Hello everyone, thank you so much for your explanations. This question had been confusing me for a long time. Thanks to the help from you and my friend Lingjia, I think I have understood it finally. And here is my summary. Please let me know if I make any mistake.
I think people who don't understand this question may have a similar thought as I did. When a peanut obstructs the airway, PAO2 in the distal alveoli decreases, so does PaO2. Why would it cause an increase in A-a gradient?
I think one way to think about it is that when there is an obstruction, there's no ventilation at all. We can simply regard the peanut as the dead end of the obstructed bronchus. In this case, if you wanna calculate the PAO2, it should be the pressure of oxygen proximal to the dead end, which is actually unchanged. However, when it comes to COPD and asthma, which are another 2 kinds of V/Q mismatch, this explanation does not fit these situations well.
A second way to put it is that during hypoventilation or at high altitude, the oxygen pressure anywhere inside of the whole lung decreases altogether. When it does not, for example, the alveolar PO2 decreases while the tracheal PO2 remains normal, consider it a V/Q mismatch.
Another way to think about it, similar to what Bakanoisha had mentioned, is that when there is an intrinsic problem of the lung, we choose V/Q mismatch.
I think the most confusing part of this whole thing, is the definition of PAO2, because, in both hypoventilation and some types of V/Q mismatch (eg. COPD), there is a decrease in the oxygen pressure in the alveoli, ie. PAO2. Then why would A-a gradient become different? Maybe when we do the calculation, we can regard PAO2 as the oxygen pressure in the trachea instead of the alveoli. Although it's not the correct definition, it helps us in this type of questions. For example, during hypoventilation, there's a weakness in breathing, so the PO2 in trachea would also decrease together with PaO2, resulting in an unchanged gradient. During peanut obstruction, COPD and asthma, the PO2 in the trachea is actually normal, since we still breathe in the air normally, if not more furiously. However, the PaO2 decreases. If we calculate the gradient between the trachea PO2 and PaO2, it will definitely increase.
Please let me know if I made any mistake so that I can stop misleading other people. Thank you again.