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Current time:0:00Total duration:11:21

we've been talking a lot about pressure-volume loops but we haven't talked about this formula Delta P equals Q times R in quite some time and you may be wondering you know what is the relationship if any between the two and so actually there is a really nifty relationship between them and I'm going to kind of try to point it out to you and see if you don't think so as well it's pretty pretty awesome if you if you stick with me you'll see that it's pretty amazing so Delta what does that mean Delta means change and here we're talking about pressure so I'm going to write it all out make sure we're very clear because as I said it's been a while since we've had to think about this stuff so that'll be kind of neat to go over it again and kind of review it and I'm going to write out the formula in a little different way we have PA and PV right and so a is arteriole and that just means what is the pressure in the arteries and then you subtract out the pressure in the veins so in another way of thinking about it you're basically saying there's a lot of pressure in the arteries when the blood leaves the heart and then it goes through the capillaries in the veins and by the time it gets back to the heart the pressure is almost gone and so that pressure drop is going to be equal to two things right this first one is blood flow blood flow we measure in volume over time or volume you could say volume per minute and the other one is resistance so this is resistance so the amount of pressure that falls is going to be equal to the blood flow times the resistance and blood flow is actually also something we can kind of break down a little bit we could say well blood flow is stroke volume and stroke volume is volume in one heartbeat so volume in one heartbeat and you multiply that by the number of heartbeats in a minute and we call that heart rate so if I say hey what's your heart rate you would say well it's you know let's say 60 beats per minute or 100 beats per minute some some number right so that's the heart rate and take all that and multiply it by resistance and you get the change in pressure so this is our formula right Delta P equals Q times our kind of spelled out for us now I'm going to make a little bit of space and now what I want to do is go back to a pressure-volume loop and I want to show you exactly how it relates to this cool equation so this is our pressure volume loop let's say and draw it nice and big so you can see everything clearly and we have volume on the bottom axis going this way and pressure on this axis going up going higher as you go up and this is of course from the left ventricles perspective so I'm just going to write LV here just so we don't forget of course that it's from the left ventricles perspective and two lines right so we have one line like this let's call this our end systolic pressure volume relationship now I want you to pay special attention to that line and this other line that kind of goes down here and we call this our end diastolic pressure volume relationship and I'm going to quickly sketch out a pressure volume loop so we've got something like this this is our pressure volume loop let's say the loop goes down and then goes up something like this I'm just kind of quickly sketching it so I apologize if it doesn't look too pretty but this is our pressure volume loop something like that right now how can we get information for our equation from this loop can it provide any information for us and the answer is it can but we have to make some assumptions if we're going to use our pressure volume loop and for starters keep in mind that we're looking at the left ventricles per you know pressure but our equation up above was about arterial pressure but of course one assumption I can make right away is that well the pressure in the left ventricle is about equal to the pressure in the arteries during ejection so remember when the blood is kind of squirting out of the left ventricle there is a continuous space between the left ventricle in the aorta which is one of the large arteries and that's during ejection so between this part of our loop our pressure volume loop this is ejection I could say well the pressure is about the same in the arteries as it is in the left ventricle and so taking it one step further I can say well you know I don't really want a bunch of numbers I don't need like you know 50 numbers or you know really I guess an infinite number of numbers here I need one number I need one number to plug into this equation how am I going to get that one number well I guess we have to do another assumption we would say well the arterial pressure remember I'm kind of assuming that during ejection the two are about the same drink ejection then arterial pressure I could say well isn't that kind of summarized or can I just use the mean the average pressure so can't I just take the mean arterial pressure and we've done that in the past right we've said well okay we've got two values here we've got our systolic value here at the top is our systolic and we've got our diastolic value at the bottom down here is our diastolic and if you kind of use these numbers and I pull out some average mean arterial pressure then that's you know good enough that tells you a little bit about kind of what the overall average pressure is and that would be fine that would be fine actually but let's say I'm having kind of a lazy day and I don't really feel like doing any math there I don't want to kind of take these numbers and plug into some other formula I don't wanna do any of that stuff I just want one number from this PV loop that's going to help me kind of get a rough sense for what the arterial pressure is remember this is what I'm after this arterial pressure because that's what's in the equation well I cool it I suppose I could just go ahead and peek at this guy this is our pressure at the end of systole I can say well what is the pressure at the end of systole and I know that that number is going to be somewhere between systolic pressure and diastolic pressure so it's going to be in the right range and that is exactly what we do so that that kind of overall end systolic pressure is what people kind of use in this equation sometimes they say well let's just assume again this is our list of assumptions let's assume that the end systolic pressure is good enough to give us information about the arterial pressure that's what we do we're going to use that number just because it's easy to get now a third assumption and I promise I will make a big long long list just a few assumptions here the third assumption is about PV it's about this number the venous pressure remember the end systolic pressure guys is really somewhere around here it's like 90 maybe it's 100 somewhere so we're pretty high for most of us right in comparison the venous pressure is going to be what let's say it's three maybe five it's going to be some small number right something very low so if the venous pressure is so low compared to the arterial pressure I could I could just assume it's zero I could say well you know the other one is so darn big that's subtracting a tiny little number like three or five or whatever the number is is not going to make a huge difference so let me just kind of assume it's zero and if it's zero then I can kind of forget about it right because a number minus zero is just the number so that's my third assumption and these assumptions again are just there to make our lives a little bit simpler so let's use these assumptions and I'm going to rewrite that equation now I'm going to just keep it like that and so our equation rewritten would be something like this it would say okay well we have pressure at the end of systole minus zero so I'm going to leave that away equals stroke volume times heart rate times resistance and I'm going to go ahead and divide both sides of the equation by stroke volume and this cancels so my final equation here I'm going to write it in a different color so it's nice and bold for you my final equation is the end systolic pressure divided by stroke volume equals heart rate times resistance so that's final what what have I done really I'm just going to move things around simplify things maybe but you're probably still looking at this in thinking a big so what who cares right what does this do for me well let me take a moment I'm just going to erase some stuff and while I erase I want you to take a good hard look at this graph and see if you can notice anything and it's a little bit of a riddle so I challenge you to see if you can kind of see how this new equation that we've written out could in some way be useful so let me just be very careful and kind of erase all this and I'll give you a moment then to think about it so go ahead and see if you can come up with anything and now I've cleaned up my my graph pretty well so I'm going to real able stuff and I guess that'll buy you a few more moments to keep thinking so let's say this point was my end systolic pressure same as before and you remember that this point was kind of where my pressure volume loop ended so I'm going to use two different colors I'm going to say okay well there's this line and that's just my end systolic pressure that's this number and then I've got this line and that's between these two right here this is my stroke volume so that's this number so I've got my end systolic pressure in my stroke volume that are now you can kind of see they're both on my graph and if I divided one over another what does that mean exactly if I have pressure over volume you might be thinking bells might be going off in your head that this sounds awfully familiar pressure divided by volume sounds like elastance and if I'm going to draw the line this is what the line would look like and this elastance is actually it's actually called exactly that it's called arterial elastance arterial arterial elastance and the reason we use the word elastance is because we're taking a pressure dividing it by a volume so it has the same units and we actually call this e with a little a a sub a so there's a line here and the point where our two lines cross this line in this line the point where they cross is our end systolic pressure so we've found a relationship now between our what's going on in the arteries namely if we're thinking about kind of the artery the arteries having a certain flow and resistance and change in pressure we have started now seeing that you can actually use our pressure volume loop which we've always thought of as being kind of a left ventricle story and that it actually tells you a little bit more than just what's going on the left ventricle we can actually use it to figure out what's also kind of going on in the our degrees as well and so we're going to keep coming back to this line this ei line we're going to revisit it in the future and you're going to see how powerful it is to have all this information on one graph