If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:13:33

I'm going to draw on this axis pressure and on the other axis I'm going to put the volume and we're going to do a little a little thought experiment so label it the way I usually do with milliliters but I'm going to leave off all the numbers just to make it a little bit easier to see what's going on so I'm not going to label the axes with numbers but you get the idea that of course pressure is going to go up this way and volume is going to go up that way now let's say I go over to the the shelf let's say I've got a shelf full of left ventricles and I just grab kind of the first one that I see and I pick it up and it's this little guy over here and he's empty to start out with but I start putting some blood in him right he's totally relaxed this ventricle is not contracted at all which is important of course right and I start filling it up with blood and as I do that I add you just kind of keep track of how much blood I'm putting in and what the pressure is inside of my left ventricle and I notice that the pressure is rising as I'm putting more and more blood in fact as I really start filling this up let's say fill it up completely with blood and try to squeeze in even more as I keep trying to stuff it with blood I notice that the pressure begins to rise and now kind of Rises really fast right so near the end it starts rising much more quickly and this is my curve and I get to name it whatever I want and so I'm going to call it the N diastolic pressure volume relationship now you might be thinking well okay pressure volume relationship that part makes sense but why do I always have to name it n diastolic why not just drop those two words right the reason I don't drop those words is because it gives you information it tells you that it's at the end of diastole that I'm doing this experiment so for example none nobody can come by and tell me well you know was there any contraction in this in this left ventricle of yours I would say no it was completely relaxed right it was completely relaxed and I can convey that information just by using the word and diastole it because it's understood that if I'm talking about something at the end of diastole the left ventricle have been relaxed and in fact one more thing I want to point out just because we're we're talking about interesting points is that remember that if this is pressure and volume that the pressure divided by volume or the slope of this line is actually equal to elastance so if I draw the line a certain way if I say for example you know what's going on over here well the slope is much higher than it is over here another way of saying that is that the elastance of my line is going up over time so just keep that in mind that the word elastance actually completely makes sense to use in this context so now we have our line or curve and I guess one thing we can think about is what would happen if I actually at this moment let's say right here this blue spot decided to let my heart contract what would happen if the left ventricle contracted well of course the pressure would rise and that's what happens with contraction right but I guess the question is what what were the conditions at the moment right so if I say this is in diastole right because of course for this situation let's call a situation a diastole just ended at that point what was the volume and let's say the volume is 125 milliliters and let's say the pressure is 10 millimeters of mercury right so that's those are the conditions at the point where I just allowed the left ventricle to contract now I could choose another point I could say well what about this point up here you know what if I allowed contraction to happen right there well that just means I waited a little bit longer right and let's call this situation B and now the the volume is higher and I'm just going to say 150 even though I guess maybe it looks like my drawing kind of is a little skewed but just let's just assume that 150 is that point and the pressure is just a smidge higher I'm going to say it's a 15 millimeters of mercury smidge higher just a little bit higher so these are the two points right a and B so I could say all right well if I want to you know talk to someone about this I could say well you know I have pressure and I have volume and the pressure for situation a let's go with a first of course a had a pressure of 10 millimeters of mercury and a volume of 125 this is how I could convey information about that spot right and if someone asks me about situation B I could say well situation B had a slightly higher pressure and a slightly higher volume and really what I'm giving them as information about what the conditions were at the time that contraction began right that's that's really what that point represents conditions when contraction began now you might think okay well this story is done right I mean what else is there to say that was very interesting but actually there's another term that people use all the time all the time to describe the conditions when contraction begins and the most common thing is that people get confused when this word is thrown around the word is preload and preload I think it's really important to define because sometimes people say well preload is pressure at the point the contraction began and other people say no no preload is volume when contraction began and I'm going to say that it's neither pressure or volume but it's something different it's something different I'm going to define preload as is being equal to the wall stress well in fact let me actually go back one step half a step maybe and I'll say not even just wall stress but I'm going to say left ventricular left ventricular wall stress wall stress when contraction began but I'm not going to say when contraction began I'm going to use shorthand I'm going to say at and diastole so at the point when diastole ended right and in situation a and B those are two different points we just we just said the point where dance li ends whatever the left integral of wall stress is at that moment is preload okay so that's how I'm going to define preload and that's that's the way I think it's most helpful to define preload but of course preload has a lot to do with pressure and volume right it's not like it's you know got nothing to do with those terms at all let me make a little bit of space and kind of build up my argument see if I can try to convince you that what I'm saying makes sense so to understand this you got to remember what all stresses remember Laplace had this law and he said well wall stress is equal to to what he said it was P pressure times the radius divided by two times the wall thickness W is wall thickness right and remember Laplace was not working with left ventricles like we are he was working with spheres he was working with spheres so he was working with something that looked a little bit more like this he was saying okay well if you have a sphere if this is your sphere I'm going to try to draw it as best I can right then if you actually take a look at the inside of that sphere let's say you take that sphere and now I'm going to just chop away half of it let's say you just cut away the top half right just kind of look at the midsection of that sphere he said what you would notice is on the inside I'm going to draw it with a white line on the inside you've got kind of a doughnut you've got something like this and and then you could actually look at it and you would see this you would see that okay if you look down at it this donut begins to look a little bit like this right the so Laplace said if you have a situation where you have some sort of a sphere and you can actually open it up and look at it well then you can actually start making some interesting observations you could say well from this point to this point let's call this the radius of the inside I'm going to call it radius in and then from this point to this point right here to here I'm going to call that W or wall thickness we said and then if you combine those you get the total radius right so you said our total equals radius of the inside plus wall thickness right something like that and remember now that oh and then of course I have to mention pressure you might be thinking well where is pressure fitted all this pressure is just kind of what's forcing out on the walls that's pressure but now remember there's a relationship an interesting relationship between volume and radius of the inside right so there's volume equals four-thirds pi r cubed and in this case when we say our I mean radius on the inside so I should say R inside and this is I wrote lowercase R but let me just make it really easy by just writing the uppercase R so that's the relationship so if you want the if you want to move things around you can actually say okay well the radius on the inside is simply the cube root of and then you flip around all the equation or you say okay 3 over 4 PI and this is V for volume and now if you know the volume if you have the volume information you can figure out the radius of the inside so we can actually do that right we can say okay what is the radius on the inside well if these are the volumes and actually calculated this beforehand so I wouldn't have to sit here and take the cube root of stuff while you wait patiently for me you can actually calculate this stuff and say okay if I have 125 milliliters then the radius on the inside ends up being what ends up being about 3.1 centimeters and remember you might you might think well how in the world do you get from milliliters to centimeters remember that one milliliter I'll just write here one milliliter equals one cubic centimeter actually that's nice because then when you take the cube root you get centimeters left behind so that's the situation a in situation B if I plug in 150 into this equation right then I get my radius on the inside becomes three point three centimeters and then I could also do the next variable I could do wall thickness and for this I kind of just assume this is kind of a fair assumption that my left ventricle is really not going to change a whole lot from heartbeat to heartbeat and that in general given my my size and my weight I'm going to be I'm going to have a wall thickness of let's say about one centimeter just to make the math kind of easy right and so then the final variable we need is the total radius the total radius which is simply the radius on the inside plus the wall thickness so this is just adding those two numbers together so I can just add those very easily and say okay well the total radius is just four point 1 centimeters this will be 4 point 3 centimeters and then finally we can calculate preload now right you can just take all these numbers and say okay well you know I've you know mr. Laplace asked me for pressure I got it right there mr. Laplace asked me for my total radius and I got it right there and mr. Laplace asked me for my wall thickness and I got it right there so all the things that we need to calculate wall stress at the end of diastole of course that's really important right we have those numbers at the end of diastole we have them and so we can actually calculate preload right which is so cool which which actually makes it just instead of a word we throw around it's actually something you can quantify so let's let's go through it let's calculate it well let's do it first situation a first in situation a I'm just going to write a now again we have 10 times 4.1 so that's 41 divided by 2 times 1 so that ends up being I'm going to I'm just going to give you a round number this is about 21 millimeters of mercury so preload another kind of interesting thing about it it's measured in pressure units and in situation B you've got we got 15 times 4.3 again divided by 2 times 1 so that math works out to 32 right 32 I'm again I'm round rounding off so 32 millimeters of mercury and so you can actually see that going from situation a to situation B and actually let me just draw on my on my doughnut here what the wall stress is remember wall stress is actually the force over area kind of pulling the heart muscle apart and that's that makes sense right in the beginning of of contraction when the heart is about to contract how much stress is there on the wall that is your preload and of course it takes into account things like pressure and volume of course and you can now say to someone well yeah we went from a preload of 21 millimeters of mercury right here to a preload thirty two millimeters of mercury right here and that's actually a very rarely done calculation but I think a very valuable one