Imagine you’re piloting a small boat. Your navigational equipment and skills are not really all they should be, but you’re still good. You’re just following the coastline or sailing around an island. If minor corrections to your course are needed from time to time, no problem. You’ll be in approximately the right place as the first landmark comes into view. You adjust your course, if necessary, and then on to the next landmark. But what if there were no landmarks? What if you decide to set sail from California to Hawaii, with no improvement in your navigational equipment or skills? This time you have a real problem. Without landmarks, over that long distance, your minor navigational deviations can build up until you are so far off course, you could bypass the entire chain of Hawaiian islands without catching so much as a glimpse of them.
What does our imaginary boating scenario have to do with algorithms and dive computers? As I mentioned in earlier posts, algorithms used in constructing dive tables, were primarily engaged in “smoothing” the Navy data. Almost any algorithm could do this in some fashion; staying relatively close to existing data, it was hard to go very far wrong. You can compare it to piloting the boat along the coastline. The use of dive computers meant that decisions – predictions, really – were being made about a wide variety of dives, some of which were far removed from the profiles in dive tables. An algorithm might work okay for dive tables but still be well out of its depth here. That’s because, rather like navigating the trip to Hawaii, you have a long series of calculations where even small inaccuracies can build up to a very wrong final result.
So, when your predictions are longer range, whenever you’re talking about a long series of calculations – whether in navigation or in dive computer algorithms – accuracy is particularly important. To construct a more accurate dive computer algorithm, you would need to see the full picture, or as much of it as is possible. Ideally, you would want full and complete data sets covering all possible dive situations, particularly those where the probability of DCS is highest. But, as mentioned in previous posts in this series, studies on humans in such high risk situations won’t, can’t, and probably shouldn’t be conducted. How, then, do you fill in the huge missing part of the picture?
What about existing data on submarine escapes? Unfortunately, this data is not only very sparse, but involves scenarios so completely different from those common to the data we use (and, to some extent, completely different from each other as well) that they don’t really provide much help.
Venous bubble counts have been used, notably by DCIEM, with some success, but they too have limitations. One limitation is that the correlation of bubble counts with DCS is not very strong (somewhat stronger for very high risk dives, weaker for low risk dives). The greater limitation is the same one that affects the Navy data sets – you still can’t use high risk situations on humans.
Looks like it comes down to animal studies. There are several problems here: The fact that animals do not, generally speaking, scuba dive is easily handled. And physiologists are used to dealing with the scaling involved in comparing animal studies to human studies. But how DCS manifests itself in animals is a little trickier. For one thing, they don’t discuss their symptoms. And, it turns out, the symptoms do vary from one species to another. Then you have the problems of which species to use and how to actually combine animal data with human data.
WHY ANIMALS DON’T SCUBA DIVE
A paper by R.S. Lillo and others in the Journal of Applied Physiology used Hill equation dose-response models to successfully combine animal data with human data to look at DCS probability in saturation dives. A saturation dive is one where the diver has been at the stated depth until fully saturated – in humans, a period of about 24 hours- and then does a direct ascent. Successfully combining them means that a model using the combined data was better at predicting the results of a different series of human saturation dives (not included in either set of data used to predict it) than was the human saturation data alone.
On the graph below I’ve put in the DCS probability for saturations dives at 33 fsw, 40 fsw, and 50 fsw, that Lillo found using the Hill equation model. On the same graph, I also show what results would be predicted for those same dives by SAUL, by a SAUL version that incorporates the effect of bubbles, by the Navy’s LE1 model, by a typical parallel (Haldane) 2-compartment model, and by the USN93 model. (The Hill equation model and the USN93 model are each shown as points with their associated 95% confidence intervals. Both SAUL models, the LE1 model and the Haldane-type model are shown as continuous functions. The Navy’s LE1 model and their USN93 are essentially overlapping each other.)
One thing that I hope is immediately obvious is that both SAUL models come much closer to the Hill points than any of the other models. What may take a few moments longer to notice is that the SAUL models are also the only ones that produce the same shape (called a sigmoid curve) as the Hill points would if they were joined. What’s much less obvious is why this particular comparison between different models matters, since these saturation dives in no way resemble anything recreational divers might consider doing.
It matters for several reasons. One is simply the general proposition that greater accuracy in general is good and likely to result in safer diving, even though these particular dives aren’t directly relevant. Another reason is that the particularly high “hit” rates in these dives illustrates differences in accuracy more clearly. But here’s what I consider the most important reason. Saturation dives are the very simplest of dives – at least for decompression modelling. The uptake of nitrogen is already complete. Everything that happens now relates only to off-gassing. (Unlike most other dives where the effects of both uptake and off-gassing must be accounted for.) So all the DCS rates shown on the graph (both experimental and model-generated) are directly related to the off-gassing process. And the off-gassing process appears to produce DCS rates in the form of a sigmoid curve. With models, it is always the underlying structure of an equation that dictates what shape it will produce on a graph. The underlying structure of an equation comes from the model the equation is trying to represent. Because SAUL models use interconnected compartments, the rate equations representing them are multi-exponential and this will produce a sigmoid curve on the graph. All the other models in the graph, being Haldane-based, use parallel compartments, so their rate equations are essentially single exponent equations and will produce something very close to a straight line on the graph.
The next few posts in this sequence will deal more directly with recreational diving and how SAUL relates to dive-related myths/anecdotal knowledge and to other models or decompression tables.
(Before we get to those posts, we may switch course briefly for a few “The Doctor is In” segments. )