Alveolar gas equation - part 1

Let's say this person is lying here in front of me. And I'm thinking about how the air is passing through their nose and their mouth and entering their lungs. And specifically I'm interested this time in how much oxygen is actually getting to their alveolar sacs. So, deep inside their lungs they have these branches, they're conducting in respiratory bronchials. But at the end, of course, they have these alveolar sacs that we've talked about. And I'm interested in thinking about how much oxygen is really down there at the very ends. And you have to excuse this alveolar sac. It really is that. It looks a little bit like a three-leaf clover, I guess. But that's the issue. How much oxygen is deep down in here where the x is? So how do we figure this out? I want to first think about the air this gentleman is breathing in. He's breathing in air from the atmosphere. So this is atmospheric pressure air. And we say ATM for short. And we know that atmospheric pressure at sea level is 760 millimeters of mercury. It's going to be lower at higher altitudes. So, if you're at the top of a mountain, it would be less than that. And this pressure is made up of many, many different molecules bouncing around. So, I've got some molecules of oxygen. Let's say this is about 21%. This is my oxygen. And before I move on, I should mention FiO2. You might come across this. And FiO2 stands for the fraction-- which in this case was 21% or 0.21-- fraction of inspired, meaning how much oxygen you took in or air you took in-- fraction of inspired oxygen. And the fraction happens to be 21%, which is, of course, much, much lower than the nitrogen. Now nitrogen-- when I draw it this way-- it's pretty impressive. All the purple is nitrogen. This is about 78% of what you're breathing in. And the last little tiny little bit, I'm going to draw the green line. This is mostly argon. And argon is-- in Greek, it actually comes from the term lazy. But it basically reminds me when I think of that, that argon is not going to do much. It's not going to react with anything that is in our body. And of course, you have other. You have less than 1%. And this would be things like carbon dioxide. So, this is a breakdown of the air that my friend is breathing in. This is my friend breathing. And if I want to now think about how much oxygen they're taking in, all I have to do is a little tiny bit of math. I can say OK, pO2-- this is the partial pressure of oxygen-- is just 0.21, or 21%, times 760 millimeters of mercury. And this turns out to be 160 millimeters of mercury. Now, that oxygen kind of goes down in his lungs. And it goes through his trachea and into his-- all the little bronchials and down into the alveolar sac. And when it gets there-- on the way over there, an interesting thing happens. The body temperature here is 37 degrees Celsius. He's got a normal body temperature. And what that does is-- the air is going through these bronchials and trachea. And as it does, there's a lot of moisture in the respiratory tree. There's moisture there. And that moisture, when it starts heating up-- and of course, 37 degrees is pretty warm-- It's going to start leaving the liquid phase and going into the gas phase. So all of a sudden you have now little molecules. I'm going to draw them as little dots of water. That's here. And it's going to start entering and mingling with the gas that's going through. So, the gas that got taken in, that he inhaled is now mingling. And what happens as a result, is that water has what we call a vapor pressure. And that vapor pressure is going to change depending on the temperature. But at 37 degrees, that vapor pressure ends up being 47 millimeters of mercury. In other words, if the temperature is 37 degrees, then we can expect that some of those water molecules will leave the liquid and enter the gas phase. And it turns out that the amount of molecules-- or the number of molecules-- that leave are going to generate a pressure that is 47 millimeters of mercury. And this is pretty standard. This is known off of a table. And in fact, if you think about it, if you just generated lots of heat-- let's say you actually were boiling water-- that would be 100 degrees Celsius. And the vapor pressure there would be very high, because it's boiling. And it would be 760. So boiling is actually 760. So just keep that in mind. Boiling water has a vapor pressure of-- And what do you think 760 reminds you of? That is atmospheric pressure. So it's interesting. Vapor pressure is going to equal atmospheric pressure when you are boiling water. And that's actually exactly what's happening as you boil. But I don't want to get too distracted. We're not boiling water inside of our bodies or our lungs. We're actually much cooler than that. But we are warm. We're at 37 degrees. And so you do have some of these little water molecules that have entered the gas phase. And so if overall it's got to be-- this whole thing has got to be 760. So, on average, our lung pressures are going to be the same as atmospheric pressure. But now you've got water taking up 47. So if water's taking up 47, the rest of those little gas molecules have got to be 713. So this is the rest. What was in that rest? It's going to be the same as before. It's going to be-- and I'm going to try to sketch it as best as possible-- this is going to be my oxygen right here. This is 21% of 713. And then we have lots and lots of nitrogen still. Same kind of break down as before. And remember this is all air that is being inhaled. So we're not talking about breathing out. We're just talking about breathing in. And this purple right here-- and this is 78%. Again, this is 78% percent of 713. And we still have a little bit of that argon, and those other gases-- I won't write it all out, but you get the idea. That basically now because water is taking up some of the overall pressure, all of the other gases are going to have a lower partial pressure. So what is the partial pressure of the air that's entering into that alveolar sac? It's going to be basically FiO2, which is 21%. I'll write that here. And then we have the atmospheric pressure. This is atmospheric pressure over here. And we said that was 760. We can draw a little arrow so we know what's pointing to what. 760 millimeters of mercury. And then, from that to account for the partial pressure of water. Because now we have some water vapor in there. We have to subtract out 47. So, so far, if you've kept up with this math, you see that we have-- what does that work out to be? About 150 millimeters of mercury. Now this is the partial pressure of oxygen, at this spot. Let me just make it very clear with my arrow, not at this orange x. So far, we've figured out that we have a partial pressure that's a little bit lower than when we started. And that was because of the partial pressure of water. Let's pick up there in our next video.