Presenter:	For me, it's also a pleasure to be here, and how the tables have turned. Now I'm here in the front, and two of my best professors ever, in engineering, Professor [Sadiki 00:00:12], Professor [Orthly 00:00:13], we're now on the other side, and thank you for coming. One of the things that I was thinking about is how, what would I have said to myself back then, when I was sitting in your chair. Actually, what one of the lectures that was given by a friend of Rachel's, I don't know where Rachel went, Andy B. Wiener, he was actually recording sprains in the bones of running horses, and I was like, wow. 
	Then I remember taking a class with Professor Sadiki, and I said, "Well, we have to use final elements for a bridge. Can I use you for a bone?" And he said, "Sure. Why not." So, I started looking at the intersection between engineering and biology, although I didn't really think about it in those terms at the time. What I want to let you know is that if you go to my website, there I have actually my class on neuro muscular systems is available. You can go there and click on the webcast of all the lectures and see them, and so you are, a lot of this information is already there. Let me begin by saying that back then, biomedical engineering existed, but my main message is that if you are a biologist and you thought that, that's a good way to stay away from mathematics, my message to you is if you want to be at the cutting edge of biology, you will need engineering and mathematics. 
	Likewise, if you think you're an engineer that can stay as far away from the problems of humanity, problems in health, that's nice. You can go hide away in your cave, but the world is actually driving engineering mathematics and biology to collision, and what a collision there will be. It will be great. Let me tell you about what I've been working on. First going to give you a glimpse of California, and I invite you all to visit. We have a lot of exchanges with say, the Claremont Colleges, and USC, even though you haven't heard much of USC, the past 30 years have been a revolution of USC becoming, essentially, a power house of engineering, mathematics, biology medicine. At parr with Cal [State 00:02:39] and Stanford, so stay tuned. Come over to USC. I recommend that. 
	Let me talk a little bit about homo sapiens. As a species, we often talk about having this wonderful identity. We are animals, but not in that sense, right? We are biological beings, and we often give these specializations that we have as animals, the reason of our so closely guarded identity, which is cognition. You know, we needed a big brain. We also look at speech as one of the great enablers. Neanderthals, for example, are thought not to have had as great speech capability, and of course manipulation, so if you realize what happened was that humans are humans because of these brain body coadaptations, and so that has always interested me. Evolution is brain body [quevolution 00:03:40], so of course you have all heard of Darwin, but the biologist here, who's heard of Wallace? 
	Good, because Wallace actually came up with the same stuff, and the published papers together, and we should actually call it the Wallace Darwin Theory. Anyway, the questions that I'm interested in, some of them have to do with, okay, so we have newer mechanical systems. Well, how do these newer mechanical systems live in the physical world? At the end of the day, that is where the rubber meets the road. You have an organism that has to work within the laws of physics, and that's great. Now, if you look at it from the clinical perspective, I think there are a couple of chairs, there's one here, if you wanted to come in. 
	If you look at it from the clinical perspective, a clinician will want to know, do I cut here, do I cut there? Is it the brain that's the cause of the problem, or is it the muscles? What should the rehabilitation be about? Should it be a chemical rehab with a medicine, or should it be physical rehab, and what kind? Et cetera, so there's lots of questions at the interface of engineering and biology. My scientific approach to these areas, is to actually have no single approach, but rather surround the problem from as many directions as I can. I can actually credit by liberal arts education with this, because often times you educated as an engineer, so you're indoctrinated into thinking and being an engineer, and this is how you are, this is how you think, this is how you approach problems. A clinician will approach the same problem in a very different way. 
	It's actually a cultural problem. It's almost a sociological problem that science has now. How is it that you can get biologists, and mathematicians, and engineers, and clinicians, to talk to each other and understand each other, so I'm very happy to hear that it seems that engineering and biology will actually be housed in the same building, shortly. That's going to be great. 
	If anything, this is a reflection on the fact that engineering is ... I've gone to many engineering conferences from national academies, et cetera, and we engineers think of this century, as the century of biology and medicine. This is where engineering is going to go. So, get ready. Might as well get on the ground floor with this, and you are actually going to be leading a revolutions, because you don't have those preconceived notions of what an engineer should be, or what an engineering problem should be, or what is strictly biology independently of computer science, right? It's good. Keep that open mind.
	The purpose of this talk is to be informative, but also to be provocative about the role mechanics, essentially what you learned in E6. How many engineers do we have here? So you've all taken E6 and passed I hope? Yeah, this is good. What do we have to say about these problems? Then, provide some examples about how very straight forward mechanics can help, and also help define the area of neuro mechanics. You've heard of biomechanics, but neuro mechanics is a combination of neuroscience with engineering. Some aspects of it. At the heart of the problem is the fact that both mutant and Darwin, are ultimately unforgiving. 
	Yeah, come on in, there's standing room in the back, and a seat here. Just come right in. 
	This is actually an issue that is often lost on people, because what an organism needed to do to guarantee its survival, and it's subsequent of illusion, is to deal with the loss of mechanics. In fact, the nervous system is thought to have evolved for motility in the very first place. This is a very interesting idea, and so when you look at organisms as they are today, you wonder how did they solve these problems over time? I approach these questions at two time skills. One is, locally, what is a problem that a brain is really solving when it's controlling a body? The other is, if you roll back evolutionary time, and you're at the point where we are neanderthal or homo algamies, whatnot, what evolutionary pressures drove us to our current state? This is a particularly subtle point for evolution to say manipulation. 
	You look at our huge brain, and a lot of it is devoted to the hand. You ask, well, why do we have such a big brain? Well, that's to be dexterous, and why are we dexterous? Well, because we have such a big brain. This is a circular argument. I actually don't see many people asking what drove the nervous system of a chimpanzee in this particular direction, our direction, and actually, it's not very clear how that happened. Those are the kinds of questions I'm interested in. When you look at problems like this, often times you say, "Well, where do I begin? I'm only an undergraduate biologist," or "I'm only an undergraduate engineer." I get that with the students who come to work with me who say, "Well, I'm a computer scientist, and of course I don't know any physiology or neuroscience, or mechanics, so can I even begin to work here?"
	What I tell them is, that's fine. You need to be strong in an area, and then come to the problem from that direction. From your sort of comfort zone, and then start collaborating with others. An important thing, especially for you, is what questions should you be asking? When I was reading the book "The Help," you may have seen the movie, it's a funny movie. The book's also pretty good. One thing that didn't make it to the movie is that there was this young writer. She wanted to be a writer in a newspaper, and she goes to this editor and she says, "Well, you know, I want to write. I want to be famous. What do I write about?" She gave her this particular answer, like, get an entry level job, and then when you're not making mimeographs, this is an ancient word that even I had to look up, which is the precursor of the photo copying machine, right? The precursor of PDF. 
Speaker 2:	You just missed it by one year. 
Presenter:	Yeah, I missed it by one year, yeah. He said, "While you're doing that stuff that young people are asked to do because they don't have that much experience," he says, "Don't waste your time on writing about obvious things. Write about what disturbs you. Particularly if it bothers no one else." It's funny to me to have read that now, because at the time I saw that, that's partly what happened to me. I was studying engineering and neuro science at Stanford, and people were talking about the great problems that the brain solves, and for reasons that will become apparent soon, I stared thinking, "Oh my God. They're worrying about that problem, but the problem I'm working on has many more muscles, and it just doesn't make sense what they're saying." 
	Very [aeriodite 00:10:59] people talking about the problem of neuro science is how the brain solves under determined systems, essentially, how it optimizes and thinks like that. I was like, that doesn't make sense, so that stayed with me. In retrospect, that's actually what drove a lot of my career, so when you read information, now that information is so ambitious, it's even bothersome, right? Try to figure out, what is it that bothers you, but others are taking for granted? I would give you that advice. 
	One of them is why do we have so many muscles? If you look at your arms, got a ton of muscles, who's done the dissections? Who's done the mink dissection and all of that? There's a ton of muscles, so it makes you wonder why is there so many? The popular view, many of you don't live in this world of motor control, or sensory motor neuro science, but the popular view is that we have way too many muscles to operate for joints in the arm. We have 20 some muscles. That's kind of silly. That means that to control them, I need to find one solution out of the infinite number of solutions that exist. I'll show you how that happens. 
	Therefor the nervous system is faced with tough competition of problem of decision making, or optimization. Preferably quadratic optimization, because that's the kind of optimization we can do. This is actually paradoxical with evolutionary biology and clinical reality. The reason is, that if we are so redundant and we have that many muscles, which muscle would you like to donate? Which muscle would you like to paralyze? We have Botox at our disposal. Who of you here is an athlete? You're being told that you have too many muscles, that your brain has to figure out how to control them all. Well, right before the race, or the day before the race, Botox a few of your muscles so your brain doesn't have to worry about them, right? You wouldn't do that. Neither would evolution do that, or if it did it, it did it a while ago. There would have been a version of you with your muscles, that would have eaten you as lunch, back in evolutionary time, because you're wasting energy, you're encoding more DNA, you have to repair those muscles, you have to nourish them, et cetera. 
	There's a disconnect here. On the one hand, we engineers are thinking oh, this is an optimization problem that neuro science, that the nervous system is solving, whereas people go seek medical help even if one muscle is out of whack. You start limping, well what's going on? Can you fix me? So, what's the disconnect? The heretical proposal that I've been writing about recently, you can go to my website, all my papers are there, is that in natural behavior, what's called ethology, we seem to have barely enough muscles. That's why you wouldn't want to paralyze any one of your muscles. You want them all, thank you very much, and it's really only by adding many muscles that you can be made functional and robust, under the context of realistic functional constraints. 
	I'll discuss that in a second. Essentially, that evolution has brought us here for a good reason. Somehow as engineers and neuro scientists, we've been missing the point of why the structure of the body is the way it is, and the function of the nervous system. Again, this is an idea that ... the crux of the matter here is that when we started looking at biological systems, the mathematics that we had available to us, and we still only have available to us, is that of robotics. Who does robotics here? So, you have a motor that drives a joint, and you have another motor that drives the other joint, and so the mathematics is perfectly fine when you look at it from that perspective. 
	However, the nervous system is not controlling a motor, rather, it's controlling tendons. So, like we're marionettes. When you're controlling marionettes, you can then simplify that problem to one of having a single actuator, a single moment at the joint, or a couple at the joint. That's not what the brain is doing, but that's what mathematics would say if you wanted to simplify the problem and be perfectly correct at it. The idea here is I started to think about tendon driven systems as tendon driven systems and not as a simplification into the motor, torque motor [domain 00:15:32]. Stay tuned, so Springer UK is going to publish my book. 
	The title is still not resolved, but something like Neuro Mechanics, the Problem the Brain Solved, so that's coming up. Going to be a short book, don't worry. The idea is this, that if neuro muscular system has muscles, and they receive an input from the nervous system, the nervous system says to the muscle, "Go," right? This is a muscle activation space. Think of it as a space, why? Because I have many motor commands coming in, so I'm selecting one point in that space. It's a solution. Then the muscles converted into muscle forces through the miracle of sacromere behavior. Then those muscle forces produce tensions at the tendons, and then they produce joint torques, and then those joint torques are transmitted through the bones, and then you get your output. This is the chain of events, the causal sequence from a neuro command to say a force, or a movement in your body. 
	What I'm going to do, is I'm going to present the analysis at this level, between tendons and output. We could talk about this another time. If you look at that, this looks like a very complicated figure, but up here is a limb. A very simplified limb. It has one joint, another joint, and it's in the plane. There has to be muscles. Look at muscle number one. You could say, where does muscle number one pull? Well, it has a tendon, and that tendon crosses both joints up there. Then say, "Oh, okay. That's fine. What does that mean?" Now, I introduce you to muscle force space, so here you have muscle one, muscle two, muscle three, and so this is like an XYZ plane. 
	Here, if you were only pulling with muscle one, that's if you were producing that little of force in that three dimensional space. Then, if you look at the torque that is produced at each joint, this is a torque that joins one. The torque at joint two, you see that this muscle crosses two joints, and it produces a positive action at those joints, a positive torque as per the right hand rule. You see that it's moving in the positive and positive direction, that's how that muscle points in torque, and this is the output force it would produce. This is a crash course from what you'll see in the going forward lectures of my class, but suffice it to say that muscle one has that action. Well, what about muscle two?
	Muscle two crosses two joints also, now that's pointing over there. Now, it's action is like this, and then that's its particular output, right? Then muscle number three. Muscle number three is a simpler muscle. It only crosses one joint, but it crosses that joint sort of on the other side, so it's like a negative action, and so that's why it's pointing strictly to the left, and that's it's mechanical output. This is in the force it can produce, the torques it can produce, and the output at the [inaudible 00:18:50]. 
	Notice something that muscles can really only pull. They can't push. This is a very strong assymetry that muscles have. You can pull on the tendon, but you can not push the tendon. This is already embedded in this, because these forces are always positive. The torque space here is kind of an in between space where you can talk about a lot of these issues here, but let's go to a more realistic system. Here you have a very simplified limb, like a finger. Again, the right hand rule applies, and now it has five muscles. The question that I'm working on here is, what are the set of all feasible actions this system can produce? Not, which is the optimal combination of commands to produce an output, but really, what is the set of feasible commands and feasible outputs? Okay.
	Well, if you have that system there, by the same analogy that we were talking about, you can look at muscle one. Here's muscle one pointing in that direction, and then if you only have muscle one and muscle two, that means that you could do every possible linear positive combination of those two muscles. You remember in high school you learned about the [inaudible 00:20:13], you know, the two vectors, how the two vectors act. If you only have two muscles, you can produce any combination of torques over this, in this little [inaudible 00:20:27]. 
	If you have three muscles, then you can go to more regions of the space. This is torque output. Positive and negative output at the first joint, and positive, negative output at the second joint. Intuitively, what is it that you would like? You would like to produce torque in every quadrant, right? But, muscles have this funky relationship to, in that they can only pull and things like that. Then let's add another muscle. Okay, if you added muscle for here, you grow the range of feasible actions, and then you can say, "Well, technically that's nice. I can produce positive and negative torque at every joint, but then you say well, what if I want to grow in this direction? Then you can add muscle five, and you see each muscle grows your set of feasible outputs in a very particular way. This actually called a Minkowski Sum. 
	This takes us into the world of competitional geometry. Let me give you a very simple definition of versatility. What would you call versatility? Well, versatility for limb is to produce forces in every direction. Those of you who rode bikes, or mountain bikes, you know that you want your leg to be able to push forward, backward, up and down. You could call that a versatile limb. Or, if you have a finger, you want it to pull up and push forward, and pull in, and push down, right? That's a very conservative way of defining what is versatility. You could also talk about this in terms of controllability for the electrical engineers in the room. 
	Versatility is that the feasible torque set include the origin, so that's a very simple, graphical description of what versatility is. Actually, we know how to obtain this versatility from the tendon routings, so if you gave me the limb of any animal, and you showed me how the anatomical layout of the tendons is, I can tell you if it's versatile or not, and I can tell you in which directions it's more versatile than not. If you were looking at a horse, it probably has a different shaped region than say a mole that wants to produce high forces only in one direction as it digs, et cetera. 
	You can begin to do that, and there's a theorem in competitional geometry, that on their linear mapping, a convex set remains convex. If your feasible torque set includes the origin, then your feasible force set, your feasible output set, will also be including the origin. You could say that by looking at the anatomy, you know the controllability of a limb. You know how versatile it is in different directions. That's fine, now, I know that to be controllable, a limb that has two joints needs, at the very least, how many muscles? It will need at least three. Three well routed muscles, and so that's fine. This is the minimum number I can have to be versatile. The problem here is that engineers tend to like this solution. If you look at how robots are being made, when you have tendons driving them, engineers say, "Well, let's have on tendon on each side of the joint, because then that way I can control that joint independently, and let's have another set of two tendons on the other joint so I can control that joint independently."
	You can actually get away with three. Three well routed muscles. Wait a minute. N plus one is already greater than M, so you already start to have more muscles than degrees of freedom. What this means that adversative torque set, implies muscle redundancy. From the get go, for your limb to be versatile, it already has to be redundant. What do I mean by redundancy? Any point in the interior or this output space, can now be generated by an infinite number of combinations. Muscle redundancy is not an accident of evolution, but it's rather an appropriate structural adaptation for versatility. 
	Then we should start looking at the number of muscles, really as a wonderful solution, instead of a competitional problem. This is the message that I have for clinicians and biologists. You say, "Well, N plus one is enough, so why do we go to five?" Let me just revisit this other issue that if in your behavioral repertoire you wanted to produce more forces in those directions, because that's how you dig, or that's how you jump or run, then it's good to have more muscles. More muscles are actually a necessary evolutionary adaptation. Every muscle, every tendon, necessarily effects, enhances the size and shape of your feasible output, and that's why you wouldn't want to give up any muscle. 
	In spite of the competitional load, you say, "Well, this is exactly what I need." So, you wouldn't give up any muscle, because you're actually now directly saying, "Well, what's my cost benefit of having a muscle there or not?" Evolution, I think, works at that level of trying to find the directions of feasibility and versatility, rather than at the level of how many muscles do I have. Then, let's say you have a lot of muscles, but I haven't addressed the issue that it's still a competitional problem, because I still have an infinite number of solutions to produce any given output, and so I still have to agree that you need to somehow optimize. 
	Let's revisit that question a little bit. Does redundancy imply robustness? We often think of redundancy as robustness, like if you have an airplane you have two engines. Why? Because if one shuts down you can still fly, et cetera. We think about it in that sense, so we say, "Okay, then redundancy is also there for robustness." Working with Jason [Cutch 00:27:05], who actually grew up not ten miles away from here in Delaware. He was a post op with me, and now is Assistant Professor at USC. Let's revisit this question of the solution space, because what I'm going to tell you, graphically, is this idea that a solution space for a given task is actually very well structured. There's a very interesting structure to how you can control the muscles, and this is actually what I think the nervous system is learning.
	It's finding those feasible solution sets, the structural solution sets, and that's how you learn to move, and walk, and run, et cetera. If you have three muscles, again, muscle one, muscle two, muscle three. This are their outputs, muscle one, muscle two, muscle three. What are the set of all feasible inputs? What are the set of all feasible commands? Well, if we can assume that our muscles activated between zero and one, it's maximal action, then your set of feasible commands is a positive unit cube. Any point inside that cube is a feasible output that you can send to the limb. 
	This actually what I did for my PhD. I said, "What if I have such positive unit cubes in high dimensions. 7, 32, whatnot, what kind of output do they produce." They said, "Well, that leads to this set of feasible outputs." Okay. So, this is the feasible input, at the numeral level, and those are the feasible outputs at the mechanical level. Then you say, "Well, that's fine." Now, let's say that I want to produce that force output. It's a submaximal force, say in that direction. Okay, fine. Let's find the solutions that can produce that. It turns out that here at the output we say, it's a constraint that the X [inaudible 00:29:08] be that big. It turns out that that constraint at the output, is a hyper plane in this three dimensional space. Meaning that every point that is on the plane, that's in the cube, can produce a force whose output on the X coordinate, is that magnitude.
	You say, well, that's okay, but I don't want to just produce forces nilly willy, I want also to produce that Y magnitude. That's another constraint plane. Now you see that you have two constraint planes, so then the question to you is, what is a set of all feasible commands to produce that submaximal force? Well, is the intersection of one plane with the other plane that's in the cube. That is actually a line, because the intersection of two points of space is a line, if it exists, and it's bounded by the cube. Then you can say, "To produce that particular output force, I can use an infinite number of commands." Sorry, this is supposed to be an interactive talk, can someone tell me what that infinite set of possible commands is? Yeah? It's the points in the line. How many points are there on the line? Well, there's an infinite number, right? 
Speaker 3:	[inaudible 00:30:34]
Presenter:	But are the nilly willy, related to each other? No, they have a very strong structure. It has to be points that lie on that line. You say, "Okay, so is there muscle redundancy?" Yes. Is muscle redundancy infinite? Sorry, I didn't catch your name, but per ... sorry?
Speaker 3:	Ali. 
Presenter:	Ali. Infinite. Is it infinite, yes. Why? Because there's an infinite set of points, but is there a structure to it? Is there a way to encapsulate that infinity of points in a simple way and say yeah, it's points in a line. So, that's one step. The next step is to say okay, let's run through this argument. That's the line. What does that structure look like? Well, one way to look at that is to say what other projections of that line onto the coordinate axis. You say well, what does that mean? The solution space for that submaximal force is this. This is the so called bounding blocks for that line. And so it said, okay, can I get rid of muscle two? Does a solution exists where I don't have muscle two? And you say well, it does exist, because you just drive muscle two to zero. 
	Because the set of feasible activities for muscle two touches zero, then sure. You can get away with doing this without muscle two. Can you also get away without muscle three? Yes, because not two and there are the same time, right? Likely. Either of these muscles is not necessary for the task, but this muscle is necessary, so can I get rid of muscle one? You need it, right? But not only do you need it, for this submaximal force, it didn't look like a lot of force, it looked like maybe 40% of output. Guess what? Muscle one must be active to at least 40%, and no weaker. The sooner you weaken that muscle below a 40% line, the task is no longer possible. This actually very important, because when you have people suffering disability, or aging into a disability, or after stroke, or cerebral palsy, or just immobilization, whatnot, all of a sudden you can't do something. People have been thinking, well, you can't do something because you're not smart enough to find a solution. Whereas in reality, you need to know that there are muscles that have lower bounds, even for apparently weak tasks. 
	You can imagine that that's just for that direction. What if you were to look at force in a different direction? Then that solution space structure is going to change. This is where you start thinking, okay, so redundancy is not a problem of the limb. Redundancy is an issue related to the task, meaning, as soon as you define a task, what does that task mean mechanically? You say, well, the X and Y components of my output vector should be like this, should be like that, and then you internalize those mechanical constraints, and then they define the structure of the feasible neuro commands that are actually very well defined. My speculation is that that's how evolution works. When we started to learn to walk, it wasn't trivial. You needed to get up, and then you fell a couple times, and when you're starting to learn a new task, you try to figure it out, and then by trial and error you land inside that solution space, ever so briefly.
	Why knows how to ski? Who learned how to ski late in life? Okay, so did it. It was harrowing. The reason it was harrowing is because there's this task that you obviously see my kids doing as if it didn't matter, and then here I am trying to learn it, but it doesn't feel right, and you keep falling, this and that. Then you realize, by chance you land on the one little bit of the solution space, and you say okay, I have to remember this, and you actually learned by memory. Trial and error and memory. To me that's more a reasonable approach to biological learning, than that of trying to optimize some quadratic function. All you need is trial and error, and memory. This is now what is called machine learning. You may have seen, those of you in CS know about machine learning. 
	At any rate, I showed you this toy system, now, by the way, this is a cadaver hand. In this case we wanted to demonstrate what you can do with trying to define the feasible output of a finger, so how do you do that? Well, you actually take a real system, and then we cut the hands right there. Then we tie strings to the tendons and we try to tie those strings to a motor. Now the hand is my marionette. I am now the brain, spinal cord, and muscles, and the plant, as people call it in control theory, the actual system to be controlled, is a real macoy. Then, we're doing nothing other than what people were doing in the 16th century. This is the beginning of medicine as we know it, which is dissection, where here Dr. [inaudible 00:36:11] is yanking on a tendon and saying, "Whoa, it does this. This muscle does that." We're doing nothing other than that, but using computer science and using competitional geometry and mechanics. This takes a team of people. 
	For example, we have a hand surgeon from Paris, a hand surgeon from Stanford, myself, a hand surgeon from Italy, a computer scientist, a mechanical engineer slash mathematician, another mechanical engineer, so it takes a team of people to do this kind of stuff, so at the end of the day, if a finger has seven muscles, then if you just wanted to produce force to the side, these are the projections to the solution space. Now, if you wanted to produce force to the side, but in this other plane, you see how it's starting to have a lot of structure? Muscles are starting to encode these correlations among them, that come from nothing else other than the mechanics. Then if you want the force to point straight sideways, and it does [inaudible 00:37:15], this is the structure that you get. 
	Interestingly, you get muscles that are not necessary, because some of these can be turned off, but then, some muscles need to be turned on at a given submaximal level, and others need to be turned on at a yet higher level. Others have a wider range. This is the structure. This is how the nervous system solves its problems. Yes?
Speaker 4:	Is the proximity of the solution for any muscle requiring a solution, does the proximity to one mean it's really in danger of overloading, or the motion has to be necessarily weak in that direction or [inaudible 00:37:53]?
Presenter:	No, I think we're loading them at a very low level, but damage is not the problem. It's really more that there's a lower bound to their contribution. 
Speaker 4:	Okay. 
Presenter:	Yeah. It really is that to perform this task, which is not a maximal task, there's a lower bound to some muscles, and that's why you see limping in people. People who well, you know, I had a stroke, or I haven't been running recently, and I'm aging, or whatnot, all of a sudden one of your muscles can not give you that lower bound, even for that normal task. This is an idea of trying to explore how that happens. Another thing that we did, is we said if you were to lose any one muscle at random, just pick a muscle. Imagine you were to miss that muscle. So this is the set of all feasible outputs by that finger. If you were to lose any one muscle at random, which is the minimum that would survive for six muscles? That's that green area. This is a robust area, which is small. In evolutionary process, like if you had a mutation that loses one muscle, or another mutation that would lose another muscle, it will come at a price. Will the system be unusable? No. You could still produce forces within that range. 
	This is the Russian roulette that mutations are playing on muscle retention. Then, you can get to the structure of how those muscle activities are related, et cetera, I won't get into that now. Then, we did some [inaudible 00:39:34] assimilation to show that it's not a problem with our model, that it's a very simple, or very bad model, but rather, if you start changing parameters around, you still only have a very small region. This is a Russian roulette evolution is playing with the maintenance of muscles. 
	Just so people wouldn't think well, this is because fingers are so weird, most systems in nature have legs and limbs, and arms, and wings, and fingers are just these very specialized things in primates, well, not really. If you take a leg, and that leg has 14 muscles, the robust region is also small. You go and play rugby, and someone's going to hit your leg and make one of your muscles sore, you don't know which muscle they're going to hit, so the probability of what can you do the next day with your leg, starts getting small. This is another way of looking at the mechanics of systems. Versatility requires redundancy. Redundancy does not imply robustness, either. Every muscle contributes uniquely to function, and then form the structure of the solution space, we can begin to see co contraction. I won't get into this, but this idea that anatomist and antagonists are active at the same time, and even calling things agonists and antagonists loses meaning. 
	If you opened your textbook on biomechanics or on neuro muscular control, or a, who has [inaudible 00:41:06] here? Do people use that? If you open those books, they first start out by saying, "Here's a limb. This is the agonist because it pulls the joint in this direction. Here's the antagonist because it goes in that other direction." That language is meaningless for real world tasks. It's a nice language to use when you're teaching, and you have things on the bench, but in terms of being useful, it's actually not useful. Synergist muscles are not obvious or invariant. There is now a culture in neuro science saying, "Oh, the nervous system controls muscles by synergies." Very famous people have said this is how the spinal cord is organized and things like that. That's not necessarily the case, and so on. 
	What I would submit to you is, we have barely enough muscles for real world tasks. This begins to explain why we have muscles with so many limbs. There's a sense to the evolutionary process that brought us to this point in terms of structure, and so the next [inaudible 00:42:14]. 
	Part two. If you just very quickly [inaudible 00:42:27] we have 15 minutes left, so how does the brain interact with he spinal cord to produce dexterity? We talked a lot about it form the structural point of view, so I don't want you to think that this world of neuro mechanics, or my work is really about the mechanics of the system, let's talk about control. What is dexterity? Switching gears a little bit, dexterity with the fingertips is to be able to produce these kinds of interactions with objects, and dexterity with the legs is to be able to interact with the ground in a dynamical way. Part of what I learned here at [Hix 00:43:05] is that, how can you define dexterity?
	One of the things is that the one and only thing that a finger can do to an object is to produce a force vector, and what is a force vector? It's something that has direction, magnitude, and sense, right? It has a magnitude, but it should also be able to change directions. My definition of dexterity is that it is the ability to dynamically regulate the direction of vectors with the fingertip. Here I have a toy for you. I brought one to look at. Hold onto the string, because it will fly out of your hands. This is an impossible spring. Don't feel bad if you can't compress it all the way. Just try compressing it, and it's much like a common buckling, but under a follower load, but it's actually close to a chaotic system. Just try it. 
	The compression of this spring that actually required little force, is a measure of the integrity of my nervous system, muscle, spinal cord, brain, to be able to control an instability. The more you can compress, the higher the instability. It undergoes a bifurcation actually, a little flutter, like a [inaudible 00:44:23] we think. It's actually a sub critical, so pass it around. I need it back at the end. Hold onto the string. This is one way in which you can test dexterity. Yours truly is owner of patent six million something or another to use a compression spring, to estimate the integrity of the nervous system. We also have it for legs. 
	You can also try to, I think the technical term for this is squirly. You try to compress is and you can't, but that's actually what's going on in real life. One of the things that we started doing is what is the role of the brain in doing this? At the time, we knew that several parts of the brain controlled the fingers and whatnot, and that's fine, but then we started doing these experiments, where we said, "What if I gave you a spring, that is either very wide, and not prone to buckling, compared to a spring that is more slender?" I learned all about slenderous ratios here. What happens if you confront the nervous system with these four springs? What would you see?
	What you actually see, there's a paper with [inaudible 00:45:35], is that you see the brain light up in different ways. We still don't know why we have such a big brain, or why would you need such a big brain to control your hands. What this begins to say, is that you have contact sensitive networks in the brain that are bilateral. Not only unilateral, but actually are necessary to control different types of instabilities, or different ways in which you're handling instabilities. What this work provided, was a tool that can more precisely interrogate the function of a human brain, in terms of manipulation. Again, the conclusions from FMRI work, is that we now have the ability to detect and differentially interrogate multiple brain networks. 
	This little toy that you have has given us this ability, and then we find these very strong nuance differences in how the brain reacts in different instability context. This begins to explain the potential of evolutionary pressures that drill the need for multiple brain areas that interact in different ways. That's why it takes so long, perhaps, to be dexterous. How long does it take a child to learn to use their hands? A very long time. This is how long it takes. What we did, is we look at people over the life span. We gave these kinds of springs to children who are as young as four, and adults as old as 92, and here you can see the progression of dexterity in healthy humans. 
	You can say well, tell me something I don't know. You start out not knowing much, and then you get better, and then you get worse. That's end of story, right? What is there to see here? Well, if you look at other measures of hand function, like pick and place task, so if you talk to any occupational therapist or physical therapist, they'll say, "Well, we have these measures for dexterity." Those saturate to around the ripe old age of 10. If you have a 12 year old and a 14 year old, you cannot really see differences in their dexterity. However, using the system, you can see that dexterity continues up into early adulthood. Not late adolescence, early adulthood. Then, how it begins to decline, and how the decline is actually so relatively slow. This is by simply looking at how far you can compress that spring and hold it for ten seconds. That's what we do.
	You need a brain to be dextrous, right? Let me say something else here that's important. You may have read the literature. I know that some children like to quote their parents. Okay, you're a teenager, and you're not completely with it, right? People say well, that's because my frontal lobe is not completely connected yet. There have been a series of papers in the 2000's saying how in adolescence there is still a very strong growth spurt for brain connectivity. People hadn't seen any consequences of that brain connectivity to behavior. People thought it was all cognitive about taking the car when you shouldn't and things like that. In reality, this is the first time that we see a behavioral consequence to that continual maturation of the brain into young adulthood. 
	Then, how do we explore relationships between finger and dexterity across ages and genders and stuff, so what is the relationship between leg dexterity, and finger dexterity, and so we had a paper of writer collaborators. For example, as you compress a spring, and you look at the little ripple in force as you compress it, this is a 32 year old and this is an 83 year old, so you see that the dynamics of control are actually different between these two calculations. We're starting to study, yeah Zach failed right? We're starting to study, for example, can you detect Parkinson's disease early by seeing the departures form this tight control to a more erratic, or some very specific frequencies of behavior? In this pseudo face, phase space. 
	Or other things, like we found a difference, we found little difference between right or left. Neither hands nor legs, which is weird. Well, we're supposed to have a dominant hand, and the non dominant hand. Well, in this task there is no difference of that [inaudible 00:50:14]. There is correlation between legs and fingers, but we also found, and this is the third rail of science, we found the difference between girls and boys. We found that girls were not able to control the spring, on average, like girls. Now, there's a growing literature in neuro science, about differences in brain connectivity between boys and girls. I say boys and girls because we're talking people younger than 21, which were in our age, our still children. Not here of course, but we can actually begin to study these issues. 
	Then, let me propose to you a very particular utility of this. As you know, non contact ACL injuries are common in young populations. What people don't usually know, is that girls are disproportionally more at risk to ACL injuries. Had anyone heard about that? Yeah. This actually, from Title Nine, where you have a need for sports of equal representation of men and women, et cetera, we now know that women are between 6 and 10 times at a greater risk of an ACL injury. People have been wondering for about 30 years, what is the difference between boys and girls in terms of, you know, from the waste down. Where shall we begin, right? The [inaudible 00:51:51] angle, different strengths, different location of center of mass, different landing strategy, different exposures, et cetera, but what we've actually found is that maybe there's a difference in the circuitry in the spinal cord. 
	You know when you land, you have immediate response by the tissue. This is the immediate mechanical response. Then you have a long latency, quote unquote, voluntary level of response. What we are arguing in a variety of papers now, is that compressing this leg sprain, gives you a window, not into the brain activity, but rather into the spinal cord activity. This is good news. We could actually identify, hopefully, women who are at risk of an ACL injury, and then we can create these training protocols. There are many others. You may have heard of training protocols about teaching women how to land and not to let the leg, the knees buckle in. There's lots of training protocols like this. How about a video game that asks you to push from this funky spring for 15 minutes a day? That could actually be training your spinal cord to respond in the appropriate way to an instability. 
	That's another direction in which we're moving. The last thing I'll say, it will take me five minutes, is okay, what about the spinal cord? The spinal cord, it was very popular in 1898, 1906, when Sharington was the hero of the day. Who has heard of Sharington? Sharington was the one who started this idea that behavior is essentially a sequence of reflexes that are all encoded in motor primitives in the nervous systems of mammals and vertebrates, et cetera. Then along came the brain, and the brain is much sexier to a lot of people. People say well, the brain you can scan it, you can stain it, you know, it's a wonderful world out there. What I'm telling you now, is that the spinal cord may actually be at play in every day life, for dexterity and manipulation. 
	One of the things that I want to do is can we understand this circuitry? Why is this important? Because if you look at say cerebral palsy or Parkinson's disease, we want to mitigate these neurological disfunctions. Here the girl can not really reach out smoothly and touch the microphone and make a noise. She sort of goes like this. She can't really aim her arm very well, and here the other older person has problems with tremors and things like that. How can we begin to understand? These are actually dystonias that are often associated with what's called hyper reflexia, so a disruption of the reflexes in the spinal cord. What we're doing is, we're following finements maxim, which is what I cannot create, I do not understand. If you look at how much we know about spinal cord circuitry, you get books that are this thick. 
	We actually, we have a grant from NIH to encode them as populations of spiking neurons in FPGA's or very fast [inaudible 00:55:15]. We have been driving muscles that behave, I'm sorry, motors that behave like muscles, and they in term drive a cadaver hand, so what we're doing, is we are recreating, it's like synthetic biology, but of a different kind. We are creating synthetic spinal cords that drive synthetic muscles that operate on the real system. For example, we started by computer controlled cadaver hands, so for this cadaver hand to move the finger up and down like this, these are the excursions of the tendons, but look at the forces that are needed. These are the forces that each of those tendons, as you were performing the simplest of tasks. 
	Winslow, in 1732, he had the most popular anatomy book, and he was dissecting the hand, and he said, "The function of the small muscles of the hand in live humans, will never be understood." He's still right. We still don't know how we coordinate all of the muscles in the hand and the forearm to produce the simplest of tasks. What we're doing here is we're actually seeing some solutions that allow you to do that. On top of that, what we're creating here are these synthetic systems where, here's a finger, quote unquote, that's driven by two tendons. Each of which is driven by a population of neurons. They're spiking away, and they're just behaving as if there were these reflex arcs. Guess what? What they're giving you is this very stable behavior that's very similar to what you can see in bot drivable robots that have inter lubes running at about 10 milliseconds for the control of impedance. 
	People do that. If you talk to Neville Hogan, and other people who manufacture robots, the way they solve the problem is by having these inter loops, looking at forcing the motor versus displacement in the joint at about 10 milliseconds, and just continually setting a stage for the system. Here you just have populations of 128 neurons on one side, 128 neurons on the other side. They're sensing the displacement as per the muscle stimuli. They're just spiking away, and this as antonymous. We don't touch it. It's just that. This is what neurons could give you if their spiking behavior were there. Here's another way in which you can ... You can actually extract the simulated EMG. Those of you who may have, let me play that again for the biologists in the room, that's as if you were recording from a lamprey. If you were recording from a single board of units in the [inaudible 00:58:06], so we're recreating the system, and again we have a team of people sort of doing this, engineers, undergrads, engineers, neurologists, neuro scientists, surgeons, and this is actually the first ever hardware implementation of reflex pathways. We say is you have reflexes. 
	You have these populations of neurons just spiking away, and then we say, now we're going to tell you to go right, or to flex, or extend. Then we have a volley of single say extend, and at the same time we extend we need to silence the neurons on the other side to allow the extension. The simplest neuro muscular system you can think of, two muscles being told to move right or left. Completely autonomously. What's interesting to me about this, is this is the most unprincipled way to look at this. Other than being faithful to the neuro anatomy, we're not dialing in any control loss. This is what's called emergent behavior. This behavior emerges naturally from the properties of spiking neurons and the sensors that we have in our muscles, and that's it. 
	What I like to do is recapitulate the evolutionary process, and find out what such a simple spinal cord can not do, and then that means I need a basil [inaudible 00:59:31] to do that, and what the [basadanga 00:59:31] cannot do, then you need a frontal lobe, and premortal cortex, and [inaudible 00:59:36]. So, actually follow the evolutionary process form the very low level of firmware, call it, to see where the brain fits in. At which point do we need a brain for behavior, that give you capabilities that the spinal cord couldn't. This, of course, very ambitious, but we have to start some place. 
	In conclusion, this view of tendon driven systems, helps us explore the challenges that the nervous systems faces. This also challenges the dominant cortical centric view of motor control. Everybody loves the brain. I love the brain, too, but let's move to more biologically reasonable distributed hierarchical embedded controllers in systems that are in organisms. There's also an issue of socio biological coevolution of objects. Are we dextrous because we designed the objects of everyday life? We think of ourselves as so dexterous, right? Every object that you manipulate, was designed to be manipulated, so we cannot really call ourselves dexterous. Who plays the violin or viola here? And who plays a guitar?
	Why do you have frets? To completely sidestep the problem, having to play the finger right at the right spot, right? So, we co evolve the body with, sorry, we co evolve the environment with our bodies and our capabilities, and so this is another broader view of the problem. This actually expands the meaning of what is disease? What is ability? What is treatment? What is rehabilitation? The take home message is that engineering is critical to make the 21st century the century of biology and medicine. An important contributor to this will be neuro mechanics, in the context of clinical rehabilitation, and hopefully evolutionary systems and the like. I'd like to thank the many people who worked on this. Always looking for outstanding students in post ox, and my funding sources over the years, and thank you for your attention. 

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