How does gas equilibration occur in the alveolus, numerically?

Question

I am attempting to model gas exchange across the alveolar membrane. My main question is there a direct exchange of O2 molecules for CO2 molecules? If so, then my model predicts (assuming alveolar PO2 107mmHg and CO2 40mmHg; and venous PO2 40, PCO2 46) an arterial PO2 107mmHg, but PCO2 of only 37mmHg (taking into account pH change and equilibration with bicarb and haemoglobin carbamates). If I remove the plasma bicarb equilibration process (as this takes ~15 seconds, but alveolar transit time is ~0.75 seconds), then the arterial PCO2 is even lower, ~33mmHg. The expected results should be somewhere in the range of an arterial PO2 of 107 and PCO2 of 40.

The only alternative I can think of is that there isn't a molecule for molecule exchange, with the O2 absorption and CO2 removal being separate processes. If this is the case then overall there will either be a reduction in alveolar air pressure and/or volume during gas exchange. However, I can find no references to inhaled tidal volume being different to exhaled tidal volume. Nor does there seem to be any evidence for N2 or H2O molecules to participate in this process (at standard atmospheric pressure).

Any ideas??

Ultimately I want to then extrapolate model to deal with pathology (eg high alveolar CO2, high venous CO2 etc).

EDIT to include references... Mechanistic physicochemical model of CO2 transport in the blood https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5341128/

Modeling of the oxygen transfer in the respiratory process https://hal.archives-ouvertes.fr/hal-00714239/document

Modeling pulmonary gas exchange and single-exhalation profiles of CO https://www.frontiersin.org/articles/10.3389/fphys.2018.00927/full

Respiratory Physiology https://derangedphysiology.com/main/cicm-primary-exam/required-reading/respiratory-system

Other materials I have read include:

• Pilbeams Mechanical Ventilation
• Nunn's Applied Respiratory Physiology
• Guyton and Hall Medical Physiology

Answer 1

There is no known mechanism for exchange of $\ce{O2}$ and $\ce{CO2}$ in a one-for-one fashion. Their transport across the alveolar membrane takes place by diffusion alone: both of them attain their equilibria with blood independently.

Note that it is not necessary for inhaled and exhaled tidal volumes to be the same. In fact, under physiologic conditions, the exhaled tidal volume is slightly less than inhaled tidal volume. This is because humans normally produce slightly less $\ce{CO2}$ than they consume $\ce{O2}$. In other words, the respiratory quotient is less than $1$.

Thus, we see that the assumption of preservation of alveolar volume and pressure is not valid. Apart from inspiration and expiration, the diffusion of gases to and from blood also affects alveolar volume.

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Reference and further reading:

Boron WF, Boulpaep EL, editors. Medical physiology. 3rd ed (international edition). Philadelphia: Elsevier; c2017. 1297 p. (I found this textbook an excellent resource for learning physiology in general and respiratory physiology in particular.)

Answer 2

No direct exchange, but there is interaction.

I used these wikipedia articles:

https://en.wikipedia.org/wiki/Hemoglobin

https://en.wikipedia.org/wiki/Bohr_effect

For Oxygen transport nearly all is transported bound to hemoglobin. Only one part in 71 is transported as soluble unbound oxygen.

For carbon dioxide, only about 20-25% is transported by hemoglobin. But it sticks to the amine groups and so doesn't directly compete with oxygen which binds elsewhere.

The Bohr effect causes the oxygen to bind more strongly where there is little CO2 and vice-versa. The wikipedia article has a mathematics treatment of this.

The rest of the CO2 is transported as hydrogen carbonate through the action of a carbonic anhydrase. CO2 is not very soluble at body temperature.

The volume of CO2 in the breath is still small.