Integrative and Comparative Biology Advance Access originally published online on May 27, 2007
Integrative and Comparative Biology 2007 47(1):16-54; doi:10.1093/icb/icm024
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Neuromechanics: an integrative approach for understanding motor control
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*Department of Biological Sciences, California State Polytechnic University, Pomona, CA 91768; Concord Field Station, Museum of Comparative Zoology, Harvard University, Bedford, MA 01730, USA; Department of Biology, University of Antwerp, and Department of Movement and Sport Sciences, University of Ghent, Belgium; Department of Biology, Harvey Mudd College, Claremont, CA 91711; Department of Biology, Case Western Reserve University, Cleveland, OH 44106; aDepartment of Biology, University of Washington, Seattle, WA 98195-1800; °Department of Integrative Biology, University of California, Berkeley, CA 94720-3140; #Department of Organismal Biology and Anatomy, University of Chicago, Chicago, IL 60637; £Department of Physiology, Emory University, Atlanta, GA 30322; **Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH 44106; Department of Biology, University of North Carolina, Wilmington, NC 28409, USA
Correspondence: 1E-mail: Kiisa.Nishikawa{at}nau.edu
Correspondence: 2E-mail: biewener{at}fas.harvard.edu
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Synopsis |
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Synopsis
IntroductionNeuromechanics seeks to understand how muscles, sense organs, motor pattern generators, and brain interact to produce coordinated movement, not only in complex terrain but also when confronted with unexpected perturbations. Applications of neuromechanics include ameliorating human health problems (including prosthesis design and restoration of movement following brain or spinal cord injury), as well as the design, actuation and control of mobile robots. In animals, coordinated movement emerges from the interplay among descending output from the central nervous system, sensory input from body and environment, muscle dynamics, and the emergent dynamics of the whole animal. The inevitable coupling between neural information processing and the emergent mechanical behavior of animals is a central theme of neuromechanics. Fundamentally, motor control involves a series of transformations of information, from brain and spinal cord to muscles to body, and back to brain. The control problem revolves around the specific transfer functions that describe each transformation. The transfer functions depend on the rules of organization and operation that determine the dynamic behavior of each subsystem (i.e., central processing, force generation, emergent dynamics, and sensory processing). In this review, we (1) consider the contributions of muscles, (2) sensory processing, and (3) central networks to motor control, (4) provide examples to illustrate the interplay among brain, muscles, sense organs and the environment in the control of movement, and (5) describe advances in both robotics and neuromechanics that have emerged from application of biological principles in robotic design. Taken together, these studies demonstrate that (1) intrinsic properties of muscle contribute to dynamic stability and control of movement, particularly immediately after perturbations; (2) proprioceptive feedback reinforces these intrinsic self-stabilizing properties of muscle; (3) control systems must contend with inevitable time delays that can simplify or complicate control; and (4) like most animals under a variety of circumstances, some robots use a trial and error process to tune central feedforward control to emergent body dynamics.
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Introduction |
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Movement science is a vast topic that spans a wide range of disciplines, not only within biology (e.g., biomechanics, muscle physiology, neuroscience), but also in other fields including engineering, medicine, sports, mathematics, and psychology. A major goal of movement science is to understand how movement is controlled. This area of research seeks to understand how muscles, sense organs, and the central nervous system interact to produce coordinated, dynamically stable movement under steady conditions, as well as when animals negotiate complex terrain and experience unexpected perturbations. Applications include ameliorating a wide range of human health problems, from prosthesis design to brain and spinal cord injury, as well as design and actuation of mobile robots. Historically, studies of motor control developed mostly within the field of neuroscience (e.g., in the areas of behavioral neuroscience, central pattern generators (CPGs), neurophysiology, proprioception, psychophysics). Over the past 20 years however, the ideas that muscle and body mechanics also contribute to control of movement have become well-established (Chiel and Beer 1997
; Full and Koditschek 1999; Loeb et al. 1999).
A significant impediment to understanding control of movement is the formidable complexity of animal bodies (i.e., high-dimensionality, nonlinearity) (Full and Koditschek 1999). From a design perspective, it seems clear that algorithms for controlling a system must take into account the details of how that system works. Although it might seem that the complexity of animal bodies would mean that the algorithms for controlling complex bodies must necessarily be complex, an alternative view is that the mechanics of the moving parts in relation to their interaction with the environment may actually simplify control (Loeb et al. 1999; Koditschek et al. 2004; Ting and Macpherson 2005).
Motor control fundamentally involves a series of transformations of information among different levels and components of the neuromuscular and skeletal systems. Sensory information (proprioceptive and exteroceptive) is transduced by sensory structures that in turn transfer a subset of their information to the central nervous system which, following yet another transformation, issues a set of motor commands. The motor commands trigger force development in muscles, which drive movement and control the mechanics of the body. The mechanical coupling between musculoskeletal elements and the muscles controlling them is yet another transformation of information in the system. Muscles, via joint torques, drive the body's motion, whose inertia and shape determine its trajectory in space. Importantly, external forces from the environment, as well as intersegmental forces, also influence the trajectory of movement. That trajectory and its time history determine the visual and mechanical information that is available to the system. Finally, the mechanics and physics of sensory structures determine the bandwidth of information that is available to the nervous system for control (Göpfert and Robert 2002). Understanding how control is achieved, therefore, depends on knowledge of the specific transfer functions that describe each transformation. In turn, the transfer functions depend upon the rules of organization and operation that determine the dynamic behavior of each subsystem.
The inevitable coupling between neural information processing and the emergent mechanical behavior of animals is a central theme in neurobiology today. Such "neuromechanical" approaches ask how mechanical systems may offload some tasks of the neural system; how size, shape, structural properties, and even the physics of the medium may determine how the neural system functions to control movement; and how processing of sensory information may limit the range or rates of movement that are feasible.
In this review, we discuss relevant work in neuromechanics, although we refer more extensively to work carried out in the authors’ laboratories. In doing so, we consider the contributions of (1) muscles, (2) sensory processing, and (3) central networks to motor control, (4) use examples to illustrate the interplay among the central nervous system, musculoskeletal system, sense organs, and the environment in the control of movement, and (5) describe advances in robotics and neuromechanics that have emerged from application of biological principles in robotic design. We end with a discussion of the emerging principles of neuromechanics and their implications for understanding motor control.
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Part I. Contributions of muscle to motor control |
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Skeletal muscle is often treated as a simple black box through which a neural signal passes to produce a mechanical output. The mechanical behavior of a given muscle is typically assumed to be predictable, given its anatomy, stimulation pattern, and/or basic contractile properties. Musculoskeletal anatomy alone is often used as an indicator of muscle function. For example, it seems straightforward to infer the functions of the biceps brachii muscle (i.e., elbow flexion) and the triceps brachii muscle (i.e., elbow extension) from the basic anatomy of their origins and insertions.
In addition to anatomy, the activation (or stimulation) pattern experienced by a muscle also influences its force output. Whereas a single stimulus results in a small twitch contraction, multiple stimuli at a low frequency produce higher forces. Very high forces, as during a tetanic contraction, can be elicited using high frequency stimuli. Finally, the basic contractile properties of a muscle, such as its contraction kinetics, force–length relationship, and force–velocity relationship, are also known to affect its mechanical output (Josephson 1999).
Although muscles are often viewed as motors that produce movement by shortening to perform mechanical work (termed "actuation" in engineering and robotics), they may serve a variety of other functions during movement. They may stabilize motion at joints, store elastic energy in connective tissues (e.g., tendons or apodemes), and absorb work as well as perform it (Biewener 1998; Biewener and Roberts 2000; Dickinson et al. 2000). Whereas swimming and flying require substantial positive work to produce the fluid forces needed for movement, steady locomotion over level ground often involves the use of muscles to produce force economically; muscles facilitate elastic energy recovery to achieve minimal net work output. When movement becomes nonsteady or requires changes in grade, shifts in motor recruitment will reflect the changing need for muscles to perform or absorb work. The function of a muscle during movement may also depend on the biomechanical context (e.g., position or mechanical advantage; Sutton et al. 2004; Uyeno and Kier 2005; Novakovic et al. 2006).
Muscle as a device for translating a control signal into a mechanical output
Although it is well-established that muscles can perform a range of functions in addition to actuation, it is less clear what factors determine the particular role(s) that a given muscle will play during movement. The hindlimb muscles of the death-head cockroach, Blaberus discoidalis, illustrate this problem. In the hindlimb of Blaberus, muscles 178 and 179 are two of six muscles positioned to generate extensor moments at the coxa-femur joint (Carbonell 1947). These two muscles have very similar anatomy and nearly identical moment arm relationships with joint angle (Full and Ahn 1995). Because a single motor neuron innervates both muscles (Pearson and Iles 1971), they also experience identical activation patterns during running in vivo and during nerve stimulation in situ (Ahn et al. 2006). In addition, muscles 178 and 179 have similar contraction kinetics, force–velocity relationships, and force–length relationships (Ahn et al. 2006).
Despite these many similarities, mechanical energy production in situ differs between muscles 178 and 179 (Fig. 1). Full et al. (1998) used the work loop technique (Josephson 1985) to investigate the functional role of muscle 179, using activation and strain patterns determined in vivo during running. Ahn et al. (2006) subsequently examined the work loop, force–velocity and force–length properties of muscle 178 in comparison with muscle 179, again based on activation and strain patterns observed during running. Results showed that muscle 178 generates mechanical work during one part of the cycle and absorbs an equal amount of mechanical work during the other part of the cycle (Fig. 1). Thus, muscle 178 generates no net mechanical work or power output during a cycle (1.79 ± 4.58 W kg–1; Ahn et al. 2006). In contrast, muscle 179 mainly absorbs mechanical work during a cycle (–25.4 + 22.9 W kg–1, Full et al. 1998; –19.1 ± 14.1 W kg–1, Ahn and Full 2002).
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Although in vivo activation and length-change patterns are identical, the strain amplitude differs slightly (18.5% for muscle 178 and 16.4% for muscle 179). This difference in strain amplitude, however, does not account for the difference in mechanical output. Even when the imposed strain is identical (15% strain amplitude), muscle 178 generates mechanical work (10.1 ± 11.5 W kg–1) whereas muscle 179 absorbs it (–14.7 ± 13.1 W kg–1; Ahn et al. 2006
). Although muscles 178 and 179 are positioned similarly, stimulated identically, and possess similar basic contractile properties, their mechanical functions during dynamic contractions differ considerably.
Not only can different muscles innervated by the same nerve exhibit different functions during movement, but different muscle segments within a single fascicle may also exhibit different mechanical output during a single contraction (Ahn et al. 2003). The semimembranosus muscle of the American toad, Bufo americanus, is a simple, parallel-fibered muscle positioned to generate extensor moments about the hip joint during hopping (Kargo and Rome 2002). In vivo muscle activation patterns in adjacent seg-ments (central and distal) of the semimembranosus show no differences in electromyogram (EMG) onset, duration or amplitude during hopping (Ahn et al. 2003). Length changes, however, differ between central and distal segments. As the central segment shortens during hopping, the distal segment simultaneously lengthens before shortening (Fig. 2A). When the toads hop a distance of one or two body lengths, the magnitude of shortening of the central segment (–14.0 ± 4.9%) always exceeds shortening of the distal segment (–6.5 ± 3.2%; Fig. 2A; Ahn et al. 2003).
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This strain heterogeneity of adjacent segments observed during hopping in vivo is also observed during cyclical contractions in vitro, suggesting that adjacent segments along the length of this single muscle perform different mechanical functions (Fig. 2B). In vitro percentage heterogeneity, or the percentage of a sinusoidal cycle during which adjacent segments strain in opposing directions, differs from that of passive cycles at all stimulation phases except phase 0, when the muscle is stimulated halfway through shortening (Ahn et al. 2003
). Maximal percentage heterogeneity occurred when the muscle was stimulated at phase 50, or halfway through lengthening (34.0 ± 9.2%). A small tendinous inscription, where the muscle attaches to the tibia near the knee, corresponds to the region of heterogeneity observed in the whole muscle. Despite the gross simplicity of the semimembranosus muscle, differential expression of protein isoforms and/or the architecture of linkages between muscle fibers and intramuscular connective tissues may influence the pattern of strain during dynamic contractions (Edman et al. 1988). These studies demonstrate that a single neural signal can produce variable mechanical outputs, not only in adjacent muscles but also in adjacent segments within a single muscle. The mechanical output of skeletal muscle depends on many factors, some of which we understand well (i.e., anatomy, kinematics, neural stimulation, contraction kinetics, force–velocity characteristics, and force–length relationships), but many of which we do not yet understand. Some of the more poorly understood factors that may influence the mechanical behavior of skeletal muscle include submaximal stimulation, muscle architecture, history-dependent properties, interfilament spacing, and variable expression of protein isoforms. We are only now beginning to understand these less frequently studied parameters, even though they may substantially influence the mechanical output of a seemingly simple neuromuscular system. As a device for translating a neural signal into a mechanical output, muscle is clearly a remarkable material that has not yet yielded all its secrets.
Muscle as a smart material with intrinsic self-stabilizing properties
In addition to generating force and producing or absorbing energy, muscles also play important intrinsic, self-stabilizing roles during movement due to their force–velocity, force–length, and viscoelastic properties (Loeb et al. 1999; Richardson et al. 2005; Lappin et al. 2006). For example, when subjected to a higher force, the force output of skeletal muscle increases automatically to resist the imposed load. Similarly, if a muscle is suddenly unloaded, its rate of shortening increases and its force production decreases (e.g., Rassier and Herzog 2004). This self-stabilizing behavior results from the inverse force-velocity relationship exhibited by all striated muscles, as was first described by A. V. Hill (1938).
The force output of striated muscles is also well known to depend on sarcomere length (Gordon et al. 1966). This length dependence also means that, when operating on the ascending portion of its length–tension curve, a muscle's intrinsic force capacity will increase to resist further stretch when it is stretched to a longer length. Hence, the intrinsic force–velocity and force–length properties of striated muscle provide immediate impedance responses that help to stabilize movement in response to perturbations, prior to the subsequent action of force-dependent and length-dependent reflexes that incur time delays and are known to modulate motor recruitment during ongoing tasks. Several recent studies demonstrate that these intrinsic musculoskeletal properties, including force–length and force–velocity behavior, can stabilize movement and simplify control (Brown and Loeb 2000; Jindrich and Full 2002; Aoyagi et al. 2004; Richardson et al. 2005).
Recent studies by Lappin et al. (2006) demonstrate that the viscoelastic properties of active muscle also provide self-stabilization during perturbations in load and contribute to active motor control. Using ballistic mouth opening in toads (Fig. 3A), they investigated elastic recoil in skeletal muscle and associated connective tissues. During ballistic mouth opening, transfer of momentum from the rapidly opening jaws to the tongue is used to project the tongue from the mouth to capture prey (Mallett et al. 2001). Prior to mouth opening, the muscles contract slowly for 50–250 ms as they store elastic energy in connective tissues at their origin and insertion, as well as in series elastic elements within the muscles themselves (Lappin et al. 2006). Lappin et al. (2006) modeled the toad jaws as a damped mass-spring system. In their model, muscle (Fig. 3A, red) is represented as a force generator (i.e., cross bridges) in series with a spring (i.e., series elastic component in the muscle). Extramuscular connective tissues at the origin and insertion are represented together as a separate spring in series with the muscle (Fig. 3A, blue). These muscle and connective tissue springs are attached to the cranium and suspend an external load.
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Muscles themselves have been thought to contribute relatively little to the power of fast movements because they shorten rapidly only under very low loads (Alexander and Bennet-Clark 1977
; Burrows 2003). This argument follows directly from Hill's (1938) force–velocity curve: the velocity of muscle shortening increases hyperbolically with decreasing load. Lappin et al. (2006), however, demonstrated that muscles can produce an order of magnitude more power during elastic recoil than during isotonic contractions at the same load. Compared to stiffer external connective tissues, such as tendon or cuticle, muscles themselves can contribute more in terms of strain (Fig. 3B) and, via elastic energy stored in their intrinsic connective tissue components, nearly as much in terms of energy, to animal movements.
The apparently low power output of muscle is an artifact of Hill's (1938) after-loaded isotonic paradigm for generating the force–velocity curve. During natural movements, muscles can begin to shorten after relatively long periods of activation. In Hill's (1938) isotonic paradigm, however, not only does the load moved by the muscle vary, but the duration of muscle stimulation prior to movement also varies with the load. At the smallest loads, the muscle is stimulated for very short durations prior to shortening (as little as 10–15 ms) whereas at the largest loads the muscle is stimulated for much longer durations (>250 ms). For natural movements of humans and animals, particularly those with time varying patterns of force and length change and variable periods of activation prior to shortening, a muscle's isotonic force–velocity behavior may well not be relevant.
During active shortening, muscles behave as springs in which displacement increases and stiffness decreases nonlinearly with the change in load (Lappin et al. 2006). When the external load changes unexpectedly, the total stiffness of the mass-spring system adjusts automatically and instantaneously without requiring neural input, due to the load-dependent, nonlinear stiffness of actively shortening muscle (Fig. 3C). The system becomes stiffer when the external load increases, and becomes less stiff when the load decreases (Fig. 3C). Because the stiffness of the extra-muscular connective tissues is relatively constant within the physiological range of movement, the load-dependent, nonlinear elastic properties of the mass-spring system arise from the behavior of muscle during active shortening. Furthermore, because the external load is relatively constant, the forces that develop in the muscles prior to movement determine the elastic properties of the system.
Lappin et al. (2006) suggested that the central nervous control of ballistic movements might be relatively simple in principle. The number of motor units recruited, as well as the frequency and duration of their activation, will determine the force attained by a muscle prior to movement (Loeb and Gans 1986). Due to its nonlinear, load-dependent stiffness, the force attained by a muscle prior to movement will determine both the total displacement (i.e., of both extramuscular connective tissues and the muscles themselves) and the total effective stiffness of the mass-spring system. The force attained by antagonistic muscles will resist movement and may also influence elastic properties. By activating a trigger at the appropriate time, the nervous system can specify the timing of rapid unloading. In principle, it appears that the nervous system could control ballistic movements simply by specifying the forces attained by muscles prior to movement and the timing of rapid unloading. The distance and speed of the resulting movement will be determined by the intrinsic, load-dependent, nonlinear elastic properties of the mass-spring system (including muscles, tendons, and skeletal elements).
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Part II. Contributions of sensory processing to motor control |
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It has long been appreciated that sensory feedback to muscles from force sensors and length sensors of muscles, as well as from other sensory inputs (e.g., vision, balance, proprioception), acts to provide appropriate changes in muscle activation and force to control and stabilize motion (e.g., Eccles et al. 1957
). Such feedback also serves to reinforce the self-stabilizing properties of skeletal muscle described earlier in this article (and see subsequent text). An important principle of neuromechanics is that the mechanics of the sensors and the neural circuits in which they are embedded affects the timing and dynamics of receptor input. Cellular and network properties of the sensors, interneurons, and motor neurons determine the timing and strength of activation of homonymous muscles, as well as of agonists and antagonists, within the limbs and other motor systems. A second principle of neuromechanics is that cellular and network properties necessarily introduce timing delays within sensorimotor circuits used to control motor behavior. A robust controller must account for these timing delays, so that interacting components are integrated into an effective control scheme for the system as a whole. These principles are illustrated by the following examples.
Mechanics and function of force sensors and length sensors
Motor coordination results from the interactions among commands from the central nervous system, the mechanical properties and conditions of body and environment, and sensory feedback. Sensory feedback from the muscles, skin and joints provides a critical link that communicates information to the central nervous system about the mechanical and metabolic changes that accompany the evolving movement. Some of this information is utilized for future planning of subsequent movements, and some is used for regulation of the ongoing movement. In the latter case, the fundamental mechanical variables of force, length, and velocity are monitored within muscles by Golgi tendon organs and by muscle spindle receptors, respectively. The corresponding neural signals are returned to the spinal cord, brainstem, or (in animals that possess one) somatosensory cortex to adjust patterns of motor neuron activation.
The adequate stimulus for each receptor is determined by the mechanical arrangement of the receptor and the muscle fibers, namely, in-series connections for the Golgi tendon organs and in-parallel connections for the muscle spindles (Fulton and Suner 1928). It has been argued that combining length and force feedback together at the motor neuron could regulate muscular stiffness (Matthews 1959; Houk 1972; Nichols and Houk 1976) and thereby promote stability and mechanical performance. Indeed, neural feedback does appear to regulate muscular joint and limb stiffness, but understanding how these receptors contribute to this regulation requires a deeper knowledge of their response properties and the synaptic distributions of the pathways emanating from them.
Golgi tendon organs can detect small contractile forces in motor units (Houk and Henneman 1967) and as a population, they provide a measure of total muscular force (Crago et al. 1982). There is some disagreement about the extent to which firing rate is linearly related to force (Jami 1992), but the relationship appears not to depend on previous movement history (Haftel et al. 2005). In contrast, the responses of muscle spindle receptors are related nonlinearly to changes in muscle length. First, these receptors are more sensitive to stretch than to release of muscle (Houk et al. 1981). Second, muscle spindles are responsive to small, rapid changes in length (Matthews and Stein 1969; Hasan and Houk 1975) and as such are particularly sensitive to vibration (Matthews and Watson 1981). Third, an assessment of sensitivity to velocity reveals a fractional power relationship between discharge rate and velocity. Finally, the responses of muscle spindles are influenced by prior mechanical history (Haftel et al. 2004). When the muscle is subjected to three sequential stretches, which take the form of triangular trajectories, the receptor responds with an initial burst followed by a dynamic response. For subsequent stretches delivered with little or no delay, no initial burst is present and the dynamic response is characterized by a reduced firing rate.
All the aforementioned nonlinear properties of the length sensors can be attributed provisionally to the mechanical properties of intrafusal fibers, the special muscle fibers within the spindle capsule that are associated with the sensory nerve endings (Matthews 1972). The response properties of the receptor therefore reflect the passive and active stiffness of the intrafusal fibers, which can be modified by the motor innervation of these fibers. The amplitude sensitivity follows from the tendency of cross-bridges to detach during stretch and from the velocity sensitivity to the effect of movement on detachment rate. The history dependence also reflects the influence of prior movement on the rate constants for attachment and detachment (Nichols and Cope 2004). The significance of these complexities is that the responses of muscle spindle receptors, rather than linearly representing muscle length and velocity, reflect the mechanical behavior (i.e., force–length, force–velocity and history-dependent properties) of the muscle itself. Intrafusal mechanics essentially constitute a model of the properties of the parent muscle. One important implication of these findings is that any signal in the central nervous system that represents length (or joint angle) or velocity must extract this information from the nonlinear responses (Cordo et al. 2002) of a population of diverse receptors.
The functional consequences of the nonlinear properties of muscle spindles can be appreciated by comparing the mechanical properties of muscles in the presence of and in the absence of reflex action. Under resting conditions, group Ia fibers from muscle spindles have a strong and excitatory effect on motor neurons (the stretch reflex), whereas group Ib fibers from tendon organs have relatively weak effects (Nichols 1999). When an active muscle is stretched, the response consists of the mechanical response of the motor units active prior to stretch (i.e., the intrinsic response) plus a component due to motor unit recruitment from the stretch reflex. The intrinsic response is an essentially instantaneous and spring-like change in force that is amplitude-limited (Joyce et al. 1969). The muscle then yields to a varying extent depending on the dominant motor unit type (Huyghues-Despointes et al. 2003a). It is at this point that the forces generated by additional motor units develop and the yield is compensated. Furthermore, the asymmetric properties of the muscle spindle receptors (see earlier text) are complementary to those of the muscle itself, so the net effect of reflex action is to provide for a response that is more spring-like and more symmetrical (Nichols and Houk 1976).
The compensatory actions of the stretch reflex can adapt automatically when the properties of muscles change. Movement tends to linearize the properties of muscle (Kirsch et al. 1994), most likely by accelerating the cross-bridge cycling rate (Nichols et al. 1999b). If muscle is stretched after a period of shortening, the intrinsic response is more spring-like and less amplitude-dependent (Campbell and Moss 2002; Huyghues-Despointes et al. 2003b). Under these conditions, the response of the spindle receptors is also modified (see earlier text), and a smaller and more delayed signal is sent to the spinal cord. The result is a spring-like response that is now dominated by the intrinsic properties of the muscle rather than by the stretch reflex. The reflex component is automatically timed and graded to maintain a spring-like muscular response (Huyghues-Despointes et al. 2003b), based on the complementary nonlinear properties of muscle and receptor. Reflex action, therefore, compensates for muscle nonlinearity through a predictive mechanism (Houk et al. 1981).
During locomotion, excitatory force feedback via a sensorimotor pathway mediating autogenic (i.e., to and from the same muscle) feedback is established (Guertin et al. 1995; Pearson 1995) and muscular stiffness increases (Ross et al. 2002). The action of force feedback, however, is simply to increase muscular stiffness, not to compensate for muscle nonlinearity, since tendon organs do not contain intrafusal fibers. Because the response properties of the muscle have already been compensated by the stretch reflex, the action of force feedback simply changes the stiffness of the muscle. Therefore, the contributions of length and force feedback are quite different. The former compensates for nonlinearity while the latter modulates the "spring constant".
Not surprisingly, length feedback is distributed locally to muscles that contain the muscle spindles and to closely synergistic muscles (Eccles et al. 1957; Nichols 1994). A group of synergists would tend to undergo similar mechanical changes and require similar extents of compensation. Excitatory force feedback, which is expressed during locomotion, also appears to be distributed mainly to the parent muscle and increases the stiffness and force output of the muscle. It may be speculated that this excitatory feedback is particularly important during tasks requiring large forces, such as walking up a slope (Gottschall et al. 2005). In contrast, inhibitory force feedback is distributed to muscles other than the muscle containing the tendon organs. These inhibitory pathways are present both during rest and during stepping (Ross et al. 2003). The rule consistent with the known distribution of this feedback is that force-related inhibition links muscles crossing different joints and different axes of rotation (Nichols et al. 1999a). From this organization, inhibitory force feedback is inferred to promote interjoint coordination and influence limb stiffness.
Timing is everything
In neuromechanical systems, time delays are inevitable (Fig. 4A). They occur in the acquisition of sensory information as well as in the processing of such information for modulating motor output. Even the sensors that encode motion information have lags in their response, which are prior to—and often much greater than—the lags in central nervous system processing (e.g., insect visual systems) (Harris et al. 1999). Some of these sensors—particularly mechanosensory structures—have inertial and viscous behaviors that lend additional delays to a system. There are further delays in the time between the stimulus provided to a muscle and the occurrence of peak force in that muscle. Because biological systems have damping and inertial components, additional time lags arise from their dynamic behavior. Thus, the time at which peak forces occur does not correspond to the time at which peak motion (speed or position) occurs, at least for very rapidly moving systems.
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A key problem is to understand the consequences of inevitable delays for control of neuromechanical systems. To explore these consequences, consider a "simple" neuromechanical system with feedback and delay: a spring and a dashpot with a delayed feedback sensor (Fig. 4B). At first glance, delay would seem to be a bad thing—compromising the ability of the system to respond to rapid perturbations. A plot of the gain (emergent motion divided by driving force) against the frequency of forcing, however, shows that delay actually increases the gain, giving a resonant-like behavior—much like the behavior of a spring-mass-dashpot system. Indeed, feedback delay acts very much like mass in forced oscillatory systems (Fig. 4C). This simple model illustrates three key points: (1) delays in neuromechanical systems can follow either from neural processing times or from the dynamics of the mechanical system; (2) delays can yield resonant behaviors; and (3) the overall dynamics of the system are understandable only in the context of information about all the delays as well as about the set of transfer functions that describe the system.
Expanding this simple control theoretic model to encompass a biological system with multiple inputs (many sensors) and multiple outputs (many actuators), each with potentially different delays, raises enormous challenges. Constructing such systems in a purely control theoretic framework requires knowledge of all the delays and a preconceived model linking specific actuators and actuator combinations to dynamic responses; this information is rarely available for biological systems. Moreover, there may be many distinct control models that maintain adequate performance under a particular set of conditions. Consideration of just one such model may not reveal the range of possible responses when conditions change, i.e., with the introduction or removal of delays from the system.
To explore the issue of delays in a neuromechanical system, Hedrick and Daniel (2006) focused on an inverse problem in the control of flight in the hawk moth Manduca sexta. Their study asked the following questions. (1) Are there multiple ways to control the wings for successful hovering? (2) Does delay in the controls of this system reduce the number of successful solutions to hovering? (3) Are there particular aspects of the feedback system for which delays are more critical than for others? Examining the effects of delay via an inverse rather than forward problem allows simultaneous consideration of its impact on the set of adequate models, as opposed to one specific control model.
The inverse problem was addressed using a micro genetic algorithm (µGA) coupled to a discrete-time, forward-dynamics simulation of flight (Hedrick and Daniel 2006). The algorithms sought sequences of wing beats that were adequate to the task of maintaining the moth's position and orientation within a small region of space, approximating hovering flight. The flight simulation followed from a set of coupled differential equations for the balance of forces and moments in the sagittal plane of the animal. A blade element wing model with experimentally derived force coefficients was used to predict the aerodynamic forces generated by wing motions (Hedrick and Daniel 2006). The resulting forces and torques were applied to a dynamic center of mass (CoM) to compute the resulting linear and angular accelerations. Wing motions for each stroke were specified as three angles: elevation, sweep and long-axis rotation. The time course of each of these angles was modeled as fixed-frequency (single component) sinusoids whose amplitude, mean frequency, and phase offset were determined by nine wing-motion parameters. A final parameter controlled the angle between the thorax and abdomen, allowing the simulated moth to change the location of the CoM relative to the wing hinge.
A genetic algorithm was used to search within the ten-dimensional space represented by the aforementioned control parameters. µGAs are a particularly effective method for searching widely within a rugged parameter space, such as that represented by the set of possible wing beats (Krishnakumar 1989). In practice, the µGA switched randomly between adequate controllers with every wing beat and, due to its stochastic nature, eventually failed to find an adequate controller and the simulated moth left the region of acceptable position and orientation.
The discrete time nature of the model adds an implicit one-wing-beat delay to all operations. The effects of delay on the simulated moth's performance were explored by adding additional delays to particular pieces of sensory information. We found that the inverse model operating under only the implicit one-wing-beat time delay due to the discrete time nature of the model can maintain steady hovering flight using a wide variety of control strategies (Fig. 5A and http://faculty.washington.edu/danielt/movies/gamoth.mov). Adding an additional one-wing-beat delay to all sensory inputs greatly reduced the number of adequate solutions and the model quickly reached failure conditions due to the stochastic noise inherent in the genetic algorithm approach (Fig. 5Aii). Restoring specific sensory inputs expanded the number of adequate solutions to the point where the model once again maintained steady hovering flight, albeit with reduced positional accuracy. The model was most sensitive to pitch rate and vertical velocity, and removing the delay in both these parameters had a multiplicative effect on the number of solutions.
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An inverse approach coupled with genetic algorithms capable of broadly searching a rugged parameter space allowed an understanding of the consequences of time delays in feedback controls of complex systems. Rather than focusing on how delay particularly determines the performance of a highly specified control system, genetic algorithms were used to uncover how delays may determine the range of reasonable solutions to a given task (in this case hovering). In a low-delay case, the results demonstrate that many controllers are capable of maintaining hovering flight in the simulated hawk moth. The existence of such diverse solutions for hovering follows from two points: (1) neuromechanical systems may accomplish a task effectively via multiple methods and (2) a behavior is specified as adequate, as opposed to being exactly determined, as it would be in a control model. Delays in the dynamics of the system on the order of one-wing-beat to all sensory systems (
40 ms) greatly reduced the number of adequate controllers. The fact that the number of successful controllers declines, however, does not necessarily imply that they are poorer controllers. The final outcomes might be "better" because of the emergent resonance properties that follow from delays in feedback control. It is likely that such controllers are more tightly tied to the exact delays in the system. |
Part III. Contribution of central networks to motor control |
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Central nervous control of basic oscillatory movements, as occurs in locomotion and feeding, involves CPGs. CPGs are networks of interneurons that are located within the central nervous system. These interneurons receive input from sense organs and send commands to motor neurons that activate the muscles. The frequency and timing of motor output are determined by the interaction between sensory inputs to the CPG network and intrinsic cellular and network properties of CPG interneurons (Grillner 1975
). Investigation of the cellular and network properties of motor circuits is a major subdiscipline of neuroscience. In contrast, many fewer studies attempt to investigate CPG function in a neuromechanical context. Within the context of neuromechanics, the goals are to understand (1) how cellular and network properties contribute to the emergent mechanical behavior of the animal and (2) how these properties are tuned to less flexible system parameters (e.g., body mass and shape, or neural delays that arise from conduction velocities and distances).
An understanding of these issues requires knowledge of the rules of operation that determine the behavior of CPGs in a sensorimotor circuit, as well as of what variable(s) are controlled via neural input. A major principle that governs the operation of CPGs is the idea that these circuits may be reconfigured to change their output. In other words, the population of interneurons that comprises the CPG may change, depending upon sensory input or other factors, and the pattern of neural output of the CPG changes with the population of participating neurons (Morton and Chiel 1994; Pearson 1995, 2000; Pearson et al. 1998). In this section, we present three examples to illustrate these points. The first example illustrates how the CPG for a swimming pteropod mollusk, Clione, is reconfigured to modulate swim frequency, and addresses the question of how the variable CPG output contributes to the emergent mechanical behavior during swimming. The second example investigates how neural (i.e., reconfiguration of shared interneuronal circuitry) and mechanical subsystems (i.e., reconfiguration of mechanical constraints) contribute to multifunctionality, or the use of evolved structures for multiple functions. This example also illustrates the principle that the function of motor neurons depends upon the mechanical configuration of the periphery. The third example discusses techniques using genetics and molecular and developmental biology to investigate the neuromechanics of swimming in zebrafish. Both spontaneously occurring mutants and genetically modified organisms have been useful for determining the roles of specific hindbrain interneurons in startle behavior and the effects of cell duplication on startle-circuit organization and function.
Central Control of Swimming Speed in Clione
In the pteropod mollusk Clione limacina, the parapodia are lateral, wing-like structures that produce relatively symmetrical dorsal and ventral bending movements to provide forward propulsive forces during swimming (Satterlie et al. 1985). The wings are flexible, and bend due to contraction of intrinsic sheets of muscle bundles found in their dorsal and ventral surfaces. Two sheets of oblique muscle bundles run across the entire dorsal face of each wing, just under the epithelium, at near-right angles to each other (Satterlie et al. 1985; Satterlie 1993). These striated muscle sheets co-contract to bend the wing dorsally. This organization is repeated on the ventral side, and bends the wing ventrally. The hemocoelic space between the dorsal and ventral muscle bundles functions as a hydrostatic skeleton for the wing, and contains three additional, less-dense layers of muscle. Two of these, the longitudinal and transverse retractor muscles, pull the wing into the body during protective withdrawal. The dorsoventral muscles, which run from the dorsal epithelium to the ventral epithelium, serve to decrease wing thickness and, presumably, to increase wing stiffness by pressurizing the hemocoel.
The swim musculature is striated whereas the other muscles are smooth. Within each swim muscle bundle, two types of muscle fibers are present. These are segregated into a slow-twitch fatigue-resistant group, which makes up the outermost one-third of each bundle, and a fast-twitch fatigable group, which forms the inner two-thirds of each bundle (Satterlie et al. 1990). This organization is repeated in all bundles of each muscle layer, and in each layer of the wings. The wing muscles are controlled almost exclusively by motor neurons within a pair of pedal ganglia. The pedal motor neurons innervate the ipsilateral wing via a stout wing nerve.
Slow versus fast swimming
Clione are negatively buoyant, so normal slow swimming consists of either "treading water" or slow forward (upward) movement. Wing beat frequencies during slow swimming are approximately one cycle per second, and if they produce forward movement, they do so at a rate of less than one body length per second. When the animal is stimulated mechanically on the tail or body wall, the wings respond with a dramatic increase in frequency (up to five cycles per second) and an increase in contractile force of the swim musculature. In addition, twisting of the flexible wings (pronation and supination) during swimming increases. Fast swimming can propel the animal forward at rates up to eight body lengths per second. The change from slow to fast swimming involves not only an increase in CPG cycle frequency, but also an increase in the force of wing-muscle contractions through recruitment of the large motor neurons that activate fast-twitch, fatigable swim musculature and enhance the contractile activity of the slow-twitch muscle.
Central control of swimming frequency
The CPG for slow swimming is comprised of two groups of antagonistic interneurons (dorsal and ventral swim interneurons—named for the bending movements they control), connected by reciprocal inhibitory synapses (Arshavsky et al. 1985a; Satterlie 1985; Satterlie and Norekian 2001). These neurons are found in the pedal ganglia and each one sends an axon branch across the pedal commissure to the contralateral ganglion. Neurons of each ipsilateral group are electrically coupled to each other and to their contralateral counterparts (Arshavsky et al. 1985a; Satterlie and Spencer 1985). Thus, dorsal swim interneurons and ventral swim interneurons form a "half-center"-like CPG in which simple alternation of activity forms a two-phase locomotor rhythm. Each interneuron fires a single broad action potential during its phase of activity and receives a single inhibitory post-synaptic potential (IPSP) from the antagonistic group during the contralateral wing contraction.
The increase in cycle frequency observed during the transition from slow to fast swimming is accomplished through a combination of cellular and circuit level modulatory changes in the swim CPG (Satterlie et al. 2000; Pirtle and Satterlie 2004). At the cellular level, swim interneurons exhibit a baseline depolarization, enhancement of post-inhibitory rebound, and spike narrowing, all of which contribute to the increase in firing frequency. At the circuit level, a contralateral pair of pleural interneurons is recruited into the swim CPG (Arshavsky et al. 1985b, 1989). Through synaptic connections between these interneurons and the CPG interneurons, the pattern generator is reconfigured to contribute to, and reinforce, cellular changes involved in increasing CPG cycle frequency. Two clusters of cerebral, serotonergic neurons have been found to produce all of the observed cellular changes in CPG interneurons that accompany the slow-to-fast transition, as well as reconfiguration of the CPG through recruitment of the pleural interneurons (Satterlie and Norekian 1995; Satterlie et al. 1995).
Neuromuscular control of swimming frequency
The swim CPG controls two groups of pedal swim motor neurons, one producing dorsal flexion of the wings, the other producing ventral flexion. This organization is duplicated in each pedal ganglion. Two types of motor neurons have been identified within each group of pedal neurons (Satterlie 1991, 1993). A single, large motor neuron (cell body diameter up to 80 µm) innervates the entire dorsal surface of the ipsilateral wing and a ventral counterpart innervates the entire ventral surface. The remainder of each group consists of small motor neurons (cell body diameter up to 30 µm), each of which has a restricted innervation field in the ipsilateral wing. Dual recordings from large and small motor neurons indicate that both receive similar monosynaptic inputs from CPG interneurons but the small motor neurons produce spikes in the appropriate half-cycle in both slow and fast swimming. In contrast, the large motor neurons show only sub-threshold synaptic activity during slow swimming and are "recruited" to the spiking mode during fast swimming (Satterlie 1991, 1993). Neuromuscular recordings confirm that small motor neurons innervate the slow-twitch, fatigue-resistant musculature monosynaptically, while the large motor neurons innervate both types of swim muscle monosynaptically.
Swimming mechanics
High-speed digital kinematic analyses of slow and fast swimming (Fig. 6) in both tethered and free-swimming Clione reveal differences in swimming mechanics at different swimming speeds. For example, the angle-of-attack changes from 42° to 52° in slow and fast swimming, respectively. The change in angle-of-attack is likely related to the innervation pattern of large motor neurons and the relative conduction times throughout the various parts of the wing. In addition, the wing-tip excursion does not appear to change from slow to fast swimming—the wing tips either nearly touch, or slightly overlap at each extreme of wing contraction at both speeds. This observation implies that the wings must be stiffer at higher swimming speeds in order to resist the increasing hydrodynamic forces acting upon them.
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Two groups of muscles appear to contribute to increasing wing stiffness at higher swimming speeds. During fast swimming, a small proportion (5–10%) of slow-twitch muscle cells change from swim-related phasic activity to high-frequency tonic firing (Fig. 7). The tonic firing appears to be associated with summation of post-spike depolarizing after-potentials, and can be triggered through serotonergic modulatory inputs to the musculature. In addition, a dense "grid" of dorsoventral muscles is present in the wings (Fig. 8), and these dorsoventral muscles appear to fire tonically rather than in phase with swimming movements. The motor neurons that innervate these muscles have not yet been identified, so their activity during slow and fast swimming remains to be measured. Together, these mechanisms likely increase wing stiffness during the change from slow to fast swimming.
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These studies demonstrate that modulation of swimming frequency in Clione involves a combination of central and neuromuscular alterations. Upon mechanical stimulation, both cellular and network-level changes in CPG configuration contribute to an increase in cycle frequency of central motor output. The increase in frequency of CPG output in turn increases swim-muscle contractility, the angle-of-attack of the wings, and wing stiffness. Together, these mechanical effects produce an increase in the speed of forward movement during swimming.
Neuromechanics of multifunctionality: feeding in Aplysia
Engineered devices are usually constructed deliberately to perform a single function. A piston within an internal combustion machine, a subroutine within a software package, or a supporting cable within a bridge, all play fixed roles. Creating devices that are functionally decomposable has great utility because designing the entire device is easier, individual components can be replaced rapidly, and it is possible to predict the effects of adding or removing a component. To create an engineered device that is multifunctional, multiple components (each of which can perform one well-defined function) are packaged together. A classic example is the Swiss Army knife. It can be used as a knife, scissors, awl, or screwdriver, among other functions. An engineered multifunctional device, however, has some drawbacks. Only one tool can be used at a time. Furthermore, if a tool has not been specifically designed, it is difficult to adapt an existing tool to a completely new function.
Evolved devices are usually capable of switching rapidly among multiple functions. The human hand can switch from pounding a stake into the ground, to unscrewing the lid of a jar, to playing piano. Turtles use their legs to paddle, walk, or scratch (Earhart and Stein 2000). The human tongue participates in swallowing, breathing, and speaking (Gestrau et al. 2005). Thus, evolved devices tend to show much greater adaptability and flexibility than engineered ones. They can be adjusted to perform new functions if the environment changes but may not perform any one function as well as an engineered device. Because evolution works on neural control and biomechanics simultaneously, it is also unlikely that evolved devices can be functionally decomposed as simply as engineered devices.
Multifunctionality in animals arises from both biomechanics and neural control. Musculoskeletal systems (e.g., limbs of vertebrates or insects), hydrostatic skeletons (e.g., worms), or muscular hydrostats (Kier and Smith 1985) have many more than the minimum number of degrees of freedom necessary to move throughout their workspace. As a consequence, there are multiple ways in which they may exert force or reach a particular endpoint. Similarly, neural circuitry shows great flexibility. Neural circuits may reorganize: connections may change or neurons may enter or leave a circuit, rapidly generating multiple motor synergies (Morton and Chiel 1994). Studies of stick insects, cats, and lampreys suggest that differential activation of pattern generators for individual joints underlies multi-limbed locomotion and allows local sensory input to shape and modify ongoing locomotor activity (Buschges 2005). Recent studies of hypoglossal neurons and motor neurons that control tongue musculature during breathing, coughing and swallowing (Gestrau et al. 2005) and of spinal interneurons during multiple forms of fictive scratching (Berkowitz 2005) suggest that shared interneuronal circuitry contributes to multifunctionality.
Feeding in Aplysia
To understand the neural and mechanical mechanisms of multifunctionality in a biological system, we studied three qualitatively different feeding responses in the marine mollusk Aplysia californica. The feeding apparatus, known as the buccal mass (Fig. 9), controls a central grasper. The grasper consists of a muscular structure, known as the odontophore, which is covered by a flexible toothed sheet of cartilage, known as the radula. The grasper can open or close and it can move toward the jaws (protract) or move toward the esophagus (retract). Protraction is mediated by the I2 muscle (Hurwitz et al. 1996), retraction is mediated by the I1/I3/jaw complex (Morton and Chiel 1993), opening is likely mediated by the I7–I10 muscles (Evans et al. 1996), and closing is mediated by the I4 muscle (Morton and Chiel 1993).
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By combining the elementary motor components (i.e., protraction and retraction, opening and closing) in different ways, the buccal mass can generate three qualitatively different feeding responses (biting, swallowing and rejection) (Fig. 10). During biting, the animal opens and strongly protracts the grasper, closes the grasper just prior to the peak of protraction, and then retracts the grasper weakly. During swallowing, the animal pulls food that it has successfully grasped into the buccal cavity by opening and weakly protracting the grasper, positioning the grasper further forward on food without pushing the food out of the buccal cavity, and then closing and strongly retracting the grasper. During rejection, the animal moves inedible material out of the buccal cavity by closing the grasper on the inedible material, protracting the grasper, and then opening and retracting the grasper.
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Mechanical control of swallowing
Swallows fall into two categories (Ye et al. 2006a