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>Posted on 2 Mar 1996 at 23:45:14 by Dan Volker >I think my point might be better described by the differences in how >much blood (which relates to surface area) can be exposed to a gradient. This is my view too. I had dreams about this all night long and woke up with a model I'm thinking of building further on. I dubbed it the 015 Unified M model (c). Important assumptions are: The fit and the unfit diver share many tissues which we'll model as compartments. The fit and unfit compartments share diffusion rates D, halftimes 1/D, gas solubility and possibly M values. Some tissues differ: especially the vascular system, % bodyfat and muscle-gas-(dissolved)-exchange-rates. I cannot for the life of me see the ongassing and offgassing go at different rates unless the membrane between vessel and tissue support a different molcular flux depending on the direction of the N2 gradient across that membrane. Within the tissue itself the diffusion is determined by the "chemical" diffusion rate. The is no information available to the thermally activated molecules which tells them to slow down or speed up. They just merrily perform random walks in arbitrary directions. (This is the opposite of what some have stated [ unfit person ongasses into slow compartments but offgas those slow ecompartments even slower]. We've seen no proofs so I take it to be wrong for now ). However, there is a remnant of the above problem in a dive that starts out with the fatty tissue warm and where the fat diver chills throghout the dive. Diffusion will slow if the temperature drops but the biggest effect is probably due to the capillaries themselves shutting down the flow of blood in cold tissue. I am unware of bubble formation being a problem if it should occur outside of the vascular system. It's size should it occur in elastic tissue would seem to have an upper bound equal that of the host cell and it can't travel anywhere. I.e., it has no effect as far as DCI is concerned. Where does this lead us. Well, the fit diver has the same set of compartments as the unfit diver. Having a vastly better circulatory system with more surface area and shorter distances over which the N2 gradient can drive N2 in or out of tisse the fit diver has more a higher percentage of his total mass in the faster compartments. But that's all we can get from the compartmentalization. Now the diffusion rates. These are given when the compartment half times are given. Solubility remains the same (assuming same chemical build-up of "same" tissue in fit and unfit person and barring temperature effects). However, a compartment that ongassed "warm" and now offgas "cold" must be treated as two different compartments. This poses no particular problem for now. We're left with the M values. If the probability of a bubble forming in the vascular system supplying that fatty tissue is p(fat) per litre of fatty tissue then a person with m kg of fat will see a total probability of bubble formation due to the fatty tissue as pM = P(fat). Similarily, the fit person has more risk of bubble formation in the muscles and the vasculatory system itself just by having more of it and light of it's faster rate of offgassing. Being a model with adjustable M parameters I'll also incorporate some of the "chilled diver" effect mentioned above into the M values. The M values are therefore functions of compartment, relative compartment mass, depth, gas/mixture, temperature and possibly more if the model is refined to include max depth, level of excersise etc. Fat and VO2 will input through the relative compartment mass dependence. In this model then the fit person can afford to lower the M values of certain (all?) slow compartment but must increase the M values of the relevant fast compartments. I could argue further that a fit person can take a bit more bubbles in his system (a larger percentage of the bubble laden blood is circulated into non-critical tissue) but this must be weighted against the increased risk of bubble nucleation in the more volumios an possibly more vigorous vascular system of the fit diver. The change in M values does support Dan's need for deep stops and the unfit person's needs for spending time shallow. Some might argue I built it into the model right away :-). Comments welcome. john
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