NDL and Decompression Tables, Algorithms, and Dive Computers

I realize it’s been far too long since my last blog post.   I have been working very hard,   getting SAUL ready for inclusion in a dive computer and attending to other scientific work.   I’ve also managed to get in a little relaxation and diving – Aloha from Hawaii, everyone.   I’ll try to keep the posts coming with a little more regularity now.

I promised some posts about SAUL’s validation, and these will be happening.  But before they do, we need a prequel of sorts – a little background information that every diver should know about decompression tables, NDL’s, algorithms, and dive computers.  What makes it hard, is that we divers are such a diverse lot.   Some of you will already know much of what’s in today’s post, and in greater detail.  To a very few of you, the information may seem entirely new.  Most of you will probably fall somewhere in between those two extremes.    So, let’s talk about..

NDL and Decompression Tables, Algorithms, and Dive Computers

You and your buddy are doing almost exactly the same dive.  His dive computer is telling him to surface; yours is still allowing the dive to continue.

Or you’re a commercial diver working different sites.  Some employers are using the U.S. Navy tables, others the DCIEM tables.  The tables differ in how long you’re supposed to work at a particular depth and, for decompression diving, the time spent at each decompression stop.

In recreational diving, some of you may deliberately use one dive algorithm (or dive computer) for certain types of dives and a different algorithm (or dive computer) for other types of dives, knowing they will differ in what they allow.  What’s going on here?

All dive tables, algorithms and dive computers are based on data from actual dives.  Until very recently, the largest data bank for this purpose, which will be referred to below simply as Navy data, had been produced by the U.S. Navy, in collaboration with DCIEM, and the Royal Navy.  (While the total amount of data collected in recent years under DAN’s PDE program greatly surpasses it, the Navy still holds the most systematically varied and organized databank.)   So, most dive tables, algorithms, and dive computers spring from the Navy data.   This leads to the obvious question: If they come from essentially the same data, why are they different?

We could try to finesse the question by comparing it to different artists painting the same harbor scene and producing very different paintings, but that’s not really a satisfactory comparison.  Paintings are art; dive tables and algorithms are supposed to be science.

Without getting into any esoteric questions like the exact natures of science, truth or meaning, we just want to know why the same huge data bank leads different scientists to different conclusions.   Some of the answer lies in how scientists think, in the theories they use to interpret data.    But a large part of the answer lies in the nature of all data, in the nature of data from living things, and in the particular complications involved in collecting data from people.

We’ll talk about data first.   Data in general is a collection of measurements made under specified conditions.  In the case of diving data, the measurements collected would essentially be the determination of  “bent” or “not bent”  or “niggles” (which refers to having mild symptoms of the bends, but the symptoms disappear on their own, without recompression therapy), while the specified conditions would be all the details of the dive.  For each set of specified conditions – e.g., 80 feet for 30 minutes bottom time, breathing air, coupled with a descent rate of 75 feet/min and an ascent rate for the direct ascent to the surface of 30 feet/min – you would see the total number of divers and the number who got  “bent” or “niggles”.  For each set of specified conditions, you could then work out the probability of getting “bent”.   (“Niggles”, usually considered a partial case of the bends, would be assigned an appropriate part-value:  less than the “1” reserved for being “bent” but greater than the “0” for “not bent”.   Typically, a niggle would count as one tenth of a hit.)


Okay, it’s a little slow going – but we’re getting there.

So, you’ve got your data.  What does it tell you?  In the example above you would now know what percentage of the sample of divers measured under that particular set of  specified conditions got “bent”.   But, of course, you didn’t measure an infinite number of divers.  If you did the exact same study again, you might get a somewhat different percentage.  There are statistical methods that are used to determine how close the result you got is likely to be to the hypothetical “true result” – the result you would find if it were possible to measure an infinite number of divers.  This is how the possible difference between the results of a study and a “true result” might be shown on a graph.

The dot or circle indicates the actual result of the study  – in this case, some of the results from DAN’s Project Dive Exploration – while the lines sticking out from the top and bottom of each dot or circle show the range within which the “true result” is probably located.   So, while the circles are, in each case, your best guess at the “true result”, you’re 95% certain that the “true result” lies somewhere in between the top and bottom of the two lines sticking out from each circle.  The results for AIR are based on approximately103,000 single dives while the results for NITROX are based on approximately 7,000 single dives.  In general, the larger the sample size, the closer it is likely to be to the “true result” (and the shorter the lines sticking out from the circle are likely to be).

There are other ways of talking about this same issue of a sample measurement versus a “true result”.    When public opinion polls show their results, they will usually contain a statement something like: “These results are accurate to within 3 percentage points, nine times out of ten.”

The fact that the results of a study are only an estimate of some “true result” is an issue that applies to all kinds of data.


Take heart! We’re getting closer now.

Notice that, in our earlier example, we were talking about only one set of conditions where depth, bottom time, the rate of descent, the rate of ascent, and the breathing mixture were each specified.  So our data refers directly only to dives under that exact same set of conditions – almost as if it were a single question on a public opinion poll.  If you were to change any one or more of those conditions – 60 feet instead of 80, 40 minutes instead of 30, etc. – or if you were to add an additional condition – say, making the dive multi-level, or adding a safety stop – each and every change would be like adding a completely new question to the opinion poll.   (Making for a completely unmanageable opinion poll, of course.)

While the Navy data contains a large number of sets of different specified conditions, it would have to be infinitely large to cover all possible sets of specified conditions.

There are two points that should be sandwiched in here before we go on (in the next posting) to deal more specifically with data from living things, particularly people.

The first is a comment on the nature of diving data.  As you can see from the above, diving data is inherently probabilistic to begin with.  That is, you have the number of divers in a particular set of conditions, and you have the number who got “bent”, which is easily expressed as a percentage of the number of divers, and which amounts to an estimate of the probability of getting bent under those particular conditions.   Why do I bother emphasizing this rather obvious conclusion?  (And no, it’s not primarily because SAUL is a probability-based model.)

It seems that a substantial number of divers may not be aware, or may not totally accept the fact that, if you dive there is always some probability, however minute, that you will get bent.   Anecdotally, I have heard from a number of diving doctors about patients who resist a diagnosis of decompression illness, protesting that they can’t possibly be bent, as they’ve never exceeded the tables or their dive computers.  But the truth is, unless you avoid diving altogether (or, possibly, if, while diving, you never exceed a depth in the general neighborhood of 15 feet – a feat which may be even more difficult than avoiding diving altogether) there is always some non-zero probability of getting bent.  True, for most recreational diving, that probability is very small.  On the other hand, the probability of winning a major lottery prize is even smaller.  Yet, for each such prize, there is at least one winner.

The other point we need to mention here is this:  Even though data from each separate set of diving conditions must be looked at as a completely separate question, we know, both intuitively and logically, that,  inevitably, there must be some relationship or connection between these disparate “questions”.  And that, of course is where algorithms, decompression tables, etc. come in.   But before we get to those, we need to deal with the particular problems that arise when your data comes from living beings, particularly people.

So my next post will start with that issue and go on from there.  And, while I can’t say exactly when that next post will appear, I promise it won’t be as long delayed as this one was.


Leave a Reply

Your email address will not be published. Required fields are marked *

Captcha Captcha Reload