From: mayne@creat.cs.fsu.edu (William Mayne)
Subject: Re: Mixed gas algorithms
Reply-To: mayne@cs.fsu.edu
Organization: Florida State University Computer Science Department
Date: Mon, 4 Jan 93 17:21:27 GMT

In article <1993Jan3.071852.14542@freenet.carleton.ca> aa372@Freenet.carleton.ca (Mike Dusseault) writes:
>
>I was wondering if anyone would know how the existing deco models
>and algorithms could be adapted to diving with other gasses such
>as helium, etc.  I assume the tissue half times and M values would
>have to be changed.  Any info out there?

For all the nitty gritty details (at least a lot of them) read
"Decompression / Decompression Sickness" by A.A. Buhlmann, published
in English and German by Springer-Verlag. A good university library
should have or be able to locate a copy. Although published as
a monograph it is quite readable. All the math is high school level.
Formulas, tables of constants for the ZHL-12 version of Buhlmann's
model, and algorithms are given. There is enough information there
to write a program to compute tables for air, nitrox, heliox, or
trimix, for programmers with sharp algebra skills willing to do
the work.

If you just want tables or the ability to generate them there is now
a commercial program to do it. The program uses the Buhlmann ZHL-16
model and is being marketed by Jim King. (Sorry, I don't have the
name or address of the company handy.) It costs about $275 and you
must attend a one day class on its use in order to buy it. Jim King
gave an introduction to it at the NACD workshop last November and
will no doubt be presenting it at Tech '93 and DEMA. It has a bunch
of other features including calculation of gas requirements, the
ability to tweak safety factors, and much more. This is a real bargain
compared to buying custom tables. Some of my friends have bought copies.
It is clear to me that most of the programming effort for this program
went into the user interface. The actual decompression calculations
are really easy to program. The price is reasonable but I am writing
my own, without the nice interface, because I like to do it and it
will give me even more control.

Here is a quick introduction to how the Buhlmann model for mixed
gas works, assuming you are already familiar with basic decompression
theory. For nitrogen-oxygen mixes it is basically a variation
on conventional Haldane models. The units are different, measuring
pressure in bar and applying some algebraic manipulations. These
are just superficial. Buhlmann has A and B parameters which can
be converted to M_0 and deltaM. The real research which went into
the Buhlmann models consists in determining and testing the values of
the constants. These determine the minimum depth to which a compartment
can be decompressed safetly. Gas pressures in compartments are calculated
by the same exponential-in exponential-out formulas as in all Haldane
type models. I don't have time to go into that here.

When more than one inert gas is involved (i.e. when using trimix
or heliox) each compartment has a separate halftime for each gas.
The halftime for nitrogen is always 2.65 times the halftime for
helium.  For example a compartment with a 1 minute halftime
for helium has a nitrogen halftime of 2.65 minutes. The sum of
the partial pressures of both inert gases is used to determine
the depth to which a compartment can be decompressed. There are
separate A and B parameters for nitrogen and helium, though they
are the same for several compartments. For compartments where
they are different each is the weighted average of the nitrogen
and helium values, where the proportion of each gas in the tissue,
not the breathing mix, is used as the weight. Note that in the
limit of 0% helium this is equal to the nitrogen-only model
most people who know a little about decompression theory know.

There really aren't any pure helium uses of the model since even
heliox divers have residual nitrogen in their bodies when going
on heliox and they use nitrox mixes for decompression. So heliox
is treated just like trimix, but with 0% nitrogen in the bottom
mix.

It is easy to see how the same principles would apply using
other inert gases. The only problem is getting parameters to
plug in. I've never seen any except for helium and nitrogen,
nor do I need any others.

If there is interest in rec.scuba I'll fill in some more details
as I have time. But I urge anyone with a serious interest to
go directly to sources like Buhlmann's book. I believe that it
is both interesting and valuable for mixed gas divers to understand
the theory in more detail than is taught in IANTD trimix classes or
the recently published mixed gas book by Tom Mount, Bret Gilliam,
et. al. (Copyright 1992, 1993. Same source and some of the same content
as "Deep Diving". This is so recent it has snide comments about hypocracy
and politicians alluding to the 1992 Presidential campaign. I'll review
it when I have time.) Actual use of gases other than nitrogen-oxygen
mixes in scuba diving, while not rocket science, is only for
professionals and very committed technical divers. I am just starting
to actually mix and dive trimix and do not pose as an expert.

Needless to say study of the theory is not a substitute for practical
training. I do plan to dive the tables I compute. I would welcome
discussion with anyone out there about this, but would not recommend
that anyone go out and compute tables for actual use without being an
expert programmer and thoroughly studying original sources. Otherwise
use Jim King's program and/or tables from professional sources.

Finally, I'd love to hear from anyone who has the ZHL-16 parameters
so I could plug them into my program.

Bill Mayne
Newsgroups: rec.scuba