 Hello, and welcome back to the Sports Biomechanics lecture series, as always supported by the International Society of Biomechanics in Sports and sponsored by Vicon. I'm Stuart McCurlay-Nailer from the University of Suffolk, and today I'm really, really lucky to be joined by Walter Herzog, who is a professor at the University of Calgary. And he's also currently on sabbatical leave at the Federal University of Santa Catarina in Florianopolis in Brazil, if I said all of that correctly. Walter, well, thinking where do I start in terms of introducing Walter, but he's a previous winner of the Jeffrey Dyson Award from ISBS, the Borelli Award from the American Society of Biomechanics. He's also a fellow of the International Society of Biomechanics. And in terms of muscle mechanics, which today's lecture will be on, Walter pretty much did write the textbook on certain aspects of this and as he said, talking to me a few minutes ago, today's lecture, maybe 20 years covered in 45 minutes, so it might be a bit of a rollercoaster but yeah, strap in and hopefully will enjoy the ride. Yeah, thank you very much, Walter, and over to you. Thanks a lot, Stuart, and here we go, and maybe just a word to the Jeffrey Dyson Award. I remember when I was in Jim Hayes' lab, one of the first lectures I ever saw by an international colleague was actually by Jeff Dyson. And not only that, I knew several athletes that were coached by Jeff Dyson in track and field. There was a very nice honor to have at the time. But let's get started here on muscle mechanics and applications in sport. And as Stuart was mentioning what I'm going to be doing is talk a bit about some basic principles in muscle mechanics, some basic properties. And then at the end of the talk, it gets a little bit more, more researchy and maybe a little bit more complex for people that are not directly in the area of muscle mechanics. But the first part, I hope, with going through some basic aspects of muscle mechanics, I cover a little bit things that everybody can understand and gets to the same level in this particular lecture. This is my outline that I'm going to have for today. The basics, I'm going to be talking about the structure of muscle a little bit, then the crossbridge theory a little bit, which is the basic theory of how a muscle contracts. And then I talk about three basic properties, mechanical properties, the force lengths, force velocity and history dependent properties of skeletal muscle and try to put them into framework of the crossbridge theory and also into the framework of some sport applications. So let's get started with structure. Here you have a skeletal muscle in the arm as it happens. And muscle is made up of smaller bundles of muscle fibers called fascicles shown here. And then these fascicles are made up of fibers and the fibers in the muscle is a multi-nucleated cell that has these organelles, these contractile organelles called myofibrils shown here. There's about 2,000 to 5,000 myofibrils in a single muscle fiber. And the interesting thing about a myofibril is it has all sarcomeres arranged mechanically in series. So it's a very beautiful preparation because if you can measure the end, the force at the end of the myofibril, then you know what the force in each single sarcomeres. And so here then we have a sarcomere as it's typically shown with two contractile proteins, the myosin in the middle here, and then the actin at the end going into the z-line, the basic contractile unit of a muscle. Here we have a myofibril. This is a single myofibril that we used in our laboratory. We do a lot of testing with single myofibrils. And you see the very distinct dark and light striation pattern where the dark is the myosin or abans, and then the light is the abans or the actin filaments in a single sarcomere, in a single myofibril. Here you have an electron microscope of the structure that's perpendicularly cut to the fiber. And what you see here very nicely is the thick filaments, the myosin, surrounded by actin filaments, and you see you have exactly six actin filaments in a nice hexagonal array. The next slide here, this comes out a little bit better. In the schematic drawing there is the myosin filament here, these little ears are indicating the cross bridges, so the cross bridges reach out every 60 degrees. So you have six directions of cross bridges from the myosin filament interacting then with the six hexagonally arranged actin filaments. So each myosin filament supplies six actins, and each actin filament is supplied by cross bridges from three myosin filaments. So a very nice structural arrangement invertebrate skeletal muscle. And what I like to point out as well is that today we don't only think about the sarcomere of the myosin filament in green here and the actin filament in red. But we also think about it, about a third filament and that's called Titan shown here in blue. So Titan goes from the middle M line of the sarcomere is fixed rigidly on the myosin filament, and then runs freely along here until it attaches to the actin at the very end, and then together is the actin goes into the Z band, this connective tissue band. The interesting thing about Titan is that here in the middle in the eye band region, it has elastic properties and can elongate really long, and then the refold again, when a sarcomere or a muscle gets longer or shorter. And we know that we have you know different types of muscles is very different shapes. We have muscles where the fibers run essentially parallel to the long axis the muscle as shown here, and in this fusiform muscle. And then we have muscles where the fibers run essentially at a very distinct angle to the longitudinal axis so here's the longitudinal axis, but the fibers are very distinct angle. There's one distinct direction of fibers we call that unipenate, when there's two distinct directions in fibers we call it bipenate, and then in the human deltoid muscle for example you have fibers going in several distinct directions. That's called a multi-penate muscle. And you ask people why would you have the structural arrangement. And of course you can imagine if you have a fusiform muscles, then where the fibers run parallel to the long axis they're relatively long fibers relative to the muscle. And here, the fibers are relatively short. And when they are short they take up less volume and therefore you have more fibers in parallel. And therefore for a given volume in a unipenate muscle, you probably have more fibers in parallel, but they are of shorter length. And then if you look at the mechanical implications for that then I try to indicate that here in the schematic drawing, where we have a muscle one and the muscle two. And this one has a large cross-sectional area with short fibers and we assume that the volume is about the same. And here muscle two has a small cross-sectional area and long fibers. And what that means is because of the large cross-sectional area, the maximum force that the muscle can exert is greater than for muscle two. But since muscle two has these longer fibers, it has a greater excursion. That means it can exert force over a bigger range. So the disadvantage of being weaker is made up by the fact that you can get force exerted over a larger range. And then if you look at the work potential of these two muscles, if we assume that they are about the same volume, then they have the same work potential which can be calculated as the area on the green curve, or the area under the pink curve, and they should be about the same in this particular case. So let's very briefly look at how muscles contract. And that goes back to the 1950s with the sliding filament and the cross bridge theory. So we think that acting filaments are shown here schematically slide relative to the myosin filament. So we have here the myosin filament, here the acting filament, and these are thought to slide relative to one another. In 1953 and 1954, when Hugh Huxley and Andrew Huxley proposed this particular arrangement, the idea was that the myosin filament was shortening and was pulling along all the rest of the sarcomere, and therefore shortening and force production was produced by a collapse of molecular bonds here in myosin that will make it shorter. But that ended up not being the case. So Andrew Huxley then shown here, this is why Regenda in 1957 was the first one to formulate a mathematical description of how this relative sliding of the filaments might be occurring. So here we have an acting filament and here we have a myosin filament. And Andrew Huxley thought that we have these side pieces or cross bridges on the myosin filament that would cyclically interact with certain attachment sites on the acting filament. And he assumed that this all happened based on rate constants of attachment called F and rate constants of D attachment called G. So when this cross bridge is here, then it has a certain probability of attaching to this attachment site here, and that's governed by these rate constants. The important in the cross bridge theory is that these rate constants are dependent on this X here, where X indicates the distance of the attachment side of acting the nearest attachment side to the equilibrium position of the cross bridge, where equilibrium is this spring that the cross pitch is attached to is not carrying any force and is relaxed, whereas here it's slightly off from the equilibrium position, and there is force in the end in this, in this link. So here from Andrew Huxley was that this is a linear spring. Therefore, the force gets bigger, the bigger this X distance is and that's how we produce force in a muscle so that's Huxley's formulation and then the little modern more modern version is that there's a myosin here, the elastic link here, the cross bridge head there, and it interacts with acting, and it has this rotational movement that pulls the acting past the myosin filament. And it does that by hydrolyzing ATP in, and so the hydrolysis of ATP gives us the energy for the muscle contraction. And it's usually assumed that there is one ATP per cross bridge cycle. And if you go further here, then Huxley in 1957, as I said, express this cross bridge theory mathematical terms, I'm not going to go into this at all this is one of the simplest equation that you put down there. They get a little bit more complex if you go into it. But what I wanted to show here is with this example that there is a framework, a mathematical framework where you can do simulations based on the cross bridge theory, and then you can make an experiment with a muscle or a fiber or a sarcomere, and then test whether or not what the cross bridge theory predicts happens is actually happening in reality. So having talked about all that, I would like to now go and talk about the three basic properties of skeletal muscle. And the first one is the force links relationship. So the force links relationship describes how much maximal active isometric steady state force and muscle can exert as a function of the muscle links. And here we have force on the vertical axis. And in this particular case sarcomere links on the on the horizontal axis. And this is the basic, the very famous paper by Gordon Huxley and Julian Journal of physiology 1966, where they show this very distinct behavior where we have a plateau where a muscle can exert maximum force. And if you get stronger it has less force until it reaches a zero active force, and also when it gets very short, it has a zero passive force. So the cross bridge theory at least the plateau and the ascending sorry the descending limb can be explained very nicely. For example, if you start at the links see here, where there is no active force anymore. That happens when the acting and the myosin filament overlap stops, and therefore these cross bridges here cannot interact is acting anymore. There is no force. And the muscle gets shorter now, and overlap between acting and myosin filament increases linearly and visit there's a linear increase in the number of cross bridges that can potentially interact with the acting filament, and therefore you have this linear increase in force, until you have a maximum overlap of cross bridges with the acting filament, which is shown here in B. And then the reason why you have this little plateau here is because in the center of that myosin filament you don't have any cross bridges. And so when the sarcomere shortens from here to here, which is about point two microns per sarcomere. Then there is no decrease or no increase in force for that particular reason. The skeletal muscle, the in vivo force-length relationship of muscle looks a bit different, because we have non-uniformity we have elastic elements and so on. This is much more rounder. So this is an estimate of a force-length relationship of a human lateralis muscle. So it looks a bit different, but still it has kind of a plateau region and then a descending limb and an ascending limb. And for most in vivo human skeletal muscles, you will find that. Another thing to observe here is that when you do this for submaximal activation, the force-length relationship at 10% or 20% of activation changes quite dramatically. It's not just a decrease in force, but it's also a change in shape of the force-length relationship. And very often people who model muscles for this particular purpose, they don't consider that, so be aware of that. So in terms of sport, of course, you know, if you're an athlete, you would always like to have your muscles at optimal lengths when you perform whatever you do. And that would be ideal because if your muscle is long and you're very weak or short and very weak, that obviously would not usually be good for muscular performance. So we asked ourselves in a variety of different sports, where do people work on the force-length relationship? And one of the questions we asked very early on some 15 years ago probably is, do cyclists use muscles in the optimal way according to force-length considerations? In this particular study we took 15 cyclists and had them on a strength-testing dynamometer. We measured fascicle lengths and we measured the moments that they exerted, and then from that, these some assumptions estimated the force. And then we also had these people cycle at different intensities, including the maximal intensity, and we measured fascicle lengths in the power phase of cycling as indicated schematically here. So here the cycling and the muscle is moving, and we continuously measured and offline the lengths of these fascicles. And when we did that for these 15 people, we got a quadriceps force-length relationship, fascicle-length relationship that looked about like this. And now the question was, where are the fascicle lengths in a maximum effort cycling trial? Here we have the force-length relationship, and here in green we have the fascicle lengths at the beginning of the power phase of cycling, and then of course the muscle shortens, and here is at the end. And so the fascicle lengths, this happens to be for the vastest lateralis, goes from about 125% of optimal lengths to about 90%, and that covers reasonably nicely the plateau region. And I would argue the cyclists could not really have chosen a better way of cycling in terms of at least this particular muscle, when cycling at 80 revolutions per minute for a maximum effort. So we also did some functional force-length relationship in other sports that we were interested in, for example, in double-polling of cross-country skiing, where we had people going into the different phases of cross-country skiing, and then we measured the forces they could exert on the poles as shown here. So this is the beginning of the pulling cycle, the first 10%, 20%, the people are very, very strong, and then they become weaker. However, the total force in the poles, of course, is not as important for them as the propulsive force, and here the poles are at a certain angle, and the propulsive force, of course, will be the projection along the horizontal here, along the ground, because that's where the skier wants to go. And if you now calculate the propulsive force, the projection of this particular force, then at the beginning the efficiency is not very good. It's probably only about a third of the force that's propulsive, but then as you go on, more and more of the total force becomes propulsive, and towards the end, the poles are swung out in the back, and they are essentially perfectly parallel almost to the ground, and therefore the entire force of the pole is also propulsive force. And so what this means, for example, in cross-country skiing is that you have a very long range over which the propulsive force is about constant, despite the fact that your force-length relationship in this functional task is quite different. That's an important thing for cross-country skiers to know, because very often they say, oh, well I'm strong at the beginning, but really weak here, so I'm not going to do anything here at the end anymore, but this end phase is actually very important and good skiers will utilize that to the full extent. Another way how we looked at the force-length properties is in cycling, where we had people exert maximum effort forces at different crank angles in an unconstrained case, which where we ask people to just push into the direction that they prefer without thinking about it. So we also asked, and then we calculated the tangential component of that, and then we also asked them to push perpendicular to the crank, which is suggested by some people, some coaches and athletes try to do that, and we realized that this force is much smaller. But the principle point that I want to make here is, if you look at the different joint angles in the power phase, and let's say you look at the yellow arrow, the result needs smaller here, gets bigger to 60, gets bigger to 90, and then at 120 degrees and 150 degrees, it's smaller again, the force perpendicular to the crank, same thing, it's smaller here, gets bigger, and it's about the same, and then it gets small and very, very small at 150 degrees. So depending on the position of the bike, you have different possibilities, different capacity of the leg extensor muscles to produce force. And as I indicated here, not only that, but in which direction you push is also depends on how much force you can exert. So here is an example for a 30 degree crank angle at the very beginning of the power phase of cycling. You have the maximum forces that a series of cyclists exerted in these different directions, and you can see pushing in a downward direction is much allows them to exert much, much more force, for example, then pushing in a perpendicular direction to the crank. So, not only does the force length property here play a role in what joint configuration your leg is, but it also depends on which position or which direction you actually want to exert the force. And if you describe that like for example in cycling and you want somebody to push perpendicular crank in this particular, in this particular configuration, the force that the person can exert is very, very, very small, and could easily be achieved very easily by pushing a slightly different direction. So, in terms of the force lengths relationship. What did I want to tell here well the first thing I wanted to say is it derives directly from the cross bridge model, at least the plateau and the descending limb ascending limb is slightly different and has a certain explanation as well. It's important in sports where the working range can be selected, you know, perfect example might be a spring start, you can go into a joint configuration in the print spring start any way you want or in cycling, you can adjust the seat height, and that will affect where on the force relationship, you are going to be working. And the force lengths properties also we have shown and other people as well, they adapt to the chronic or sport specific demands. I'm not going to show you examples here but we have done a couple of studies, where in athletes we found that the force lengths properties of certain muscles were distinctly different, and they were different in a way that they kind of took advantage or adapted to the chronic demands. You know that were required by the specific sport. Next, let's talk about the next mechanical property and that is the force velocity relationship. So here you have the force velocity relationship force as a function of velocity, and the force velocity relationship essentially describes the maximum steady state force and muscle can exert at optimal classical lengths as a function of the speed of shortening. So here, and this was first popularized by Hill in 1938 classic article there. And so the idea here is when we have an isometric contraction, we are very strong. Then if you shorten the muscle, we get weaker very very quickly, until we reach a point where the muscle shorten so fast that you really cannot exert any external force anymore. I want to point out that if you only shorten at 20% of the maximum velocity of shortening, you're already have lost about half the muscle force available isometrically. So the punishment of shortening your muscle in a movement of producing work is very very big. That's something to keep in mind. Then people also are interested in power as a function of velocity, and you can construct the maximum power velocity curve by taking each of these maximum points from the force velocity curve, multiplying them with one another. If you do that, you get this characteristic curve where power here, of course, is zero, because the velocity of shortening is zero, and power here is zero because of the very fast shortening velocity you have no force, but then somewhere in the middle, 30 to 35% of the maximum velocity of shortening, you reach a maximum power output. And if you are a jumper or a weight lifter or a shop putter or you want to do something very quick over a second or so. So in the ideal case, you probably would like to work in an area where the power output is maximal for your muscles. Of course, you cannot always choose that, but in the ideal case you would. So the optimal parameters would be that you shorten the muscle in such a way that the power output or if you integrate power, the work of a muscle over a certain amount of distance or also over a certain amount of time would be maximized. I'm bringing here the cross pitch model back in because I think it's important to understand that the force velocity relationship does not really come naturally out of the structure of the of the cross bridge theory. But in 1957, Huxley adapted these rate constants in such a way the rate constant of attachment and detachment in such a way that his model fit the 1938 hill force velocity relationship. Essentially, he did a data approximation and data smoothing, and he filled around with the rate parameter such that he got this nice hyperbolic shape that he had observed in 1938. And therefore, yes, you get the force velocity relationship from the cross bridge model, but you get it because the rate constants are chosen or have to be chosen in a way to make that happen. So in this particular slide, I also want to talk about this part of the force velocity relationship, the eccentric part, because here the concentric part that was mostly covered by me and also by healing 1938. You have this decreasing force, but what you probably know is that when you have an eccentric contraction force raises quite rapidly. 10% of eccentric contraction velocity from the maximum you have 50 or 60 or 80% more force than isometric. And if you shorten at the same rate and you're down to 50% or so. So there's an enormous punishment. If you shorten the muscle slowly, or if you increase or if you're lengthen the muscle actively slowly, you get much, much more force. And I get asked very often, you know, why is that actually the case, can we explain based on the cross bridge model, why you get more force essentially compared to concentric way, and explanation based on the cross bridge model is actually very simple so in the concentric contraction, imagine the cross bridge has attached here, and this is the right hand side of a sarcomere, then the acting filament will be moving in this direction. If the acting film moves in this direction, this x distance becomes smaller, and therefore the force in this spring element becomes smaller. In a concentric contraction, you continuously decrease the force available to a cross bridge. And not only that, the rate constant of detachment here when you shorten becomes about four and will be up here. And so it's very, very high. So cross bridges detach very quickly in an in a concentric contraction. If we now go to an eccentric contraction, we have exactly the opposite. Here the cross bridge is attached. And now the acting filament will be in going to the right, make this x distance bigger. And therefore, the force in the cross bridges that are attached will tend to increase the detachment constant G here is relatively slow, and therefore the detachment is relatively slow. And therefore you have the simple answer, according to the cross bridge theory, why is the eccentric force greater than the concentric force for a given shortening velocity or lengthening velocity. It is greater because N, which is the proportion of cross bridges is greater in the eccentric and x, the amount of force in a cross bridge on average is bigger. So we have more cross bridges attached, and each of the cross bridge on average produces more force, according to the cross bridge theory, that's why eccentric is better than concentric in terms of being able to produce force. We also looked a little bit at some examples here. For example, we looked at double polling in cross country skiing and the force velocity properties that you might have. And again, this is more a functional property, not that of an individual muscle. But how does the skiing speed affect the power, the work, the force that you can exert in cross country skiing. So here, for those of you who are not cross country skier, this is a double pole action. And the force on the ground comes exclusively from the poles. There's no pushing off backwards with the skis. So this is the technique. People ski this technique in most world lopets, like in the beer cabiner that is over almost four hours long for elite skiers. And they ski in this particular technique for the entire four hours. Imagine that. We did that in the laboratory where we have people on a treadmill and they, we asked them to push as hard as they could about 20 times in a row and having the treadmill go at different speeds. And then we did that. Then we ended up for two different techniques of polling with these two curves and you can see, especially the red curve here looks a little bit hyperbolic very similar to the isolated muscle. Before that, before that curve, we then look at the power velocity relationship. Then we see that for these skiers, which were elite Canadian and Alberta skiers when we look at them, they reach a maximum power output in double polling at about 18 kilometers per hour of skiing. The problem for them, of course, is that they normally in a fast race, they ski on average at about somewhere between 27 to 30 kilometers per hour in the double pole. And so that means they already lose about 30% of the power output, because that's what they are supposed to polling at. In the old days, old days, meaning before 2017, people could use longer poles and that would slow down their frequency of polling and also their movement during polling. Unfortunately, that's not allowed anymore, because since 2017 the pole restriction length is that the poles cannot be longer than 83% of the body height of a skier. And therefore they get punished in this particular event by having to do it faster and therefore the power output is reduced compared to if they could use longer poles or if they were skiing at a slower speed. This is not from us. People, including Tony Sergeant have made these kind of force velocity relationship in cycling. So here we have pedaling rate, which is kind of a measure of velocity and crank torque as a measure of force. And then people have done these relationships in cycling. They essentially find a linear rather than a hyperbolic relationship. But in this particular example, you have to realize that there is nothing measured below about 60 pedaling, 60 pedal revolutions per minute, and nothing up here. And my hunch is that this would actually fly out now like this, and probably hear a little bit like that as well and that it would be slightly hyperbolic. But nevertheless, what you can do now is you can also calculate the power output here. And of course the power output for a straight line would be maximal if you multiply the crank torque by the pedal rate, it would be maximal right in the middle. So this scale goes from zero to 250. The middle would be about 125. So the maximum power output would be right about there, at least theoretically speaking. And of course, that's what people have found in laboratory experiments as well, where maximum power output in cycling seems to be somewhere between 100 and 130 revolutions, pedal revolutions per minute. There's another application of the force velocity relationship where when you pedal faster and faster and faster, the torque that you can exert becomes small, when you pedal slower and slower and slower, the torque that you can exert gets bigger same principle. So the force velocity relationship as a discussion does not arrive naturally from the cross bridge model, but it's usually contained by appropriate choice of the rate constants. Concentric is stronger than concentric and then now somebody asks you why and you will be able to give them a perfect answer, because it's more cross bridges are attached and they exert the greater average force. And something that might be interesting from a coaching and athlete point of view the maximum power output for muscles is achieved when they shorten at a velocity of about 30 to 35% of the maximum velocity of shortening. And then functional force velocity relationships in sport, like the double pulling example or the pedaling example, they show the same characteristics the faster you make a movement that the less force the more the less power the less work rate, do you have available that principle holds and again can be adapted in some sports. Most simply for example in cycling, you know you can cycle at a faster and faster and faster speed, but always keep the same pedaling rate by changing the gear, for example. So there are certain sports where you can artificially determine how fast your muscle contraction will be and then of course in sprint running you cannot do that because you want to run really fast so that means your muscle shortening velocity has to be fast as well. Once but not least, let's talk about some history dependent properties and just to take it right from the very front and make it quite clear the history dependent properties. First of all, are not contained at all in the cross bridge theory, they are not explainable with the acting mice in thinking, and second of all, there is very very little to know work that has been done in sport. There is a fair amount of work on these particular properties and I want to show them what we mean by them and I want to maybe point out a couple of things why they might potentially be important and why people in sport might want to look at them. So here we have an isometric contraction of a muscle and we activated to get a certain amount of force. We now take that muscle at a shorter length and we stretch it actively, then we get this hill, eccentric force, but then after we reach a steady state isometrically we have more force. And if you pull the muscle for a longer distance, we get more force, or if we shorten the muscle from a longer links to that same links we get less force. The basic principle here is that here we have an isometric contraction, exactly the same activation, and we get completely different amount of forces and of course that force is not only here at steady state when we measure it, but it's also here, and here, or, or right here at the end of the stretch and shortening, and therefore will affect the performance or the capacity of a muscle that you have quite dramatically. I want to talk a little bit particularly about this force enhancement property, the one where you get more force with eccentric contraction. And we think that has primarily to do with this third filament that I already mentioned this Titan, we think that Titan is an adaptable spring. It doesn't have one stiffness, but it has multiple stiffnesses, and the stiffness is adapted, we propose by activation of a muscle, which means by calcium, and also by active force production. That means acting and myosin cross bridge interactions. And why do we think that? Well, I'm going to give a couple of examples. So here, the first thinking is that you have a Titan filament here and you stretch it passively and it just elongates and we know that Titan provides all the passive force in a sarcomere, not in a muscle, but in a sarcomere shown here. If we now activate the muscle and we add calcium, we have shown that calcium combined to certain specific elements of Titan and make it stiffer. That means the unfolding of certain molecular bonds is harder, and that then gives you more force. And I'm going to show you a couple of examples how we did that. So here we have a single myofibril and we stretch the single myofibril with arresting calcium concentration and with an activating high calcium concentration. And then that looks something like this in a high and low concentration or in a higher concentration and we then stretch this and we measure the force with this lever that appeared on the left hand side. And then we do that and we see that for the high calcium concentration, we get more force during the stretch that stays there for a long, long time. And for the low calcium concentration, the resting calcium concentration, we get less force. And so we know that this is happening. Of course, in this particular experiment we had to inhibit actin myosin interaction that normally happen with calcium, but you can do that by blocking it chemically, or by genetically modifying it and we have done it in both ways. There's no actin myosin force here. This is only the force of Titan, because Titan is the only passive force producer in a single myofibril or a single sarcomere where these experiments were done. We then took some of these segments of Titan and perform atomic force microscopy and if somebody's interested, this is the immunoglobulin domain 27 that we took. So we took several of these immunoglobulin domains and we measured with atomic force microscopy, how much force does it take to unfold these elements and it was maybe somewhere between 180 and 200 piconewtons. That was the control with no calcium. If we then added calcium, we required about 20% more force. And we have previously shown that calcium binds to these immunoglobulin domains. And here we showed that indeed the unfolding of this spring element becomes harder, and therefore the spring becomes stiffer. We have shown the same in other elements of Titan, so it's fairly well accepted that calcium binds to Titan and influences the mechanical properties, particularly the stiffness. The second thing that we thought might be happening is the following. We thought that since Titan is already attached to actin here, maybe it can attach at other places as well. And then make this part of Titan, what we call the proximal part, inextensible, and then you would be left with a short free spring, and of course a shorter spring then would produce more force would be stiffer when stretched by the same absolute amount. And in order to test this, we put an antibody that was fluorescently labeled at a crucial point on the Titan segment. We put it on the so-called PEVK area, which is where we thought the binding might be occurring. And here you see a myofibril with these antibodies that are also labeled fluorescently. So these are all these PEVK markers, the bright strip that you see there. And now we can stretch this myofibril passively and actively, and we can see if the elongation of Titan occurs in the same way. So here we have first a passive stretching, and so we measure the distance from the z line here to this particular marker on Titan on the PEVK area. And when we do this passively, we find that this element is elongating all the way, which is shown by the raw data here that we measure, it's elongating all the way. If we now do this actively, so now we have this calcium activated and force is produced, and again we measure the same distance. Then usually what happens is that we can stretch it a little bit and it elongates, so it seems that this part is elongated a bit, but then it seems to bind, Titan seems to bind to act in. And all of a sudden it's not elongating anymore, and the whole elongation is taken up by this much shorter spring, which then of course would be much stiffer and add an enormous amount of force to the elongation. I'm just going to show this once more. So here we have a little bit of elongation, it binds and then the whole elongation is taken up by this segment exclusively. And so we think that this might be happening in Titan when it's activated, and therefore produce, you know, more force, produce force enhancement, and have all these applications. So what about sport applications of history dependent properties well. Craig McCown did quite a bit of work in implementing history dependent properties in in in an open sim model, and he applied it, for example to cycling and the counter movement were vertical jump. And he found that the difference between in cycling were up to 40% in power output per pedal cycle, and that was due to the force depression that occurs in the shortening cycle. And he also showed that the slower you pedal and the higher the power output is the more that force depression therefore the punishment would be. As in a counter movement jump he showed that for some muscles, for example, the gluteus medius maximus here that the force enhancement property that are coming about by Titan increased the force of the gluteus maximum by as much as 50% and therefore were a substantial component of the jumping performance in a counter movement As I said, there has not been done much in sport but I want to propose a couple of applications here what and how we might be able to look at history dependent effects. Particularly I would be very, very interested to see what happens to Titan in exercise and disuse. So for example, when a heart is paced and exercised, we know that the Titan is a form in the heart can change in a rat skeletal muscle it has been shown that when there is a disuse atrophy by hand lip suspension, then the Titan is a form is not changed, but the number of Titans. Per myosin is reduced. What does that mean, there is less passive stiffness, there is less force enhancement, there is less force transduction across the sarcomere and presumably also less stability and therefore the muscle might be more vulnerable to injury. What happens to calcium and activation regulation to the force enhancement effect in exercise or in this use. Nobody has ever used really looked at that. So particularly in exercise adaptation are Titan isophores are Titan numbers changed. Nobody has ever looked at that in humans and I think that would be a fabulous area to look at that because that might potentially affect the force enhancement properties that could influence sport performance particularly through the stretch shortening cycle, because it has been shown recently by one of my postdocs and by other people as well that it appears that the stretch shortening effect that is the additional amount of force that you get in shortening following a stretch. But that is primarily you to tighten and primarily due to the residual force enhancement that you have at the end of the stretch. So it would be fabulous to look at whether or not that can be affected in a systematic way by certain exercise and some people have looked at the strength training and the decrease or the stiffening of the muscle and that might have something to do with that, but I don't think anybody has ever looked in the con in that context at isoform numbers and Titan, Titan isoforms and Titan numbers. What happens to the risk of muscle injury? As I said in the rat model we know that this use is associated with a loss of about 50% of Titan and these muscles are much, much more vulnerable to instabilities and injury in the rat model. What about humans when they have athletes that are, that have, that break a leg, that turn into a crucial ligament and then their muscles are disused and now they try to go back to training what special considerations might there be to consider there for these type of athletes. So I'm coming to the end. In summary, I'd like to, I wanted to talk a little bit about the cross bridge model and explain how that works. And particularly wanted to make you aware of that there is a third filament that Titan that I think is going to become very, very important and will be included more and more in textbooks and I think will receive more attention in muscle mechanics, basic muscle mechanics and also in applied and sport biomechanics. I talked about the force lengths relationship and the possible application to sport on examples of cross country skiing and cycling. I did the same for the force velocity relationship. So I'm going to explain the difference between eccentric and concentric attraction. And here at the very end talked a bit about history dependent properties. And I think the enormous potential of looking at history dependent properties in applied situation, including sport. And with this, I would like to thank Stuart once more for the kind invitation and give it back to him. Thank you, Walter. Yeah, that was fantastic. Even better than I expected. Yeah, thank you ever so much. And there's a lot of people giving positive comments and thanking you on YouTube in the comments I'll send those over to you afterwards. There are also quite a few questions. So I'll start with just the first ones that came in and just kind of try and run through them. So if I scroll through the first one here was from Bram van den Bosch, who said, What implications does the hexagonal structure of the filaments have on the force production, because we always see models in one plane in images or textbooks. So how does the hexagonal structure make a difference? Well, of course, you know, a muscle, of course, is three dimensional and we know there's a third dimension there but I know we always show sarcomas like I did here with like two actins and one myosin. And the hexagonal array really what it means is that an actin filament is not only supplied by cross breaches from one myosin but from three myosins and then you say, Well, why is that important? It's important because I think very few people realize how few cross breaches interact with a given filament because we know that the spacing of the cross breaches is about 43 nanometers in a given direction. So every 43 nanometers you have a cross bridge that can interact with one actin. And then if you calculate that over the 720 nanometers of a half myosin, then you realize that there's only about 17 or 18 cross breaches that can interact with one actin filament. But now you triple that number because in the hexagonal array, you are supplied by cross breaches from, you know, from three different myosin filaments and so it increases the force production quite dramatically by having that alignment. Having said that, I have to point out that the structure I showed you is for vertebrate mammalian skeletal muscle. In insect muscle, you also have six actins relative to the myosin but they are rotated by 30 degrees, they're not in the same configuration. In some invertebrate muscles, you have a completely different structure with up to 12 actin filaments surrounding one myosin filament. So the structure I showed you is the one that will be relevant for you for human and mammalian skeletal muscle work but not necessarily. It's not a preserved property across all species. Thank you. And yeah, the second question that came through just after that from Nick Ward. When you were talking about cycling at different crank angles and with the different lines of action asked, is that the same or different on flat versus going up a hill, for example, you've only looked at that in the flat. And so, so I cannot answer that question directly. But I do know that some cyclists, some very famous cyclists, they do adapt their C-type when they go uphill and of course the best cyclist ever to live in this world, Eddie Merckx was famous for that, that whenever going uphill, he would slightly change, he would slightly change the C-type to a lower position, thereby obviously reconfiguring where his muscles would be working. And so my hunch is that it would not be exactly the same. Then of course in uphill cycling can also go out of the seat and that's a completely different beast in itself. But we have not looked at it so I don't really have an answer. Please do so and let me know what you find. I thought you were going to say Lance Armstrong then and get me into trouble, but I'm glad you settled through Eddie Merckx. Yeah, then. Yeah, I wouldn't be able to say that. So, CAU Motion Lab, who I know have been watching a lot of these lectures and helping to promote them. So yeah, thank you for that. They've asked, what's the role of fatigue in these models that you presented? Yeah. I am not a fatigued person and so I'm probably not a very good person to talk about that. But in fatigue, of course, we know that the force lengths and the force velocity properties are changed quite dramatically and they start looking, not only is the force getting lower, but the shape of the force lengths and force velocity relationship starts to look more like that of submaximal activation. And so we know that the interesting thing is in the force enhancement property, when you are fatigued, or when you use a partial inhibitor of cross-bridge attachment and you mimic chemically fatigue, then that property is not affected and you get the same absolute amount of force enhancement and since the isometric force that you are normalizing this to in fatigue is becoming lower, the force enhancement, the relative force enhancement will stay higher. So in other words, in eccentric contraction and then we think that Titan system comes into place, that seems to be much less affected than in concentric or isometric contraction. I think that was an excellent detailed answer for somebody who says it's not their area of expertise. I'm reading these things, it's not, it's not, you know, I'm always hesitant when I haven't done my own experiment. The force enhancement experiment we did, but in the isometric fatigue and the concentric fatigue, those are other experiments by other people. Okay. Yeah, the next question, and apologies if I say this incorrectly, from Hylian Debrito Fontana, who asked whether there are strong experimental evidence that in eccentric contractions, number one, more cross-bridges are attached, and number two, average force per cross-bridge is greater. Is there strong evidence for that? Yeah, there are. People have done, and again this is not from our group, but the Italian group under Vincenzo Lombardi, they have made experiments in using also low angle x-ray diffraction where they estimate the number of attached cross-bridges and they have found that yes, the stiffness is greater in e-center compared to concentric and the estimated number of cross-bridges that they see through the low angle x-ray diffraction supposedly is higher as well. So there is experimental evidence there that yes, in eccentric contraction, there's a greater number of cross-bridges attached. I'm not sure if they ever try to estimate the number of cross-bridges in concentric and eccentric and then calculate an average force estimate and whether or not they have determined that the average force per cross-bridge was greater as well. That I do not know, but in eccentric there should be more cross-bridges attached and yes, there is some evidence for that. Thank you. I'll read the next question out. Recently, the groups of HD EMG described the redistribution of muscle activity within muscles such as the medial gastrog. Do these findings make sense and match with muscle fibre modelling in order to maintain a load? Can you please read the first part of the question again? I'm not sure if I fully understand the question. I'm just saying that in order to maintain a load, there has been EMG evidence describing the redistribution of muscle activity within muscles and does that fit with the models that you've described? That particular observation and that has been made, I'm aware of observations that have been made at very, very low load levels like 5%, 10%, 15% where people have measured individual motor unit activity and then they can show that some motor units are active for five minutes and then they drop out and then other ones come in. So there is kind of a sharing of the load over very long periods of time and I assume that's maybe what the questioner asks about, but that really would not directly relate to the model that I think we are proposing here, because that's really a control problem and not really, I would argue, a mechanical problem on the myfibrillar or the molecular level, really how force is produced. I think that's just really a clever way of a muscle saying, OK, I have lots of motor units available. This is a maximal contraction. I'm only using 10% of my motor units. I might as well switch them a little bit so they don't have one of them do the work for the entire time and all the other ones are just sleeping. But I think that's more a motor control problem rather than a mechanical force transmission, force capacity problem. Thank you. Then, yeah, there's a really interesting question and then conversation actually between Ross Miller and Dario Cazola who gave a lecture as part of this series on in silico modelling. They're asking what you would suggest for implementing the Titan like effects in a hill based muscle model. And whether you think that's possible to incorporate. Craig McCowen has done that. He essentially took in the use an open sim model, and he essentially took properties that we had measured on isolated cuts of the muscles enhancement properties and depression properties that different amounts of magnitude and shortening velocities are different. All kinds of conditions we have tons of data available on this particular muscle and how it behaves on a variety of different conditions. And then he just implemented that essentially phenomenologically into that model. And then there is a cross bridge model out there that actually on a half sarcomere on the sarcomere level used Titan and the Titan, the Titan adjustments with calcium and with calcium. And this Titan binding to acting and that is a model by an Austrian mathematician. Her name is good room shop. And if anybody is interested in a particular paper you, you don't know how to spell shop. You can send me an email. And I'll send you the paper that has been implemented on a half sarcomere and sarcomere level but not on a whole muscle level. So I think there is two possibilities. You just added them phenomenologically and Craig McCowen and David core and a couple of other people have done that or, or you actually look at the molecular events and good room shop has done that. So it has been done. But I don't think really systematically and systematically being used. Thanks. Yeah, it's a really useful answer. And we're now up to the point where I'd made notes of people's questions as the lecture was going on. Apologies if I miss any out as I scroll through the ones that have come through since, but there's one here from Brian Glancy that asks if there's any direct evidence that a single myofibril runs the entire length of a muscle cell. I would not know that. And I do not know that. We do know that muscle cells often don't run the entire length of fascicles, but I don't think I don't think I could be wrong here but I don't think anybody has ever looked at myofibrils and looked at them. I don't know how long they are and whether or not a single myofibril truly goes the entire, I don't know, three, four, five centimeters of a of a muscle fiber. What I do know is that we have to mechanically make the myofibril shorter because we like to work with myofibrils from one sarcomere up to about 20 sarcomers. They undergo a very rigorous and somewhat tough and mechanical breaking protocol that you get them at that length because otherwise they are very, very, very long, but whether or not they truly span the entire length of the fiber I don't know. Thank you. I'm conscious I don't want to keep you too long with us to throw another question in there from me. I mentioned earlier on that the force length properties of athletes, for example, might adapt based on their chronic demands. I wondered if you could just explain that in a little more detail or maybe say, what would those adaptations look like in terms of a molecular level or some of the models that you described. So that the first study that we did in that area was where we tried to compare the rectus femoris force lengths relationship between cyclists and runners. And the reason for that was because cyclists have usually a fairly flexed hip angle, and they shorten the rectus femoris, much more than a runner would. And the idea was the hypothesis was that maybe the rectus femoris in cyclists would be strong at short lengths and weak at longer lengths, so we have like a negative force length slope. Whereas we would expect the opposite in the runners, where the rectus femoris would be relatively weak at short lengths and then we have a positive slope and become relatively strong at long lengths. This was a small study only with four athletes in each group, but the surprising result was that we found exactly that for each of the athletes a negative slope, force length slope for the cyclists, and the positive one for the runners. The explanation for that we thought and we didn't measure it directly there because it would not be impossible, but the explanation was that this had to do with sarcomere genesis, so that in the fascicles of cyclists, you would have fewer sarcomeres, and therefore an individual sarcomere would be relatively long, and therefore will be acting on the descending limb of the force length relationship. And in the runners, at the same fascicle lengths, you would have more sarcomeres through sarcomere genesis, and therefore each sarcomere will be at a shorter length, and therefore fall more on the ascending limb of the force length relationship. And that this can happen, this sarcomere genesis with chronic exercise or with other chronic interferences of muscles has been shown in animal models, but I don't think anybody has ever really shown it carefully in humans. Thanks. And yeah, there's always one person to ask the awkward question. And, yeah, Josh Walker has asked, what about triathletes then if we've got one adaptation for runners and one for cyclists. You know, you know, that's not an awkward question at all. I think that's a, that's a question that I actually get a lot. And, and my answer always is that, and I have no scientific proof for this really, but, but I believe very much, having seen these adaptations in muscles and the force length adaptations for example, having seen that I would argue that a triathlete will be independent, you know, that the muscles of a triathlete will adapt to the cycling to the running and to the swimming, whereas the whereas for a cyclist they will adapt to cycling and for a runner alone they will adapt to running. And therefore it's been my contention and I'm happy to make a big bet on that, that no triathlete will ever be able to break the world record in the in a 10k run. And that is, even if the triathlete runs as much as the runner, and on top of that swims and cycles, the adaptations of the muscle would always be such that it would not be maximized or optimized for running. Therefore, a runner will always be faster than equivalently talented triathlete and cyclist will always be faster than an equivalent trained triathlete because you use the muscles in a different way. And therefore you don't get that very very specific adaptation that I think is required to run, you know, 26, or let's take the 5k world record which was just broken beautiful beautiful world record and 5k 12 minutes and 35 seconds. And as a triathlete, you just cannot come close to that, you just cannot. I would admire any triathlete who comes within a minute of that, within a minute which is, you know, would be lapped. You know, for a runner would be a fairly average national level performance. And, you know, so a runner, so a triathlete probably can come maybe to a 1335 and be a good average national runner, but never ever a world elite runner. So if we do happen to have any elite triathletes watching then the challenge has been set. I put some money on it if a triathlete runs a world record in the 5k or 10k, I give him $1,000. Yeah, the last question that's just come through now from Marco Aurelio-Vaz asks, continuing the theme of adaptations to training. What effects do you think specific eccentric training might have on muscle adaptations? That's, that's a very good question. And of course, Marco, thank you for the question. He has actually done work on different athlete groups and looking at adaptations of force. Thanks relationships and I'm very aware of that work. And I think specific eccentric training in some instances has been shown to result in an increase in sarcomere number and in other studies it has not been shown to do that sarcomere number stayed the same. And in the studies that I'm aware of the increase in sarcomere number was relatively modest, you know, two or 3%, which I think would have probably a relatively little effect on on on changing substantially for slings properties. So I know people have tried it. And I know there is probably some sarcomere genesis, but from what I know it's not going to be very big and I think functionally probably not all that relevant. Thank you. And yeah, I'll leave it there for the question and answers. But if anybody does watch this back kind of tomorrow or next week or anything and does have a burning question. I think it's the best way of getting in touch with you or. Yeah, just by email. And if you go on Google, you find my email it's all over the place but it's w herzog at you Calgary dot ca w herzog at you Calgary dot ca but just go on Google and type in my name and it comes up left right in center so Well, if you Google you there is also an actor called Walter Herzog as I discovered earlier on when I'm planning the introduction. And the very famous German filmmaker called Werner Herzog, who people always mix me up please. Thank you ever so much again Walter that was brilliant and thank you for your time in both preparing and giving the lecture and I think thanks to everyone watching as well for what was a really good discussion afterwards and some really good questions. And yes, the last sort of request from me is anyone watching. If you enjoyed it, please either share it or if you use it with students, try and make sure that as many people can benefit from that excellent lecture as possible because that is after all really what we're trying to do with this series is just help out as many people as possible, especially as a lot of us move towards online teaching. So yes, thank you very much everyone that's watching and especially thank you to you Walter. Pleasure. Thanks to it.