Dear Diver0001:
Tall order
I am not sure that I am aware of all of the variables in the model and I believe that there are different versions of it depending upon the complexity one ill will to incorporate. I can tell you what I know off the top of my head and, if something is unclear, let me know.
Two Phase Model
This model is a two-phase model, meaning that it deals with not only nitrogen (or helium) in the dissolved state but in the gaseous phase as well. Let us look at what are referred to as limits in the world of physics. If there we no micronuclei (microbubbles) present in tissue, then the Haldane model would be applicable since it assumes that they are absent in the first place. If there really were no microbubbles, and water had its theoretical tensile strength (how much force is required to push water molecules apart and make a hole in the liquid), you would not really need a decompression table. You could surface directly from several thousand feet beneath the ocean. This is not the case and Haldane assumed incorrectly that a stable supersaturation was possible. It is not really true because there actually are micronuclei present.
The basic concept here is that, if there were no microbubbles, all of the dissolved gas would find its way into the capillaries and be carried away by the blood.
Case With Nuclei Present
If we were to have an infinite number of microbubbles present, it is clear that nitrogen molecules, randomly diffusing through tissue, would bump into one of them before reaching a capillary. This being true, none of the inert gas would be eliminated. It would all get sequestered in the tissue.
Now, the real case is somewhere in between. There are in reality only some tissue micronuclei present, and some of these are so small (and have such a high internal pressure from surface tension) that they would never expand in a real decompression. Therefore one needs to guess what fraction of nitrogen molecules will go into the microbubbles and which into the capillaries. The whole thing is adjusted such that the nuclei remain small (no expansion by Boyles Law, or only minimal expansion) so that nitrogen is not sequestered or trapped. The pressure drop or elimination gradient must be reduced the more micronuclei that are present.
When ever a dive situation is thought to produce an enlargement of micronuclei, then there must be a slower ascent or a stop inserted to allow the dissolved nitrogen to diffuse into the blood stream. This reduction in the gradient is where the model derives its name.
How Much to Reduce ?
How much of a reduction is derived from an examination of real decompression data. A true ab nihilo model is not possible, since that would require the prior knowledge of the number of nuclei and their size distribution and the relationship of these to the capillaries. The problem has essentially too many variables to be defined a priori. Dive data can give a realistic estimate of variables needed.
The pressure reduction (gradient) is reduced in those situation in which micronuclei are thought to be present or created, especially if the nuclei are enlarged and have a smaller Laplace pressure (from surface tension). Thus deep dives and repetitive dives will need a reduced gradient. The case of reverse profiles needs apparently special rules such that large reversals are not performed. Apparently this will lead to decompression problems.
How Well Does It Work?
From what I read, it works very well. On cannot venture outside of the boundaries from which the algorithm was made. That means do not strain when reentering the boat after a dive and no beach volleyball between dives.
It would take a laboratory test program to determine if the underling concept is correct. Field data probably only demonstrate the utility but not the veracity of the model.
If that does not answer the question, please ask again and I will try to unravel what I can. There is most likely more to it than I am aware
Dr Deco :doctor:
