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John Crea <johncrea@de*.co*> sez: > Please read the work of Buhlmann. Gas elimination and and absorbtion > is modeled exactly the same (mirror images) in an exponential manner. > The US Navy model (Haldanian) also utilizes 2 factors, both the "M" > value and the "delta-M" values, much like Buhlmann does. 1) I have. 2) Yes, Buhlmann uses the same rate for uptake and elimination, but most moderm implementations of the Buhlmann model do not. I thought it important to mention theis shift in thinking, but I did not want to get so intricately detailed in the history of deco model development. 3) Again, I did not really want to write a detailed history of the development of dive tables. While you are correct wrt the Navy model, these features are mostly thought of originating with Buhlman in the mind of the advanced diving public (in my experience). I was not interested in getting all of these detailed attributions correct, but rather getting a general point accross (as mentioned in the disclaimer-like heading I put on that section). > UDT only markets the DCIEM tables. They were not the developers of > the DCIEM tables. The DCIEM tables evolved from work done by Kidd and > Stubbs back in the early years trying to develop a mechanical diver carried > decom computer. They came up with the concept of 4 compartments, linked in > a serial manner. This (with much tweaking) produced a diver carried > computer that produced decompression profiles that were acceptable in risk > and rate of DCI. The latest DCIEM tables were computer generated by a modern > version of the Kidds-Stubbs model, still utilizing 4 compartments linked in > a serial manner. The main advantage of the DCIEM tables is that they were > extensive doppler tested (on human subjects) in a cold, high workload > environment. Yes, all correct, but mostly incidental to my point. Note that the 4-compartment model is extensively tweaked to produce the actual tables. Simply using the model in its straight math form will not generate the tables, and that is significant. Note that the *tables* were extensively tested *NOT* the *model*. > Serial gas movement is probably a component in gas uptake and elimination > (tissue to tissue interchange/exchange), but the fact remains, that arterial > blood is delivered to the tissues in a parallel fashion (and this is > probably the major route of in gassing and outgassing). You have missed the entire point of my post. Let me state it simply: Producing mathematical models starting from "first principles" of very complex mechanisms which are not wholly understood is misguided. Sure, you can defend a parallel model in as much as it makes sense by what you stated above. You can also defend a serial model, in that tissue types border other tissues. You could even extend this to serial-parallel models. Or slab models, like the BSAC model (I believe, don't have ref's here). Or even take a different approach, and look at things from a bubble nucleation/growth perspective, like Hills (again, this is now raw memory, as I don't have ref's here). All of these approaches "make sense" to us as they trigger some identity with things we know about physics. I thought by showing how the three models I chose (Haldane, Buhlmann, DCIEM) all also "make sense" you could see the problems with this type of modeling. Another way to look at it would be thus: if a model really was "correct" in the sense that it was founded on physics, we should see some evidence of this in trials. Namely, if a particular "compartment" is overly supersaturated, we should be able to correlate the compartment with a real tissue. But we can't; there is no correlation. In fact, people such as Buhlman who have tried modeling from that approach have found it not to work (as I mentioned in my post). What this says to us is that the models are way to simple. Let's look at what these models "say" causes DCI: All these models say that there is a dirrect correlation between inert gas supersaturation and DCI. All models say that there are no other variables (no other variables appear in the math). In other words, from the math perspective, no dive on a dive table should ever result in DCI, and every dive off the table should result in DCI (no matter what other conditions there are). Does this really make sense? Of course not -- we know that DCI is related to temperature, work load, stress, and many other factors. But these things do not appear in the models -- so how can we say that the models are pictures of reality? The models are not even "pretty close" to reality: people still get "unearned hits" when diving on the tables, and others get off scott free when it seems that they "deserve" to take a hit. This is where the advantages of a nnet approach come in: a properly trained nnet will "discover" these relationships on its own -- as long as they have an input. But at least we can give these factors as an input to the nnet. Building useful models is a difficult task, and sometimes interpreting them is even more so. There is always a danger that people will ascribe more meaning to a model than what is really there: remember that a model is nothing more than a curve fit to existing data, which is then used for predictive purposes. Remember also that models need not necessairly be built from first principles to be useful: we don't use Einstein's relativity to launch satelites, we use Newton's (less "correct") Laws of Gravity. But if we were in a situation where all we had were Newton's Laws, and they were not good enough (as I contend that today's deco models are not), it would be much cheaper/easier to build a useful nnet model than to come up with Relativity. > Hate to rain on your interesting and lengthy post, but it would be best > if you would do a little extra research before making some of your > statements. Hate to rain on your career, but it would be best if you researched and understood a tad bit more about what models are and what they aren't. Especially in that you sell implementations of models to people... > John > Submariner Research, Ltd. > (johncrea@de*.co*) -frank -- fhd@pa*.co* | So far as the laws of mathematics refer to reality, they are 1 212 559 5534 | not certain. And so far as they are certain, they do not 1 917 992 2248 | refer to reality. 1 718 746 7061 | -- Albert Einstein, _Geometry and Experience_
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