Question Should OC and CC divers respect the same limits for breathing gas densities at depth?

[Bernie_U]

This posting in fact addresses two interlinked questions:

1. Is there scientific evidence that the limit for breathing gas densities at depth (commonly 6.2 g/l) is the same for OC and CC diving?
2. Is the work of breathing (WOB) the predominant factor that sets this limit?

Background of my question(s):
The often cited article "Respiratory Physiology of Rebreather Diving" was published in the conference proceedings "Rebreathers and Scientific Diving" (2016). As the title and the conference suggest, this article was written about closed-circuit diving. Based on a series of rebreather test dives, the authors recommend to keep the gas density of the breathing gas below 5.2 gram per liter at depth. Further, they set the hard limit at 6.2 gram per liter.
I consider this article as scientific evidence in the sense of my first question (see above), although one might criticize the small sample size. But again, that article refers only to CC diving, there is no statement regarding OC diving.

However, these limits (5.2 and 6.2 g/L respectively) have been picked up by many and became widely adopted by SCUBA training agencies, dive computer manufacturers and other for both CC and OC diving. There are many articles published in dive magazines or online, in which the authors claim the general validity of the limits for both CC and OC diving. All articles I have read so far refer to the original article "Respiratory Physiology of Rebreather Diving". I don't consider these articles as scientific evidence, because the authors are neither scientists in that area, nor do they provide new knowledge or data. These magazines are secondary or tertiary literature.
Here are some examples:​

• DAN
• Shearwater
• BSAC

Now, I move over to the second question and explain the link between my two questions.

On page 68 of "Respiratory Physiology of Rebreather Diving", the authors state​

"... but a significant contribution to the process occurs because of the increase in the work of breathing that occurs during diving",​

followed by more than one page about what is affecting the WOB.​

​

If WOB set the limits, then I would expect a limit on the WOB and thus different recommendations for maximum gas densities for CC divers and OC divers. As for modern regulators, the WOB is around 0.8 Joule per liter at testing conditions, compared to 1.8 Joule per liter of a rebreather (JJ or X-CCR). OC divers have a lower WOB base level, thus more capacity reserves to the maximum tolerable WOB. Following the thoughts of the authors, one would expect different gas density limits for CC and OC diving. I am not the first person who stumbled upon this, the question has already been touched on SB. But the forum members who wrote that they knew an article about gas density and OC did not provide the link to it.​

I already did some Google search on my own, but the most promising scientific articles are behind the pay-wall. Don't get me wrong: I would buy a copy if I had the certainty to find the answer in there. On the other hand, the authors of "Respiratory Physiology of Rebreather Diving" probably would have mentioned any source published earlier than 2016.

Is anyone aware of a scientific article (primary literature only) on the critical breathing gas density explicitly for open circuit diving?

 

[Bernie_U]

I am afraid that only the presenter (Simon Mitchell) can provide the definite answer.

Here is my best guess:

• K denotes most likely a constant with physical units, and its value is not necessarily the same in both equations. Although these equations are not provided in the same slide, it is likely that both K are identical, because of the similarities of both equations.
• I think, your first approach is correct: delta P equals R times V° --> delta P = R * V°
• Hence, as you wrote, R = delta P / V°
• IMHO, delta P is the pressure difference along the length of the alveolar airway.
• The resistance 'R' is probably an analogy to Ohm's law: R = U / I. The voltage U is an electric potential, similar to the mechanical pressure. The electric current I is similar to the gas volume flow V°.
• Then, R means 'the pressure drop per volume flow rate', in SI-units: Pascals per (cubic meters per second)

The pressure drop equation does not look like the technical equations for pressure drop in pipe flow applications. On the other hand, our airways do not look like rigid pipework either. I assume these equations have been derived from experimental data.

 

[CG43]

• IMHO, delta P is the pressure difference along the length of the alveolar airway.
• The resistance 'R' is probably an analogy to Ohm's law: R = U / I. The voltage U is an electric potential, similar to the mechanical pressure. The electric current I is similar to the gas volume flow V°.
• Then, R means 'the pressure drop per volume flow rate', in SI-units: Pascals per (cubic meters per second)

Thank you, that's exactly it and it also fits with the units. So R is the pneumatic resistor !

I am interested in the delta P formula because I want to calculate the limits within which the greater density can be compensated by slower breathing. In the case of a complete compensation with a known well-tolerated value for delta P, one can then determine the volume flow that should lead to the same tolerable delta P and therefore the same change in the soft bronchi.

The pressure drop equation does not look like the technical equations for pressure drop in pipe flow applications. On the other hand, our airways do not look like rigid pipework either. I assume these equations have been derived from experimental data.

I have already started with the tube formula and will compare these results with Dr. Simon Mitchell's formula.
There is also a very convenient online calculator for the pipe formula.

www.druckverlust.de/Online-Rechner/dp.php