ZHL-16 Calculations

[bvanant]

I think that half-life choice is based on a wealth of pharmacokinetics experience in the medical world and the assumption that physiological decay curves are indeed mostly driven by concentration gradients.
Bill

 

[tlj3071]

I think that half-life choice is based on a wealth of pharmacokinetics experience in the medical world

This sounds reasonable to me.

...and the assumption that physiological decay curves are indeed mostly driven by concentration gradients.

But this doesn't - any number of statistical models can be used for concentration gradients - half-life is only one such model.

Tom

 

[Charlie99]

I have always wondered why Haldane, Buehlman, et al all used half-life as the basis for on- and off-gassing formulae rather than other statistical models (e.g. time-constants).

It's just a different way of expressing the equations. There is NO difference mathematically.

It's kind of like using natural logs for some things, base 10 logs for other things, and base 2 logs for some things. It does not change the underlying math.

The relationship between a halftime and an exponential time constant is very simple. Halftime = TimeConstant * ln(2)
or halftime = timeconstant*0.693

=============================

You can see this same back and forth between halftimes or half lifes and exponential time constant in other fields. For example, in radioactive decay it is common to talk about the halflife of decay products. When doing equations on computers, it is nowdays general easier to use the decay time constant. Same relationship as decompression halftimes and time constants.

The physics doesn't change when you flip back and forth.

 

[dmainou]

I am not a mathematical person therefore I can not explain why they used one model rather than the next.

I know that half times are used in many things including nuclear reactors.

If you wish to read about the history of decompression and how they went about it you may wish to read Deco For Divers from Mark Powell. It is written quite well and has little math in it.

D

 

[cofford]

I made this spreadsheet yesterday during my lunch break. Basic ZH-L16, no gradient factors (or GF 100/100), changes in depth are instant. I "planned" a 200ft dive with it. It's fun to play around and see how the limiting compartments change during deco. It's also interesting to see the huge difference 32% makes over 21%.

Disclaimer-This is NOT a planning tool. Use it for educational purposes only.

 

[Dr Deco]

Hello dmainou:

Haldane

Haldane writes in his paper “The Prevention of Compressed-Air Illness” [J. Hyg. Camb. 1908, 342-443] “Now the weight of blood in man is about 4.9% of the body weight…,” and then he proceeds to show how by using the blood volume, the weight of a man, and the circulation time of blood, one can estimate the nitrogen content of the tissues as a function oftime.

He states, “On following out this calculation, it will be found that half the total excess of nitrogen would have entered the body after 23 rounds of the circulation, three-fourths after 46 rounds, seven-eighths after 69 rounds, and so on. The progress of saturation of the body with nitrogen is thus a logarithmic curve…” The log curve is another representation of halftime. Time constants are not "statistical."

Surprisingly, half times, by that name, do not enter his paper and are mentioned nowhere in his paper. He does use the term “half-saturation” and is as close as you can come. The half-life term was just beginning to enter the world of physics with respect to the decay of radioactive elements.

Halftime

Half time comes from studies of the uptake and elimination of biomolecules and drugs in the body. Experimentally, it is very commonly observed process. There is a discussion of which diffusion process should be used for calculations in the body but no disagreement with respect to halftimes.

Dr Deco :doctor:

 

[Charlie99]

I made this spreadsheet yesterday during my lunch break. Basic ZH-L16, no gradient factors (or GF 100/100), changes in depth are instant. I "planned" a 200ft dive with it. It's fun to play around and see how the limiting compartments change during deco. It's also interesting to see the huge difference 32% makes over 21%.

Disclaimer-This is NOT a planning tool. Use it for educational purposes only.

Very nice!

At 200' it doesn't have much effect, but at shallow depths the calculation for ppN2 should subtract out the CO2 + water vapor pressure in the lungs before multiplying by the fraction N2. I don't have any references handy at the moment, but I think Buhlmann used something like 1.8fsw. Edit: I googled a bit and only got more confused. I found a reference saying Buhlmann used 0.627msw/ 0.0627 bar/ 2.041fsw, Workmann/USN used 1.848fsw and Schreiner says 1.607fsw is the right value. I thought Buhlmann was the 1.8FSW, and USN was 2.0.

This also effects the initial loading of the compartments, reducing to to around 0.73 ata rather than 0.79.

You would notice this change only if you looked at ZHL16-based tables to validate your spreadsheet. I did some quick and dirty checking vs. DSAT/PADI NDLs and it looks good. (Different model, so I wouldn't expect exact correlation.)

The other tweak I did is to copy the halftimes as labels above the compartment numbers, to make it easier to see which halftime compartment is the limiting one for different situations.

 

[tlj3071]

Hello dmainou:

Haldane

Haldane writes in his paper “The Prevention of Compressed-Air Illness” [J. Hyg. Camb. 1908, 342-443] “Now the weight of blood in man is about 4.9% of the body weight…,” and then he proceeds to show how by using the blood volume, the weight of a man, and the circulation time of blood, one can estimate the nitrogen content of the tissues as a function of time.

He states, “On following out this calculation, it will be found that half the total excess of nitrogen would have entered the body after 23 rounds of the circulation, three-fourths after 46 rounds, seven-eighths after 69 rounds, and so on. The progress of saturation of the body with nitrogen is thus a logarithmic curve…” The log curve is another representation of halftime. Time constants are not "statistical."

Surprisingly, half times, by that name, do not enter his paper and are mentioned nowhere in his paper. He does use the term “half-saturation” and is as close as you can come. The half-life term was just beginning to enter the world of physics with respect to the decay of radioactive elements.

Halftime

Half time comes from studies of the uptake and elimination of biomolecules and drugs in the body. Experimentally, it is very commonly observed process. There is a discussion of which diffusion process should be used for calculations in the body but no disagreement with respect to halftimes.

Dr Deco :doctor:

Thanks Doc, the [apparent] fact that biological saturation follows a logarithmic function seems to more than adequately support its use in the dive calculations.

As for time constants not being statistical, you are - of course - correct. In my fervor to make a point, I was semantically inaccurate. There is nothing that would preclude using time constants in the calculations [other than the previously stated biological reasoning], but they are definitely not a statistical tool (for those not familiar, they are used to calculate - among other things - the instantaneous charge on a capacitor).

Tom

 

[Dr Deco]

I am happy that you found all of this usefull.

 

[Mark Guccione]

Hello Dr. Powell,
We met many 25 year ago in Washington, when you were studying the effects of making multipliable dives for multipliable days, (simulating live aboard diving). I found reading your published material quite useful in my training.
It was my pleasure in meeting you and your staff, thanks for allowing me, to be your "guinea pig"
P.S. I have just recently learned how to navigate through these forums, anything else you've published I should read?

Thanks for your time,
Mark Guccione