached, so we started our gradual ascent.

Before we left, however, we paused to photograph a most quirky and – I warn you – somewhat scary feature. Some people sure have a sense of humour!

The dive profile and log can be found below as usual. Hopefully, I’ll soon find some time to post some pictures from the subsequent dive. Hope you enjoyed this one. Until the next, happy & safe diving!

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