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let's go ahead and use our pressure-volume loop I'm going to sketch out how afterload would make things change on this so let's just quickly sketch this out I'm going to put pressure over here and I'm going to start out with just two lines first and this is probably the one I want you to keep an eye on this is the end systolic pressure volume relationship and then I'm going to also put on there the end diastolic pressure volume relationship something like that and so these are kind of the the first two lines that we know are going to be helpful in sketching out our pressure volume loop and then we have this other line right we have this ei line this is arterial elastance and there's a good formula here that is very very helpful it's the pressure at the end of systole over stroke volume remember any elastance is kind of thinking along lines of a pressure over a volume and this red dot represents the pressure at the end of systole and this other red dot here is going to kind of show you where it crosses the x-axis the volume and that's helpful because then we can kind of quickly figure out what the stroke volume would be this would be our stroke volume here so we have it sketched out and I can actually take this and now draw in the PV loop which would be something like this kind of chugging along and you know you might be tempted to make it cross right there at the point where the purple line is but remember we have to go a little bit further because that's not where the volume is going to be the volume is actually gonna be a little bit further along so to be true to that I'm just going to draw a little bit further but I wanted to draw the first line just to show you how you might have thought it looked but that is not where it crosses and then of course you have contraction and you have ejection of blood into the aorta so this is our pressure volume loop right this is what it looks like and at the top of this loop we have ejection right this is where blood I said is coming out of the left ventricle and going into the aorta and if I actually just kind of trace around this part of it this is ejection you would probably remember that this is where something important is taking place and specifically I'm talking about afterload remember we actually defined afterload according to this part of the pressure-volume loop we said and this is going back to Laplace we said that afterload is basically wall stress wall stress happening during ejection so during the entire ejection phase the wall stress is what our afterload is and we actually simplify this - or not simplify but kind of wrote this out I should say to Laplace's law which is pressure times radius of the left ventricle during ejection divided by 2 times the wall thickness during ejection so this is the formula for afterload and we have to remember that it's occurring during the entire ejection during the entire part I trace down but for simplicity because a lot of times we don't actually you know sit there and calculate all the different points we oftentimes kind of look to this value this pressure at the end of systole because of course this is the last this is definitely one of the points during ejection the you could say the final moment of ejection would be that point right there that problem where the pressure is n systolic and so we often use that value to kind of be a marker for what afterload is doing and remember we we know that pressure and afterload are very closely related you can see it in the formula right there so we do use the end systolic pressure as a marker and I guess now the question I want to pose is what would happen if we actually increased that number what if we increased the pressure at the end of systole what would happen so you know on the graph it would basically look maybe something like this where now your value is higher this is our new pressure this is the new pressure at the end of systole I'll put P Prime and if that's the new pressure at the end of systole then we have to think through what would what what else would change I guess that's that's the question and you know of course the first thing to think about is the fact that this is going to drop down this line and if our pressure has gone up then you know our stroke volume has gone down so our stroke volume is going to be a little bit more contracted or smaller and you remember now we have a formula may actually just jot down the formula for us just make a little bit of space maybe I'll maybe I'll just actually leave it that way you can see everything but I'll put the formula over here we have our formula which says that elastance or tree elastance equals pressure and n systole divided by stroke volume and all that equals heart rate times resistance right and in this case I'm saying that I'm going to increase this number and I'm going to decrease this number so what I've done is basically changed the slope so I know that the elastance is going to change and if I've done that the only way to really accomplish that would be to either increase the heart rate or increase the resistance so already I'm getting some interesting information about how this might have happened I can ask you know hey did that person's heart rate go up or are there blood vessels you know more constricted you know because one of those two things must have happened to cause this increase in afterload that I'm drawing for you and either way to draw it out it would be kind of the same you'd basically say okay well if this is my new end systolic pressure I know that I need to draw it so that the point where it crosses the volume axis is the same and I can make it kind of extend on the other side too I can say something like that and this is what would happen so one of the things I want to point out is there is a difference between e a and there's a difference between EA and afterload so let's talk about that difference when I talk about afterload I really want you to keep remembering or keep in mind the fact that we're talking about the entire line so this entire area where this entire part of the curve which I'll redraw here which would look something like this right that entire thing is the afterload and we kind of simplify that I keep reminding us that we simplifying that down to just pressure it and systole but really afterload is just is more than just at one point but we use that as kind of a a marker for how afterload is doing it every other point and we can see pretty clearly that of course you know the after load has gone up at every point including the very the very last point which is n systolic and the new curve of course if I was just just draw it in would look like this let me just keep a blue line so it stays steady the new line would look like this and would actually come up like this and do this that would be my new line so the pressure-volume loop does change and you can see that if afterload is pressure and systole if that's what we're using is our marker actually maybe I should put it in quotes just to make sure we don't actually think that that's afterload because we know that the definition of afterload is much more than just that then EA is going to include part of that it's the end systolic pressure but it's also includes include stroke volume so one of them is the pressure over volume and the other is just the pressure and if we're thinking about that remember that many things are going to affect then this end systolic pressure many things including you know things like contractility will affect this and preload will affect this so many things are going to affect after load but not too many things are going to affect our ei so remember if you're having a change in ei the things that are going to change ei would be like heart rate and resistance so truly when you're when you're breaking this down just try to keep this in mind that the formula you want to always remember is this guy and this will always kind of get you to the right answer that if you are thinking about afterload you're really talking about everything that could affect afterload including preload and contractility because all of those things can affect which direction this goes because they are going to change stroke volume whereas if you're going to talk about the elastance then really the only things that are going to change the overall elastance this whole thing are going to be things like heart rate or resistance so it's actually pretty simple when you look at the formula but I know a lot of times people confuse the word elastance arterial elastance with afterload and they think you know it could be the same thing and it's true that they're very related but they're not exactly the same thing so as a final point in this case we increased the arterial elastance by either changing the heart rate increasing it or increasing the resistance but we could also decrease the heart rate or resistance and we would have seen a smaller arterial elastance