Confused about alveolar air/gas equation...

[CBG23]

So, I am reading about how changes in Alveolar ventilation affect both PACO2 and PAO2. I understand how a change in alveolar ventilation would affect PACO2- by looking at the alveolar ventilation equation, mutiplying the alveolar ventilation by "x" will cause the PACO2 to change by a factor of "1/x". I am confused however about how exactly a change in alveolar ventilation will change the PAO2. What is vexing me is that I have read the following in multiple sources:

Halving the alveolar ventilation will double the PACO2. However, halving the alveolar ventilation will MORE THAN halve the PAO2. I have been playing around with the aveolar gas equation for the past couple of hours and have even searched for a a mathematical explanation of this using the equations, but have not had any luck. I think the fact that there is another variable to add (FIO2) in the alveolar air equation that is really confusing me (whereas is the alveolar ventilation equation all the variables are multiplied or divided and not added or subtracted) and preventing me from seeing this relationship between a change in "V dot A" and PAO2. I don't know if I explained that clearly.

I am trying to come up with a general relationship that says if I multiply alveolar ventilation by "x", I will cause a change in PAO2 by more than x or less than x.

Maybe I am missing something really simple here, but I couldn't figure it out even after a couple of hours...Any one have a good handle of this concept and is wiling to share their understanding? Any help would be very much appreciated,

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[switcheroo]

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[TexasMDtobe]

You have to use the Alveolar Gas Equation to predict Alveolar PO2 based on Alveolar PCO2:

Alveolar PO2 = (Inspired PO2) - (Alveolar PCO2 / R)

where R = (CO2 production) / (O2 consumption)

In a normal person, R = 0.8, but it depends largely on diet.
For Carbs R = 1.0
For Protein R = 0.8
For Fat R = 0.7
If you know the proportions of a person's diet, you can calculate their exact R number, but if not, just use R = 0.8

The dividing Alveolar PCO2 by 0.8 is what makes the Alveolar PO2 slightly more than halve when Alveolar PCO2 is doubled.

 

[CBG23]

So, for the following I just am multiplying by the reciprocal of 0.8 instead of dividing by 0.8 directly, hence the 5/4...

Alveolar PO2 = (Inspired PO2) - [(Alveolar PCO2)*(5/4)]

So, now I double Alveolar PACO2.

--> (Inspired PO2) - 2*[(Alveolar PCO2)*(5/4)] = ???

Why does the R value even matter? If I double the Alveolar PACO2, i have to divide by 0.8 (or multiply by 5/4), but before I even doubled the PACO2, I still had to divide the original PACO2 by 0.8.


I am trying to compare this somewhat to the alveolar ventilation equation:


Alveolar ventilation eqn: PACO2= [(VdotCO2)/(VdotA)]*K
If we halve VdotA, we double PACO2. Even though we are multiplying the above variables by some constant,K, less than 1.

I am getting hung up on why the constant (R=0.8) would make a difference when calculating the change in Alveolar PO2 using the alveolar gas equation, but not when calculating the change in Alveolar PCO2 using the alveolar ventilation equation.

 

[TexasMDtobe]

I see what you mean now. Dividing by R = 0.8 exactly halves PAO2 when PACO2 doubles

PAO2 = 150 (inspired air) - (40 / 0.8) = 100
PAO2 = 150 (inspired air) - (80 / 0.8) = 50

This gives standard values of PACO2 = 40 and PAO2 = 100

Varying R will change the PAO2 as it relates to doubling PACO2

A fattier diet will lower R:
PAO2 = 150 - (40 / 0.7) = 92.85
PAO2 = 150 - (80 / 0.7) = 35.71
PAO2 is more than halved when PACO2 doubles

A more carb-rich diet will raise R:
PAO2 = 150 - (40 / 0.9) = 105.56
PAO2 = 150 - (80 / 0.9) = 61.11
PAO2 is less than halved when PACO2 doubles

As to combining the Alveolar Gas Equation with the Alveolar Ventilation Equation, I haven't bothered trying to do it (too many other things to memorize).

Hope this helps!

 

[theWUbear]

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[Polish Farmer]

Alveolar pCO2 concentration is determined by minute ventilation and CO2 production

Alveolar pO2 concentration is determined by the too long to remember alveolar gas equation.

I am not aware of a mathematical formula that can predict the pCO2 from the pO2, at least not one that is clinically relevant. The reason that elevated alveolar pCO2 causes lower pO2 is simply a volume/pressure problem in the alveolus. From Boyle's law if two gases exist in a closed structure (alveolus), increasing the volume or pressure of one leads to a proportional decrease in the other.

Minute ventilation does not determine oxygenation for any other reason than this.