Compliance and elastance

All right, so you take a little balloon, let's assume. You see it on the table, and you can't resist yourself. You take that balloon. And you start to think about how to do a little experiment with it. Maybe that's not what you're thinking, but that's certainly what you should be thinking, because we're going to have a lot of fun checking out and learning about this balloon by giving it some air. So imagine if you put some pressure into that balloon, what would happen? It would, of course, get larger, right? So you know that the volume of the balloon is going to go up as you put pressure into that balloon. But you actually want to measure it, let's say. So you go ahead and give a small amount of pressure, maybe a small breath. And this balloon gets a little bit bigger. And you note that a small amount of pressure is over there, and it gets a little bit bigger over there. So you put a little x right there. Very good. Now, you go back and give it a little bit more pressure, a little bit bigger breaths. And you do the same thing. You say, well, there's my pressure. And now it's a little bit bigger, so I am going to put a little x right there. And you do this again with a large, large amount of pressure. And you notice the balloon is getting much bigger now. So you figure out that as you put in more pressure, the balloon is getting bigger and on top of that, it's happening at a linear rate, right? So the more pressure you're putting in, you're getting a direct amount of volume for that. Now, not all balloons are going to behave this way. But let's assume, for the moment, that this balloon does that. So it gets bigger and bigger as you put more pressure. Great. This is my balloon. Now, you notice that there's one more thing sitting on the table, and you grab it. And it's a plastic wand, like this. And you dip it in soap, and you make a balloon-- or, a bubble, rather. Not a balloon this time, a bubble out of the soap. So you give it a soft breath, just like you did before. And you notice that even with a soft breath, you get kind of a large volume. So that's interesting, right? So kind of a large volume. And then you give it a medium-sized breath. And you get even a larger volume. Let's say, something like this-- even a larger volume. And you can see where this is going to go, because I'm going to give it a large breath. And maybe it'll fill out this entire corner, something like that. You get this enormous bubble, and it doesn't burst, let's assume. So now you have three little blue x's for the bubble, and you connect them just as you did before. And this is my bubble line. And you can already see something interesting, right? You can see that the balloon has a smaller slope than the bubble. The bubble is rising more quickly. And so thinking about this, you could actually say, well, this is a formula for the soap-- rise in volume over run, which would be pressure, in this case. And if you do rise over run, you get the slope. And in this case, we're going to call the slope compliance-- really interesting and important word. Seems pretty simple, right? It's just-- how big does something get when you give it a certain amount of pressure? And you can see, in this case, that the bubble has more compliance than the balloon. Good. So now we've figured out a couple things, and I'm going to add one more new word, which is actually just the inverse. What if I flipped it around? What if I put pressure over here, and volume over here? I can do that, right? I can just take the same data, the same information, and just flip the two axes around. And if I did that, then in this case, the balloon line would be over here, something like that, right? Because all I'm doing is just flipping the way we look at this chart. And the bubble line would be over here, something like that. So now my bubble and my balloon have switched places because the axes have switched. In a way, you could literally just tilt the graph over, and you'd get the same thing. So there's nothing magical. But the thing that is different about this is that now, if I'm calculating rise over run, or the slope, I actually have flipped the volume and pressure, right? So now my pressure is on top, and the volume is down below. And if you have it like this-- pressure over volume-- we actually call that elastance. So the first one, we called compliance. And this one, we call elastance. And so you can see that elastance and compliance are basically just inverses of one another. They're just the flip of one another. And so these two words, you're going to hear them, but I want you to see how they're very, very much the same kind of thing. It's just that one is the inverse of the other one. OK. So now we've gotten that. I'm going to make some space here, like that. And I'm going to bring up one final point. And that might be this-- what if you have an artery? So instead of balloons and bubbles, let's talk about blood vessels for just a second. What if you had an artery, like that? And here's my artery. And you decide that you want to block it off on one end, maybe with your hand, like this. And here's your hand blocking it off. And let's say you do the exact same thing with a vein. You decide you want to take a vein, and block it off on one end. I'm trying to draw these two to be the same size. So if they look different, then please assume, for the moment, that they're the same size, same length. Block it off. So that end is blocked off with your hand, and nothing can leak out, right? So you only have one open end. And now let's assume that you cover up this end. Let's say you cover it up. And you have just one tiny opening here. You cover up the vein. You do the same thing. You have one tiny opening here. And this opening-- let's have it go down, so it looks the same-- this opening is to a bicycle pump. I know this is sounding very strange. Why in the world would you have a bicycle pump attached to an artery or a vein? Well, you'll see in just a second. Here's my bicycle pump. And I'm going to actually pump up my artery and pump up my vein much the same way that I did before with the balloon and the bubble. And you're going to start seeing some really interesting parallels, I think. So let's say I pump up the artery. Immediately what happens? Well, if I put a certain amount of pressure in there, let's say I put the large amount of pressure that I had put in the balloon. Well, I'm going to get something like this, where this artery is going to start swelling up. And this goes away. So now, my artery looks a little fat, like a plump little sausage. And if I give that same amount of large pressure to the vein, it's going to do something like this. It's going to get enormous. And I have to erase these little lines to make it clear that my vein is getting huge. So with a little bit of pressure, the artery gets a little bit bigger. But then a vein gets a lot bigger. So with the same amount of pressure, you see a difference in the volume. And this is actually a critical point, right? Because the artery and the vein are really behaving just like the balloon and the bubble. And it's actually very, very similar. So if I was to make a volume pressure loop with this, I could actually erase the word balloon and bubble. And really, replace them completely with artery and vein. I could just write the words artery and vein. And essentially, they would be behaving this way. Artery up here, artery over here, and then vein in the other two spots. So you can now see that the artery has lower compliance than a vein, and higher elastance than a vein. And now, just speaking to the compliance issue, imagine that you had a really rigid iron pipe, something completely solid that's not going to budge, no matter what you do. Well, for that solid pipe, you'd actually get something like this. You would have even less compliance. So if you're ever thinking about the issue of compliance-- and we talk about stiffness-- think about these curves, and the fact that where the slope is tells you how complaint something is, and that arteries are going to be more compliant than a stiff pipe, certainly, but less compliant than the veins.