Why do people add a few minutes to their last deco stop?

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I would speak about supersaturation if you go over the theoretically M-value
The literature uses "supersaturation" for anything above inspired partial pressure (though sometimes meant to be above total ambient, see above). The M-value line is "critical supersaturation". Anything above that is... well... "above critical", although I can see "supercritical" working. :)
 
What word?

for what?
Significant.

H0: pDCS(TDT) = pDCS(TDT + 5) = pDCS(TDT - 5)

H1a: pDCS(TDT + 5) < pDCS(TDT)
H1b: pDCS(TDT - 5) > pDCS(TDT)


But I don't believe you or anyone could prove with existing data that it is statistically significant differences across a wide range of profiles, and and exposures with such small changes in TDT, and I doubt there is much of a measurable practical significance either.

I agree that longer TDT should reduce risk, and that the distribution of stops should favor shallower stops over deeper stops but:

If you have a 30 minute dive to 100ft(30m) on Nx32 what is the pDSC if you complete a 20ft stop of 0, 5 and 10 minutes. Each increase in TDT time likely lowers the chance of DCS but by how much, both in absolute terms and relative to each other.

If you have a 30 minute dive to 150ft (46m) on 21/35 with nx50 as a decompression gas with a TDT of 30 minutes determined by whatever algorithm you want, what's the pDSC for shortening your 20ft stop by 5 minutes, or lengthening it by 5 minutes.
 
Saturation, is when the tissue is holding as much of a gas as it can stably hold at a given pressure. It is independent of the partial pressure of that same gas in the inspired air. The saturability of a fluid/tissue is not affected by the presence or absence of the gas in the inspired air.
Saturation is not a measure of whether gas is flowing into or out of the solution. It is a measure of how much is in solution as compared to how much can be in solution.

Think about it this way, If I take a blood sample and place it in a sealed container. Inspired partial pressure is now irrelevant. And yet, the tissue is still either sub-saturated, saturate, or supersaturated with gas. If it is supersaturated, gas bubbles will form in the sample over time. If it was sub saturated with bubbles, the bubbles will dissolve. If it is saturated, bubbles will not form or dissolve.
 
Significant.

H0: pDCS(TDT) = pDCS(TDT + 5) = pDCS(TDT - 5)

H1a: pDCS(TDT + 5) < pDCS(TDT)
H1b: pDCS(TDT - 5) > pDCS(TDT)
If H0 is true, iterate.
  • Since pDCS(TDT) = pDCS(TDT - 5)
  • TDTnew = TDT -5
  • Apply H0 to TDTnew: pDCS(TDTnew) = pDCS(TDTnew - 5)
  • pDCS(TDT) = pDCS(TDT 5 5) = pDCS(TDTnew) = pDCS(TDTnew-5) = pDCS(TDT + 10)
  • repeat till TDTnewest = 0
  • pDCS(TDT) = pDCS(TDTnewest) = pDCS(0)
  • Obvious falsehood.
  • Therefore H0 is false.

But I don't believe you or anyone could prove with existing data that it is statistically significant differences across a wide range of profiles, and and exposures with such small changes in TDT, and I doubt there is much of a measurable practical significance either.
Then you haven't looked at any of the data. Why do you think we do any last stop at all? Why do you think we even have a value for a last stop time at all? Do you think someone just arbitrarily picked a number out of the air?

I agree that longer TDT should reduce risk,
Wait, you just said that there is no significant evidence of that.

and that the distribution of stops should favor shallower stops over deeper stops but:
Again inconsistent with your statements above.

If you have a 30 minute dive to 100ft(30m) on Nx32 what is the pDSC if you complete a 20ft stop of 0, 5 and 10 minutes. Each increase in TDT time likely lowers the chance of DCS but by how much, both in absolute terms and relative to each other.

If you have a 30 minute dive to 150ft (46m) on 21/35 with nx50 as a decompression gas with a TDT of 30 minutes determined by whatever algorithm you want, what's the pDSC for shortening your 20ft stop by 5 minutes, or lengthening it by 5 minutes.
So your position is that since we cant quantify the number (pDCS), we shouldn't act as if the number exists? That for a 30 minute dive to 150ft (46m) on 21/35 with nx50 as a decompression gas, there is no statistically significant difference between a 25 min stop and a 35 min stop at 20 ft?

ETA:
A 25 min stop is approximately GFHi/GFLow = 80/65.
A 35 min stop is approximately GFHi/GFLow = 60/50.
You are saying there is no statistically significant difference in pDCS between these two dives.
 
If I take a blood sample and place it in a sealed container. Inspired partial pressure is now irrelevant.
It's not total pressure that dictates saturation, it's the inert partial pressure. In your sealed container, "inspired" is effectively the layer of gas above the blood. If that has a lower partial pressure, then gas will move out of the blood until the partial pressure above the surface of the blood equals that below. If you fill up the container completely with blood, then obviously there will be no net movement assuming the gas is distributed homogeneously within the blood.

This is a table from Deco for Divers:
1705075564362.png

He states in regard to the 20 m row:
We can now see that tissue 1 is supersaturated as its tissue nitrogen pressure is higher than the inspired nitrogen pressure and is also higher than the ambient pressure. As a result Tissue 1 starts to off gas. Tissue 2’s nitrogen tension is now higher than the inspired nitrogen pressure and so it too starts to off gas although the nitrogen tissue tension is not yet higher than ambient pressure.
You will note the use of "supersaturated" to mean tissue pressure higher than inspired pressure as well as synonymously with "off gas".
 
Saturation, is when the tissue is holding as much of a gas as it can stably hold at a given pressure. It is independent of the partial pressure of that same gas in the inspired air.
Again, the part I bolded is completely wrong. A simple rebuttal: for someone at sea level, nitrogen saturation is 0.79 atm precisely because the partial pressure of nitrogen in the inspired air is 0.79 atm. If you breath EAN50 long enough while sitting on the couch, your tissues will be saturated at 0.5 atm. All this without changing the total ambient pressure.
 
Do you think someone just arbitrarily picked a number out of the air?

Yes, to an extent. Go look at the primary research on safety stops.

So your position is that since we cant quantify the number (pDCS), we shouldn't act as if the number exists?
You keep putting words that people never said into their mouth.

That for a 30 minute dive to 150ft (46m) on 21/35 with nx50 as a decompression gas, there is no statistically significant difference between a 25 min stop and a 35 min stop at 20 ft?

ETA:
A 25 min stop is approximately GFHi/GFLow = 80/65.
A 35 min stop is approximately GFHi/GFLow = 60/50.
You are saying there is no statistically significant difference in pDCS between these two dives.
I'm saying I don't know what the difference is or if it's significant. If you do please publish it or at least share so I can incorporate it into my diving practices.
 
Again, the part I bolded is completely wrong. A simple rebuttal: for someone at sea level, nitrogen saturation is 0.79 atm precisely because the partial pressure of nitrogen in the inspired air is 0.79 atm. If you breath EAN50 long enough while sitting on the couch, your tissues will be saturated at 0.5 atm. All this without changing the total ambient pressure.
Take that blood. place it in a sealed container. Will nitrogen bubbles form? what will be the pressure in those nitrogen bubbles? What will the pressure be in the container?

Make it a 1 litter sample. inject a 1 ml bubble of pure nitrogen. Will the bubble grow, collapse, or stay the same size?

The solubility of nitrogen is determined by pressure and temperature. If the nitrogen present is above the solubility, the solution is supersaturated and gas will come out of solution. If it is below the solubility, it is sub saturated and additional gas will dissolve into the solution.

Equilibrium =/= saturated.
 
The solubility of nitrogen is determined by pressure and temperature. If the nitrogen present is above the solubility, the solution is supersaturated and gas will come out of solution. If it is below the solubility, it is sub saturated and additional gas will dissolve into the solution.

Equilibrium =/= saturated.
This is not how the buhlmann algorithm is implemented in all modern deco software and dive computers. Assuming you consider supersaturation and off-gassing as synonymous (as I and others do), then supersaturation (and the rate of off-gassing) is determined by calculating the pressure gradient between partial pressures in breathing gas vs tissues. Ambient pressure doesn't come into the equation (it does when calculating M-values, but not when calculating off-gassing/saturation).
 
You keep putting words that people never said into their mouth.
So how would you edit those words to match your actual position.

I'm saying I don't know what the difference is or if it's significant. If you do please publish it or at least share so I can incorporate it into my diving practices.
Try these:

Fraedrich DS, Validation of algorithms used in commercial off-the-shelf dive computers, Diving and Hyperbaric Medicine, V48 No 4 , 2018
Doolette DJ, Gerth WA, Gault KA. Redistribution of decompression stop time from shallow to deep stops increases incidence of decompression sickness in air decompression dives. NEDU TR 11-06, Panama City FL; 2011.
Howie, LE, Weber PW, Hada E, Vann RD, Denoble PJ, The probability and severity of decompression sickness, PLoS ONE 12(3): e0172665,2017
Balestra C. Dive computer use in recreational diving: Insights from the DAN-DSC database. In: Blogg SL, Lang MA, Møllerløken A, editors. Proceedings of validation of dive computers workshop. 2011 Aug 24 Gdansk. Trondheim: Norwegian University of Science and Technology; 2012. p. 99–102.
Van Liew HD, Flynn ET. A simple probabilistic model for standard air dives that is focused on total decompression time. Undersea Hyperb Med.2005;32:199–213.

Do you have a single citation that even suggests that the difference between the two dives above (GF's=80/65 and GF's = 60/50) might not be significant?
 
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