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Alveolar gas equation - part 2
In our last video, we were kind of getting to the idea that there's a partial pressure of oxygen that is a little bit lower in the bronchial tree than you would expect by just comparing it to the air that you breathe in. And the reason is because we said, well, of course you have a little bit of water vapor. And that's what this little pH2O represents. This is the partial pressure of water in your lungs, because, of course, it's pretty warm in there. This is the 37 degrees that I had drawn up here. So I had said, well, of course this works out to 150. And just to go over that math very quickly, it was because this FIO2 is 0.21. And we multiply by 760 millimeters of mercury. That's this atmospheric pressure. And subtract off 47, because that was the partial pressure of some of that water vapor that we get in our lungs. And that's how we got our 150 answer. But I had said in the last video that actually, that's not the alveolar oxygen. This is the partial pressure of oxygen. But that's not this. Watch this And there's a subtle difference. And the difference is this capital A. This A means the alveolar, because it's capitalized just like this A over here is capitalized. So how do we calculate the alveolar oxygen concentration? Let's start where we left off, and I'll wrap things up. I'll show you how you do it. You basically have to think about it from a person's point of view. Let's imagine that you're a little person, and you're standing here inside of this little alveolar sac. You can see on the one hand, you've got some oxygen coming in. That's what I circled at the red arrow. And that's all this stuff. This is all the stuff coming in. But you also can see that, of course, alveoli are going to be releasing oxygen to a little blood vessel nearby. So of course if there's an alveolar sac right here, you must also have some blood rushing by. And there might be some gas exchange. Of course, there probably will be some gas exchange. So you have some stuff coming in oxygen-wise, but you also have some oxygen going out. And so if you have some oxygen going out, you have to subtract from this formula the oxygen that's leaving. And that would be the second part of this equation. We have to figure out how much is leaving. Because again, if you keep your eye on that x, you really want to know what is the steady state of oxygen in the alveolar sac. How much is coming, but also how much is going? So at any point in time during inhalation, what is the actual alveolar partial pressure of oxygen? So we have to remember in and out. So how do we figure out how much oxygen is leaving? Well, the first trick is remembering that you have some carbon dioxide in here as well. So here you have some carbon dioxide. And I'll refer to that as PACO2. And you also have carbon dioxide in here. And I'm going to refer to this one as PaCO2. And it turns out that in the blood vessel in the alveolar sac, the concentration of carbon dioxide is basically the same. Because it equilibrates really well. In that number turns out to be 40. So the partial pressure of arterial-- and I could just as easily say alveolar here-- but arterial CO2, because that's what we measure is 40. So that's the first clue as to how we're going to figure out how much oxygen is leaving. Now, how do we use the carbon dioxide number to calculate how much oxygen is leaving the alveolar sac? Here's where things get fun. It turns out that there's a relationship, and we call it the respiratory quotient. And respiratory quotient-- actually sometimes they end up shorthanding it to just RQ. So sometimes you'll see RQ. And what RQ is, is it's a relationship between oxygen and carbon dioxide. It's a relationship between those two things. So for example, let's say my diet is all sugars. Let's say that's all I ever eat. For every 10 molecules of oxygen that I breathe in and use, my body cells are going to make 10 molecules of carbon dioxide. So my ratio-- and this is my ratio of CO2 to O2-- my ratio is going to be what? It's going to be one. That's 10 versus 10 is a ratio of 1 if you divide the 2. Now let's say instead of sugars, my diet consists of, I don't know, let's say fats and lipids and things like that. So a slightly different diet. It turns out that now my body is actually a little bit more efficient. And by that what I mean is that with 10 molecules of oxygen used, your body only makes seven molecules of carbon dioxide. So it's actually a lot better than before. Less waste. And so the ratio ends up being better-- 0.7. So the ratio is actually lower with lipids. And of course, we have diets that are probably mixed. Most people have a mixed diet, not just one thing or another. So if you have a mixed diet, they've estimated something in between, and said, OK, well maybe a ratio of oxygen to carbon dioxide is something like 0.8. So if I know, going back to our formula then, if I know that carbon dioxide, the partial pressure in the alveolus or the arterial is 40-- so let me show you that on this picture. That basically means that if we have then-- let me do it in a different color. Carbon dioxide is going from the blood vessel-- 40 millimeters of mercury-- that's the partial pressure. But that's of course a reflection of how many molecules there are, then I can just divide by the respiratory quotient, which is 0.8-- that gives me a ratio to think about. And I can say, ah, then that must mean that this is going to be 40 divided by 0.8 which is 50 millimeters of mercury of oxygen, O2, that must have left. So if I want to figure out how much has gone out-- that's what these purple arrows were-- I could say, ah, it must be basically 50 millimeters of mercury worth of oxygen left. And I base that on the fact that I know 40 millimeters of mercury of carbon dioxide came in. So because of that relationship-- see this ratio is really cool, because you can say, ah, well if you know that there's this relationship between the two, I can just measure this thing, this guy. And I immediately can get a good sense for how much oxygen left my alveolar sac. And so then just plugging into the formula you could say, OK, 150 millimeters of mercury is where we're left here, and then subtract off 50, because that's about how much oxygen is leaving. And the net amount-- my PaO2 is going to be 100 millimeters of mercury, like that.