Skip to main content
main-content

Über dieses Buch

This book provides a conceptual and computational framework to study how the nervous system exploits the anatomical properties of limbs to produce mechanical function. The study of the neural control of limbs has historically emphasized the use of optimization to find solutions to the muscle redundancy problem. That is, how does the nervous system select a specific muscle coordination pattern when the many muscles of a limb allow for multiple solutions?

I revisit this problem from the emerging perspective of neuromechanics that emphasizes finding and implementing families of feasible solutions, instead of a single and unique optimal solution. Those families of feasible solutions emerge naturally from the interactions among the feasible neural commands, anatomy of the limb, and constraints of the task. Such alternative perspective to the neural control of limb function is not only biologically plausible, but sheds light on the most central tenets and debates in the fields of neural control, robotics, rehabilitation, and brain-body co-evolutionary adaptations. This perspective developed from courses I taught to engineers and life scientists at Cornell University and the University of Southern California, and is made possible by combining fundamental concepts from mechanics, anatomy, mathematics, robotics and neuroscience with advances in the field of computational geometry.

Fundamentals of Neuromechanics is intended for neuroscientists, roboticists, engineers, physicians, evolutionary biologists, athletes, and physical and occupational therapists seeking to advance their understanding of neuromechanics. Therefore, the tone is decidedly pedagogical, engaging, integrative, and practical to make it accessible to people coming from a broad spectrum of disciplines. I attempt to tread the line between making the mathematical exposition accessible to life scientists, and convey the wonder and complexity of neuroscience to engineers and computational scientists. While no one approach can hope to definitively resolve the important questions in these related fields, I hope to provide you with the fundamental background and tools to allow you to contribute to the emerging field of neuromechanics.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Neuromechanics is a perspective that highlights how real-world behavior emerges from the intimate relationship between the mechanical structure of the musculoskeletal system, the mechanical requirements of a task, and the feasible neural control actions to produce it. To understand these interactions, it is necessary to consider the anatomical fact that muscles act on vertebrate limbs via tendons. This is different from the more common mathematical formulation that focuses on analyzing the net action of all muscles at each joint. This deliberate consideration of tendon-driven limbs allows us to articulate the problem of neural control in a way that promotes the debate and refinement of current theories. This perspective has important consequences to understanding healthy function, disability, and rehabilitation; and to the design of novel versatile robots.
Francisco J. Valero-Cuevas

Fundamentals

Frontmatter

Chapter 2. Limb Kinematics

Abstract
The purpose of this chapter is to introduce you to the kinematics of limbs. Kinematics is the study of movements without regard to the forces and torques that produce them. In essence, it is the fundamental description of the articulations and motions of which a limb is capable. This chapter serves as the foundation upon which we can build a common conceptual language, and begin to discuss limb function in the context of mechanics.
Francisco J. Valero-Cuevas

Chapter 3. Limb Mechanics

Abstract
Limb mechanics involve limb kinematics, and the forces and torques that cause limb loading and motion. Mechanics can be both static and dynamic depending on whether motion is prevented or not, respectively. Studying limb motions that result from applied forces and torques falls within the realm of rigid-body dynamics, which is a specialized branch of mechanics. However, I will mostly consider the case of static mechanics because it suffices to illustrate and debate important concepts in neuromechanics. This chapter focuses on presenting some fundamental concepts of how limbs produce static forces.
Francisco J. Valero-Cuevas

Chapter 4. Tendon-Driven Limbs

Abstract
The purpose of this chapter is to introduce you to the fundamentals of tendon-driven limbs, and to begin to explore how they affect our understanding of vertebrate and robotic limbs. Many robotic limbs are driven by motors or pistons that act on the kinematic degrees of freedom (DOFs, e.g., rotational joints) either via linkages, cables, or gears. These actuators can exert forces and torques in both clockwise and counterclockwise directions, symmetrically in either direction—which in the robotics literature are idealized and analyzed as torque-driven limbs. The term ‘tendon-driven’ comes from the robotics literature where limbs are actuated via a variety of motors or muscles that pull on strings, cables, or tendons that cross the kinematic DOFs. Thus, these actuators can only pull on, or resist stretch in, the tendons. But they cannot not push on the tendons. This discontinuity and asymmetry in actuation makes tendon-driven limbs distinctly different from their torque-driven counterparts with symmetric actuation. While this asymmetric actuation in tendon-driven limbs might have some mechanical disadvantages and complicate their analysis, it can also have advantages such as being light weight, and allowing remote actuation and flexibility of tendon routing. As the reader will discover, varying tendon routings and moment arms can enable multiple solutions for specific functional requirements, especially when size and power constraints are critical. More importantly, because the nervous system is unavoidably confronted with the need to actuate and control the tendon-driven limbs in vertebrates, the nuances of tendon-driven limbs provide insights into the nature of neural control, evolutionary adaptations, disability, and rehabilitation that is not available in the torque-driven formulation. Note that throughout this book, I use the terms muscle when relating specifically to the behavior, forces, or state of the muscle tissue, musculotendon when relating to issues that involve the muscle and its tendons of origin and insertion, and tendon when relating specifically to the behavior, forces, or state of the tendon of insertion of the muscle. For most mathematical and mechanical analyses, however, the term tendon suffices as it applies to both robots and vertebrates. When the analysis continues on to consider muscle mechanics and its neural control, I will prefer to use the term musculotendon.
Francisco J. Valero-Cuevas

Introduction to the Neural Control of Tendon-Driven Limbs

Frontmatter

Chapter 5. The Neural Control of Joint Torques in Tendon-Driven Limbs Is Underdetermined

Abstract
This chapter introduces the mathematical foundations of the classical notion of muscle redundancy. As presented in Chap. 4, a sub-maximal net torque at a joint actuated by tendons can be produced by a variety of combinations of individual forces at each tendon. We see this already in the simplest case of a planar joint with 2 tendons—one on each side of the joint. Of course, each combination of tendon forces will produce different loading at the tendons and joint, and will incur different metabolic or energetic costs, etc. But in principle there are multiple solutions to the problem of achieving a given mechanical output. This underdetermined problem is called the problem of muscle redundancy, and it begs the question of how the nervous system (or a robotic controller) should select a particular solution from among many. This has been called the central problem of motor control and has occupied much of the literature in this field. The main goal of this chapter, however, is to introduce and cast this problem for high-dimensional multi-joint, multi-muscle limbs (it is often only presented in simplified joints). This will serve as the foundation of subsequent chapters where we critically assess this classical notion of muscle redundancy—and challenge its assumptions and conclusions. As mentioned in Chap. 1, however valuable and informative the concept of muscle redundancy has been, it is also paradoxical with respect to the evolutionary process and clinical reality, and should be revised.
Francisco J. Valero-Cuevas

Chapter 6. The Neural Control of Musculotendon Lengths and Excursions Is Overdetermined

Abstract
This chapter introduces the mathematical foundations of the concept of obligatory kinematic correlations among joint angles and musculotendon lengths. As presented in Chap. 4, tendon excursions are overdetermined because the angles and angle changes of the few joints uniquely determine the lengths and excursions, respectively, of all musculotendons. This is the opposite of redundancy: there is a single and unique set of tendon excursions that can satisfy a given limb movement. This begs the question of how the nervous system controls the excursions of all musculotendons so that the limb can move smoothly. Essentially, if for some reason any of the musculotendons undergoing an eccentric contraction fails to lengthen to satisfy the geometric requirements of the joint rotations, at the very least the limb motion will be disrupted, and at worst the limb can lock up. Physiologically, the failure to accommodate the necessary length changes could be due to anatomical interconnections among muscles or tendons, neurally mediated resistance to lengthening due to short- or long-latency reflexes, or spinally- and cortically-mediated commands to the muscles. This chapter lays the foundation for understanding the interactions between muscle coordination and reflex mechanisms necessary for natural movement by providing a mathematical framework for the overdetermined nature of tendon excursions. This is done for the simplified case with no anatomical interconnections among muscles or tendons, but the conclusions and intuition provided reinforce the notion that the neural control of movement for tendon-driven limbs is in fact not as redundant as is currently thought. Recall that, as mentioned in Chap. 4, the term tendon suffices for most mathematical and mechanical analyses as it applies to both robots and vertebrates. When the analysis continues on to consider muscle mechanics and its neural control, I will prefer to use the term musculotendon.
Francisco J. Valero-Cuevas

Feasible Actions of Tendon-Driven Limbs

Frontmatter

Chapter 7. Feasible Neural Commands and Feasible Mechanical Outputs

Abstract
Having understood the basic concepts related to the structure and function of tendon-driven limbs, we can now revisit and appreciate the question: ‘How does the nervous system control a tendon-driven limb?’ Chap. 5 shows why it is reasonable to consider optimization as a means to resolve the muscle redundancy that exists for the control of joint torques. But Chap. 6 paints an alternative picture when we see that orchestrating tendon excursions among muscles is severely overdetermined—which is the opposite of redundancy. In this chapter I begin to explore in detail the working hypothesis that having numerous muscles does not make them as redundant as proposed by the classical notion of muscle redundancy. I do this by introducing you to the concepts of how feasible muscle activations produce feasible mechanical outputs. This perspective grows out of the fusion of linear algebra, geometry, mechanics, and anatomy. It shows how the anatomical structure of the limb together with the constraints that define a mechanical task naturally specify a set of feasible neural commands. The fact that this set of feasible neural commands has a well-defined structure compels and allows us to revise and extend the classical notion of muscle redundancy, and propose a more general approach to neuromuscular control that emphasizes compatibility with evolutionary biology and clinical reality.
Francisco J. Valero-Cuevas

Chapter 8. Feasible Neural Commands with Mechanical Constraints

Abstract
In this chapter I refine the notion of feasible neural commands by introducing the concept of functional constraints. Chapter 7 presented the geometric principles that allow us to find the structure of the sets of all feasible neural commands and feasible mechanical outputs as a function of the natural bounds on muscle activations, strengths of the muscles, routing of the tendons, and mechanics of the limb. From that perspective it is clear that producing maximal mechanical output—shown for the case of static force production—can only be achieved by a unique muscle activation pattern (i.e., there is no muscle redundancy). But producing sub-maximal mechanical outputs can be done by multiple muscle activation patterns (i.e., there is muscle redundancy). This chapter explores the nature of those multiple muscle activation patterns, and the relationships among them. I emphasize that considering the properties of the limb plus the functional constraints of the task (which can be mechanical, metabolic, physiological, etc.) allows us to define and find families of valid and related solutions—instead of unique solutions in isolation. These concepts continue to challenge the classical notion of muscle redundancy but, most importantly, provide perspective and computational tools to explore mechanisms by which the nervous system controls the limbs for specific tasks. That is, muscle redundancy is a function of both the limb and the task. This is directly relevant to the central questions of motor control such as optimization, learning, adaptation, dimensionality reduction, synergistic control, etc. More generally, these concepts build a case to argue that exploring and exploiting feasible activation sets is likely a more biologically tenable way in which the nervous system operates in the context of muscle redundancy and multifaceted real-world tasks.
Francisco J. Valero-Cuevas

Neuromechanics as a Scientific Tool

Frontmatter

Chapter 9. The Nature and Structure of Feasible Sets

Abstract
An engineering perspective is inherently incomplete when applied to science. However, as per the words of Galileo Galilei at the beginning of this book, science is also not complete without a mathematical foundation. Our large community applied this mathematics-based perspective for decades to understand motor control. This has resulted in a large, informative, useful, and fruitful body of work. I now comment briefly on how the neuromechanical framework of this book applies to some current tenets, theories, and debates in motor control. In particular, if we agree that the mechanical principles outlined in this book are relevant to the structure of vertebrate limbs, then the nature and structure of the feasible sets they allow are relevant to their neural control. In this chapter I present brief descriptions of how our community has approached understanding the nature and structure of the high-dimensional feasible activation sets.
Francisco J. Valero-Cuevas

Chapter 10. Implications

Abstract
This book is deliberately a short introduction to the mathematical and anatomical foundations of neuromechanics. My hope is that you will take these concepts and challenge, modify, extend, and leverage them to advance the science of neuromuscular control and its related areas, such as robotics, musculoskeletal modeling, computational neuroscience, rehabilitation, and evolutionary biology. Having established a common language, conceptual framework, and computational repertoire, I discuss several implications of this neuromechanical perspective. My intent is that my presentation of several issues, research directions, tenets, and debates, however brief, will inspire and encourage you in your research.
Francisco J. Valero-Cuevas

Backmatter

Weitere Informationen