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    Alveolar gas equatiion

    Split from the Near drowning and Rescue thread - http://www.rebreatherworld.com/showthread.php?t=12601

    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  View Original Post
    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.




    Last edited by sadave; 23rd June 2007 at 03:45. Reason: Made font in quote larger, more readable

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    Studies In Pulmonary Physiology

    Quote Originally Posted by dteubner  View Original Post
    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.

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    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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    Re: Alveolar gas equatiion

    Quote Originally Posted by apitkin  View Original Post
    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

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    Re: Alveolar gas equatiion

    Quote Originally Posted by dteubner  View Original Post
    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

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    Re: Alveolar gas equatiion

    Quote Originally Posted by dteubner  View Original Post
    I have put the Fenn paper on my website
    Many thanks. Lots to read here.

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