Need help figuring halftime compartments, please!

[Charlie99]

Firstly we are talking about Haldanes theories. We are also talking about nitrogen loading in theoretical tissue compartments under pressure, which do not have any other part of breathing gas in them as it is either metabolised or exhaled and is not a foctor in decompression sickness and nitrogen loading, in this model. ....

As a TDI Decompression proceedures Instructor and PADI Course Director I too have read quite a few different articles. I am not going to say your math is wrong, but it does not pertain to the problem at hand and is overcomplicating a simple calculation that is the basis of haldanean thoery which is used as a base model for all decompression tables and computers.
......

IMO, taking into account the fraction of N2 in the breathing gas is not overly complicating things, but instead it taking into account something that is VERY important in decompression.

I also don't consider the use of the normal absolute pressure units to be unduly complicating things.

Both you and the original poster have discussed nitrogen loading, which is important. The PADI text excerpt you quoted talks about total pressure, which is not nearly as important.

 

[Requiem]

I am not getting into a heated argument about trying to help someone understand a part of a course. We are not talking aboutr decompression (as in stops and exceeding safe nitrogen loading limits) where other factors such as other gases in percentages of breathing gas do make a huge difference, we are talking about the basics of "compression" if you like, how gas in this case N2 that is not metabolised by the body, is absorbed into the tissues under pressure.

When you do decompression stops or deep dives with extended time (which PADI does not do), factors such as the humidity of the lungs, the absoption of gases across the gas membrane, the fraction of other gases due to the blocking of the exchange of gases across the gas membrane and in the tissues etc. become a very big factor.

In an earlier post you said [The PADI excerpt is about some non-standard concept call tissue pressure, which doesn't seem to depend upon FN2.]

The basis of all of the article is in fact that "non-standard concept"
If you re-read the article in question he starts off with:

The reason you should read the above papers is to understand the historical context and development of the dissolved gas model, which is necessary to understand Bühlmann's implementation of the model. Key points are as follows: (I hope you read the articles he reffered to )


Haldane established the concept of various "tissue" compartments within the body in
which the gas loading behaves according to the law of exponential decay found throughout nature. Haldane also established the concept of "ascent limiting criteria," in
his case it was through supersaturation ratios.


Workman used the research data of the U.S. Navy to establish the the concept of
"M-values" for the ascent limiting criteria. These are expressed as a linear relationship
between tolerated supersaturation in the "tissue" compartments and ambient pressure.
Workman's M-values are based on the partial pressure of the inert gas in question, not on the total pressure of the breathing gas. Workman explained the concept that fast half-time compartments tolerate a greater supersaturation than slow half-time compartments. Workman also developed a detailed calculation procedure which is the foundation of those used today. A colleague of Workman's, William R. Braithwaite, later modified Workman's procedure to include the calculation of "tolerated ambient pressure" as a means to determine a "trial first stop."


Schreiner explained the decompression model in terms of actual physiological elements such as gas transport in the blood to the tissues, solubility of gases in body fluids, fat fractions and composition of "tissue" compartments, and alveolar partial pressures of gases. He established the very important concept that the total inert gas partial pressure in a compartment is the sum of the partial pressures of all inert gases in that compartment, even if they have different half-times. Another major contribution that Schreiner made was to solve the differential equation for gas exchange when the ambient pressure changes at a constant rate. This is the general solution to the differential equation, of which the familiar instantaneous equation is only a subset. The general solution makes it possible to directly calculate the inert gas partial pressure of a compartment, as a function of time, for any linear (constant depth) or stepwise ascent or descent (at a constant rate). There are many other insights into decompression physiology given in this paper including a basis for
the half-time constant, k.

 

[Azza]

Yep. Your math gives the same N2 loading independent of whether the gas is air or nitrox.

Using EANx32 at 18msw we are not "theoretically" at 18msw. We are now at 14.1 msw using the EAD.

So 5, 10, 20, 60 minute halftime compartments, after 60 minutes at 18 MSW on EANX32

60 / 5 = 12 halftimes. Tissue is saturated after 6 halftimes. Answer is 14.1 MSW

60 / 10 = 6 halftimes. Tissue is saturated after 6 halftimes. Answer is 14.1 MSW

60 / 20 = 3 halftimes.
• Halfway to 14.1MSW is 7.05MSW. (1st halftime)
• Halfway from 7.05MSW to 14.1MSW is 7.05MSW. 7.05MSW + half of 7.05MSW (3.5MSW) = 10.5 MSW. (2nd halftime)
• Halfway between 10.5 MSW and 14.1 MSW is 3.6MSW, 10.5MSW + half of 3.6MSW (1.8MSW) = 12.3 MSW (3rd halftime)
• Answer is after 3 halftimes 12.3 MSW

60 / 60 = 1 halftime. Half of 14.1MSW is 7.05MSW. Answer is 7.05MSW

I suggest if you are going to give advice to people about Divemaster issues, then you should become one first.
Also if you are going to get into Haldane Decompression Modelling then you do some kind of decompression course so you can try your theories out yourself.

What you have done is take a very simple concept that is part of Divemaster training and turn it into something very complex. This will not help schoc369 in his/her Dm exams, if that is indeed the reason they wanted to know.

 

[pete340]

Yep. Your math gives the same N2 loading independent of whether the gas is air or nitrox.

No, he just forgot to mention that he's talking about PPN2, not total pressure. <g>

 

[Dr Deco]

Hello readers:

Halftimes

Many thanks to all of the responders to this question.

This is not a part of the answer to the original question, but, from a pedagogical perspective, I might like to add the following about tables in general.

• Halftimes were the logical choice for JS Haldane since he was well aware that blood did not flow equally to all organs (tissues) during a given period.
• Tissue halftimes in all algorithms (with the exception of the NASA model) are “time invariant,” which means, they do not change depending on the activity level of the individual.
• All halftime compartments are assumed to be present in all individuals at all times.
• All inert gas is assumed to be constantly in the dissolved state unless the "supersaturation threshold" has been exceeded.
• A free-gas phase (i.e., tissue nuclei or microbubbles) are not acknowledged to be present in the Haldane scheme, and therefore surface tension effects are unnecessary.
• With Haldane, nuclei are not present, and their concentration can not be changed by the physical activity of the diver.

Dr Deco :doctor:

 

[DepartureDiver]

Hi Schoc369. Not to get involved in some good debates ... the answer depends on the question. Azza's approach is the easiest and simplest. Beginning half-time compartment lessons will just be interested in the "uptake" or "elimination" as it is an easy reference point and visualization of the model. Since you are only interested in the uptake, then the surface pressure does not matter. Azza's approach is a very simple and correct way of learning this. You can then take this number and multiply it by .79 if needed for the nitrogen only uptake (assuming an air dive). Again, it depends on how the question is phrased. If you need the total gas load, then you can take Azza's approach and then add 10 meters (or 33 feet) for the surface pressure and then multiply it by 79%. For an example, the 60-foot dive for 60 minutes results in a single half-life for the 60-minute compartment as everyone has correctly pointed out. This results in the 60-minute compartment now having an extra "30 feet" of pressure. This can be converted into psi or any other unit if desired. If the total nitrogen pressure is needed, simply add the surface pressure of 14.7 psi (equivalent to 33 feet of water pressure) and a total pressure of 63 feet is reached (30' + 33' = 63') and then multiply this by 79% which yields 49.8 feet of nitrogen pressure ... which is then an easy conversion to 22.18 psi of nitrogen pressure (by multiplying the water depth times the .445 psi per foot of pressure). Hopefully this did not make things more confusing ... if so let us know and it can be cleaned up some more.

 

[Charlie99]

No, he just forgot to mention that he's talking about PPN2, not total pressure. <g>

There's a couple points of confusion. The original poster asked "In feet of pressure, how much nitrogen would the 5, 10, 20 and 60 minute halftime compartments each have after 60 minutes at 60 feet?"

I answered the poster's questions. Other have answered the question for total pressure, which is apparently what is asked on the PADI DM quiz.

The other confusion is that "feet of pressure" is normally expressed as absolute pressure in fsw rather than feet of depth. The difference is the 33fsw total pressure at sea level.

Haldane established the concept of various "tissue" compartments within the body in which the gas loading behaves according to the law of exponential decay found throughout nature. Haldane also established the concept of "ascent limiting criteria," in
his case it was through supersaturation ratios.

These supersaturation ratios were, of course, calculated in absolute pressure, rather than in feet of depth.

 

[Azza]

There's a couple points of confusion. The original poster asked "In feet of pressure, how much nitrogen would the 5, 10, 20 and 60 minute halftime compartments each have after 60 minutes at 60 feet?"

I have to admit I know nothing about the Imperial systems of measurement. Its all so convoluted it makes no sense.

However I do know about halftimes. These halftimes came into being because John Scott Haldane theoreticised (sp) that due to differences in perfusion (blood flow), diffusion (rate of gas flow from one place to another) and other factors, the inert gasses we breathe are dissolved into our different body tissues at different speeds.

As he was first asked to help Caisson workers, who worked under pressure building the foundation of bridges, he based these halftimes on breathing air as this was the surrounding gas they worked in. So to account for using higher oxygen content gasses one must use the EAD formula to get the correct tissue loading.

I answered the poster's questions. Other have answered the question for total pressure, which is apparently what is asked on the PADI DM quiz.

There is only Nitrogen pressure in the tissues as we do not "store" oxygen, this is metabolized and expelled as Carbon Dioxide. Any other gasses such as Neon, Argon, Krypton etc are in such miniscule amounts they can be discounted, especially from someone going into a DM exam.

The other confusion is that "feet of pressure" is normally expressed as absolute pressure in fsw rather than feet of depth. The difference is the 33fsw total pressure at sea level.
These supersaturation ratios were, of course, calculated in absolute pressure, rather than in feet of depth.

I gave them in ATA absolute, at the bottom of my answer. 1 ATA being the surface, then 1 ATA on top of that for every 10MSW.
Also I dont see that we were talking about "supersaturation ratios". The tissues cannot be supersaturated until the outside pressure decreases, i.e the diver starts to ascend, and we havnt spoken about that yet. We are talking about the tissues at depth and as such they are either Saturated or on-gassing, not supersaturated.
When we start talking about supersaturation we move into M-Values and they are quite out of date these days with the "acceptance"t of Dual Phase models, which account for free phase gas, something Haldane didnt account for.

 

[Charlie99]

There is only Nitrogen pressure in the tissues as we do not "store" oxygen, this is metabolized and expelled as Carbon Dioxide.

OK, now I see the difference in our thinking. I assume that at depth, there will indeed be O2 dissolved into the various tissues.

 

[Shoc369]

Thanks everyone for your help! I passed my PADI Divemaster physics exam yesterday with a 95% (on the first try)!