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Current time:0:00Total duration:10:26

so we're going to talk about the left ventricle I'm going to draw out the left ventricle here and I'm going to draw out the rest of the heart as well but I'm just kind of going to leave dashes here just to make sure that we kind of focus in on just that one chamber the left ventricle and this is of course next at the right ventricle and above both of them you know you have the two atria right these are the the chambers of the heart that are going to kind of hold onto the blood until it's time to refill the ventricles this is our right atrium and our left atrium now a question that came up to me and might come up to you is why in the world does the left ventricle never have a rip or tear I mean if I look at my genes or anything else you know you always get these kind of rips and tears over time and why is it that you don't get these tears in the left ventricle I mean it would be disastrous of course because the blood would start gushing out of the left ventricle but what prevents that from happening and and also what are the stresses on the left ventricle I mean what does it have to deal with exactly so to think about this I actually wanted to split it up into two categories you've got diastole right and you've got systole and diastole of course is when you have have refilling of the heart and systole is during kind of the squeezing of the heart and when I say the heart I should really be more specific I mean the squeezing of the left ventricle because now I'm going to talk in just the perspective of the left ventricles now diastole what is happening there well blood is really refilling that left ventricle and so the volume of that chamber is going up up up and during systole pressure is going up up up so these are the two major issues right now of course you have volume in systole and of course you have you know some pressure and diastole it's not what I'm saying but what I am trying to get to is the idea that the major issue in diastole is the fact that you've got a full heart it's especially by the end of NASA you should have a full left ventricle the fullest it's going to be and in systole the highest pressures that the left ventricle is going to see so keeping this idea in mind let's actually know go back about 200 years to someone who thought about a very similar situation around kind of the stress of the wall and what pressure and volume will do to that so this guy I'm going to draw up his picture bring it up this guy is a French mathematician and his name was Laplace and we actually still honor him by kind of talking about his formulas today and Laplace was a brilliant mathematician he actually gave a lot of thought to shapes and the shape that we're going to be kind of focusing on today is this sphere or a ball so you just think of a ball like a baseball I'm drawing you kind of orange like a basketball I suppose and this ball is essentially a hollow sphere right and I'm going to draw on the side and actually me write that sphere here I'm going to draw on the side a left ventricle or kind of my image over left ventricle right something like that and actually starts looking quite similar to the sphere so the idea is that he Laplace thought about spheres but a lot of the the ideas he put forward actually applied beautifully to the left ventricle as well so you've got something like this where you can you can see the obvious similarities now Laplace thought about this in terms of what would happen if you actually cut away part of that sphere and let's say you could actually now kind of look down at the cross-section of it something like that so he actually thought about in those terms and of course I said that this is a hollow ball so you've got a no fill it in you've got something like an inner circle I suppose like that right in fact let me draw it on the side here so you can make it really nice and easy to see I don't need to have to try to figure out what it is I'm drawing something like that right this is our cross-section of the ball or the sphere and you could do the exact same thing with the left ventricle now the first thing that Laplace thought about was volume he knew that volume is going to put some sort of stress on the wall and volume we know equals you can actually write the formula 4/3 PI R cubed so if you actually take away some of these numbers 4/3 and PI and these are just numbers right you can get rid of those then you can say well there's a relationship or a proportion between volume and radius and you can actually write proportion as this symbol right that means proportional to and so you can take the cube root of both sides you could just say okay what's the cube root of this side and the cube root of this side and you can say well that means that radius because that cancels right radius is proportional to the cube root of V or volume and on our two pictures let me just write it on this picture actually just to be clear this would be our radius this is our radius now a second point I'm just going to first label our picture and then you'll see how it all kind of comes together is pressure and pressure is a little simpler to imagine we know that that's just you know a force divided by an area and here I can draw a little blue arrows to signify the pressure on the walls of this left ventricle this is our pressure I say left ventricle or sphere kind of interchangeably I guess right at the moment and third is the wall itself right the wall thickness how thick is the wall and that's obviously going to affect how much stress the wall feels so wall thickness would be kind of this quantity and I'll write W for wall thickness now putting it all together Laplace came up with this he said well the stress of the wall we'll call it wall stress wall stress is equal to is equal to some of these other factors he said it's equal to pressure and write that first pressure times the radius times the radius divided by two times the wall thickness two times W so that was the relation ship and if you think about it you get some interesting kind of ideas from this you say well okay radius what is that well radius is like a length right you're going to measure that out like you know centimeters or millimeters and wall thickness is also a length right so you've got similar very similar you've got millimeters or centimeters and we we just got through saying pressure is just force divided by an area so what units are wall stress well length cancels length so all you're left with is force over area so really wall stress and this is pretty cool is in units of pressure so it's kind of a pressure isn't it but that might make you feel kind of puzzled because you think well wait a second what is wall stress exactly you might have thought that wall stress was the stress on a wall maybe it was something like this but actually it's not right because that would then just be the the P the the pressure that we had in the first place so then what is wall stress what would it look like well wall stress you can imagine as this the stress is the we said it's a pressure think of the pressure the pulling pressure that's kind of how I think of it pulling pressure literally the pressure that's pulling apart the wall so in our first question when I open up the video I said you know what is keeping our wall from just having rips and tears and the wall stress is literally this the the force or the I shouldn't say force the force divided by area the pressure that's going to cause those rips and tears so you can see that that in a way we should have some rips in Terezin or in our left ventricular wall but we don't why don't we so these in that little white box I'm going to draw for you what's inside there and you know it's going to be little heart cells right so little heart cells are lining this wall and you've got thousands of them of course right thousands of little heart cells going every which way and you've got them crossing and going over and under each other or something like this so what happens is you literally have thousands of heart cells and they're attached to each other and these little attachments are I'm going to draw in white called desmosomes so desmosomes are one of the reasons why your heart doesn't just rip apart you've got these tiny little desmosomes and their job is to keep everything kind of tidy and tucked they want to keep the heart cells attached and that means if they're going to be attached that they're not getting ripped apart so these white little arrows are literally counteracting those purple pulling pressure arrows so this is how you can think about wall stress and why it is that our heart doesn't just rip apart lastly I want to point out that the pressure is actually going to be in our equation but we don't really have volume in our equation we have radius and the relationship is a cube root right so if you have a cube root here but pressure is direct then that means that between the two of them volume versus pressure pressure has a bigger influence on wall stress than volume does so that's one interesting point another interesting point is that wall thickness which is right here makes perfect sense because if you have more and more of these heart cells that means you have more and more desmosomes that are going to counteract the effects of pressure and radius in this equation