Time to total saturation

[canuckton]

I would like to know what the algorithm/ formula to find out time to total saturation at a given depth.

The tissue model I'm using is the Buhlmann ZL-16, but while I can find equations for no-stop times, calculating tissue half-times, and calculating decompression times for tissue, what I really want is the time to total saturation at a given ppN2

TIA

 

[Walter]

Saturation is theoretically never achieved, however it is so close to saturation after six times the slowest compartment used in the model that you are considered saturated at that point. If the slowest compartment in your model is 480 minutes, you are considered completely saturated after 48 hours. OTOH, if the slowest compartment in your model is 60 minutes, you'd be considered saturated after 6 hours. Going to the extreme, if a model had no compartment slower than 5 minutes (unheard of) you'd be considered saturated after only 30 minutes.

 

[Dr Deco]

Dear Readers:

As Walter has stated, six hours is taken as the time to completion for an exponential process. Here is how this half time business works for elimination.

100% at start
50% after one half time
25% two half times
12.5% three half times
6.25% four half times
3.125% five half times
1.563% six half times

In the uptake mode:

0% at start
50% after one half time
75% two half times
87.5% three half times
93.75% four half times
96.875% five half times
98.438% six half times

Dr Deco :doctor:

 

[Walter]

Close Dr Deco, but I never said, "Six hours." I said, "six times the slowest compartment." That equates to six hours only if your model's slowest compartment is 60 minutes. That is true for the RDP, but most models have slower compartments.

 

[Liquid]

I think the longest half time used is 12 hours, and a tissue is considered saturated after at least four half-times. that makes it 48 hours.

Any better numbers?

 

[Dr Deco]

Dear Readers:

Oops!

It is definitely true that six hours is not saturation except for the sixty minute compartment. I read something in Walter’s reply that was not there. Six times the longest half time is considered saturation. For most diving tables with a 240 minute compartment , that would be twenty four hours.

Some tables carry this out to much longer times. I believe that the Bulhmann table has a 600 minute compartment. This would require more than two for complete saturation under this model.

This refers to the time to load and unload inert gas with respect to the biomarker of decompression sickness. It does not refer to those parts of the body that might not exhibit DCS. It is also very possible that the unloading times are for separated gas in a bubble.


Dr Deco :doctor:

 

[The Iceni]

Hi everyone,

I believe the NITROGEN half time for the slowest tissue compartment 16 on the Buhlmann ZH16 algorithm is 635 minutes.

Thus 6 x 635 = 3,810 minutes or 63.5 hours (two and a half days)

Also the equivalent helium half time is 240 minutes.

Thus 6 x 240= 1,440 minutes or 24 hours.

This is obviously why Trimix diving (with helium) gives different deco times.

On gassing and off-gassing are thought to be exponential, like radioactice decay or the cooling of a liquid. The smaller the differential the slower the rate of gas transfer, the lower the rate of radioactive discharge or the change in temperature. This can be expressed mathematically by a differential equation but I am no mathematician and do not know how this is written (I did not study maths at "A" level.)

This is a good practical rule of thumb, but as Dr deco rightly says the body does not consist of 16 tissue types and some ill-perfused tissues will have significantly longer half times (that do not figure in DCI.)

While the slowest compartment 16 will be 98.438% saturated with nitrogen after 63.5 hours of exposure to the new pp N2 it will take much, much longer to be completely 100% saturated. (ie. in stable equilibrium with the external environment). How long does it take for your cup of tea to cool to exactly room temperature?

I understand that it is now believed that the half times for on-gassing and off-gassing differ, or at least an allowance is made in the newer deco programmes to account for a theoretical diffence (possibly due to bubble dynamics.)

If this is the case and the off-gassing half time is 1.2 times the on-gassing half time it will take 24 hours to effectively saturate the body with helium but nearly 29 hours to return to the original steady state prior to the dive.

Is that right madmole/Dr D?

 

[Dr Deco]

Dear Readers:

In some models, there is an asymmetry in the uptake and elimination rates for the inert gas. This is more a preference of the table designer than a known physical reality. It is an attempt to account for why some individuals will get DCS even when within the table limits. Thus the tables are effectively adjusted under the premise that off gassing is not as rapid. The RGBM incorporates some of this when indicating decompression for a diver performing deep dives.

The oft-quoted concept in this FORUM of conservative diving is in the realm of low musculoskeletal impact to reduce tissue micronuclei concentration. It is another way of stating some aspects of what these models are based on. You can, of course, always attempt to minimize physical stress (why not try to take it easy?) when performing post-dive activities.

Micronuclei will, in some cases, sequester nitrogen in its gaseous state (= form). When this occurs, the elimination rate is greatly reduced. It is probably this phenomenon that accounts for the long halftimes in some of the models. It is biophysically difficult to imagine tissues with such long halftimes. One must thing that these are living tissues. Such a long time to bring in oxygen and food, and to eliminate carbon dioxide and waste metabolic products would not readily be conducive to life.


Dr Deco :doctor:

 

[canuckton]

Ok, I like where this is going. Another question.

If a given party was, for all intents and purposes, saturated with nitrogen....

what would happen, physiologically, if they switched to a mixture with a different diluent gas...say helium.

Would the off-gassing of the nitrogen be a seperate issue from the on-gassing of the more soluble helium? Or would the helium help to flush out the nitrogen?

Not that I'm planning to use the idea, I'm just wondering whether or not there is a tissue compartment relationship with any combination of non-metabolised gases.

Does a tissue half-time for helium remain the same when it is partially or fully saturated with nitrogen? And vice versa?

 

[The Iceni]

Hi Canuckton,

In case you have never heard of him Sherlock Holmes was a famous, fictional, Victorian British detective who teased his friend, Dr Watson remorselessly.

When some totally obscure clue was blindingly obvious to him he would say "It's elementary my dear Watson!"

So may I tease you a bit? How about doing a search on isobaric counterdiffusion and come back to us with the answer to your own question?

I won't keep you in suspense too long!

As a clue to help, Trimix divers do what you suggest all the time - that is they change from breathing one gas mixture to another.

Kind regards,

ut: