Alveolar gas equatiion

dteubner · 23rd June 2007, 02:19

Split from the Near drowning and Rescue thread - http://www.rebreatherworld.com/rebre...tml#post122149

The alveolar gas equation describes the partial pressure of O2 in the alveolus, which is essentially the same (in a fit person) as that in the arterial blood. It says

PAO2=FIO2(PA-47)-PaCO2/R

Where
PAO2 - alvoleolar partial pressure of O2 (in mmHg)
FIO2 - fraction of inspired oxygen
PA - ambient pressure in mmHg
47 - saturated vapour pressure of water at 37 degrees celcius
PaCO2 - arterial partial pressure of CO2 (in mmHg)
R - respiratory quotient (assumed to be 0.8)

If you are breathing surface air then it works out that

PAO2 (in mmHg) = 147-1.2xPaCO2

Now if the PaCO2 is 40 (which is normal) it means that the PAO2 is about 100 - which is fine. With very severe hypercapnea the CO2 may rise to more than 100mmHg and in this case the PAO2 in air is only 27, which is not really enough to support life and so hypercapnea causes lethal hypoxia.

BUT, you can see that by raising the FIO2 or the ambient pressure the CO2 becomes essentially irrelevant to the oxygen. In the case described we have

PAO2 = (0.7*760-47)-1.2xPaCO2
= 485-PaCO2
or 440 odd with a CO2 of 40 but still 365 or so mmHg with a CO2 of 100 - so no hypoxia at all.

Quote: (Originally Posted by Abbo)

I am rather hijacking the thread for a biochemistry lesson on hypercapnia, but this equation says CO2 crowds out the O2. Anyone able to explain how?

Indeed the CO2 does crowd out the O2 - unless there's lots of O2.

The equation is derived mathematically, and basically depends on the respiratory quotient. It seems to have first been published in the American Journal of Physiology in 1946 by Fenn, Rahn and Otis.

If anyone is interested in looking at this paper email me off line and I'll send it - it's a 2 MB pdf and well worth a read. It was described rather lyrically in a 1979 textbook-

Quote: (Originally Posted by Herman Rahn)

Fenn’s second masterpiece, the O2-CO2 diagram, did for pulmonary gas exchange what the [pressure-volume] diagram [his first masterpiece (11)] did for respiratory mechanics. With it he could represent all parameters of the alveolar gas and ventilation equations. He never claimed to have originated these equations, but he derived them independently, made sure they were correct, and put them in graphic form. As somebody put it, “That’s when he made them sing.” On the diagram he could show all possible compositions of alveolar gas and the arterial blood under any specified set of conditions. He could indicate normal ranges and limits of survival as well as the pathways followed during hyperventilation and asphyxia and during exposure to CO2, altitude, or hyperbaric pressures. It could be used to demonstrate ranges of normal and impaired performance. It was indeed a theme that could be sung with many variations.

Gene_Hobbs · 23rd June 2007, 18:40

Quote: (Originally Posted by dteubner)

The equation is derived mathematically, and basically depends on the respiratory quotient. It seems to have first been published in the American Journal of Physiology in 1946 by Fenn, Rahn and Otis.

This was US Air Force - School of Aviation Medicine research so it is free from copyright.

It is included as a part of this report series (LARGE DOWNLOADS):

STUDIES IN PULMONARY PHYSIOLOGY: CHEMISTRY MECHANICS, AND CIRCULATION OF THE LUNG
Rahn and Farhi, 1960
RRR ID: 3421

STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME I
Rahn and Farhi, 1963
RRR ID: 3422

STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME II
Farhi and Rahn, 1966
RRR ID: 3423

STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME III
Rahn and Farhi, 1970
RRR ID: 3424

STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME IV
Rahn and Farhi, 1974
RRR ID: 3425

NOTE: Thanks to Bill Hamilton for sending these to us for inclusion in the RRR.

apitkin · 24th June 2007, 08:30

Dave,

Thanks for posting that useful summary. It's been a while since I did my exams, and I haven't got a copy of Nunn's Respiratory Physiology to hand, but I seem to recall that there are several versions of the alveolar gas equation. The simpler ones (including the one you quote that we all remember) make some assumptions to allow their simplification.

What I have forgotten is what those assumptions are, and therefore whether they are still valid in a hyperbaric environment, and I doubt in this case they would materially affect the result. Any thoughts?

A copy of the paper would be much appreciated.

Andy

dteubner · 24th June 2007, 23:23

Quote: (Originally Posted by apitkin)

Dave,

Thanks for posting that useful summary. It's been a while since I did my exams, and I haven't got a copy of Nunn's Respiratory Physiology to hand, but I seem to recall that there are several versions of the alveolar gas equation. The simpler ones (including the one you quote that we all remember) make some assumptions to allow their simplification.

What I have forgotten is what those assumptions are, and therefore whether they are still valid in a hyperbaric environment, and I doubt in this case they would materially affect the result. Any thoughts?

A copy of the paper would be much appreciated.

Andy

Hi Andy,

The equation is a simplified version amongst other things it
1. Omits a correction factor (F) which is only about 2 mmHg
2. Assumes FICO2 to be zero (which may not be true at all for rebreather divers)
3. I have seen one version of it which includes a FIN2/FeN2 ratio with no explaination see Riley et all ON THE DETERMINATION OF THE PHYSIOLOGICALLY

EFFECTIVE PRESSURES OF OXYGEN AND CARBON DIOXIDE IN ALVEOLAR AIR -Am J Physiol 147: 191-198, 1946

Apart from the FIO2 thing my understanding is that it does apply in the hyperbaric environment.

I have put the Fenn paper on my website (after all, it's 60 years old and the authors probably won't get cross with me about copyright) see "Fenn paper" at the bottom of the page at - Research etc

Gene_Hobbs · 25th June 2007, 00:32

Quote: (Originally Posted by dteubner)

after all, it's 60 years old and the authors probably won't get cross with me about copyright

It would be the journal and not the authors but as I mentioned above, this was US Air Force research and is free from copyright. If anyone says anything, it is a part of this USAF-SAM Technical Report:

STUDIES IN PULMONARY PHYSIOLOGY: CHEMISTRY MECHANICS, AND CIRCULATION OF THE LUNG
Rahn and Farhi, 1960
RRR ID: 3421

Abbo · 25th June 2007, 01:00

Quote: (Originally Posted by dteubner)

I have put the Fenn paper on my website

Many thanks. Lots to read here.

23rd June 2007, 02:19	#1 (permalink)
dteubner Pedant Current Rebreather/s: Sport Kiss Classic Kiss Other Rebreather/s: Join Date: Mar 2005 Location: Adelaide, Australia Posts: 217	Alveolar gas equatiion Split from the Near drowning and Rescue thread - http://www.rebreatherworld.com/rebre...tml#post122149 The alveolar gas equation describes the partial pressure of O2 in the alveolus, which is essentially the same (in a fit person) as that in the arterial blood. It says PAO2=FIO2(PA-47)-PaCO2/R Where PAO2 - alvoleolar partial pressure of O2 (in mmHg) FIO2 - fraction of inspired oxygen PA - ambient pressure in mmHg 47 - saturated vapour pressure of water at 37 degrees celcius PaCO2 - arterial partial pressure of CO2 (in mmHg) R - respiratory quotient (assumed to be 0.8) If you are breathing surface air then it works out that PAO2 (in mmHg) = 147-1.2xPaCO2 Now if the PaCO2 is 40 (which is normal) it means that the PAO2 is about 100 - which is fine. With very severe hypercapnea the CO2 may rise to more than 100mmHg and in this case the PAO2 in air is only 27, which is not really enough to support life and so hypercapnea causes lethal hypoxia. BUT, you can see that by raising the FIO2 or the ambient pressure the CO2 becomes essentially irrelevant to the oxygen. In the case described we have PAO2 = (0.7760-47)-1.2xPaCO2 = 485-PaCO2 or 440 odd with a CO2 of 40 but still 365 or so mmHg with a CO2 of 100 - so no hypoxia at all. Quote:* (Originally Posted by Abbo) I am rather hijacking the thread for a biochemistry lesson on hypercapnia, but this equation says CO2 crowds out the O2. Anyone able to explain how? Indeed the CO2 does crowd out the O2 - unless there's lots of O2. The equation is derived mathematically, and basically depends on the respiratory quotient. It seems to have first been published in the American Journal of Physiology in 1946 by Fenn, Rahn and Otis. If anyone is interested in looking at this paper email me off line and I'll send it - it's a 2 MB pdf and well worth a read. It was described rather lyrically in a 1979 textbook- Quote: (Originally Posted by Herman Rahn) Fenn’s second masterpiece, the O2-CO2 diagram, did for pulmonary gas exchange what the [pressure-volume] diagram [his first masterpiece (11)] did for respiratory mechanics. With it he could represent all parameters of the alveolar gas and ventilation equations. He never claimed to have originated these equations, but he derived them independently, made sure they were correct, and put them in graphic form. As somebody put it, “That’s when he made them sing.” On the diagram he could show all possible compositions of alveolar gas and the arterial blood under any specified set of conditions. He could indicate normal ranges and limits of survival as well as the pathways followed during hyperventilation and asphyxia and during exposure to CO2, altitude, or hyperbaric pressures. It could be used to demonstrate ranges of normal and impaired performance. It was indeed a theme that could be sung with many variations. __________________ Dave T Hanlon's Razor - Never attribute to malice that which can be adequately explained by stupidity. Last edited by sadave : 23rd June 2007 at 02:45. Reason: Made font in quote larger, more readable
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23rd June 2007, 18:40	#2 (permalink)
Gene_Hobbs Resident bibliophile Current Rebreather/s: Not Bought Yet Other Rebreather/s: Not Bought Yet Join Date: Sep 2006 Location: Durham, NC, USA Posts: 122	Studies In Pulmonary Physiology Quote: (Originally Posted by dteubner) The equation is derived mathematically, and basically depends on the respiratory quotient. It seems to have first been published in the American Journal of Physiology in 1946 by Fenn, Rahn and Otis. This was US Air Force - School of Aviation Medicine research so it is free from copyright. It is included as a part of this report series (LARGE DOWNLOADS): STUDIES IN PULMONARY PHYSIOLOGY: CHEMISTRY MECHANICS, AND CIRCULATION OF THE LUNG Rahn and Farhi, 1960 RRR ID: 3421 STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME I Rahn and Farhi, 1963 RRR ID: 3422 STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME II Farhi and Rahn, 1966 RRR ID: 3423 STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME III Rahn and Farhi, 1970 RRR ID: 3424 STUDIES IN PULMONARY PHYSIOLOGY MECHANICS, CHEMISTRY, AND CIRCULATION OF THE LUNG. VOLUME IV Rahn and Farhi, 1974 RRR ID: 3425 NOTE: Thanks to Bill Hamilton for sending these to us for inclusion in the RRR. __________________ http://rubicon-foundation.org/ Home of the Rubicon Research Repository. For help getting started with the Repository, please visit our FAQ page. PLEASE support our work. "Oxygen is addictive and deadly. Everyone who uses it will eventually die" --RW Hamilton, PhD 1991
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24th June 2007, 08:30	#3 (permalink)
apitkin New Member Current Rebreather/s: Prism Topaz Other Rebreather/s: Join Date: Feb 2005 Location: Cloud Cuckoo Land Posts: 102	Re: Alveolar gas equatiion Dave, Thanks for posting that useful summary. It's been a while since I did my exams, and I haven't got a copy of Nunn's Respiratory Physiology to hand, but I seem to recall that there are several versions of the alveolar gas equation. The simpler ones (including the one you quote that we all remember) make some assumptions to allow their simplification. What I have forgotten is what those assumptions are, and therefore whether they are still valid in a hyperbaric environment, and I doubt in this case they would materially affect the result. Any thoughts? A copy of the paper would be much appreciated. Andy
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24th June 2007, 23:23	#4 (permalink)
dteubner Pedant Current Rebreather/s: Sport Kiss Classic Kiss Other Rebreather/s: Join Date: Mar 2005 Location: Adelaide, Australia Posts: 217	Re: Alveolar gas equatiion Quote: (Originally Posted by apitkin) Dave, Thanks for posting that useful summary. It's been a while since I did my exams, and I haven't got a copy of Nunn's Respiratory Physiology to hand, but I seem to recall that there are several versions of the alveolar gas equation. The simpler ones (including the one you quote that we all remember) make some assumptions to allow their simplification. What I have forgotten is what those assumptions are, and therefore whether they are still valid in a hyperbaric environment, and I doubt in this case they would materially affect the result. Any thoughts? A copy of the paper would be much appreciated. Andy Hi Andy, The equation is a simplified version amongst other things it 1. Omits a correction factor (F) which is only about 2 mmHg 2. Assumes FICO2 to be zero (which may not be true at all for rebreather divers) 3. I have seen one version of it which includes a FIN2/FeN2 ratio with no explaination see Riley et all ON THE DETERMINATION OF THE PHYSIOLOGICALLY EFFECTIVE PRESSURES OF OXYGEN AND CARBON DIOXIDE IN ALVEOLAR AIR -Am J Physiol 147: 191-198, 1946 Apart from the FIO2 thing my understanding is that it does apply in the hyperbaric environment. I have put the Fenn paper on my website (after all, it's 60 years old and the authors probably won't get cross with me about copyright) see "Fenn paper" at the bottom of the page at - Research etc __________________ Dave T Hanlon's Razor - Never attribute to malice that which can be adequately explained by stupidity.
(Offline)

25th June 2007, 00:32	#5 (permalink)
Gene_Hobbs Resident bibliophile Current Rebreather/s: Not Bought Yet Other Rebreather/s: Not Bought Yet Join Date: Sep 2006 Location: Durham, NC, USA Posts: 122	Re: Alveolar gas equatiion Quote: (Originally Posted by dteubner) after all, it's 60 years old and the authors probably won't get cross with me about copyright It would be the journal and not the authors but as I mentioned above, this was US Air Force research and is free from copyright. If anyone says anything, it is a part of this USAF-SAM Technical Report: STUDIES IN PULMONARY PHYSIOLOGY: CHEMISTRY MECHANICS, AND CIRCULATION OF THE LUNG Rahn and Farhi, 1960 RRR ID: 3421 __________________ http://rubicon-foundation.org/ Home of the Rubicon Research Repository. For help getting started with the Repository, please visit our FAQ page. PLEASE support our work. "Oxygen is addictive and deadly. Everyone who uses it will eventually die" --RW Hamilton, PhD 1991
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25th June 2007, 01:00	#6 (permalink)
Abbo Nicholas Smith Current Rebreather/s: Megalodon Other Rebreather/s: Join Date: Aug 2006 Location: Tokyo Posts: 445	Re: Alveolar gas equatiion Quote: (Originally Posted by dteubner) I have put the Fenn paper on my website Many thanks. Lots to read here.
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