The origin and use of positional frames of reference in

BEHAVIORAL AND BRAIN SCIENCES (1995) 18, 723-806 Printed in the United States of America

The origin and use of positional frames of reference in motor control Anatol G. Feldman Institute of Biomedical Engineering, University of Montreal, Montreal, Quebec, Canada H3C 4A7 Electronic mail: [email protected]

Mindy F. Levin Research Centre, Rehabilitation Institute of Montreal, Montreal, Quebec, Canada H3S 2J4.

Abstract: A hypothesis about sensorimotor integration (the \ model) is described and applied to movement control and kinesthesia. The central idea is that the nervous system organizes positional frames of reference for the sensorimotor apparatus and produces active movements by shifting the frames in terms of spatial coordinates. Kinematic and electromyographic patterns are not programmed, but emerge from the dynamic interaction among the system s components, including external forces within the designated frame of reference. Motoneuronal threshold properties and proprioceptive inputs to motoneurons may be cardinal components of the physiological mechanism that produces positional frames of reference. The hypothesis that intentional movements are produced by shifting the frame of reference is extended to multi-muscle and multi-degrees-of-freedom systems with a solution of the redundancy problem that allows the control of a joint alone or in combination with other joints to produce any desired limb configuration and movement trajectory. The model also implies that for each motor behavior, the nervous system uses a strategy that minimizes the number of changeable control variables and keeps the parameters of these changes invariant. Examples are provided of simulated kinematic and electromyographic signals from single- and multi-joint arm movements produced by suggested patterns of control variables. Empirical support is provided and additional tests of the model are suggested. The model is contrasted with others based on the ideas of programming of motoneuronal activity, muscle forces, stiffness, or movement kinematics. Keywords: control variables; equilibrium points; frames of reference; kinesthesis; motoneurons; motor control; multi-muscle systems; pointing; proprioception; redundancy problem; synergy

1. Introduction According to the traditional view of motor control, the central nervous system (CNS) plans and executes movement in terms of biomechanical variables (movement trajectory, joint angle, final joint position, movement amplitude, velocity, amount of muscle activation or electromyogram [EMG] activity, stiffness, force or torque, etc.). The limitations of this approach are illustrated by the following analogy. Imagine that aliens have come to the earth and are trying to understand the mechanism of the behavior of, in their view, earth's most numerous creatures - cars. First, they would quantify the interactions of cars with the environment in terms of speed, displacement, forces, power, tire and road quality, and other directly measurable external variables. The observation of cars sliding on icy roads or accidentally colliding would convince the aliens that cars are unable to specify directly their movement trajectory or traction force to negotiate the environment. After years of such empirical studies they would conclude that the explanation of the behavior in terms of external variables represents the description of effect without the indication of the cause. Looking inside the car, one alien might discover some levers but it would take him some time before he could conclude that they might be the key to the solution of the problem. Finally, he could deduce that the active © 1995 Cambridge University Press

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behavior of cars occurs because of the independent specification of the levers' positions by an intrinsic part of the car, the driver. Unlike aliens, we neuroscientists are more interested in finding control variables (CVs) underlying the active motor behavior of the driver. For the most part, research has focused on analyzing active movements in terms of external variables without looking more deeply to reveal the independent "levers" used by the CNS to produce these movements. Even though we can directly record neuronal activity in the CNS of vertebrates during different motor tasks, do such studies provide information regarding the nature of CVs that produce active movement? An intensive discussion of this problem in several BBS target articles has been confounded by the lack of a consistent definition and experimental verification of CVs (Berkinblit et al. 1986; Bizzi et al. 1992; Gottlieb et al. 1989; Stein 1982). A distinctive definition of CVs (also called central commands) has been developed in the framework of the \ model (Feldman 1966a; Feldman & Levin 1993; Houk & Rymer 1981; Latash 1993) and will be discussed in detail in this target article. We begin by suggesting that CVs, first of all, characterize the ability of the CNS to produce voluntary actions and are defined as follows: (1) CVs are broadly specified by the nervous system independent of current external conditions and biomechanical variables. The terms "external conditions" and 723

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Feldman and Levin: Motor control "environment" are used synonymously and are associated with external forces (including inertial, reactive, and gravitational) acting on the body as well as their time and space characteristics. The term "independent" implies that the CNS may specify a constant value or a particular timing of a CV and maintain it regardless of the movement or changes in external conditions or afferent feedback from muscle proprioceptors. On the other hand, the system has the option to use this information to change the control pattern. As usual, the system's freedom of choice is limited. In other words, the system may be forced to change CVs under specific external conditions. For example, if somebody hits us on the back, some changes in CVs may be triggered to prevent falling. However, even in such cases, the possibility of varying the triggered control pattern still remains. In the above example, we can take a step forward, turn, fight back, or run away. Once the decision to change the control pattern has been made, the new pattern may, again, be performed independently of the current afferent feedback. (2) CVs may influence biomechanical variables. The latter are non-CVs because they are dependent on external conditions and thus do not meet criterion (1). For example, when we squeeze a cylinder, the length of hand and finger muscles remains the same regardless of our efforts. The dependence of muscle length and other kinematic variables on external conditions categorizes them as non-CVs (see also sect. 2). Note that the notion of independent and dependent variables in mathematics is conditional and as such these variables may usually be rearranged. Rearranging variables associated with active motor behavior may not be appropriate, however, because this may be equivalent to a rearrangement of cause and effect. Thus, the definition of CVs implies a functional hierarchy in motor regulation. We can conceptualize two functional levels: control and subordinate (previously called executive, see Feldman & Levin 1993). The first level specifies CVs, whereas the second continuously regulates biomechanical variables and other non-CVs as a function of CVs, afferent feedback, and external forces. This functional hierarchy may not correspond to an anatomical hierarchy in the CNS. In principle, the same CNS structures may contribute to the generation of CVs and non-CVs. Now we turn to another basic concept of the A model. In a recent interview Isaac Stem described the secret of his performance, saying that a musician "should play music in a frame of reference." This expression may touch on the strings of motor control specialists who want to know how the CNS generates frames of reference within which to specify coordinates for movements that are appropriately oriented in space. The problem of the frame of reference is closely related to the CV concept (sect. 3). It has also attracted much attention in numerous theoretical and experimental studies especially since Bernstein's work (Bernstein 1967; Bloedel 1992; Gielen & van Zuylen 1986; Paillard 1991; Pellionisz 1985; Pellionisz & Llinas 1982; Soechting & Flanders 1992). We will illustrate, in physiological terms, the central idea of the A. model, that the CNS organizes positional frames of reference or systems of coordinates for the motor apparatus and produces active movement by shifting the frames in space (Feldman & Levin 1993). Motoneuron (MN) threshold properties and proprioceptive feedback may be cardinal components of the mechanism that defines such frames of reference (sect. 3).

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Specifically, tliese components make MN recruitment dependent on muscle length when the latter exceeds a threshold length, A.. Parameter X is thus the point of origin for the positional frame of reference for the generation of active muscle force. By modifying A, the CNS specifies a new origin point of the positional frame of reference for force generating and neuronal components of the sensorimotor system. In this way, the system is forced to find a steady state (see sects. 10 and 11) that results in a new equilibrium body configuration in the new frame of reference. The hypothesis that intentional movements are produced by shifting the frame of reference will be extended to multi-muscle and multi-degrees-of-freedom systems (sects. 7 and 11.3). The A model also implies that, depending on external conditions, the same control process may be associated with different patterns of muscle activation and kinematics. Thus, these patterns are not programmed but emerge from the dynamic interaction of the system's components and external forces within the designated frame of reference. They may be a manifestation of the system's tendency to reach an equilibrium or steady state. The notion of steady states is the one defined in physics, particularly, the theory of dissipative systems in which irreversible processes play a central role (Andronov et al. 1959; Glansdorff & Prigogine 1971; Kugler & Turvey 1988; Saltzman & Kelso 1987). Like living systems, such systems are open and exchange energy and matter with the outside world to establish a macroscopic internal order. The fact that the system is open means that the environment may have an impact on the steady state of the system that is no less important than that of CVs. The equilibrium point (EP) concept is just one of the descriptors of the steady state emphasizing this constraint. For a single joint, the EP is a combination of the equilibrium joint position and the net muscle torque at this position. If an EP exists, it is defined by time-independent parameters (constants) of the system, provided that the current values of CVs are fixed ("frozen"). Because, in the equilibrium state, the net muscle torque equals the external (e.g., gravitational) torque, the EP characterizes the interaction of the joint with the environment and thus emphasizes that they act as equal partners in movement. The initiative to modify this interaction by changing CVs voluntarily rests with the organism. Because the EP depends on external conditions it is not a CV (see also sect. 10). It is an essential dynamic variable, however, responsible for movement production. The A model, originally published in Russian and later translated into English, has been popularized in the West. The idea of movement production via EP shifts, isolated from the other concepts of the A model, was used by Bizzi et al. (1984) in their version of the EP hypothesis. By considering the level of muscle activation as a variable underlying shift in the system's EP, cause and effect in movement production were rearranged and thus the original formulation of the EP concept was misinterpreted (for further discussion see Feldman 1986; 1992). More important, Bizzi's group did not comprehend the principles of sensorimotor integration underlying the A model (in contrast, see Houk & Rymer 1981). Criticism directed at the EP hypothesis did not, until recently, distinguish between the two versions. The tradition of confusion has been compounded by the recent target article by Bizzi et al. (1992) in which they trivialized the A model by making it quite similar and even subordinate to their model (see also Mclntyre & Bizzi 1993). We feel it is time to summarize the A model to

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Feldman and Levin: Motor control discuss its ideas, possibilities, and limitations without the confusions accumulated since its original formulation. It is quite natural in science to look for alternatives to existing views and hypotheses. However, attempting to "disprove" the X model without actually understanding it (e.g., Agarwal 1992; Bizzi et al. 1992; Bock & Arnold 1993; Burgess 1992) hardly seems to be a productive approach. 2. Pseudo-control models

T. = TK

Our approach to CVs will be both theoretical and experimental. We proceed with a discussion of models that try to explain movement production in terms of variables we consider to be non-CVs. We therefore call these models pseudo-control models. In all examples the system is presumed to be intact. 2.1. Torque, force, stiffness, kinematic, and inversedynamic models. Suppose we lift a weight from position a to b as shown in Figure 1A. At position a, we create a greater muscle torque and begin to lift the weight. When the weight approaches position b, we decrease the muscle torque and decelerate the movement until it stops in the desired position, b. From a physiological point of view, the description of this behavior in terms of classical mechanics disregards a specific problem. Note that the net muscle torque (equalling the gravitational torque of the arm) is the same in the two static positions in Figure 1A, that is, the two states of the system are indistinguishable in terms of muscle torques. Clearly, however, the nervous system discriminates between them: after a short external perturbation, say, in position b, the arm returns to the same position but not to position a. What variable(s), then, predetermined position a in one case and position b in the other? The question cannot be answered in terms of torque control models. Similarly, force control models (e.g., Bock 1990; Bock & Arnold 1993; Meyer et al. 1982; Schmidt et al. 1979) are unable to explain how the CNS chooses between different positions under isotonic conditions. Models treating muscle stiffness as a control variable have similar problems because stiffness is related to muscle force (e.g., Feldman & Orlovsky 1972) and may also be the same in different positions. (For a definition of stiffness see sect. 4.) Hollerbach and Atkeson (1987) and Soechting and Terzuolo (1986) suggest that the nervous system chooses desired movement kinematics such as effector trajectory, and then computes the muscle torques and muscle activations (inverse dynamics) necessary to implement the program. Supporting this idea is the observation that some kinematic relationships are relatively stable in spite of considerable changes in external conditions, endpoint effectors, and EMG patterns (Bernstein 1967; Fitts 1954; Hogan 1984; Lacquaniti 1989; Soechting & Terzuolo 1986; Viviani & Terzuolo 1982). However, kinematic invariants may be an inherent property of some dynamic systems rather than a programmed property (Bullock & Grossberg 1988; Glansdorff & Prigogine 1971; Kugler & Turvey 1988; Latash 1993; Schoner et al. 1990; van Emmerik 1992; see also sect. 11). The idea of inverse computations originated from robotics for which it may be practical. It has also been used successfully to improve the description of complex, multi-segmental movements in living systems in terms of mechanics. The idea may be misleading, however, when applied to control processes in such systems (see Hasan

EMG h = EMG.

Descending Inputs

Figure 1. Failure points of some control models (A, B) and illustration (C, D) that the control variable associated with active choice of position is independent of output activity of motoneurons (MNs). A: Net static elbow muscle torque (T) is the same in position a and b. Therefore, torque control models do not unambiguously indicate the variable associated with the choice of position. B: Tonic level of EMG in position b and c may be the same, demonstrating a similar problem as in A. C, D: Shading in rectangles represents the levels of descending facilitation to a MNs in an initial (b) and a final (c) position (as in B). Shaded parts of circles show the level of tonic activity of MNs and interneurons (INs) at these positions. The increased descending input in D results in surplus a MN activation that is nullified because of muscle shortening. The system arrives at position c in which the tonic level of MN activity is the same as in position b.

1991 and Loeb 1989). In essence, such models are a variety of torque or force "control" models that, as exemplified in Figure 1A, add little to the understanding of how the nervous system chooses between different positions. 2.2. Electromyographic models. The amount of muscle activation or EMG activity as well as the variables dependent on it (e. g., muscle force and stiffness) are also not CVs because they are affected by segmental reflexes (Doemeges & Rack 1992; Ghez et al. 1990; Granit 1970; Hoffer & Andreassen 1981; Houk & Rymer 1981) and, consequently, are a function of kinematic variables. In addition, if EMG activity were a CV, it could be regulated independently of static muscle force (a non-CV). This assumption obviously conflicts with the well-known monotonic EMG/force relaBEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



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Feldman and Levin: Motor control tionship described for some muscles (Bilodeau et al. 1990; Jongen et al. 1989; Milner-Brown & Stein 1975). Consequently, depending on the external force, the EMG level on one static position of the joint may be greater than, less than, or the same as that in another static position. The case in which the level of tonic EMG activity may be the same in two different positions ("isoelectric" conditions; e.g., for arm positions b and c in Fig. IB; see also Feldman 1986) is of specific interest: it shows that the level of muscle activation is not the primary variable that permits the CNS to choose between the two positions. Let us try to explain such a process in basic neurophysiological terms. Suppose there is a tonic descending facilitation of a and/or y MNs so that the arm is stabilized at position b with a specific level of muscle activation (Fig. 1C). To change this position, the CNS presumably specifies a new level of descending facilitation of a MNs (Fig. ID). For simplicity, the descending inflow to 7 MNs and interneurons (INs) remains the same. Is there any physiological variable that may be used as a measure of the facilitation of MNs? At first glance, the resulting increase in MN output or EMG activity can be such a measure. This could satisfy proponents of central programming of EMG patterns. Consider the behavior of the system in more detail, however. The descending facilitation gives rise to an increase in muscle activation and force resulting in muscle shortening. Because of properties of afferent feedback mediated by muscle afferents and segmental INs, the muscle shortening gives rise to a decrease in muscle activation. Thus, the surplus excitation of a MNs introduced by the descending facilitation will finally be nullified at a new joint position and the movement will cease. Now compare the initial and the final states of the system (Figs. 1C and D). MN activity is the same in both positions. The only difference is that the tonic level of descending inputs to the MNs is greater for the final position (c) associated with a shorter muscle length. From this example, it is obvious that the CVs that affect the equilibrium position are defined by the descending control influences to MNs regardless of the level of MN output (the amount of muscle activation). Note that Sherringtons metaphor that the MN is the "final common path" (Sherrington 1906/1947) is usually interpreted to mean that all neuronal influences on MNS can be measured in terms of their activation. The above discussion rather favors the Bernsteinian view that descending control influences to MNs cannot be measured in terms of muscle activation (Bernstein 1935). Another class of models is based on experiments in deafferented and curarized preparations in which actual or fictive movements, including locomotion, have been observed. This has led to the concept of the central pattern generator (Brown 1914; Grillner 1975; Orlovsky & Shik 1976; Pearson 1985; Rossignol et al. 1988; Stein 1984; Taub et al. 1975). Taking into account the substantial motor deficits in deafferented subjects (Blouin et al. 1993; Ghez et al. 1990), the concept can hardly be interpreted in the sense that movements basically arise from central pattern generators with afferent feedback playing only a modulatory role. However, some models are intrinsically based on such an interpretation. In these models, MNs are condsidered linear summators such that muscle activation (a) would consist of two additive components: a reflex component (a r ) which is dependent on proprioceptive feedback, and a central one ( a j , which is independent of it:

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a = ar + ac (1) Equation (1) shows that MNs can be activated in the absence of reflexes as observed in deafferentation experiments. The results of such experiments can hardly be generalized to the intact system if one takes into account the immediate and long-term consequences of deafferentation such as sprouting and synaptic plasticity (Goldberger & Murray 1974; Hellgren & Kellerth 1989; Kaas 1991). Equation (1) is obviously inconsistent with some properties of the intact system. It is known that sudden unloading produces a silent period in the tonic MN firing of a normally innervated muscle (e.g., Angel 1973; Feldman 1986; Forget & Lamarre 1987; Gerilovsky et al. 1990; Hugon et al. 1982). According to Equation (1), unloading should only lead to the disappearance of the reflex component (a r ) but experiments show that all activity (a) is suppressed. The explanation maybe simple: because MNs are threshold elements, one input may become subthreshold for producing MN firing if the other input is withdrawn. Thus, although the idea of decomposing the output activity of MNs into reflex and central components underlies several motor control models (e.g., Bizzi et al. 1992; Bullock & Grossberg 1988; Gottlieb et al. 1989; Loeb & Levine 1990; Mclntyre & Bizzi 1993; Zajac & Gordon 1989), it may misrepresent the process of sensorimotor integration at the level of MNs. A plausible description of higher brain functions and motor production may be obtained in neuronal network models (Alexander et al. 1992; Bullock & Grossberg 1988; Douglas & Martin 1991; Fetz 1992; Grossberg & Kuperstein 1989). The problem of CVs has still to be resolved in the framework of such models. Those treating motor control in terms of the specification of kinematic variables or EMG activity seem less promising.

3. Control variables and positional frames of reference for motoneurons We can interpret the CV concept physiologically by considering the effects of a muscle stretch or a voluntary movement on the MN membrane potential. Some changes may be produced monosynaptically by muscle afferents or polysynaptically by spinal and supraspinal neurones participating in reflex loops. Whatever the specific details for different muscles, we assume there is an increase in MN depolarization during passive quasistatic muscle lengthening. We also assume there is a component of change in the membrane potential, 8VC, produced by descending systems that may be independent of muscle afferent feedback. This component is thus considered as a CV.1 It is interesting that this electrical measure may be represented in terms of a variable having positional dimensions. In Figure 2 (left panel), V is the initial membrane potential of the MN (vertical axis) at the initial muscle length, x, when descending control signals are fixed. Because of proprioceptive feedback, the state of the MN depends on muscle length (horizontal axis). A quasistatic stretch of the muscle results in an increasing depolarization of the MN as a function of x (diagonal line) because of predominant facilitation from length-sensitive afferents (i.e., muscle spindle afferents in most muscles). The slope of this line represents the positional sensitivity of the stretch reflex at the subthreshold level. The threshold membrane potential, V + , and consequently, the recruitment of the




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Feldman and Levin: Motor control

MOTONEURON Effects of inputs reflex

central

X Muscle length Figure 2. Identification of control variables at the level of the a MN in the X model. Left panel: Effects of reflex inputs on the MN membrane potential. Slow muscle stretch from initial position (x) results in a length-dependent (8Vr) increase in membrane potential (V). Threshold membrane potential (V+) is reached at length X and tonic MN firing begins. Right panel: Two measures of control variables produced by descending systems - the lengthindependent increment of MN membrane potential (8VC) and threshold muscle length (8X). The latter consists of two components: one (8Xd) is associated with direct synaptic inputs to the a MN and the other (8X:), with indirect inputs mediated by 7 MNs and muscle spindle afferents.

This notion is fundamental in the X model and may be applied to multi-muscle and multi-degrees-of-freedom control (see sects. 7 and 11.3). We continue to discuss some possible physiological mechanisms of X regulation. In the model, any type of length-sensitive afferent feedback is sufficient to provide a basis for the regulation of X via independent inputs to a motoneurons. However, 7 innervation of muscle spindles maybe an important additional source of such regulation. It is known that for skeletal muscles there are three types of MNs: a, (3, and 7 MNs. The first and the third innervate extra- and intrafusal muscle fibers, respectively, whereas the second supplies both types of fibers (Boyd et al. 1977; Matthews 1981). MNs innervating intrafusal fibers are subdivided into static and dynamic MNs affecting position and velocity gains of muscle spindle afferents, respectively. Muscle afferents may provide feedback not only to a MNs but also to static and dynamic 7 MNs (Appelberg et al. 1986; Grillner 1969; Wadell et al. 1991). Control inputs to a and 7 MNs can be coordinated in different ways depending on the motor task (Prochazka et al. 1985). In the X model, the decrement 8X results from both direct influences of the control signals on the a MN and indirect influences mediated by active static (} and 7 MNs, muscle spindle afferents, and INs. The direct and indirect components of the CV are denoted by 8Xd and 8XS. We assume that they are additive in terms of changes in X (Fig. 2, right panel): 8X = 8Xd + 8Xj

MN, will be reached at a muscle length X. The effect of a change in the tonic control signal (Fig. 2, right panel) can be measured by a decrement (8VC) in the membrane potential at the initial muscle length. Now, muscle stretch will result in MN recruitment at a shorter muscle length. Thus, the same control signal is expressed as a decrement (SX) of the threshold muscle length at which the MN is recruited. This decrement is independent of the actual muscle length, x, and thus is a CV. The above considerations illustrate that MN threshold properties and proprioceptive feedback may be essential components of the mechanism that relates basic electrical parameters of the MN to space variables so that the current and threshold membrane potentials are associated with the current and threshold muscle lengths, respectively. As a result, MN functioning becomes associated with external space. It is not the actual muscle length, but the difference between the actual and threshold length that is essential for MN recruitment. By modifying X, the control level "tells" the MN in which part of the physiological range of muscle length to work to compensate the load. These theoretical results may be understood in terms of physics. Movement of a body is defined as a change in its position with respect to another object, frame of reference, or system of coordinates. Inherent in the concept of the frame of reference is Galileo's principle of relativity of motion: movement can be produced by shifting the frame of reference. The threshold X. may be considered as the origin point of the frame of reference for positional recruitment of MNs. By modifying Xs, the control level specifies a new reference point for positional recruitment of MNs (Fig. 2, right panel) and thus produces movement (sects. 10 and 11). Thus, shifts in the positional frame of reference may underlie movement control, whereas MN activation and force production may be a consequence of this process.

Both inputs produce a broad range of shifts in the positional frame of reference for MN recruitment. As a consequence, the range of regulation of actual muscle length and force is also maximized (Feldman 1986). It is presumed that the X is affected by a change in the level of presynaptic inhibition of ot MNs by descending systems combined with opposite changes in the level of postsynaptic facilitation. It has been shown experimentally that the reflex threshold may be diminished by stretching the antagonist muscle or stimulating its nerve (Feldman 1979; Feldman & Orlovsky 1972; Matthews 1959; Nichols 1989; see Fig. 5C). Thus, some changes in \ may result from reflex intermuscular interactions (Feldman 1986; Feldman et al. 1990) mediated, in particular, by la reciprocal inhibitory interneurons (McCrea (1992). As a consequence, only the independent change in X (8X) but not X itself, may be considered as a CV. (For a more detailed description of how reflex intermuscular interaction is represented in the X model see Feldman 1992 and sect. 8.) The properties of the X model were addressed in early experiments on humans (Asatryan & Feldman 1965; Feldman 1966a; 1966b; 1979). Because CVs are independent variables, they can be held constant during postural control tasks in spite of perturbations in the external load that result in changes in joint position, force, and EMG signals. In these experiments, subjects specified the same initial elbow joint angle against a load-opposing flexion created by a weight attached to a horizontal forearm manipulandum (Fig. 3, filled dots). Thus, they specified the same combination of initial torque and position (EP) in each trial. With vision blocked, part of the load was suddenly removed by an electromagnetic device. The change in the load was varied from trial to trial. The subjects were instructed "not to intervene" or "not to correct the arm deflections." Position, torques, and EMG activity of elbow flexor and extensor BEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



(2)

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Feldman and Levin: Motor control MN recruitment (Feldman 1986; Feldman & Levin 1993). Note that when the subject changed the initial combination of the torque and angle, he made an active movement. In other words, he produced an action that could only have been made by a change in CVs. The fact that the Xs were different for different torque/angle characteristics indicates that 8\ is a CV. Three additional experiments have been used to test the hypothesis that this behavior is associated with invariant values of CVs. Two such tests were concerned with the magnitude of the load and the timing of loading. In such experiments, the magnitude of the load depended on the arm position. The coefficient of this dependency is called the positional load gradient. It was shown that the muscle torque/angle characteristic was insensitive to changes of the gradient of the load (from positive to negative values) and to the timing of unloading (single or double steps; Fig. 4 A-D; Feldman 1979). The reversibility of these effects was tested by reintroducing the load. If the reloading was gradual, the arm returned to the initial position (equifinality shown by position traces in Figs. 4 E and F). These three properties suggested that the subject did not change CVs

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Figure 3. Static torque/angle characteristics for the elbow flexors (upper curves) and extensors (lower curves) recorded in unloading experiments using the "do not intervene" paradigm. Different active characteristics result from different combinations of initial muscle torques and positions (filled circles) reproduced by the subject before unloading. Open circles show combinations of steady state values of the same variables after step-like decreases in the initial load. The dashed line shows the passive joint characteristic when both muscle groups are relaxed. Tonic EMGs of a flexor muscle are shown for one of the curves. The parameter \ for a specific active characteristic corresponds to the muscle length at which the characteristic begins to deviate from the passive one (from Feldman 1986). muscles were recorded. The results of such experiments revealed a monotonic relationship between the final (static) values of muscle torque and joint angle (termed the torque/angle characteristic). The tonic level of EMG signals was not constant, but was related to torque (Fig. 3). This implied that the spring-like behavior of the joint was mediated not by active muscles perse (as is the case in other models, e.g., Hogan 1984), but by the whole system, possibly including supraspinal structures (see Adamovich 1992 for further discussion). Similar behavior has also been observed in more recent work (Davis & Kelso 1982; Gielen et al. 1984; Gottlieb & Agarwal 1988; Latash 1993; Levin et al. 1992; Vincken et al. 1983). Figure 3 shows that when the subject changed the initial combination of torque and position, unloading revealed a different torque/angle characteristic. Although the characteristics were similar in shape, they diverged from different points of the passive torque/angle characteristic of the joint (Fig. 3, dashed line). The divergence point of the active characteristic corresponded to the threshold length, \ , for

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Figure 4. Three tests of the invariance of the static elbow torque/angle characteristics obtained as in Figure 3. A: Test 1. S, and S 2 represent families of position-dependent loads. Different families permit the measurement of different points, after steplike drops in the load, all found on the same elbow characteristic (solid line; the upper dot shows the initial combination of muscle torque and position). B-D: Test 2. The final position is the same after a 20 N load (moment arm is 0.35 m) is removed in double- (B, C) or single-steps (D). Initial position (9) and torque (T) are the same in all three series. Numbers in brackets: the magnitude of steps in Newtons. Interstep interval (msec) is shown below each pair of traces. E - F : Reversibility test in which the load was diminished and then restored. In one set of trials (E, F; only positional traces are shown) the reloading was done gradually, using an elastic load. In the other set (G), the reloading was done by a falling weight. Thus, the initial period of the reloading was associated with the absorption of the kinetic energy of the weight although the final value of the load was the same as before the unloading. Note movement equifinality in E and F but not in G (from Feldman 1979, reproduced in Feldman & Levin 1993).




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Feldman and Levin: Motor control tions during rhythmic arm movement and handwriting, respectively, resulted in phase resetting. It is interesting that Lackner and DiZio (1993) observed reaching errors (inequifinality) when subjects produced arm movements in a rotating room. They associated these errors with the action of Coriolis force. This force is zero once an arm movement ends and, according to the EP hypothesis, should not affect the end arm position. The errors may be associated with a change in perception of the target position in the rotating room, however, rather than with Coriolis or centrifugal forces. For example, during rotation of the body, the head tends to rotate passively in the opposite direction leading to a change in its position relative to the body. This may result in a gaze shift and, as a result, in the incorrect specification of CVs.

during the experiments and therefore the torque/angle characteristic was called the invariant characteristic (IC). The unloading-reloading test has also been used to demonstrate that specific load perturbations may break equifinality regardless of instruction (Feldman 1979). When, in such a test, reloading was abrupt, the arm undershot the initial position (Fig. 4G). Similar findings of the absence of equifinality in perturbation experiments have led some authors to conclude that the IC concept was not valid (e.g., Gottlieb & Agarwal 1988). However, rather than negating the EP hypothesis, these findings may merely reveal that there are limits to the subjectss ability to hold CVs constant despite the instruction not to intervene. A similar idea has been suggested by Kay et al. (1991) and van Emmerick (1992), who reported that external perturba-

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Figure 5. Families of force/length curves for m. gastrocnemius in the decerebrate cat obtained by slow muscle stretch during different levels of tonic background stimulation of various descending systems (Deiters nucleus, DN; pyramidal tract, PYR) and stretch of antagonist muscle (tibialis anterior, TA). A: Initial curve (0) is shifted to the left during bipolar stimulation of ipsilateral DN at different strengths (2, 3, and 4.5 V; 70 imp/s; pulse duration 0.1 ms; 0.2 — 0.3 mm interelectrode distance; electrode resistance ~100 kOhm). The lowest curve (not labeled) is the passive characteristic after muscle paralysis. B: The effects of isolated or simultaneous stimulation of DN and PYR. Different characteristics were obtained with isolated stimulation of DN at 10 or 12.5 V. Stimulation of PYR (2 V) has no effect on the passive characteristic (0). Combining DN (12.5 V) and PYR (2 V) stimulation results in the same characteristic as when DN alone is stimulated at 10 V. C: Shifts produced by stimulation of DN in isolation (0 - 15 V) or in combination with TA stretch (DN, 15 V + TA stretched by 0.3 and 2 kg.wt). The lowest curves in B and C are passive muscle curves. D: Electromyographic evidence for a decrease in the threshold of M N recruitment under the influence of tonic stimulation of DN. Upper curves were recorded without stimulation. Lower curves were recorded during DN stimulation at 6 V. Muscle was stretched at a slow rate of 3 mm/s (adapted from Feldman & Orlovsky 1972 and Feldman 1979). BEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



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Feldman and Levin: Motor control The absence of equifinality after deafferentation (Day & Marsden 1982) may be predicted by the X model, which assigns a fundamental role to proprioception in the normal functioning of the motor system. In particular, deafferented muscles, unlike normally innervated muscles, display a significant hysteresis (Nichols & Houk 1976), which may lead to nonequifinality of movement regardless of a specific control strategy. Additional support for the A. model comes from experiments in decerebrated cats. It was shown that X can be modified by a change in the activity of 7 MNs by selective anaesthesia of their axons (Feldman 1979; Feldman & Orlovsky 1972; Matthews 1959). Feldman and Orlovsky (1972) tonically stimulated different descending systems at the level of the brainstem (Fig. 5), imitating independent descending influences on a and 7 MNs. Under these background conditions, ankle extensors were then stretched at a slow velocity and EMG signals, muscle force, and length were recorded. At a given level of tonic descending activation, muscle EMG activity arose at a specific threshold length A. and increased with muscle stretch. Increasing tonic stimulation of the Deiter's nucleus (Fig. 5A) gave rise to a decrease in the X resulting in a shift of the static force/length characteristic to the left. On the other hand, stimulation of the pyramidal tract (Fig. 5B) or medial reticular formation (not shown) had the opposite effect. Nichols & Steeves (1986) obtained similar results observing, in addition, an independent change in the slope of force/length characteristics during stimulation of the red nucleus. Indeed, these stimulation experiments are artificial. It is not obvious that in the intact nervous system, descending signals are independent of peripheral ones. Supraspinal structures, including the motor cortex and cerebellum, may participate, possibly via transcortical loops (e.g., Goodin et al. 1990), in positional recruitment of MNs and therefore in the generation of force/length characteristics. Nevertheless, it is reasonable to assume that at least some component of these descending signals may be independent in intact subjects and may influence the threshold X. The results of these experiments are consistent with this hypothesis. 4. Positional reference frame for a single motoneuronal pool - static activation area How are the positional frames of reference of different MNs related? Because MNs are recruited according to the size-principle (Henneman 1981), there should be a strong correlation between the two geometrical factors (the size of an MN and its threshold length) with the natural conclusion that the smallest-sized MNs should be recruited at the lowest threshold lengths. Under static conditions, MNs are active in the muscle activation area defined by the inequality x- A > 0

(3)

where x is the actual muscle length and X is the threshold muscle length (Fig. 2A). In the suprathreshold area, muscle activation (a), that is, some measure of the number of active MNs and their firing rates, is an increasing function of x — A.. Each MN has its own threshold, X^, for recruitment: XO), X, . . . , X

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Commentary/Feldman and Levin: Motor control coded in terms of shifts of equilibrium states or patterns of muscle excitation that code for position and provide the required forces or in terms of some other control strategy remains unanswered. We suspect that any alien coming to earth and informed of the existence of the independently controlled variables R, C, and u will still be as confused as the rest of the field of motor control judging by previous commentaries on equilibrium point models (Cordo & Hamad 1994) and the commentaries that we envisage will emerge on this target article.

The lambda model is only one piece in the motor control puzzle Jeffrey Dean Abteilung 4/FakultSt fur Biologie, Universitat Bielefeld, D-33501, Bielefeld, Germany. [email protected]

Abstract: The lambda model provides a physiologically grounded terminology for describing muscle function and emphasizes the important influence of environmental and reflex-mediated effects on final states. However, lambda itself is only a convenient point on the length-tension curve; its importance should not be overemphasized. Ascribing movement to changes in a lambda-based frame of reference is generally valid, but it leaves unanswered a number of questions concerning mechanisms.

A major conceptual difficulty in motor behavior arises from the linkages among different parameters imposed by physics or physiology. The misunderstandings mentioned in Feldman and Levin's (F&L's) Introduction are just one example. A related problem is that many different control strategies produce behavior so similar that they cannot be discriminated experimentally (Morasso et al. 1994; Nelson 1983). Hence, an important goal is to sort out regularities by necessity from those by choice and then to understand how the nervous system makes choices where it has the freedom to do so. Faced with this problem, the inclination is to look for a model and terminology that sort things out neatly and simplify control: the coordinate system, frame of reference or control variable serving this purpose has become a kind of Holy Grail. The notion of positional frames of reference defined in terms of the lambda model is one attempt. Does it succeed? Yes and no. Animals move in space, so controlling position is obviously important. To do so, they modulate muscle forces, so dynamics and effector action are also important. Inverse kinematic and dynamic models provide a formalism for linking these levels in robotics. The prime virtue of the lambda model is that it links muscle activation and position in a manner grounded in physiology. One criterion of a good model is whether it focuses attention on significant features. The lambda model does this in several ways. First, it emphasizes that actual configurations reflect interactions between states established in the musculoskeletal system and the environment, but the further discussion does not go far enough. The difficulty is apparent in the attempt to distinguish execution and control, with control variables being independent of environmental influences. As F&L acknowledge, this distinction is clear only if high-level environmental influences, which can alter the control variables, are ignored. Moreover, the distinction need not have a clear anatomical correlate. Thus, the separation seems artificial, valid only for a narrow focus on the motoneuron-muscle level. The difficulty is inherent in the language of a control hierarchy. Considering the whole as a dynamic system would seem more appropriate. Similarly, some of F&L's arguments concerning ambiguous configurations and interpretations of motor activity, advanced to discredit alternative models (sect. 2), rely on ignoring the history of the system, that is, the sequence of positions by which a joint arrives at one position or another. Second, the lambda model underlines the importance of mo-

toneuron thresholds, whether or not one accepts the explicit association of this threshold - as a length - with a frame of reference. The flight system of locusts is a vivid example where this nonlinearity in moto- and interneurons provides a simple gating mechanism: course deviation generates a continuous turn command that only affects motor output during and close to the muscle s normal phase of activity (Reichert & Rowell 1986). In this case, however, the length associated with the threshold does not seem particularly relevant - although it can be defined; what matters is the bias on the whole cycle of oscillation in the neuron's potential. Focussing strongly on lambda as a position, rather than as a parameter useful for describing muscle activity, gives it too much importance. Third, I agree completely that approximations rather than brittle, exact specifications may be adaptive in biological systems, even if they do not satisfy an engineer. However, this fact also allows control algorithms quite different from the still rather exact, analytic lambda model. In the stick insect, one tarsus is placed near another based on neural comparisons much simpler than exact trigonometric calculations (Brunn & Dean 1994; Dean 1990). A second criterion is whether a model simplifies discussions. Here, too, I think making lambda the basis for a shifting coordinate system or frame of reference, although formally correct, places too much emphasis on one particular point of the motoneuron-muscle response curve. To the extent that lengthtension curves for different lambdas maintain equal separations with changing muscle length, lambda is the most convenient descriptive parameter. To the extent that they are not parallel, it seems the focus should be on the part of the curve where the system is operating. If the state is close to the length lambda (which may frequently be the case), then fine. If not, and lambda must be changed to achieve the desired behavioral output, lambda seems less useful as a frame of reference; that is, if you have to change the frame of reference to achieve some goal, then by implication the goal is defined some other way and you might as well use that system as a frame of reference. A more appropriate focus is on the actual state of the system and its change with time, in terms of dynamics and attractors given various internal and external conditions. Similarly, lambdas do change when internally specified movements are made, but viewing the change in coordinates as the primary cause rather than a possible descriptive framework is not helpful and the appeal to Galileo s principle is not pertinent. The decomposition of control activity into reciprocal and coactivation components is also analytically correct and useful, but the system need not explicitly make this separation. A third criterion is whether a model simplifies solutions. Here, more is promised than delivered. The section on three-joint movements promises a solution to the redundancy problem but relegates this solution to the selection of weights for alternative synergies, and this, in turn, to the conservative control principle. Once the weights are determined, the lambda model does lead to appropriate motor commands, but this is not the same as solving the redundancy problem (see Cruse et al. 1993, and references therein). Even casual observation reveals that angles are not chosen randomly in postures and movements. The systematic choices can be described as an optimization based on separate cost functions for each joint (see Cruse et al. 1993). This criterion represents a reduction in the degrees of freedom, but one that does not correspond to a conservative control in the framework of the control variables discussed here. For arm movements (Cruse & Briiwer 1987; Dean & Briiwer 1994) and for walking in the stick insect (Eltze 1994), a variety of different criteria, expressed in different frames of reference, affect movement and movement planning. What counts for the animal is not merely simplicity of control, as Feldman and Levin authors imply, but performance, and the latter usually reflects a combination of criteria that vary according to task requirements.




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Commentary/Feldman and Levin: Motor control

Natural unconstrained movements obey rules different from constrained elementary movements Michel Desmurget, Yves Rossetti, and Claude Prablanc INSERM Unite 94, Vision et Motricte, 69500 Bron, France. prablanc@f rmopi 1 .cnusc.fr

Abstract: The concept of a conservative control strategy minimizing the number of degrees of freedom used is criticised with reference to 3-D simple reaching and grasping experiments. The vector error in a redundant system would not be the prime controlled variable, but rather the posture for reaching, as exemplified by nearly straight displacements in joint space as opposed to curved ones in task space.

The concept of "sensory motor integration" proposed by Feldman and Levin (F&L) can be credited with being one of the most heuristic theoretical constructs in the field of motor control. However, the empirical arguments supporting this hypothesis derive mainly from very simple planar movements generally restricted to one joint and one degree of freedom, and the X model has received little experimental support in multi-joint control. We would like to discuss here whether it is possible to understand complex motor behaviors by focusing only on elementary motor responses. More specifically, we will describe evidence that shows that the rules governing redundant unconstrained motor systems may be quite different from those acting on completely constrained motor systems. The generalization from single- to double- and triple-joint pointing movements proposed by F&L calls for the concept of "conservative control strategy," which defines the tendency of the control level to "minimize the number of modifiable CVs" (sect. 11). One of the main correlates of this hypothesis is "the minimization of the number of degrees of freedom - or joints - used in a motor task." Such a strategy, which analytically provides a considerable simplification of motor control processes, is generally implemented in robot arms (Hollerbach 1988). It has also received support from the experimental data on bi-dimensional movements, showing a proximo-distal dissociation when subjects are asked to point along the sagittal plane toward visual targets presented at different orientations (Soechting 1984). However, this tendency to "minimize the number of joints participating in the movement" (sect. 11.3) does not apply to unconstrained behavior, as demonstrated by a recent experiment (Desmurget et al. 1995). Indeed, when subjects were asked to reach and grasp a cylinder presented at different tilts in the fronto-parallel plane, the final posture reached by the upper limb was different at both proximal and distal joints. In other words, all the available degrees of freedom were used by the CNS, although avoiding combined azimuth, elevation, and rotation movements at shoulder level would have simplified the control pattern by circumscribing hand orientation to forearm rotation. This result rules out the concept of "conservative control strategy" as being a general rule used by the CNS to program the movement; it rather favors other general strategies such as the minimum torque change hypothesis (Uno et al. 1989) or static quadratic minimizations of muscle force over joints (Cruse et al. 1990; Hogan & Mussa-Ivaldi 1992). Another topic we wish to address in this commentary concerns the general problem of trajectory formation: it is worth noting that the F&L model as well as many models of the saccadic oculomotor system (Becker &Jiirgens 1979; Robinson 1975) refer implicitly or explicitly to the notion of motor error (ME), but this shared conceptual referent conceals fundamentally different ways of encoding ME. In the oculomotor system this motor error is simply derived from the retinal vector between the initial direction of gaze and the target. Recent motor control hypotheses depict saccadic eye movements as resulting from displacement codes rather than positional codes and do not require knowledge of initial gaze position. Such a notion has received electrophysiological support: the superior colliculus, the main structure controlling

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the eye saccade, contains neurons that drive vectorial displacements of the gaze axis irrespective of its initial position (Munoz et al. 1991). This vectorial mode of operation for gaze saccade control also works in a same way under kinematically redundant eye-head coordinated gaze shifts. Indeed, if a combined eye-head saccadic orientation is experimentally perturbed by suddenly blocking the head (Fuller et al. 1983; Guitton & Voile 1987), the gaze shift is correctly achieved by increasing the on-line contribution of the eye displacement caused by the mechanical redundancy. Thus, seeing the motor error as a Control Variable (CV) also applies fully to gaze shifts. Concerning the skeleto-motor system, there is no general agreement for the existence of a motor error signal, though this parameter has often been proposed as the control signal for driving the hand to the target (Hoff & Arbib 1992; Jeannerod 1988; Pelisson et al. 1986; Prablanc & Martin 1992). Referring implicitly to this "vectorial" conception, F&L's model presupposes, to construct the velocity vector (the derivative of motor error), the knowledge of the initial hand position through a direct transformation of the shoulder-elbow system. This initial prerequisite contrasts with the absence of an a priori knowledge of the final postural state to reach. F&L's conception thus directly contradicts other models referring both to the concept of equilibrium point (as underlined in sect. 1; Bizzi et al. 1992; Hatsopoulos 1994; Polit & Bizzi 1979) and to the general idea that the posture to achieve is computed before movement onset (Flanders et al. 1992; Rosenbaum et al. 1993). The advantage of F&L's hypothesis is that there is no need for an inverse transform computation, which becomes all the more complicated because there is joint redundancy. However, as previously emphasized, the X. model was initially developed on very simple, constrained motor behaviors and its generalization to complex, unconstrained movements is not obvious. Again, Desmurget et al. s above-mentioned experiment seems incompatible with F&L's model, and with the general idea that movement is programmed as a vector in task space. Indeed, when grasping movements were performed toward a cylinder presented along different orientations in the fronto-parallel plane, the hand path was highly curved, contrasting with the straight paths obtained under planar constrained movement (Flash & Hogan 1985; Morasso 1981). The "motor error vector" was therefore, in our unconstrained task, not directed toward the target as postulated by F&L. Moreover, despite a curved hand path in task space, the trajectory observed in joint space was nearly straight, indicating a linear relationship among most degrees of freedom implicated in the movement. This general synergy was accompanied by a strong invariance of upper limb final posture with respect to object tilt: when object orientation was unexpectedly modified at movement onset, the final angular configuration of the limb was identical to that obtained when the object was initially presented along the orientation reached after the perturbation. This result would lead to a reformulation of F&L's hypothesis, and to the suggestion that natural movements could be encoded as a linear transition in joint space between an initial and a final limb posture, rather than a transition between an initial and final endpoint location and orientation in the task space.

The lambda model and a hemispheric motor model of intentional hand movements Uri Fidelman Department of General Studies, Technion, Israel Institute of Technology, Haifa 32000, Israel, [email protected]

Abstract: The lambda model of Feldman & Levin for intentional hand movement is compared with a hemispheric motor model (IIMM). Both models imply similar conclusions independently. This increases the validity of both models. The Lambda model implies that intentional movements begin before their final destination is determined, and the final destina-




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Commentary/Feldman and Levin: Motor control tion is computed during the movement (sect. 11 of the target article by Feldman & Levin [F&L]). A similar conclusion follows independently from a hemispheric motor model (HMM) of intentional hand movements. The probability of obtaining the same conclusion independently at random is small. This observation increases the probability that both models are correct, including details that are part of only one model, but do not contradict the other one. The HMM is presented in Gilad & Fidelman (1990) and Fidelman & Gilad (1992). In these studies, the performance times for manual micromovements by right-handed males were correlated with their scores on tests for the right hemisphere. The subjects removed 12 objects, differing in shape and size, in a fixed sequence from one task board and replaced them in the appropriate recesses on the other task board. The hand movements were divided into the following four components (micromovements): Reach, Grasp, Move, and Position. Reach and Move are defined as spatial motions, whereas Grasp and Position are defined as exact motions. The experiment was filmed by a movie camera and the performance time of each component was determined by counting the frames. Two tests were applied for the right hemisphere. The first was the enumeration of dots presented simultaneously during 64 milliseconds (subitizing). The second test was a similar enumeration of different figures. The performance terms of the micromovements and the scores on the right hemispheric enumeration tests were correlated. Most of the correlation coefficients were positive, that is, the more efficient the right hemisphere, the slower the hand movements. This effect is larger for the left hand (controlled by the right hemisphere) than for the right hand (controlled by the left hemisphere) with a 2-tailed significance of p = 0.0212. That is, this effect is not related to a nonright hemispheric factor. According to Guiard et al. (1983), movements are performed with a smaller constant error when using the left hand than when using the right. We explained this finding and our own by the existence of two alternative strategies for operating the hands. One strategy is a slower but more accurate one, related to the right hemisphere (the left hand). The second is a fast and inaccurate movement related to the left hemisphere (the right hand). Because the right hand (left hemispheric strategy) is less accurate, it requires more corrections, which are performed by the left hemisphere. The exact motions (Grasp, Position) are more compound and require more adjustments. Conversely, the spatial motions, Reach and Move, require fewer adjustments while the hand is moving. That is, we may expect the positive correlations between the scores on the right hemispheric tests and the performance times of the spatial motions to be larger than the correlations related to exact motions. This hypothesis was confirmed experimentally with a 2-tailed significance of p = 0.004 for the right hand and p = 0.0212 for the left hand. These observations are explained by the HMM as indicating that the right hemispheric strategy is to compute a representation of the spatial goal state; then the hand is sent to its spatial target with minimum corrections. The left hemispheric strategy is to begin the motion before the right hemisphere completes the computation of the spatial goal state; the left hemisphere performs corrections quickly by feedback monitoring (Gilad & Fidelman 1990, p. 160). The longer performance time of the right hemispheric strategy is caused by the later initiation of the movements. The logical reason for this later initiation is that although the right hemispheric goal state of a subject serves both hands, the right hand is less accurate and faster. That is, the right hand does not fully apply the goal state and may begin its motion before the goal state is fully imprinted in the right hemisphere. It therefore applies the correction mechanism more extensively to correct the deviations. It should be noted that there is no clear distinction between the two strategies, and they may change continuously. We may accordingly expect that most subjects (except, perhaps, most extreme right hemispheric subjects) begin moving their hands before the computation of the destination is complete.

According to the conservative control strategy of the Lambda model, a movement may be initiated without determining its distance. The distance may be determined during the movement by computing the time needed to come as close as possible to the target. That is, the central control of the movement comprises two components: the determination of the direction and of the duration of the movement. This model is in line with the HMM. The spatial direction may be determined by the right hemisphere, whereas the temporal analysis may be performed by the left hemisphere. The spatial direction may be identical to the spatial goal state of the HMM; the arresting of the movement using temporal coding may be related to the left hemispheric corrections of the HMM. This arresting of movement is extended by F&L to double-joint and triple-joint movements. This extension may be identical to the left hemispheric series of corrections existing according to the HMM. According to the HMM, the more efficient the right hemisphere is, the more time that is required to compute the direction of the movement. This is explained by the necessity to inhibit the former goal state of the movement imprinted in the right hemisphere. This inhibition is more difficult if the right hemisphere is efficient (Gilad & Fidelman 1990, p. 159). An additional factor causing the longer time for the right hemispheric strategy may be related to a negative correlation between the efficiency of the left and right hemispheres caused by the influence of sex hormones (see references in Fidelman & Gilad 1992). A right hemispheric subject, therefore, has an inefficient left hemisphere that requires more time to compute the duration of the movement. This movement is hence slower, to allow more time for computing its duration. That is, even extreme right hemispheric subjects may begin their hand movements before the computation of their duration is complete. We observe that the Lambda model and the HMM can be integrated. Each of the models contributes details to the unified model.

Moving models of motion forward: Explication and a new concept Thomas G. Fikesa and James T. Townsendb department of Psychology, University of Puget Sound, Tacoma, WA 98416. [email protected]; b Department of Psychology, Indiana University, Bloomington, IN 47405

Abstract: We affirm the dynamical systems approach taken by Feldman and Levin, but argue that a more mathematically rigorous and standard exposition of the model according to dynamical systems theory would greatly increase readability and testability. Such an explication would also have heuristic value, suggesting new variations of the model. We present one such variant, a new solution to the redundancy problem.

We find ourselves in an interesting predicament: we would like to believe that the theory put forth in the target article is essentially correct, but we are still not quite sure we understand it. Apparently we are not alone - Feldman and Levin's (F&L's) complaint is that others have consistently misrepresented the model as well. Unfortunately, the present paper does not appear to remedy the problem. Our commentary takes the form of a suggestion and an illustration. First, we suggest that the proponents of this and similar models (e.g., Bizzi et al. 1992) make better use of the mathematical conventions of dynamical systems theory. This would substantially improve clarity of the model and issues surrounding it. Perhaps Feldman and his colleagues believe that the use of quantitative notation will obstruct communication. In this instance, we suspect exactly the opposite is the case. Second, we illustrate the heuristic utility of this suggestion by taking another look at the redundancy problem (sect. 11.3 of the target article), briefly sketching an apparent misprediction from his theory. Then,




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Commentary/Feldman and Levin: Motor control we indicate the anchor point of our own (incipient) theory in the context of a \ model-compatible solution motivated by dynamical systems theory. The language of dynamics. Our suggestion for clarification of Feldman's theory breaks down into two parts: 1. Develop the mathematics of the model (sans physiological evidence) concisely, rigorously, and in one location (rather than scattered throughout the paper); 2. Make a more thorough use of standard dynamical systems theory language and plots. For those already familiar with the conventions, this tack would make the assumptions of the model unambiguous; for the unfamiliar, standard texts abound (e.g., Abraham & Shaw 1992; Hale & Kocak 1991; Hirsch & Smale 1974; Jackson 1989). We understand that any model of such a complex system is itself likely to be complex, but there is no reason to make it unnecessarily so. For example, if we allow that muscle activation a is monotonically related to muscle force, equations 8, 9 and some of the text in section 4 yield:

(1)

dt2

otherwise

where b = km. Equation 3 immediately follows as a special case (velocity = 0). This equation could easily be integrated with respect to time from a number of initial conditions to produce a (slightly more standard) phase diagram in the spirit of Figure 12. There is a growing tradition of dynamical systems theory application in behavioral modeling (e.g., Busemeyer & Townsend 1993; Schoner 1994; Schoner & Kelso 1988), and the level of mathematical sophistication is increasing. In addition to precision and pedagogy, explicitly phrasing a model in the language of dynamics offers another benefit: new solutions and alternative (dynamical) hypotheses suggest themselves. We illustrate this point by reconsidering the redundancy problem discussed in section 11.3.

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Figure 1 (Fikes & Townsend). A comparison of synergy and attractive manifold hypotheses. A simplest redundant effector (A), a synergy solution (B), and an alternative solution based on the notion of an attractive manifold (C, D). See text for discussions.

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Commentary/Feldman and Levin: Motor control Another look at redundancy.1 Redundancy, the ability to solve a problem in more than one way, is a problem that faces actors whenever the number of degrees of freedom (df's) of the effector are in excess of the number specified by the task (i.e., most of the time). Although excess effector df's allow for flexibility in performance, they present the problem of selecting among an often infinite number of possible realizations. One solution is to constrain the effector df's in some fashion to make the task of effector mapping 1:1 (eliminating redundancy). This can be done by introducing a cost function (e.g., minimizing energy or distance) or equations of constraint (Feldman's synergies in sect. 11). However, these solutions violate certain characteristics of biological movement. We illustrate this in the context of a simple, redundant, dynamical system, and then offer a sketch of an alternative solution within the context of the authors' theory (Fikes & Townsend, in preparation). Consider the system in Figure 1A, a two-joint arm operating in Cartesian two-space with shoulder fixed at the origin. To create a redundant situation, we specify a one-df task, to locate the end effector at a particular value of y. For simplicity, we treat the dynamics in terms of the joints rather than muscles and consider only a first-order system (thus, we can plot the phase space for both joints in a plane). Figure IB depicts the phase-space of a constraint-based solution, a synergy in which the joints are constrained to equal one another. A goal of y = 2 was selected, and a manifold corresponding to the forward kinematics (y = f(d), 3 = dy = d2; b°ld line) plotted. The two stable equilibrium points of the system are at the intersection of y = 2 and this manifold. Note that, if unperturbed, the system will move to a new goal slate along this manifold to the nearest fixed point; if perturbed, it moves back onto the manifold and onto one of the same fixed points. Thus, the system exhibits equifinality in both task-space and joint-space (by equifinality, we mean simply that the system comes to the same equilibrium position in spite of perturbations). This violates a characteristic of human movement, namely, that we tend to equifinality in task-space but not effector-space (e.g., see Folkins & Abbs 1975): the system does not seem to care how the task is achieved, as long as it is. As an alternative, consider the strategy depicted in Figures 1CD. In short, the strategy is to determine a 1-df manifold in jointspace that represents all possible joint configurations that would yield a desired goal (y value), and to define a phase space in which this set is an attractor (specifically, a continuous set of fixed points). In Figure 1C, we represent the collection of such manifolds for — 1 < y < 4. Specific manifolds (contour lines) are drawn fory = {—1, 0, 1, 2, 3} on the three-dimensional structure in Figure 1C. In Figure ID, we define a vector field (gradient system) that produces trajectories toward the nearest point on the solution manifold for y = 2. Note that the vectors along the manifold are zero length - if the system is perturbed along the solution manifold, it will not compensate, but if it is perturbed off the manifold, it will restore onto it. Thus we produce equifinality in task but not effector (joint) space. We believe this second solution is more reasonable as a model of biological movement, but we would like to emphasize that it is through the use of the language and conventions of dynamics that the two solutions are rigorously distinguishable conceptually. Again, we think the X model is probably a close approximation to what biological systems actually do, but we await a rigorous, concise, and coherent development of the mathematics, followed by qualitative and quantitative testing of the theory. NOTE 1. We wish to thank Gregor Schoner for many helpful discussions on the topic of dynamical systems theory and its application to behavioral research during his stay at Indiana University in the summer of 1994. Many of the ideas presented in this section can be traced, directly or indirectly, to these conversations.

Grip force adjustments during rapid hand movements suggest that detailed movement kinematics are predicted J. Randall Flanagan,8 James R. Tresilian,b and Alan M. Wing b 'Department of Psychology, Queen's University, Kingston, Canada, K7L 3N6; "Medical Research Council Applied Psychology Unit, Cambridge, CB2 2EF, England, [email protected]

Abstract: The X model suggests that detailed kinematics arise from changes in control variables and need not be explicitly planned. However, we have shown that when moving a grasped object, grip force is precisely modulated in phase with acceleration-dependent inertia! load. This suggests that the motor system can predict detailed kinematics. This prediction may be based on a forward model of the dynamics of the loaded limb. As outlined in the target article, a central notion of the X model is that the kinematics of movement arise as a result of changes in control variables (CVs) and need not be explicitly planned. Feldman and Levin (F&L) appear to accept that CVs must be sensitive to parameters such as overall rate, direction, and displacement that define a task but they suggest that the central nervous system (CNS) does not need to be concerned with detailed kinematic features. Thus, for example, the smoothness characteristic of reaching movements is viewed as a natural consequence of dynamic processes rather than a planned feature of the motion trajectory (cf. Hogan & Flash 1987). Nevertheless, under certain conditions, it may be desirable to predict detailed kinematics accurately. For example, such a prediction would enable the motor system to make precise adjustments for potentially destabilizing loads that depend on kinematics. Recent results related to anticipatory grip force adjustments during rapid arm movements with hand-held loads (Flanagan & Tresilian 1994; Flanagan et al. 1993; Flanagan & Wing 1993) suggest that motion planning may involve the prediction of detailed kinematics. In these studies, subjects held an object in a precision grip with the tips of the index finger and thumb at its sides. In this case, grip force (normal to the objects surface) permits the development of frictional force to counteract gravitational and movement-induced loads. We have shown that when moving an inertial (acceleration-dependent) load, grip force is finely modulated in phase with fluctuations in load force arising from the movement; grip force rises as the load increases and falls as the load decreases. The tight coupling between grip force and load force is observed in vertical and horizontal movements made at varying rates and in different directions (see Fig. 1). Despite marked differences in the form of the load force function across conditions, grip force adjustments anticipate changes in load force in all cases. Moreover, the tight linkage between grip and load is observed within conditions. For example, there are strong correlations between peaks in grip force and load force both in timing and amplitude. Finally, we have demonstrated that changes in grip force parallel fluctuations in inertial load regardless of the articulators subserving the motion of the object. These results indicate that the motor system is able to predict accurately the time of occurrence of the peaks in the acceleration profile of the hand-held object and the load properties of the object. (On the basis of this information, the load force can be predicted and the grip force adjusted accordingly.) Thus, the results suggest that the motor system is able to predict detailed features of the kinematics. It seems unlikely that detailed kinematics can be directly predicted from changes in CVs underlying the movement. The X model suggests that the trajectory of the actual hand will, in general, deviate substantially from the trajectory of the equilibrium position of the hand (equilibrium trajectory). Moreover, the extent of deviation will depend on the load and the form of the CVs themselves. At least in the case of rapid movements, the equilibrium trajectory of the hand would appear to be




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Commentary/Feldman and Levin: Motor control Grip and load forces in up and down movements.

o LL

involves prediction of arm kinematics, such a prediction plays no part in arm movement control in general. That is, control of grip force in moving objects held in a precision grip may be a special case and, if objects are encompassed in a full grasp or if there is no hand-held object, there is no requirement for the CNS to predict kinematics. We believe that this position is not tenable, however, because of findings that there are anticipatory postural adjustments associated with arm movements (Belen'kii et al. 1967; Bouisset & Zattara 1987). These, it has been argued (Friedli et al. 1988), serve to minimise the dynamic consequences of the arm movement for remote body segments. This suggests that an internal model of limb dynamics may serve whole body posture stabilisation just as an internal model might facilitate stabilisation of a hand-held object during arm movement. Finally, we would point out that the notion that the motor system has an internal representation of limb dynamics is, in some sense, already assumed in the X model. In particular, to deal with gravitational (or elastic) loads, CVs must be adjusted because the relation between actual positions and equilibrium positions is altered. This adjustment will depend on the position-dependent load properties of the arm. Thus, it seems reasonable to suppose that this information, at least, is used in motion planning.

Reciprocal and coactivation commands are not sufficient to describe muscle activation patterns C. C. A. M. Gielen and B. van Bolhuis

0.8

Figure 1 (Flanagan et al.). Grip force (thin) and vertical load force (thick) records from single upward (top panel) and downward (bottom panel) point-to-point movements. The load force represents the sum of the inertial and gravitational loads. The peak load occurs early in the upward movement and late in the downward movement. The peak grip force coincides closely in time with the peak load force (dashed lines). Note that in the downward movement, grip force starts to rise at the start of the movement and there is a "bulge" that coincides with the peak in negative load (shaded area). This prevents slip as the object is accelerated rapidly downward. In slower downward movements, where the load is always positive, grip force does not increase until later in the movement and, in fact, often decreases at the start. insufficient for predicting kinematics; a fortiori, the equilibrium trajectory is insufficient for control of grip force during transport of grasped objects. We suggest that the prediction of object acceleration may be based on an internal model of the dynamics of the loaded limb. This is not necessarily inconsistent with the X model. In particular, the motor system may use an internal forward model of dynamics to predict kinematics from planned CVs. The forward model could thus provide the basis for coordination of arm movement and grip force (and other postural adjustments). Forward models may be distinguished from inverse models, which translate planned kinematics into the forces required to achieve the plan. Thus, whereas inverse models hold that kinematics are planned, forward models suggest that kinematics are predicted. The idea that there is an internal forward model of dynamics preserves the basic idea in the X model that the motor system plans in terms of CVs rather than kinematics, but, at the same time, provides a way in which grip force can be coupled with load forces that depends on kinematics. Of course it might be argued that, even though grip force

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Department of Medical Physics and Biophysics, Katholieke Universiteit Nijmegen, Geert Grooteplein Noord 21, The Netherlands. [email protected]

Abstract: Recent results have shown that the relative activation of muscles is different for isometric contractions and for movements. These results exclude an explanation of muscle activation patterns by a combination of reciprocal and coactivation commands. These results also indicate that joint stiffness is not uniquely determined and that it may be different for isometric contractions and movements. It was one of the attractive features of the X model that the threshold muscle length X was the only control variable (CV) necessary and sufficient to characterise the activation of muscle (by the difference between muscle length and X) and its contribution to stiffness. When several muscles are involved, just as many control parameters are necessary, one for each muscle. With these CVs it was possible, according to the model, to control the position of a limb (by the position at which forces by external loads and those exerted by the limb are in equilibrium), hmb velocity during movements (by controlling the rate of change of X), and EMG patterns. Recent experiments have provided evidence that nature is more complicated than the simple view described by the X model. These new studies have shown that the relative amount of EMG activity in human arm muscles is different under conditions in which subjects are instructed to exert an isometric force at the wrist or to move the hand very slowly against the same external force (see Miller et al. 1992; Theeuwen et al. 1994a; 1994b). In terms of the X model, this implies that the rest-length of these muscles is changing in a different way for each of these instructions. The important point is that the amount of EMG changes in a different way for different muscles: for some muscles the recruitment threshold of motor units decreases (and as a result the corresponding EMG activity increases); for other muscles, the recruitment threshold increases corresponding to a decrease of EMG activity. Further experiments by Theeuwen et al. (1994b) revealed that for movements assisting an external load the relative activation was different from that in isometric contractions and from that observed for movements against an external load. These results demonstrated that the relative activation of muscles is different for various motor tasks.




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Commentary/Feldman and Levin: Motor control Tax et al. (1990a; 1990b) did an experiment in which the instruction to the subject was either to control force at the wrist or to control position of the wrist. In this way the physical state of the wrist (position, velocity, and force) was the same; only the instruction to the subject was different. The results revealed a different relative activation of human arm muscles, indicating that the differences were the result of a different central command, not simply of changes in reflex-induced activity. Any explanations to describe the different relative activation based on the forcevelocity relation or the muscle-length relation could be excluded (see Theeuwen et al. 1994b). Because both position and force are the same under all conditions, the only explanation provided by the target article could be based on a change in activity resulting from a coactivation command. However, this, too, could be excluded for two reasons: (1) no change of activity was found in the three heads of m. triceps (in fact, no activity was found at all in m. triceps) and (2) this explanation cannot explain why EMG activity increases in some muscles (like m. biceps) but decreases in other muscles (like m. brachialis). Therefore, neither changes in the R nor those in C commands can explain these results and the present state of the \ model cannot explain the results described above. This review of the differential relative activation of human arm muscles in isometric and movement tasks indicates that the threshold for muscle activation is modulated differently for various muscles. More than one setting of muscle-length thresholds generates the same physical state of the arm. This indicates that the \ model cannot explain the redundancy problem (i.e., that the number of muscles is greater than the number of degrees of freedom of the arm.) There is no unique relation between muscle rest lengths on the one hand and position and/or force of the limb on the other. Several hypotheses have been proposed to explain the different relative activation of muscle by considering biomechanical constraints (Gielen & van Ingen Schenau 1992; van Ingen Schenau 1989). The activation patterns predicted by these hypotheses can be translated directly into rest lengths of muscles and changes in their rest lengths. Whether these hypotheses can really provide a satisfactory explanation remains to be seen. Although there can be some criticism of it, I really think that the \ model has been a good one. Like any good model, it has stimulated a lot of experiments trying to falsify it and we have learned a lot from the results. In my opinion, the model is outdated now, being too simple; what we need is a new model, just as good as the \ model, which incorporates all of its good ideas.

The case of the missing CVs: Multi-joint primitives Simon Giszter Department of Anatomy and Neurobiology, Medical College of Pennsylvania and Hahnemann University, Philadelphia, PA 19129. [email protected]

Abstract: The search for simplifying principles in motor control motivates the target article. One method that the CNS uses to simplify the task of controlling a limb's mechanical properties is absent from the article. Evidence from multi-joint, force-field measurements and from kinematics that points to the existence of multi-joint primitives as control variables is discussed. Feldman and Levins (F&L's) target article is an interesting description of the lambda hypothesis. However, I would suggest that several "control variables" (CVs) are missing from their description. These are: (1) a simple method for direct end-point force control and its use in a limb, and (2) the presence of (and perhaps requirement for) multi-joint primitives. Such multi-joint primitives appear to form built-in "reflex" units of behavior and may be important contributors to the execution and development of

"voluntary movement." By emphasizing voluntary motor control of human adults, and specifically arm movements and isolated joint-based controls, F&L neatly avoid any need to discuss seriously the issues of multi-joint locomotory tasks, pattern generation, complex reflexes, motor primitives, and other built-in functionality (some of which F&L have themselves participated in characterizing (Berkinblitt et al. 1986; Fukson et al. 1980; Ostry et al. 1991). In fact, multi-joint primitives may bear strongly on the issues they raise. Among these issues are redundancy in multiple muscle systems, independent joint control, "cocontraction commands," and the roles and organization of reflex intermuscular interaction. It is not at all clear that independent, single-joint controllers are the best way to perform all voluntary movements, but this seems to lie at the heart of F&L's approach. The evolution of multi-joint muscles in most articulated animals seems to fly in the face of the idea of joint isolation. Limb dynamics involve complex inter-joint effects. Multi-joint controllers of the appropriate form might simplify the organization and execution of many behaviors. Evidence for the presence and importance of multi-joint CVs in the spinal cord comes in part from experiments in the frog (Bizzi et al. 1991; Giszter et al. 1992). It has become clear that the frog spinal cord in isolation can generate a small, consistent set of muscle activation patterns, and hence, forces in its limb, in reflex spinal behaviors, and after microstimulation of the spinal cord. These patterns can be represented as force-fields. The vector fields examined under static conditions show several features suggesting that these patterns may be primitives for reflex behaviors and perhaps for other movements: (1) The field structures are fixed. Increasing the stimuli on the skin or within the spinal cord elicits stronger fields that are simply scaled versions of the singleforce pattern elicited by all stimuli applied at that point (Giszter et al. 1993). (2) The fields can be combined in some instances by vector summation, as a result of microstimulation (Mussa-Ivaldi et al. 1994) or skin stimulation (Giszter 1994). (3) The force patterns often correspond to reflex phases or postures, the limb end-point converging to the "canonical position" for flexion, hind-limb wiping placing, or back wiping placing. These multi-joint primitives specify not only a posture but also a pattern of limb compliance far from equilibrium. These results suggest that some vertebrates have built-in "basis sets" for a set of multi-joint reflex controls and postures. These could perhaps even form sets of CVs on which additional layers of control and more complex CVs could be built (Mussa-Ivaldi 1992). For example, force-fields suitable for force control could be synthesized from combinations of such convergent fields (Mussa-Ivaldi & Giszter 1992). There are two points from the experimental data that are particularly noteworthy in the context of the target article: (1) Whereas we did observe fields representing single-joint actions, most force-fields are multi-joint. (2) We discovered that the set of multi-joint primitives in the frog spinal cord includes force patterns that are parallel and almost uniform in hip-centered polar coordinates, and hence well suited to force control over areas of the work-space (Giszter et al. 1993). Thus, there may be some primitives or CVs specialized for force control, rather than position. The primitives we have described are CVs that also include effects of inter-joint and inter-muscle reflex modulation (Loeb et al. 1993). The notion of multi-joint primitives as intermediate variables in biological systems that simplify motor control is supported by work from many preparations and approaches. Masino and Knudsen (1990) have demonstrated such elements in the barn owl and neural networks organizing such primitives have been developed (Sanger 1994a; 1994b). The power of similar sets of basis functions in approximating nonlinear controls for robotic mechanical systems has also been dramatically demonstrated (Slotine 1994). In conclusion, focusing only on a global planner of movement using a single global "voluntary" mechanism based on independent joint controls is likely to fail to capture much of the richness of BEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



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Commentary/Feldman and Levin: Motor control motor behavior. The notion of a hierarchy of primitives or CVs with different levels of specialization seems plausible. The positional frames and CVs proposed by Feldman & Levin may indeed form components in such a hierarchy, but assigning any CV special prominence may be a mistake, given the variety of both voluntary and reflexive tasks performed in the day-to-day functioning of the intact motor system.

Inverse kinematic problem: Solutions by pseudoinversion, inversion and no-inversion Simon R. Goodman Department of Physiology, Rush-Presbyterian-St. Luke's Medical Center, Chicago. IL 60612. [email protected]

Abstract: Kinematic properties of reaching movements reflect constraints imposed on the joint angles. Contemporary models present solutions to the redundancy problem by a pseudoinverse procedure (Whitney 1969) or without any inversion (Berkenblit et al. 1986). Feldman & Levin suggest a procedure based on a regular inversion. These procedures are considered as an outcome of a more general approach.

The triad of hypotheses: Anatomical correspondence, positional frames of reference, and equilibrium point. The hypothesis of anatomic correspondence introduced by Feldman and Levin (F&L) postulates that the motor control system transfers positional frames of reference to the actual values of joint angles. As a result, in the absence of a special command for relaxation, the system takes up the slack of muscles. New positional frames pull up the torque/angle invariant characteristics to the desired values of the angles so that a new command can start from these values not as "\," but as "8X" (target article, sect. 3). Notions of the equilibrium point, positional frames of reference, and the principle of anatomical correspondence discussed in the target article and before (Feldman 1986; Flanagan et al. 1993) are strongly related, so they can be understood better when considered together. The triad of these hypotheses implies that the movements can be planned as a sequence of transitions from one posture to another (Abdusamatov et al. 1987). In the target article, F&L again discuss the possibility of reconstructing a movement trajectory as a sum of identical movements shifted in time (Fig. 15, sect. 11.1 of the target article). The existence of such "basic" submovements could play a crucial role in our understanding of motor control, but it would be too good to be true. Perhaps we misunderstood F&L's explanations, however, and they merely imply that in a linear approximation, any movement can be represented as a sum of impulse responses of the moving system (which in the limit leads to the Duhamel integral, see Jacobs 1993). This assertion can lead to a description of movement control by differential Equation 10 introduction in section 11.2 of the target article (although it does not look like the differential one). N-shape or V-shape? F&L distinguish between two types of positional frames of reference: one in angular space ("a referent body schema," target article, sect. 7) and one in Cartesian space ("frame of reference associated with extrapersonal space," target article, sect. 11.2). Arguing against the N-shaped patterns in the case of a single-joint movement (Latash & Gottlieb 1991), F&L hold that central control of a (reaching) movement should be simple (ramps of R and C commands; target article, sect. 11.1). A modem paradigm confirms that the motor control system does not care about the simplicity of angle trajectories but only about Cartesian ones (Abend et al. 1982; Morasso 1981; Viviani & Terzuolo 1980, etc.). In this context, the principle of Ockam s razor works for extrinsic coordinates; the shape of R commands can be quite complicated because of limb geometry. F&L themselves

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implicitly accept this fact when they suggest using the solution to Equations 10 and 13 as R commands. This means that the question of the simplicity of the CVs should be explicitly addressed to Cartesian virtual trajectories. F&L's hypothesis is that the motor control system plans these trajectories only by transferring positional frames of reference, not by taking into account external loads. The evidence for this hypothesis remains to be provided. A class of models solving the inverse kinematic problem. To comment on Equations 10 and 13, we will first recall one recent work (Berkenblit et al. 1986) with a model of the frog wiping reflex. [See also Berkenblit et al: "Adaptability of Innate Motor Patterns and Motor Control Mechanisms" BBS 9(4) 1986.] In this pioneering work, the trajectories of each joint are calculated independently but executed simultaneously. The model preserves the property of equifinality, but its path is not straight. The outstanding feature of this model is that it leads to a solution of the inverse kinematic problem without inversion (see below)! Another approach is usually used in robotics when trajectories of all joints are calculated simultaneously. These calculations use the technique of pseudoinversion (Whitney 1969). F&L consider an approach intermediate between these two extremes: they suggest first calculating the trajectories for all pairs (in a two-dimensional case) or triples (in a three-dimensional case) of joints, and then summing these weighted "partial" trajectories. This allows one to preserve the straight path and not to resort to the procedure of pseudoinverse (but only to the inverse). In fact, this algorithm can be used to solve the problem of muscle redundancy as well. This approach looks adequate for neural network realizations. Hence, contemporary models provide different ways of calculating the kinematic plan of the movement, which incorporate a procedure of pseudoinverse, or of inverse, or require no inversion at all. All models mentioned above are analytically related. Let us briefly introduce a general model including them. Analytical description. Because designing the limb trajectories in Cartesian space is one of the main goals of the movement planning system, they can be planned independently of and prior to the angular trajectories. Let us explicitly approximate the plan of the limb end-point trajectory with the solution of a differential equation (to be closer to the substrate, we can assume that this equation is embodied in a neural structure working out the solution): x'(t) = A(t)(x lar-x(t))

Here, x(t) is the planned trajectory in Cartesian space, x'(t) is velocity, x ^ is the position of the target, and A(t) is a matrix. This first-order equation describes not the actual trajectory but the plan of movement kinematics (in terms of the R-command, as Equations 10 and 13 do it in the target article). Therefore, it does not include forces and dynamic properties of the moving system. For simple matrices A(t), the equation gives trajectories fitting the experimental ones with some accuracy, which can be increased by increasing the order of Equation 1 (Goodman & Gottlieb 1995; Gutman & Gottlieb 1992; Latash & Gutman 1993). Cartesian and angular trajectories are connected through the geometry of the limb: x = F(q)

(2)

where q is the vector of joint angles and F(q) is a vector function describing the limb geometry. Let J be the Jacobian matrix {dx/dq,} of the transform F(q) (here, i = 1, . . . n, j = 1, . . . m, where n is the dimension of Cartesian space (two or three) and m is the dimension of angular space, m > n.) The end-point velocity x'(t) can be expressed as a linear transform of the angular velocity q'(t) with the matrix J: x'W = J q'(t)


(3)

Angular velocity q'(t) can in turn be expressed as a linear transform of the Cartesian velocity x'(t) with some matrix G with the size of J:



(1)

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Commentary/Feldman and Levin: Motor control q'(t) = GV(t)

(4)

Combining Equations 1, 2, and 4, we obtain a general differential equation for joint angles command (Goodman & Gottlieb, submitted): q'(t) =

r ~ F(q))

(5)

Let A(t) = I (I is the identity matrix). It can be shown (see Figure 1) that for G = J, this equation describes the model of the frog wiping reflex (Berkenblit et al. 1986; the original expression of the model is given in a form of vector cross-products.) If G T = J T (JJ T )~ 1 . the equation calculates the minimal norm pseudoinverse solution (Whitney 1969). G T can be taken in the form of Z T (JZ T )~ l , where Z is an arbitrary matrix with the size of the matrix J (Goodman & Gottlieb, submitted.) The matrix Z reflects the joint redundancy represented in a "multiplicative" form and can be called the "redundancy matrix" a. The impedance control introduced in Mussa-Ivaldi and Hogan (1991) can be expressed in terms of the model for Z T = (k — F)"1}1", where k is the inverse of the matrix of joint compliance, Fj, = 2 k

—F k , F k is the k-th dqoq component of the force applied to the limb end point. The model considered in the target article can also be expressed with the help of the general model in the following way. Let {Jk} be

Time

all possible n by n (square) submatrices of matrix J. For all these submatrices, equations can be written: = Jkqk'(t),

(6)

k

where q '(t) are subvectors of q(t) corresponding to submatrices Jk. These subvectors are found as k q

'(t) = j - y ' (

(7)

(Actually, F&L used only the direction to the target, i.e., factor x'(t)/|x'(t)| instead of x'(t).) Then, each component of the vector q'(t) is formed as a weighted sum of corresponding components of vectors q k '(t); this is analogous to calculations in Equation 13 of the target article. Such a generalization helps us to clarify the mystery of the redundancy problem. It also explains certain properties of multijoint reaching movement sometimes called "invariances." As can be shown (Goodman & Gottlieb 1995), the movement formed according to model 5 will have such properties as movement equifinality, straight path of the extrinsic reference frames, possibility of obtaining speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step target, variations of angular trajectories without variations of the limb end-point trajectory in Cartesian space, and some others (Fig. 1). Those properties are almost independent of limb configuration, target location, movement duration, and load. The general model

Time

Figure 1 (Goodman). Paths, velocity-time profiles, and joint angle-time profiles for a plan of a three-joint limb reaching movement in two-dimensional Cartesian space for different algorithms of trajectory planning. (In Equation 5, a correcting time factor A(t) = t"I was used.) A: paths of the limb end point from initial position XQ to the target location x tar and some intermediate limb configurations; elbow, shoulder, and wrist joints are represented by e, s, and w. Algorithms with a redundancy matrix Z (Z-algorithm) produce a straight path for all values of Z (see text). Upper curved path was obtained for the algorithm of the model of the frog wiping reflex (F-algorithm). B, C: time profiles of tangent velocity vtun(t) and distance between limb end point and target Ix^,. — x(t)|. Whereas Z-algorithms produce a bellshaped plan of the velocity-time profile, F-algorithm distorts it. D, E: joint angle-time profiles for two different redundancy matrices in Z-algorithm. Both of these produce the same straight path in Cartesian space, although the angle-time profiles are different. Elbow, shoulder, and wrist joint angle trajectories are e(t), s(t), and w(t). F: joint angle-time profiles produced by the F-algorithm.




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Commentary/Feldman and Levin: Motor control can also be used for simulations of movements that are more complex than reaching. For example, in the study of movements involving moving targets.

Shifting frames of reference but the same old point of view Gerald L. Gottlieb Neuromuscular Research Center, Boston University, Boston, MA 02130. [email protected]

Abstract: Models of central control variables (CVs) that are expressed in positional reference frames and rely on proprioception as the dominant specifier of muscle activation patterns have not yet been shown to be adequate for the description of fast, voluntary movement, even of single joints. An alternative model with illustrative data is proposed. During the last 30 years Feldman and his colleagues have progressively developed and elaborated a model for posture and movement for which "the central idea [is] that the CNS organizes positional frames of reference or systems of coordinates for the motor apparatus and produces active movement by shifting the frames in space," where "MN threshold properties and proprioceptive feedback may be the cardinal components of the mechanism which define such frames of reference." Although they have shown how this mechanism could be consistent with kinematic and EMG patterns associated with a limited set of voluntary movements, the model offers no compelling reasons to believe that this is true and it remains seriously incomplete and inaccurate in many of its predictions. Feldman and Levin (F&L) fail to confront the two primary functions of models of this sort: first, their model does not give us insight into how the CNS will specify its CVs to perform various purposeful tasks such as moving different distances at different speeds with different external loads. While remaining dogmatically rigid about one aspect of its control scheme (namely the behavior of R, its shifting reference frame), the model has proven to be simultaneously flexible, extensible, and vague about others (Cj, C 2 , u.) that are no less important. Second, it does not provide a unified interpretation of EMG patterns and experimentally observed kinematics, although that is one of its fundamental claims. One of the most serious errors of the X model is reversal of causality in its attempt to explain EMG patterns in terms of observed kinematics. Kinematic patterns are the consequence of the interaction of muscle activation (which we suggest is mostly centrally driven) and muscle and load compliance (Gottlieb et al. 1989a). The nonutility of the X model is illustrated by the following experimental fragment. Figure 1 shows three "fast and accurate" elbow flexion series by one subject using all the usual protocols (Gottlieb 1994). The dashed line movements are inertially loaded (M). A viscous load (M + B) has been added by a torque motor for the solid line and an elastic load (M + K) has been added for the dotted line. We have proposed that the CNS adjusts the CVs (described in terms of excitation pulses and steps) to the expected load based on its knowledge, acquired through practice, of task dynamics (Gottlieb 1993; Gottlieb et al. 1992). According to this model, the differences in EMG patterns are primarily consequences of this "educated" motor controller. Kinematics are an "emergent" property of this central control pattern and of muscle, reflex, and load dynamics. Our interpretation of this figure in terms of the X model is that all three loads are initially moved by the same R command that rises at a fixed rate for 100 msec or less, producing identical EMG and torque patterns initially. The final value of R for the K load is greater and is reached later than for the other two loads to accommodate the static load of the external spring. Subsequent differences in muscle activation and force arise from proprioceptively driven differences in kinematics and presumably by differ-

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ent C and u, commands, but the X model offers little guidance as to how these parameters will be specified. With two (actually at least three) free control variables, one might expect the X model to be able to do the job but it cannot. To take one specific example, the X model does not correctly predict, at even a qualitative level, the antagonist EMG patterns illustrated. Kinematic feedback alone will not produce the largest, earliest antagonist EMG burst (and the shortest agonist burst) for the slowest movement (M load). The latency of the antagonist burst increases monotonically with increases in inertial or viscous loads or distance or decreases in intended speed. Of all these task variations, only increases in inertial load will increase the area of the antagonist burst (Gottlieb et al. 1989b). Increases in viscous load decrease the antagonist burst, as do decreases in intended speed. The only thing Figure 13 of the target article gets right is the decrease in antagonist area. The X model makes similar errors simulating movements of different distances. In retrospect, we discovered that the kinematics of the inertially and viscously loaded series were virtually identical although the torque and EMG patterns differed considerably (as they must to produce similar movements with different external loads). On the right are plotted velocity, net muscle torque, and the EMGs with angle as the independent variable. Phase-plane plots have sometimes been employed to show how proprioceptive information may be used by the X model (velocity scaled by |JL) to generate muscle activation patterns that are load adaptive (e.g., Fig. 12B of the target article). I am skeptical that the different torque and EMG patterns shown in the lower panels can be explained by the kinematic differences between the phase plane trajectories. (The difference toward the end of the elastically loaded movement is caused by a different CV.) In that case, as in our own model, the central commands must be adapted to load dynamics by an "educated" central controller. Whether this is best described in terms of a complex shift of reference frame (Latash & Goodman 1994) and auxiliary CVs or in more explicit terms of forces as we have suggested is an issue we have previously addressed in this forum (Gottlieb 1992). The X models' hallmarks are elastic invariant characteristics mediated by reflex mechanisms. Only lip service has been paid to intrinsic muscle properties. (They are absent from their own simulations [St.-Ongeetal. 1993].) After 30 years, there are hardly any published data to support the contention that spring-like reflex mechanisms provide any explanatory power about the initiation of a fast, voluntary movement. Neither observations of movements against known inertial or elastic loads nor simulations have provided such data. A class of experiments that has been more revealing has used unexpected load changes imposed during voluntary movements. The affirmative conclusion in Levin et al. (1992) rests more on computational methodology than data. Smeets et al. (1990), Gottlieb (1994; 1995a; 1995b; Latash 1994) and others show data that does not support the X model (although Latash's interpretation is more generous, as seen in his commentary on F&L, this issue). Equilibrium point models, even rephrased in terms of shifting reference frames and auxiliary control variables, are conceptual tools for understanding posture and slow or quasi-static movement. As general descriptions of the control of voluntary movements, even at the single joint, they provide little predictive utility or insight.

Twisted pairs: Does the motor system really care about joint configurations? Patrick Haggard,1 Chris Miall, and John Stein University Laboratory of Physiology, University of Oxford, Oxford, 0X1 3PT, England, [email protected]

Abstract: Extrapersonal frames of reference for aimed movements are representationally convenient. They may, however, carry associated costs




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Commentary/Feldman and Levin: Motor control -r-

100-,-

Net Muscle Torque (Nm)

Net Muscle"Yorque (FTmj

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0.4 0.5 time (s)

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Figure 1 (Gottlieb). Movements of three dynamically different loads. Average of 10 movements over 54° with known inertia], viscous, and elastic loads. Similar kinematic traces on the left are produced by very different muscle forces that emerge from different muscle activation patterns as revealed by the EMGs. Net muscle torque is equal and opposite to the sum of the motor and inertial (limb plus manipulandum) torque components. It is well correlated with the EMG patterns. Neither muscle torque nor EMG patterns can be determined from the kinematics alone without reference to the dynamics of the land moved by the limb. Kinematic, force, and EMG variables are illustrated as functions of time on the left and as functions of joint angle on the right. The instructions to the subject were only to be "fast and accurate" and it was in retrospect that the similarity of the movement trajectories (particularly with B & K loads) was noticed. In general, changes in load alter the trajectory, but the degree to which they do so is strongly dependent on the type of load, its magnitude, and the strength of the subject. This figure may be considered from two points of view. One is that EMG patterns are mostly proprioceptively driven consequences of kinematics. The other is that EMG patterns are mostly consequences of centrally specified patterns (CVs). The choice is left as an exercise for the reader.

when the movement is executed in terms of the complex coordination of multiple joints they require. Studies that have measured both fingertip and joint paths suggest the motor systems may seek a compromise between simplicity of extrapersonal spatial representation and computational simplicity of multi-joint execution.

This commentary focuses on the application of Feldman and Levin's (F&L's) EP model to multi-joint reaching movements. F&L suggest that multi-joint movements are represented as shifts of a reference frame for the limb endpoint in extrapersonal space (sects. 9 and 11.2). External space provides a representationally intuitive framework for the CNS to code target locations for movements. However, it does not guarantee a simple or intuitive system for controlling joints and muscles, because the varying kinematics and dynamics of the arm make the transformation from a set of muscle commands to locations in external space very complex. Because the human arm is redundant, representing

movements in terms of locations in external space also leaves the motor system with the ill-posed problem of selecting just one of the many possible ways that the joints can move the endpoint through external space. The selection problem is often associated with prior trajectory planning, especially in robotics, the control problem arises during movement execution. F&L's EP model does not address either problem adequately. Models based on extrapersonal representation of movement often ignore the control difficulties in generating the commands that produce such regular features (e.g., Hogan 1984). The geometrical decomposition approach of sections 11.2 and 11.3 does not truly solve the selection problem, because the set of joint-pair weightings is just as underdetermined as the joint angles; nor do they guarantee solutions to the control problem that are easy to implement. We suggest that the motor system may try to simplify the control functions required to execute multi-joint movements. BEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



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Commentary/Feldman and Levin: Motor control Preferring multi-joint patterns that are simple to execute would also help answer the selection problem. We have recently measured the spatial path of the fingertip, and the shoulder, elbow, and wrist joints during anterior posterior, lateral, and diagonal horizontal right-handed planar pointing

movements (Haggard et al. submitted). We present three results that suggest the motor system represents and selects some joint paths that simplify the control of multi-joint movement. First, we noticed a tendency for one joint to rotate much more than the others. Lateral movements were performed largely by shoulder

Joint activity in lateral movements Grand average of 5 subjects 1.0 Start

Target

0.5 o

.~

Extension

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Figure 1 (Haggard et al.). Rotation of shoulder, elbow, and wrist joints during each cm of the hand's progress along a start-target axis in lateral movements from left to right (top), and in anterioposterior movements from distal to proximal (bottom). Traces show a grand average of 12 movements from each of 5 subjects. The cumulative integral of each trace gives that joint's spatial path.

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Commentary/Feldman and Levin: Motor control rotation, and movements from proximal left to distal right were performed largely by elbow rotation. More important, the primary joint in each case moved essentially without reversals; the nonprimary joints often involved considerable reversals. This result implies a simple, invariant control strategy for the primary joint in each case, with the remaining joints accommodating the primary joint. Decomposition of an extrapersonal space representation using weighted joint pairs cannot explain this result. We suggest that the motor system may simplify reaching movements by selecting a single joint to produce the bulk of the movement. The primary joint may use simple (interpolative?) control, whereas the paths of the other joints may be coordinated so as to prevent excessively curved paths in extrapersonal space. That is, the motor system may prefer to sacrifice the representational convenience of an extrapersonal frame of reference for computationally simple pseudo single-joint movements. Second, we found that movements from distal left to proximal right, and to a lesser extent anterioposterior movements, involved more equal amounts of shoulder and elbow rotation. These movements cannot be reduced to pseudo single-joint movements, and the motor system must confront the arm's redundancy head-on. Indeed, the hand's spatial paths in these movements showed greater variability than those of movements with a clear primary joint. Analogous results were seen by Atkeson and Hollerbach (1985), but did not attract comment. This increase in variability suggests that executing coordinated multi-joint movements presents a sufficient computational problem to warrant trick solutions where possible, such as using primary joints, which simplify coordination. Extending EP hypotheses to multi-joint movements assumes that multi-joint coordination follows straightforwardly from control variables in extrapersonal space, but our variability data suggest that this transformation has a clear computational cost. Third, we averaged the amount of rotation at each joint over each cm of the hand's spatial path between start and target. In a sense, this representation corresponds to the way the motor system inverts the Jacobian matrix of the arm. It is not surprising that the resulting joint rotation patterns (Fig. 1) differ markedly between anterior posterior and lateral movements. For example, the elbow reverses in lateral but not in anterioposterior movements. Further, the contribution of shoulder and elbow rotation to the instantaneous hand displacement varies during the course of the movement. The converging shoulder and elbow traces suggest different patterns of inter-joint coordination are used to produce hand translation at different stages. F&L's treatment of the joint pairing (W^ in sect. 11) suggests the pairings are control variables that are normally calculated and fixed in advance for a given motor task. Our evidence suggests that the pairings are not held constant throughout the movement. The clear tails on the joint rotation profiles near the start and target suggest that the inter-joint coordination is actively modulated, perhaps to produce a desired hand path in extrapersonal space. In conclusion, our evidence suggests that the selection of joint activity and of inter-joint coordination patterns is not independent of the endpoint trajectory as the Feldman and Levin model proposes. Further, the motor system seems to select both joint and endpoint parameters in a way that simplifies the computations required for coordinated movement execution. An extrapersonal frame of reference is a convenient representation, but it may not be appropriate for the problems the motor system faces in controlling multi-joint movement. ACKNOWLEDGMENT The experimental data reported here was collected while the first author was supported by a Wellcome Trust Postdoctoral Research Fellowship. NOTE 1. Correspondence address: Department of Psychology, University College London, London WCIE 6BT, England.

Is X an appropriate control variable for locomotion? Thomas M. Hamm and Zong-Sheng Han Division of Neurobiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013. [email protected]

Abstract: The lambda model predicts that the command received by each motor nucleus during locomotion is specific for the joint at which its muscle acts and is independent of external conditions. However, investigation of the commands received by motor nuclei duringfictivelocomotion and of the sensitivity of these commands to feedback from the limb during locomotion indicates that neither condition is satisfied. If one attempts to apply the \ model of movement control to locomotion, the issue of what neural signals constitute the central commands for this activity is critical. The goal of forward progression of the animal is achieved by a coordinated set of angular translations at each of the joints in the limbs. In the context of the X model, these translations would be accomplished through the rhythmic shift of threshold membrane potentials for motoneurons innervating muscles that act at each joint. According to this model, it would be expected that the command received by each motor nucleus is specific to the joint at which its muscle acts. Moreover, the central command, or control variable, received by each motor nucleus must be independent of external conditions. A consideration of the mechanisms involved in the control of locomotion suggests that these conditions are not satisfied. First, consider the organization of commands to motoneurons. This can be inferred from the patterns of activity expressed by motor nuclei. During normal locomotion, this activity is influenced by feedback produced by the movement and cannot be viewed directly as an indicator of the central command. However, the activity of motoneurons can also be observed during fictive locomotion, when movements have been abolished by paralysis (Jordan et al. 1979). Complex patterns of locomotion have been observed in fictive locomotion (Bayev 1978; Grillner & Zangger 1979) and after deafferentation (Grillner & Zangger 1984), suggesting that the central commands contain many of the individual features of activity observed in normal locomotion. Such observations have prompted models of locomotion in which spinal pattern generation consists of coordinated sets of oscillators for each joint (Grillner 1981), a proposal that is compatible with the X model. This issue remains unsettled, however, and it has been argued that the complex patterns generated in locomotion depend on alternating commands to extensors and flexors, as proposed by Graham Brown (1911), with individual characteristics conferred by feedback generated by the movement (Lundberg 1981). Investigations have been conducted in this laboratory to determine how commands are distributed to motor nuclei during fictive locomotion. In this work (McCurdy & Hamm 1993) the activity of different motor nuclei during fictive locomotion was determined from recordings of selected muscle nerves in paralyzed, decerebrate cats. These recordings were analyzed in the frequency domain. Coherence spectra were computed to determine the correlation between different frequency components in the activity of the motor nuclei. Coherence spectra have been used as a measure of common central commands in the form of shared synaptic input or synchronized input to motor nuclei in several forms of motor activity (Bruce & Ackerson 1986; Christakos et al. 1991; Farmer et al. 1993; Smith & Denny 1990). The coherence spectra in fictive locomotion revealed substantial correlations between the activities of motor nuclei that innervate hip extensors and ankle extensors, indicating that common central commands were received by motor nuclei that act at different joints. Based on this observation, it appears that motor nuclei receive common central commands during locomotion that are related to the control of more than one joint rather than independently specifying the control of individual joints. Second, the central commands are not generated indepen-




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Commentary/Feldman and Levin: Motor control dently of external conditions, as required for the control variables in the X model. The transition in activity from stance to swing in locomotion depends on hip position (Grillner & Rossignol 1978), and cyclic motion of the hip entrains the pattern of locomotion (Anderssonetal. 1978; Kreillaarsetal. 1994). The central command issued by the spinal pattern generator also depends on activity in large-diameter afferents from the ankle extensors, probably Ib afferents signaling the force developed by these muscles (Conway et al. 1987; Duysens & Pearson 1980). These position- and forcedependent signals could be viewed as triggers to switch activities without influence on the commands during stance and swing. It appears likely, however, that the commands themselves are influenced by these signals (Andersson & Grillner 1981; Conway et al. 1987; Gossard et al. 1994; Pearson & Collins 1993). These studies on the control of locomotion indicate that common commands are directed to the muscles and motor nuclei of more than one joint, and that these commands are subject to regulation by sensory information regarding hip position and the force developed by extensors. Although the synthesis of reflex and mechanical properties in the X model provide a valuable approach to analyzing problems in motor control, the model does not seem to provide a suitable description of the commands for pattern generation in locomotion. ACKNOWLEDGMENT This work was supported by USPHS grants NS 22454 and NS 30013.

Do control variables exist? Nicholas G. Hatsopoulos8 and William H. Warren, Jr.b "Division of Biology, CNS Program, California Institute of Technology, Pasadena, CA 91125. [email protected]; bDepartment of Cognitive and Linguistic Sciences, Brown University, Providence, Rl 02912. [email protected]

Abstract: We argue that the concept of a control variable (CV) as described by Feldman and Levin needs to be revised because it does not account for the influence of sensory feedback from the periphery. We provide evidence from the realm of rhythmic movements that sensory feedback can permanently alter the frequency and phase of a centrally generated rhythm. Feldman and Levin (F&L) present a compelling theory of skeletal motor control because they attempt to uncover the underlying control variables (CVs) that are regulated by the central nervous system (CNS) to generate motor behavior. They argue quite forcefully that variables such as muscle activity (EMGs), muscle force, joint torque or stiffness, end-effector trajectory, and equilibrium position are consequences and not causal agents of a motor control strategy. On closer examination, the theory makes a number of standard assumptions that are shared by most approaches to motor control and should be questioned. In their introduction, F&L define a control variable as a quantity that exists and is specified by the CNS independent of the state of the periphery. That is, the locus of CV generation represents the "control" level of afunctional hierarchy that leaves out the mechanical and physiological state of the musculo-skeletal system. Time-varying CV profiles are sent as motor commands to the lower "executive" level which then executes them. The assumptions of independent specification and functional hierarchy are so pervasive in theories of motor control in part because of the influence of modern control theory. Take, for example, the servomechanistic view of control. A reference signal is specified independent of the state of the plant, and thus comprises the CV. On the other hand, the signal sent to the controller and plant depends on the difference between the reference signal and the state of the plant. This feedback loop including the controller represents the "executive" level of the hierarchy. We would like to argue that control variables as defined

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by F&L are scientific constructs that may hinder our understanding and may not even exist for certain kinds of motor tasks. We provide evidence for our view in the context of rhythmic movements by discussing three important properties: resonance tuning, frequency entrainment, and phase resetting. First, the frequency of a motor rhythm will very often scale with or match the resonant frequency of the musculo-skeletal system (Kugler & Turvey 1987). Pennycuick (1975) observed that a variety of animals in the wild walked at a stride frequency that was proportional to the square root of the reciprocal of the leg length. Holt et al. (1990) demonstrated experimentally that humans chose a preferred frequency of walking that scaled linearly with the resonant frequency of the leg. More recently, we have shown that the preferred frequency of rhythmic arm movements actually matched the resonant frequency of the forearm, which depends on the stiffness of the joint and the mass of the limb (Hatsopoulos & Warren, in press). According to the lambda hypothesis, the CNS dictates the frequency of a rhythm by adjusting the timing of the R command. The above results suggest, however, that the periphery also influences the frequency at which preferred motions should occur, presumably via proprioceptive feedback. Computer simulations modeling a central pattern generator coupled with a pendular limb have demonstrated that resonance tuning emerges with the introduction of proprioceptive feedback (Hatsopoulos et al. 1992). It has also been shown that the strength of proprioceptive feedback can modulate the wing beat frequency of locust flight (Wilson 1961) and the body frequency in dogfish swimming (Williamson & Roberts 1986). F&L might argue that the lambda hypothesis allows for the influence of sensory feedback in the temporal dynamics of the R command. In that case, however, the R command cannot be considered a CV as they define it because its dynamics are not specified independently of "external conditions." Second, frequency entrainment of centrally generated rhythms via mechanical or electrical stimulation of afferent pathways has been demonstrated in a number of systems (Andersson & Grillner 1983; Williamson & Roberts 1986). that is, if proprioceptive afferents are stimulated at frequencies close to the endogenous frequency of the central pattern generator, the latter s frequency will adjust to match the imposed frequency. Again, entrainment argues against the existence of CVs specifying the timing of motor rhythms independent of sensory feedback. Third, a number of phase resetting experiments have demonstrated that the timing of an ongoing motor rhythm can be permanently shifted by a brief mechanical or electrical perturbation (Conway et al. 1987; Kay et al. 1991). For example, Conway et al. (1987) electrically stimulated extensor afferent I fibers in hind knee and ankle joints of spinalized cats during fictive locomotion. If stimulation occurred during a flexor motor burst, the flexor burst was prematurely terminated and the onset of the following ipsilateral, extensor burst occurred earlier than expected. On the other hand, if stimulation occurred during an extensor burst, the burst was prolonged and the onset of the following ipsilateral, flexor burst was delayed. These experiments provide strong evidence against the existence of CVs as defined by F&L. We suggest that the theory put forth by Feldman and Levin should be revised. We agree with the authors that the CNS has influence over certain motor parameters and that the goal of any theory of motor control should be to discover these parameters. The hypothesis that the CNS modulates positional frames of reference by controlling the threshold lengths of muscles is a very strong candidate theory. However, the theory should incorporate the influence of the environment in shaping motor commands.




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The unobservability of central commands: Why testing hypotheses is so difficult Antony Hodgson Laboratory for Biomechanics and Human Rehabilitation, Division of Health Sciences and Technology, Harvard University-Massachusetts Institute of Technology, Cambridge, MA 02139. [email protected]

Abstract: The experiments Feldman and Levin suggest do not definitively test their proposed solution to the problem of selecting muscle activations. Their test of the movement directions that elicit EMG activity can be interpreted without regard to the form of the central commands, and their fast elbow flexion test is based on a forward computation that obscures the insensitivity of the predicted trajectory to the details of the putative commands.

The question Feldman and Levin (F&L) pose for us, phrased in terms of their car analogy, is: How does one drive a car? The problem we all faced when we learned to drive was translating our plan to travel a particular route into the appropriate manipulations of the accelerator, brake pedal, and steering wheel. F&L propose that the analogous control actions in the biological realm are changes in the membrane potentials of motoneurons that can be interpreted in kinematic terms as shifts in the length (X.) at which each muscle will become active. Although essentially I share F&L's view that motor tasks can be mapped onto \ specifications, I do not believe that centrally generated reciprocal (R) and coactivation (C) commands have the form F&L describe, nor do I believe that the tests they propose are definitive. F&L rightly point out that interaction port variables such as position or force are not specified directly by the CNS but emerge from an interplay between the central commands, the musculoskeletal apparatus, and the environment. However, because F&L understand the primary role of control variables (CVs) in generating motor activity, it puzzles me that they define R and C the way they do. In their view, C is defined as the vector of coordinated changes in the X parameters of agonist and antagonist muscles that preserves a joints equilibrium position (EP). However, because an EP is defined as the position in which the subject's muscle torque balances the environmental load, it cannot be a CV. Indeed, if the environment is sufficiently destabilizing, no EP may even exist. If the EP may not exist, then C cannot be considered a CV because it is fundamentally defined in terms of the EP; as F&L properly argue, a CV must be defined independently of environmental interactions. Even if an EP does exist for a given interaction, it is not clear to me that it would be particularly useful to have central circuits that can compute the vector of C commands necessary to keep the EP constant. If the commands to agonists and antagonists are more straightforwardly conceived of as scalar reciprocal and coactivation commands, then one could change the stiffness at the same EP through a coordinated command change. Although the change in the reciprocal command would then depend on the interaction force level, this is no more complicated than generating a vectorvalued coactivation command. Furthermore, in the presence of a position-dependent interaction force, a given change in R would not shift the EP by the same amount, so we cannot use the proposed R and C commands to get around the difficulty of mapping CVs to EPs. I appreciate F&L's emphasis on creating testable hypotheses, but I suspect that their R/C control scheme is not testable in the manner they propose in section 7. In that section they propose a solution to the redundancy problem - how the \ parameters of individual muscles are set - in which the central specification of R is expressed relative to a referent body schema. F&L claim that this hypothesis can be tested experimentally by observing EMG changes as the limb is moved in different directions. This test implicitly assumes, however, that C is zero. If C were nonzero and R did not satisfy their principle of anatomical correspondence, we might well observe precisely the same EMG patterns; in such a situation, we would have no way to distinguish the two cases.

Indeed, even if we had measurements of the motoneuron membrane potentials, the contributions of the hypothesized R and C commands would have an additive effect and we would be unable to unambiguously determine their relative influences. In a simple one-joint system with a single agonist and antagonist muscle pair, for example, any pair of membrane potentials that preserves the same interaction force at the same position (i.e., preserves the EP) can be decomposed into a fixed R and a 2-vector C, so one cannot disprove this idea based on EMG measurements. This debate raises the issue of what we can deduce about central commands or representations from measurements made at the interaction port of a system. This problem is unlike the standard system identification problems encountered in other impedance measurement tasks (Kearney 1983; 1984). In those studies, the experimenter applies torque perturbations, measures the responses, and attempts to deduce the dynamic relations between them. In the case addressed by F&L, however, the goal is to deduce the nature of the central commands through observing the kinematics of various motor tasks. Using a systems-theoretic approach, I have recently proven that observations made at a single interaction port, whether or not perturbations are applied, do not unequivocally determine the central commands (Hodgson 1994). This somewhat surprising result is rooted in the fact that responses due to the impedance of a system about its internal setpoints and responses resulting from changes in these setpoints are fundamentally indistinguishable at the point of interaction with the external world. This fundamental unobservability of the central commands affects many of F&L's arguments concerning the form of the R and C commands. I am not disputing that their model is competent to describe the behaviours they discuss; rather, I am concerned that the tests they propose do not adequately test their ideas, nor are they specific enough to discount other hypotheses. Shadmehr et al. (1993), for example, have nicely demonstrated that a twodimensional stiffness measurement allows us to predict the directions of quasi-static motion for which particular agonist and antagonist muscles will exhibit EMG activity; this is one of the tests F&L propose for their R/C control scheme. Shadmehr's analysis relies solely on stiffness measurements and a knowledge of the arm configuration - the position of the shoulder, the lengths of the forearm and upper arm, and the lines of action of the muscles - and notably does not depend on F&L's principle of anatomical correspondence. Because Shadmehr's results do not imply anything about the workings of the nervous system beyond certain interjoint reflex relationships (Hogan 1985), it would be surprising indeed if F&L's model, which in describing muscle activation is firmly grounded in physiological reality, did not accord with his observations. A second example of an inadequate test of the R/C control strategy is that proposed for fast single-joint elbow flexions. F&L claim that the R command is best characterized as a ramp from the initial to the final position. The test they suggest is a forward one: they compute the response of their model of the elbow to a rapid ramp input and compare it to experimental trajectories. However, because the ramp is so rapid (the EP reaches the target before the arm is halfway there), the input contains frequencies beyond the arm's natural frequency; this implies that the resulting trajectory will be insensitive to minor features of the command. If we invert the model and compute the command input corresponding to a measured trajectory, we will find that the input is highly sensitive to minor changes in the actual trajectory. This enhanced sensitivity of the inverse computation might explain the suggestion that the command for a fast movement is N-shaped (Hogan 1984). Although Hogan used a linearized approximation to the muscle stiffness, both his model and F&L's were otherwise similar in structure, so a ramp input to Hogan s model might well predict an actual trajectory as close to the measured one as F&L's prediction. Similarly, had F&L performed the inverse computation using their model, they might well have come up with an N-shaped EP transition.




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Commentary/Feldman

and Levin: Motor control

Finally, according to my observability theorems, the only way to compute the commands to a system is to assume a model of it. Although many of the components of F&L's model are perfectly reasonable, others are questionable. I do not believe, for example, that their use of linear damping is accurate. Muscle damping behaviour is highly nonlinear (Wu et al. 1990), and to the extent that uncertainties exist in the limb model we use, we should not identify the back-computed inputs to the model with any real inputs in a real system. However, even if we feel that their model is sufficiently accurate to back-compute commands and test the hypotheses, F&L have given us no sense of how sensitive their command estimates would be to the stiffness and damping values they assume and to the absence of those elements of the real limb that they have neglected in their model. Until they are able to put bounds on their predictions, they have not given us a testable hypothesis, but merely a conceptual model.

Frameworks on shifting sands R. lngvaldsen a and H.T.A. Whiting b "Department of Sport Sciences, University of Trondheim, Trondheim, Norway. [email protected] Department of Psychology, University of York, Heslington, York, YO1 5DD, England.

b

Abstract: Feldman and Levin present a model for movement control in which the system is said to seek equilibrium points, active movement being produced by shifting frames of reference in space. It is argued that whatever merit this model might have is limited to an understanding of "the how" and not "the why" we move. In this way the authors seem to be forced into a dualistic position leaving the upper level of the proposed control hierarchy "floating."

Feldman and Levin (F&L) propose a model (A.) of motor control in which "intentional movements are produced by shifting the frame of reference." They use as an analogy to explain their theory, the control of the movements of a car via the independent specification of the position of levers by an intrinsic part of the car - the driver. Within the framework presented, the levers are seen as control variables (CVs), set by the driver, largely independent of the environment, thereby reducing the degrees-of-freedom problem to manageable proportions. CVs, in F&L's terms, are specified by the nervous system broadly independent of the external conditions. In contrast, non-CVs, for example, biomechanical variables, are dependent on both external conditions and the influence of CVs in a functional hierarchy. The first level specifies CVs and the second continuously regulates biomechanical variables and other non-CVs as a function of CVs, afferent feedback, and external forces. CVs are seen as central aspects of F&Ls X. model with the notion that "the nervous system organizes positional frames of reference for the motor apparatus and produces active movements by translating them in space." X is considered the origin of the positional frames of reference or system coordinates for the motor apparatus. The question to which this naturally gives rise concerns the relation between CVs and X. A hint is provided in F&L's comment that the change in X may be influenced both directly and indirectly by CVs and that these effects are additive. Just when we thought we had a grip on the relation, however, we were thrown into confusion to read that "the independent change in X (8X) but not X itself, may be considered as a CV" (sect. 3, para. 6). Is this what Haken (1990) terms circular causality? According to the model, the system seeks equilibrium points (EPs) and active movements are produced by shifting frames of reference in space - modifying X by changing CVs. This results in a redefining of a situation with one EP as one with a new and different EP. Adjusting for this imbalance will bring about movements. (Continuing the car-driving analogy, when the steering wheel is turned, a series of events is set in motion that results in a

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change in the direction of the wheels in relation to the rest of the system. The system then has to adjust itself to a new EP, which it does by turning. F&L are at pains to emphasize, however, that behavioural patterns emerge from the dynamic interaction of the systems components and external forces within the designated frame of reference and are not "programmed" in the CNS. Once the initiative (decision?) is taken, what follows can be conceived of as a direct action system, that is, it is self-organized. In this way, the EP takes on the role of an attractor (Haken 1990), in the dynamical system sense. Given this interpretation, we would like to ask whether this is an attempt at a rapprochement between the synergetics approach (in Haken's 1990 terms) and F&L's neurophysiological control system. If so, is their control theory likely to encounter the same kind of problem that the synergetic approach has when it comes to an understanding of actions in context, that is, not how we move (by shifting frames of reference) but why we move (changing the CVs)? We will argue this to be the case on two grounds: (1) In the first place, X theory, like the synergetic theoretical approach, lacks a value system that can explain why organisms behave or change their behaviour (i.e., learn) at all (Ingvaldsen & Whiting, 1993; 1995) - a problem recently brought into focus by the work of Edelman (1992). (2) In the second place, F&Ls theoretical approach is far from clear in terms of enabling us to understand the relation between the controller and the system being controlled, that is, "who" issues the central commands? "Who" sets the levers? Let us focus on this second problem, acknowledged by Haken (1990, p. 29) who, in discussing (e.g.) self-organisation, makes the following observations: "note how the self creeps in." and "But what kind of self?" (Haken, 1990, p. 29). This is a problem for which Kelso (1994) tries to find a systematic solution by suggesting that information is not separate from action; a solution may have its own problems but is, at least, a systematic attempt to cope with the problem (see, also, Beek & Van Wieringen 1994; Michaels & Beck 1994). In searching F&Ls target article for an answer to this particular problem we find it impossible to unearth a consistent standpoint. On the contrary, the authors suggest a variety of relations between levers and the agent responsible for their setting. We are left with the feeling that the hierarchical system that F&L describe falls into the category of a homuncular theory. If this is, indeed, their position, the traditional questions must be asked: How is it possible for the homunculus to get its hands on the steering wheel? Given that homuncular theories are more anachronism than theory today, such a construal on our part may perhaps be misplaced. We may, indeed, have been misled by the car driving analogy F&L use as their departure point. If, however, the interpretation of their model is so unclear and the analogy with which they start out so misleading, what is the significance of their model when it comes to an understanding of the upper level of the control hierarchy? What could be meant, for example, by the statement that the initiative to modify this interaction by changing CVs rests, voluntarily, with the organism? Even if one assumes a driver in the seat, why and how could an initiative be taken? In F&L's we detect signs of the more traditional, dualistic position, as well as the alternative monistic one and we therefore find it difficult to resolve our dilemma. In using statements such as "intentional movements are produced by," "the system s freedom of choice," "the decision to change," "the initiative to change," "the decision to change the control pattern," "he has to modify CVs," and so on. F&L signal a dualistic standpoint. In contrast, by statements like "the CNS organizes," "dynamical events leading to," and "levers which are used by the CNS," we are led along the monistic road. We cannot expect F&L to provide a solution to this problem (body/mind), but we could have hoped for a more consistent approach. The shifting positions, as presented, make the model unnecessarily weak. By a more stringent selection of analogies (if




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Commentary/Feldman and Levin: Motor control such analogies from everyday life that match the model they present, are, indeed, to be found) F&L would have steered clear of many of the problems to which their interpretation of the control of skilled actions gives rise.

Frames of reference interact and are task-dependent Bruce A. Kay Department of Cognitive and Linguistic Sciences, Brown University, Providence, Rl 02912. [email protected]

Abstract: The problem for the CNS in any particular movement task is to coordinate the various frames of reference appropriate to the task. Control variables are determined by this coordination. The coordination problem varies greatly from task to task, and so no single set of control variables is likely to account for a broad range of movement tasks.

unnecessary after the completion of a movement, that is, at the endpoints. However, depending on the external state of affairs (actually, the relation of the actor to the external world), cocontraction may be required to stabilize the endpoint. ("Completing the motion" usually means to reach a target area and stay in it for a prescribed time.) A better statement of the frame of reference of the task problem would alleviate such problems. Perhaps a solution to the problem of varying environmental constraints and varying tasks might be to take the problem of frames of reference a bit more seriously and to realize that the CVs at work are determined by the coordination of the frames of reference, which are in turn determined by the task (Saltzman & Kelso 1987).

Equilibrium-point control? Yes! Deterministic mechanisms of control? No! Mark L. Latash

The idea of identifying control variables (CVs) and frames of reference is very useful, and Feldman and Levin (F&L) have done a great service by presenting a worked-out example of how to define and use these terms. I do not think, however, that the authors have identified "the" CV for movement in the setting of muscle threshold lengths. I think that we are going to find (as if we have not already - see Stein's 1982 BBS target article and responses) that CVs and their frames of reference are highly taskdependent. For point-to-point motions in which the dynamics are unchanging or are briefly perturbed, the lambda model may suffice (but see below). However, for many other classes of movement, these are neither the appropriate CVs nor the appropriate frame of reference. The key problem with F&Ls analysis is that the frame of reference for the task has not been treated thoroughly enough. What the CNS is trying to do is to control the relationship between the body and the world around it; this means coordinating the various frames of reference in a task situation (Saltzman & Kelso 1987). The coordination of the frames of reference also determines what the CVs are. I would claim that this coordination varies considerably from task to task. For tasks involving forceful interactions with the environment, such as tool use, a very important class of movements - the frames of reference for the actor, the tool, and the workpiece - must relate in a very tight interaction. That interaction varies substantially from task to task and can only be understood by understanding the relationship between the actor and the environment. The CNS must somehow coordinate internal and external frames to use tools in various situations, and the CVs might be quite complex. A movement task may have very little to do with muscle lengths or even forces per se, and so an altogether different frame of reference may be necessary. In timing tasks, for example, the goal is to get a limb segment to a particular place - or to produce a particular force, or whatever - at a particular time. In these tasks the CNS is trying to control when certain muscle events occur, in relation to other internal or external events; controlling threshold muscle lengths to do so would be very cumbersome and an inversion of the problem to be solved. A frame of reference based on time would be more appropriate for this task. Not having a good description of the framework for point-topoint tasks also causes F&L to have a problem with their hypothesis of anatomical correspondence. How can the actual joint angles equal the threshold angles for any and all body postures? This would mean that no muscles are active when in a static posture in which there is a constant external force, for example, gravity. This solution to the redundancy problem does not make sense when you put the body's internal frame together with the external (e.g., gravitational) frame. A related problem is that, as F&L have presented it in section 5, cocontraction commands are

Department of Physical Medicine & Rehabilitation, Department of Molecular Biophysics & Physiology, Rush-Presbyterian-St. Luke's Medical Center, Chicago, IL 60612. [email protected]

Abstract: The equilibrium-point hypothesis (the X-model) is superior to all other models of single-joint control and provides deep insights into the mechanisms of control of multi-joint movements. Attempts at associating control variables with neurophysiological variables look confusing rather than promising. Probabilistic mechanisms may play an important role in movement generation in redundant systems.

The fate of the X model is really weird! When I first learned about it from Anatol Feldman at the end of the 1970s, it immediately appealed to me as an extremely attractive, elegant, and powerful physical model of a complex system that makes a lot of sense. Since that time, I have been genuinely perplexed, witnessing the stubbom resentment of the motor control community toward this model, which is obviously superior to all the other models in the area. The target article presents an extensive and deep exposition of the basic concepts of the X model, and attempts at expanding the model to multi-joint movement control suggesting an ingenious solution for a particular case of Bernstein's problem of redundancy. Predictably, I agree with 95% of what is said in the target article, and admire its clarity and depth. Let me focus on the remaining 5%. Single-joint control. I understand the desire of Feldman and Levin (F&L) to come up with a clear neurophysiological substrate for the originally metaphorical variable \ . I am not impressed by the suggested scheme, however, and see it as a potential source of more confusion and misunderstanding. Such attempts seem to be at odds with the original complex system approach to motor control underlying the X model: a formal description of a system at a certain level of complexity implies that the variables used in the description cannot be reduced to variables describing elements of the complex system, in our case, membrane potential of the ot-motoneurons (—MNs). Let me add one more comment to a recently published critique of this neurophysiological interpretation (Latash 1993). According to F&L, X is associated with subthreshold a-MN membrane depolarization. Thus, X is stripped of its CV status, which is assigned to its central component. This decomposition of X into central and reflex components looks dubious to me. Note that F&L argue against attempts at decomposing muscle activation into central and reflex components (sect. 2.2, para. 4). Some of their arguments, with which I totally agree, can equally be used against the decomposition of X (a-MN membrane depolarization) suggested in the target article. I do not understand why X has to be associated with a neurophysiological variable such as a-MN membrane depolarization. The X model seems to work fine with X being an abstraction, a




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765

Commentary/Feldman and Levin: Motor control metaphorical CV reflecting the activity of many neurons and providing solid means for the hypothetical central controller to produce predictable, functionally significant shifts in the equilibrium state of the neuro-motor apparatus. It is very tempting to engage in a lengthy discussion about the alleged N-shape of the equilibrium trajectory (ET). However, to be brief, I will mention only that since our original publication (Latash & Gottlieb 1991), we performed a number of studies supporting the idea of nonmonotonic equilibrium trajectories (reviewed in Latash 1993; also see Latash 1994; Latash & Goodman, 1994). Multi-joint control. The motor control community has been in urgent need of a hypothesis that would specify CVs used by the brain to control multi-joint movements and simultaneously suggest a solution for Bernstein's problem of redundancy. The solution suggested in the target article has two distinct components: (1) The basic principle of controlling multi-joint movements by shifting positional frames of reference, and (2) The principle of anatomical correspondence, which suggests a neurophysiological mechanism for the implementation of the first principle and finds a deterministic solution for the problem of muscle redundancy when there is no kinematic redundancy. This is indeed a very elegant and appealing approach. On closer examination, however, the principle of anatomical correspondence leaves one with an uneasy feeling of being too prescriptive. The variability of motor patterns (including muscle activation patterns) during repeated attempts at performing a motor task suggests that the CNS does not prescribe unique patterns of muscle activation to achieve a single, desired outcome. I think that Bernstein's problem does not have a deterministic solution similar to such problems at other levels. For example, find which motor units will be recruited and at what frequencies for a given level of muscle activity. Such problems have only probabilistic solutions, which are constrained by what may be called "coordinative rules." Henneman s size principle (Henneman et al. 1965), for example, is a coordinative rule that favors certain patterns of motor unit recruitment without generating a deterministic solution. I think that a less rigid version of the principle of anatomical correspondence may actually be a coordinative rule for multi-joint motor control. As such, it is likely to constrain the distribution of probabilities for the changes in the CVs for individual muscles involved in a multi-joint task while leaving room for variability of these patterns.

What does body configuration in microgravity tell us about the contribution of intra- and extrapersonal frames of reference for motor control? F. Lestienne, M. Ghafouri, and F. Thullier Laboratoire de Biologie et Physiologie du Comportement, URA-CNRS 1293, UniversM Henri Poincar6, Nancy 1, F 54 506 Vandoeuvre-Les-Nancy Cedex, France, [email protected]

Abstract: The authors report that the reorganization of body configuration during weightlessness is based on an intrapersonal frame of reference such as the configuration of the support surface and the position of the body's center of gravity. These results stress the importance of "knowledge" of the state of internal geometric structures, which cannot be directly signalled by specific receptors responsible for direct dialogue with the physical external world.

In section 9 of their target article, Feldman and Levin (F&L) provide a welcome reaffirmation that the X. model is based on an intrapersonal frame of reference (called referent body scheme) combined with extrapersonal frames of reference organized for any sensorimotor modalities, in particular from vestibular, proprioceptic, and visual systems.

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In an attempt to illustrate the notion of referent body scheme, F&L remind us that, upon exposure to weightlessness, the position of different parts of astronauts' bodies shows a large range of body configurations regardless of their orientation in space. Based on studies of postural activities in weightlessness during three space missions, body configuration and the modification of postural muscle activity have been well documented and quantified by our group (Clement et al. 1984; 1985; Gurfinkel et al. 1993). Because of the absence of longitudinal constraints and static torques in the joints caused by gravity, it was in fact reasonable to predict modification of postural attitude resulting from a fuller potential range of angular excursion for each joint. In other words, the "unbolting" of the multi-joint kinematic chain would permit a large diversity of postural forms (Lestienne & Gurfinkel 1988). However, we do not see clearly how F&L can identify a frame of reference attached to a body whose configuration can vary widely. Fortunately, F&L have begun to address this question by proposing that geometric invariance may underlie the "neuronal" body scheme, taking into account that some parameters, such as segment length, remain invariant. Maioli and Lacquaniti (1988) have also suggested that limb length is one of the determinants of postural control in cats. In our view, the theoretical importance of an invariant structural organization depends on the premise that the localization of the origin of this structural organization must be defined within the body architecture. From neurophysiological and psychological data under various experimental conditions, investigators have localized the origin of the frame of reference at different anatomical sites: head-centered, shoulder-centered, and trunkcentered (Blouin et al. 1993; Jeannerod 1988; Soechting & Flanders 1992). If one accepts the above claim, we think it appropriate to emphasize the importance of the "knowledge" of the state of internal geometric structures that cannot be directly signalled by specific receptors responsible for direct dialogue with the physical external world. As mentioned previously, if this internal geometric structure is characterized by the length of the body segments, it also includes the sequence of the segment linkage, the configuration and the dimensions of the support surface (subtended polygon), and the position of the center of gravity of the body (localized at the level of the trunk). It must be mentioned here that investigation of the stabilization of human body position has indicated that the component of the body that is the main object of regulation for maintaining vertical posture is the trunk (Gurfinkel et al. 1981). At this point, we would like to report a very interesting result concerning the reorganization of body configuration during space flight (Lestienne & Gurfinkel 1988). The basic idea is that neural mechanisms must work to correct posture by shifting the barycenter of the body (Lestienne et al. 1994). This assumption is supported by the highly simplified multi-segmental model depicted in Figure 1. In this study we draw particular attention to how the postural attitude is reorganized after seven days in flight to maintain a stable standing posture with feet attached to a platform. This series of sketches shows the postural position in two situations: normal terrestrial standing and voluntary tilting, both in stabilized vision. It is clear that on day two (middle column), the exaggerated forward position of the body was totally incompatible with the existence of a gravitational field. However, at the end of the flight (day seven, right column), the straightening of the body in the two situations is generated by an identical ankle-hip strategy: hip and ankle extension associated with a slight flexion of the knee and a distinct ventroflexion of the neck. The execution of this complex reorganization was not totally successful in obtaining an erect posture. Nevertheless, this nonerect posture, characterized by the semi-flexed position of the joints to minimize the consumed energy, was in equilibrium with respect to a "hypothetical" field




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Commentary/Feldman

and Levin: Motor control

What can we expect from models of motor control? Gerald E. Loeb Bio-Medical Engineering Unit, Queen's University, Kingston, ON K7L 3N6, Canada, [email protected]

Abstract: The lambda model of servocontrol seems superior to the alpha model in terms of dealing with the mechanical complexities of nonlinear and multiarticular muscles. Both, however, can be trivialized by noting that the "control variable" may simply be the sum of descending influences at propriospinal interneurons in the case of the lambda model or in the muscles themselves in the case of the alpha model. The notion that the brain explicitly computes output in terms of any such control variables may be an engineering metaphor, useful for conceptual understanding but not for generating predictive hypotheses about higher motor circuitry.

Figure 1 (Lestienne et al.)- Body configuration in normal gravity and in weightlessness. Multi-segmental, two-legged human model showing the angular combination among four joints (neck, hip, knee, and ankle) before (left) and on day two (middle) and day seven (right) of a seven-day space flight. Upper figures: "normal terrestrial" standing posture. Lower figures: voluntary 7° forward tilt. In both situations goggles were used to stabilize the visual surroundings (stabilized vision). Notice the exaggerated forward posture on day two. In this posture, the projection of the body's center of gravity is located very far from the subtended polygon. On day seven, immediately following postural reorganization, the body is in equilibrium with respect to a hypothetical field of terrestrial gravity, whereas the execution of the postural reorganization was not totally successful in attaining an erect posture (adapted from Lestienne & Gurfinkel 1988).

of terrestrial gravity. The resulting angular combination among the four joints highlighted the mechanism of movement production by bringing backward the barycenter of the body mass into the vicinity of the foot support. This reorganization of body configuration has been confirmed by the redistribution of tonic activity of the leg muscles controlling the ankle, knee, and hip joints during space flight (Clement et al. 1984; 1985; Lestienne et al. 1994). In conclusion, we believe that the experimentally testable arguments developed here reinforce the statement of Feldman & Levin concerning the role of the neuronal body scheme, which "forces the neuronal structure to find a new steady-state distribution of activity which restores the correct geometric relationship associated with the new body configuration" (sect. 6, para. 2). ACKNOWLEDGMENT This work is supported by CNES (Grants 88/CNES/1218 and 94/CNES/0408).

The lambda model for sensorimotor control is clearly a much richer source of biomechanical and neurophysiological insights than the oversimplified alpha model that now dominates many textbooks. Rather than concentrating on the lambda model's mathematical details (which may have frightened off those who demand simple explanations for complicated phenomena), let us concentrate on its general features. Consistency with anatomical facts. It is certainly a great step forward to recognize the importance, even predominance, of motor command pathways that interact with segmental sensory feedback before they reach the motoneurons (Illert et al. 1981; Jankowska et al. 1973). such interactions have often been viewed as a descending modulation of local reflexes, but Feldman and Levin (F&L) imply correctly that the same circuitry permits the motor output to be generated during the event by the proprioceptive signals themselves, played out around an interneuronal set point established by the descending signals. What is less clear is the need for any direct, unmodulated command signal to motoneurons to act as "the control variable." Even monosynaptic excitation of motoneurons is often subject to presynaptic inhibition from somatosensory afferents (Hultborn et al. 1987). By appropriately weighting the relative effects of descending and peripheral signals on the various interneurons, it should be possible to account both for the presence of motor output in the absence of sensory feedback and for its obvious pathologies. Such a unified approach would also account more gracefully for the obvious differences in dependence on proprioceptive feedback in systems such as the eye and neck that, despite F&L's fancy footwork, seem to operate in a very different mode from limbs. As F&L point out, the lambda hypothesis actually makes it plausible for the motor cortex to generate descending commands in end-point coordinates, as suggested by Georgopoulos (1991) and colleagues. If the complex distribution and sequence of activation patterns of motoneurons had to be computed explicitly by the brain, there would simply not be enough computational machinery between the motor cortex and the spinal cord to perform the transformation. Instead, the brain can shift the operating point of the spinal interneurons that actually elaborate the observable motor program. The spinal circuitry can also take into account the posture-dependent background of afferent activity and can generate rapid and goal-directed responses to perturbations. It is worth noting that these "preenabled" responses are often far more sophisticated than might be expected from the simple homonymous reflexes that are usually associated with spinal cord circuitry (Cole et al. 1984; Gracco & Abbs 1985). This is, of course, the result of the widespread convergence and divergence of inputs and outputs mediated by the same spinal interneurons responsible for conveying most of the descending control to the motoneurons (Schomburg 1990). Consistency with biomechanical facts. The lambda model is probably better than the alpha model at coping with the mechanical dynamics of multiarticular limbs and muscles, but much work remains to be done. The analyses presented by F&L assume that




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Commentary/Feldman and Levin: Motor control motoneuron activation (as measured by EMG) is closely related to force output, an assumption that breaks down for large and rapid movements and brief perturbations. The effects of cross-bridge dynamics and connective tissue elasticity are large and complex, but they weigh much more heavily on alpha-like models that must compute motoneuronal activation explicitly. It will also be a challenge to see whether the lambda model can account for the activation of muscles on the basis of their ability to cause acceleration at a particular joint, as opposed to torque. Zajac and Gordon (1989) have pointed out that, depending on posture, activating a muscle can produce accelerations at joints that it does not cross; even more paradoxically, it may accelerate a joint that it does cross in a direction opposite to that predicted by its torque. Such complexities seem to be dealt with appropriately by the nervous system but they are completely beyond the scope of alpha models. For the lambda model to account for them, it seems likely that it will need a considerable refinement of the rudimentary but promising approach to kinesthesia presented by F&L. Consistency with scientific method. It is distressing to see how quickly attempts to cope with reality tend to trivialize all such models into tautologies. For the lambda model, elimination of private line paths to inotoneurons causes the control variable in the brain to become simply the sum of all descending influences on spinal circuitry. For the alpha model, the motoneuronal output to the muscles themselves is the control variable, resulting in a trajectory of purely mechanical equilibria (which are under no constraint to be either realized or realizable during a movement). Neither constitutes a testable hypothesis, so what is an experimentalist to do? At these levels of abstraction, models are more like metaphors than theories. When we read an inspiring novel dealing with a universal theme, we believe that we have gained insight, but we do not insist on going out and reliving the life of the protagonist to test its validity. Instead, we hope these insights will lead us indirectly to make wiser choices in our daily lives. Both the alpha and lambda models are metaphors for aspects of the much richer workings of the real brain. Personally, I find the former like a child's cartoon and the latter like an intriguing short story. Even if someone writes a great novel, however, it would not be the only book I would ever read to understand all there is to know about life or motor control.

Can the X model benefit from understanding human adaptation in weightlessness (and vice versa)? P. Vernon McDonald KRUG Life Sciences, Houston, TX 77058-2769. [email protected]

Abstract: Parameters of the lambda model seem tightly linked to certain characteristics of human performance influenced by weightlessness. This commentary suggests that there is a valuable opportunity to probe the lambda model using the changed environment experienced during space flight. The likely benefits are a better model and a better understanding of the consequences of weightlessness for human performance. The consequences of the changed inertial environment of space flight for human performance are not fully understood, but both the scientific and anecdotal evidence indicate the consequences can be profound. Reports of space motion sickness, disturbances in motion control and spatial orientation, visual disturbance, and experiences of vection are common during the adaptive period early in flight (Reschke et al. 1994). Many of the same disturbances also manifest themselves immediately following the crew's return to Earth. Humans in weightlessness for extended durations also exhibit a number of physiological changes, including changes in bone density, muscle mass, and strength, all of which are

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considered attributable to a changed loading history (Whalen 1993). Given that nominal contact with support surfaces during orbital flight has momentum characteristics significantly different from those experienced on Earth, Whalen (1993) argued that the significant decrease in daily external loading history is critical to the process of musculoskeletal adaptation during space flight. Because humans adapt to operate efficiently and effectively within the ambient environment, it is likely that die consequences of a modified loading history for human performance are much more extensive than the physiological changes referred to by Whalen. The dynamics observed during human-environment interactions are modulated by the inertial, stiffness, and viscosity characteristics of the musculoskeletal system. The control of intersegmental energy flow is critical in many activities, as evidenced by performance decrements seen under conditions of vibration (e.g., Burstom & Lundstrom 1994). Thus, appropriate modulation and attenuation of energy flow is critical for effective performance under conditions of multisegmental motion. Because the dynamics of human-environment interaction during weightlessness are qualitatively different from those found in the terrestrial environment, adaptation to weightlessness will entail a fundamental change in the overall viscoelastic characteristics of the musculoskeletal system. If adapting to weightlessness has implications for the attenuation of energy flow, then this adapted state will be inappropriate for effective and robust postflight terrestrial behavior. The capacity to attenuate the transmission of energy through the body at the moment of heel strike during locomotion is directly influenced by changes in the characteristics of the musculoskeletal shock absorbers, including the viscoelastic properties of joints (Voloshin et al. 1981). Together, the stiffness, viscosity, and inertial properties of the musculoskeletal system contribute to the ability to conserve, dissipate, direct, and/or exploit such energy. It is quite possible that a potent factor influencing postflight human performance is the compromised ability to attenuate energy flow through the body (McDonald et al. 1994). This maladapted effort to manage energy flow will result in inappropriate energy transfer among contiguous body segments and could cause disturbances in both lower limb coordination and head-eye coordination seen during postflight locomotion. The I model lends itself to a direct exploration of the mechanisms underlying this adaptation to weightlessness. In turn, human performance in, and adaptation to, weightlessness lend themselves to direct testing of certain predictions of the I model. The question to be posed for the I model is: How does this process of adaptation unfold? If one were to express the adaptive phenomena in light of I model parameters, where exactly should we expect to see change? For example, Feldman & Levin (F&L) admit that there is the possibility that as yet undefined control variables (CVs) may influence muscle stiffness (sect. 4, para. 3). Is it possible that such a CV is related to the energy transmissibility of the musculoskeletal system? Grillner (1972) demonstrated that the earliest response to the disturbances encountered in walking occur as a result of the intrinsic stiffness of muscle. Perhaps one feature of adaptation to weightlessness is a change in the dynamics of this response mechanism? Finally, one is naturally led to questions of a directly operational nature. For example, would a description of adaptation to weightlessness in terms of the I model lead to the identification of measures we could adopt to alleviate the deleterious aspects of adaptation? As the model currently stands, what kind of sensorimotor disturbances would the model predict in response to the changed inertial environment of weightlessness? Because the parameters of the I model seem tightly linked to certain characteristics of human performance influenced by weightlessness, there is a valuable opportunity to probe the model using the changed inertial environment experienced during orbital flight. The likely benefits are a better model and a better understanding of the consequences of weightlessness for human performance.




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Kinematic invariances and body schema Pietro Morasso and Vittorio Sanguineti Department of Informatics, Systems and Telecommunications, University of Genova, Via Opera Pia 13, 16145 Genova, Italy, [email protected]

Abstract: Generalizing the notion that muscles are positional frames of reference, a high-dimensional muscle space is defined for multi-muscle systems with an embedded low-dimensional motor manifold of functional articulators. A central representation of such a manifold is proposed as computational body schema. The example of the jaw-tongue system is presented, discussing the relation of functional articulators with kinematic invariances and control problems.

Are kinematic invariances, such as the bell-shaped speed profile of the hand trajectory in reaching, peripheral side effects of the motor control process (Feldman & Levin, F&L) or are they essential components of the central planning that precedes and prepares the control process (Morasso 1981)? In a similar vein, where is the natural site for a computational brain structure that can be called the body scheme: at the spinal or the cortical level? Although we think the centralist answer to both questions is more plausible than the peripheralist one defended by F&L, we agree with them concerning the importance of positional frames of reference in motor control and, in particular, concerning (a restricted version of) the \ model. We assume that the muscular actuators (muscles + segmental circuitry) are devices characterized by the following family of electromechanical curves: /=a(/-X)

(1)

where/is the muscle force, / is the muscle length, \ is the control variable, and the function a, the IC of the muscle, is a monotonic increasing function of the argument, which is zero for nonpositive values of the argument.1 The essential points captured by the model are (1) the spring-like properties, (2) the invertibility with respect to the control variable, and (3) the existence of a restlength. For the CNS, this is a sort of black box with two inputs (/ and \ ) and one output (/): one input is controllable (A.) and the other (/) is only measurable, but they are both expressed in the same measurement units. Muscle space. We agree with F&L that associating the set of input variables (L and A) in a multi-muscle system with a positional frame of reference is a fundamental concept for describing and understanding motor control. In more abstract terms, we may think of a muscle space (MS) with one axis for each muscle length: Any configuration of the body is identified by a point Lfz. MS, and movements are uniquely represented by trajectories L = L (t) in this space. A very important aspect (and a major source of complexity} is that biomechanical and functional constraints do not allow L to move freely in MS but force it to "slide" on a complex nonlinear manifold M of much lower dimensionality than MS. The control vector A is a point in MS, although it is not constrained to stay on M, and the brain must have some knowledge of M to generate values of the control vector that are consistent with a desired trajectory. According to F&L, such knowledge, which they call hypothesis of anatomical correspondence, is encoded by means of interneurons of segmental reflex loops. We disagree on this point because we think that it severely underestimates the complexity of the problem. We rather believe that the only possibility for the brain's acquiring a working knowledge of the geometry of M is through unsupervised learning, in line with the Gibsonian theory of affordances (Gibson 1950) and the Piagetian theory of circular reaction (Ackermann 1990; Piaget 1963): The early experience ofbabbling, guided and shaped by social interaction, allows the brain to discover regularities in the inflow of high-dimensional kinesthetic data (L = L(t)) and extract from them the geometry of the lower-dimensional manifold M. An example: Jaw-tongue model. To stress this point, let us consider a muscular hydrostat like the tongue. From the mechanical point of view, it has °° degrees of freedom and thus the principle

of anatomical correspondence would be ill-posed for supporting a coordination of the jaw-tongue muscles. Nevertheless, the jawtongue movements observed in normal speech appear to satisfy some kind of functional constraint that is not merely anatomical but must be somehow related to the nature of the task. We have investigated this problem by analyzing a database of X-ray images of the vocal tract, which allowed us to estimate the shortening/lengthening patterns of a representative subset of jawtongue muscles (3 muscles of the jaw, 3 intrinsic, and 11 extrinsic muscles of the tongue.2 The embedding MS in this example is 17dimensional and to estimate the dimensionality of M we performed a Principal Component analysis (PCA) of the 17dimensional vectors and found that 4-6 independent functional articulators are sufficient to explain the data.3 (Figure 1 shows the effect of the first 4 components, varied separately, one at a time.) Functional articulators embody much more than purely anatomical constraints: they include cognitive constraints as well, which are task-specific (speech, in this case). An immediate consequence of this finding is that such components would be "good" CVs; this suggests that the CNS should be able to "select" the particular set of CVs (i.e., the particular internal representation of body geometry) that maximally "simplify" coordinate transformations, such as one above. A relevant aspect of this second hypothesis is that the emergence of such an "optimal" representation of CVs might be explained in terms of some known computational features of cortical maps, such as unsupervised Hebbian learning (Morasso & Sanguineti 1994). We can also suppose that the same process that discovers the functional articulators Qfonc also learns the mapping L is the order parameter - observable and quantified as the difference between two phase angles. In 1:1 frequency locking, coordination patterns follow from the one-dimensional potential: V() = —acos+ vQ%, where location and relative stability of two minima (equilibria) at | = 0 (inphase) and = IT (antiphase), are scaled by b/a. The expression VQ£ denotes a stochastic force of strength Q. In the associated motion equation, = 8 — asin(J> — 2&sin2 + vQij, 5 represents possible asymmetric contributions to the coordination pattern by the two limbs and similarly affects the equilibria (Kelso et al. 1990; Turvey & Schmidt 1994). In this light, X is a control parameter - changes in X shift the threshold for the tonic stretch reflex, leading to restoring forces that either reestablish the old equilibrium or lead to a new equilibrium. The EP (equilibrium point), defined as the set of rest angles of the involved joints, is the result of this control and could be X s corresponding order parameter. But F&L's effort to achieve a precise understanding of that which controls (namely, X) is not matched by a similar effort to understand precisely that which is controlled. Defining the body reference frame as the intersection of all single-joint rest angles, leaves unaddressed what kind of observable quantifies this equilibrium. In formalizing a X-controlled gradient system, identification of the order parameter under X s influence is as essential as the identification of X itself. Conceiving X as a control parameter does not countenance F&L's definition of a control variable (CV) as purely internal and centrally regulated. In a dynamical account, control and order parameters are not internal to, or detached from, the behavior that they model, but are overt and measurable at the interface between actor and environment. Formalizing behavior through observables need not imply "pseudo-control," but it emphasizes that the relevant quantities emerge from the actor-environment interaction. Although there is a logical distinction between control and order parameter, it is not advantageous to draw this distinction along the traditional lines of internal versus external. It invokes classical, conceptions of a central, controlling unit and leads to recalcitrant problems when extrapersonal factors have to be considered. The basic technical issue, it seems, is how to elaborate on V. In the rhythmic coordination model, asymmetries from the "external" biomechanical properties of the limbs and environmental information have been integrated into V (e.g., Turvey & Schmidt 1994; Schoner & Kelso 1988). In the general case, V will be defined for tasks, that is, movements and their goals. Some important steps toward a task dynamics have been taken (Saltzman & Kelso 1987; Schaal et al., in press; Schoner 1994). They may eventually prove useful to the elaboration of X.

Origins of origins of motor control Esther Thelen Department of Psychology, Indiana University, Bloomington, IN 47405. [email protected]

Abstract: Examination of infant spontaneous and goal-directed arm movements supports Feldman and Levin's hypothesis of a functional hierarchy. Early infant movements are dominated by biomechanical and dynamic factors without external frames of reference. Development involves not only learning to generate these frames of reference, but also protecting the higher-level goal of the movement from internal and external perturbations.

Feldman and Levin (F&L) offer an ambitious and compelling hypothesis for the control of mature and well-practiced movements. But what about the development origins of control? Is their hypothesis useful for understanding the earliest acquisition of voluntary movement, as infants progress from no control of limbs and body segments to purposeful and flexible actions?




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Commentary/Feldman and Levin: Motor control Recent work on infants' learning to reach is both consistent with and informed by F&L's hypothesis. When infants first succeed in reaching and grasping objects at 3 to 4 months, their hand trajectories are jerky and tortuous. Over the next several months, their hand pathways become straighter and the trajectories contain fewer segments of acceleration and deceleration (von Hofsten 1991). Two developmental questions are important: First, how do infants first fashion goal-directed reaches from their ongoing spontaneous movements? And second, by what mechanisms do infants produce smoother and straighter trajectories? In F&L's framework, how do babies learn to generate shifting positional frames of reference and how do they acquire control that is independent of biomechanical changes at the subordinate levels? There is good developmental evidence supporting F&L's notion of a functional hierarchy consisting of a control variable (CV) level and a second level that continuously regulates biomechanical variables in relation to the CVs and internal and external forces. Furthermore, it is clear that the subordinate level is developmentally prior to the control level, and that one function of development is the progressive elaboration and stabilization of the CV from the subordinate level. Consider the nature of infant arm movements in the first three months, before the onset of goalcorrected reaching. These movements often look like expressions of the pure dynamic interactions of the system components and external forces without any imposed frames of reference. (Schoner, in press, has termed this the load level.) Load-level

dynamics alone can produce temporally and spatially patterned movements. Figure 1 shows two examples of high velocity flapping movements of a 14-week-old infant, Gabriel, as he was offered an attractive toy. This is a week before we observed his first successful capture of the toy (Thelen et al. 1993). At the sight of the toy, Gabriel activated his neuromotor system, but he was unable to impose task-related spatial frames of reference. The result was the cyclic, spring-like dynamics of the subordinate level components. These spontaneous infant movements offer a unique opportunity to look more closely at the load-level dynamics without apparent intentional constraints. I show an example of the calculated intersegmental dynamics at Gabriel's shoulder during flapping movements in Figure 2. There are large changes in the gravitational torques as he lifts and drops his arm. At the same time, his high velocity movements generated high motiondependent torques. These high passive forces were counteracted by correspondingly high muscle torques, indicating the reflex intermuscular interactions were in place, and probably played an important role in the load-level dynamics. (See also Schneider et al. 1990, for similar mechanisms in early infant leg movements.) The corresponding EMGs of shoulder and upper arm muscles were almost entirely dominated by coactivation rather than reciprocal activation patterns, consistent with many reports of extensive coactivation in young infants (Forssberg 1985; Myklebust & Gottlieb 1993; Thelen & Fisher 1983). I am especially intrigued, therefore, by F&L's suggestion that without the imposition of a set

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Figure 1 (Thelen). Top panels. Hand trajectories of simultaneous flapping movements of both arms in a 14-week-old boy, Gabriel. The left panel is 8 sec of right-hand movement and the left panel, 14 sec of left-hand movement, both depicted in the sagittal plane. Bottom panels: phase plane representations of the same movements in the x-axis, lateral to the body, and showing characteristic spring-like dynamics.




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Time (s) Figure 2 (Thelen). Top panel. Calculated (inverse dynamics) torques at the shoulder for Gabriel during flapping movements at 14 weeks. The solid line is the net torque, the dashed and dotted line is the gravitational torque, the dashed line is the motion-dependent torques, and the dotted line is the residual or muscle torque. Torques in the positive direction are extensor and in the negative direction, flexor (lifting the arm). Bottom panel. Resultant 3-D velocity for the same movement. Note the high velocity movements at about 6 sec and the resulting high motion-dependent torques. of R commands to set a single reference point for multiple muscle recruitment, reflex intermuscular interactions would favor domination of C commands. Thus, in the beginning the dynamics of generating a trajectory as a succession of frames of reference must be tightly coupled to the dynamics of the load level. Early reaches often look like they are sculpted from pure load-level dynamics; for example, Gabriel's early reaches evolved continuously from the cyclical flapping movements that preceded them. Examination of the underlying torques and EMG revealed a damping down of the high motiondependent and muscle torques in the transition from flap to reach and continued extension cocontraction (Thelen et al. 1993). This ability to get the hand in the "ballpark" of the object by damping

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forces suggests that there has been development in the load-level control as well. Indeed, one function of the spontaneous movements of the first three months may be to tune these reflex loops as infants learn about their arm dynamics. Our observations of infants' week-by-week reaching skill development over the first year suggests that the CV only gradually comes to be independent of the load-level dynamics. Load-level dynamics consisting of interaction, centripetal, and inertial forces, stiffness, and viscoelastic properties all scaled with movement speed, and movement speed had a pervasive effect on hand trajectories. First, throughout most of the first year, the speed of the reach itself was influenced by the speed of the infants' ongoing movements before they initiated the reach. (For an adult analogy,




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Commentary/Feldman and Levin: Motor control imagine beating eggs in a bowl and immediately reaching for the salt without significantly slowing down.) Not until the last months of the first year did the infants isolate the reach itself from the influence of the ongoing movement speed. In addition, for each infant, fast reaches were less straight throughout the year. Fast reaches were also associated with decreased hand path smoothness, but especially in the first few months after reaching onset. Later, hand paths were equally smooth in fast or slow movements. It appears as if the jerky and indirect character of early reaches may, at least in part, be caused by disruptions from the load-level dynamics (Thelen et al., in press), but that the trajectory becomes increasingly stabilized with continued practice. F&L's shifting positional frames of reference may not be the highest CV on the functional hierarchy, however, nor may acquiring trajectory control be the end of the developmental story. Following the theoretical scheme of Schoner (in press), I suggest that a higher, more abstract level of task dynamics, Schoner s goal level, must also develop through learning. A higher goal level is needed because spatial targets can be attained by any number of trajectories, just as trajectories have a large number of load-level realizations. In a similar manner, early in development, the goal level may not be independently controlled or stabilized from the other functional levels and only becomes a CV through learning and practice. There are several developmental examples of goal-level dynamics being captured, so to speak, by dynamics of the lower levels. At about six or seven months, when infants show relatively stable trajectories for reaching but are just developing fine manipulatory control, they often seem to wave or shake objects automatically rather than performing more object-appropriate actions. These (and other) rhythmic stereotypies look as though still unstable goals or trajectories are interrupted by load-level dynamics, particularly cyclical dynamics (Thelen, in press). An equally dramatic example is the classic Piagetian A-not-B error. Eight- to twelve-month-old infants reach for a hidden object several times in the "A" location. Then, in the full view of the infant, the experimenter hides the object at a second "B" location. The error is that infants, having seen the object moved to the second location, persist in reaching toward the original "A" location. This error is traditionally interpreted as a failure to understand that objects exist when displaced. A more likely explanation is that there is as yet imperfect stability of the highest level goal in the sense of control independent from the repeated spatial frames of reference generating the reaching trajectory. (Thelen & Smith 1994). Actions are adaptive and flexible, then, only as goals are maintained irrespective of their particular executions, just as trajectories are functionally useful only when they are not blown off course by movement biomechanics or external forces. With this additional CV level added, Feldman and Levins hypothesis for motor control is thus highly compatible with existing developmental data and furthermore, it suggests many new avenues for further research.

Equifinality and phase-resetting: The role of control parameter manipulations R. E. A. van Emmerik and R. C. Wagenaar Vrije Universiteil Hospital, Department of Physical Therapy, 1007 MB Amsterdam, The Netherlands, [email protected]

Abstract: It is argued that the equilibrium point model can lead to new insights regarding transition and stability processes in movement coordination. The role of movement control parameters on equifinality and phase-resetting is discussed; not only control but also external control parameters can affect the global dynamical regime.

In Feldman s equilibrium-point hypothesis, states of the motor system are described in equilibrium states, which are dynamically

assembled from the interactions of centrally regulated, nonlinear thresholds on the motor neuron pool and the active loading of the musculo-skeletal system. Although from an ecological psychology perspective (e.g., Gibson 1979) the mutuality between organism and environment is central, very few attempts have been made to formulate common "metries" in which perception and movement properties are scaled to a common measurement basis. One such attempt has been provided by Shaw and Kinsella-Shaw (1988), who proposed fractal geometries and attractor dynamics to provide such a metric. In our view, the EP hypothesis also offers such a metric, and is a very detailed and thorough attempt to put the dynamics of perception and movement on a common measurement basis from a neurophysiological perspective. In this commentary we discuss the role of movement control parameters in equifinality and phase-resetting from a dynamical system perspective (e.g., Schoner & Kelso 1988) and elaborate on similarities with and challenges to the lambda model of motor control as presented in the target article. In section 3, Feldman and Levin (F&L) indicate that the loading-reloading tests have been used to demonstrate that specific load perturbations can break equifinality, even under the instruction not to intervene. As Figure 4G of the target article shows, abrupt reloading can lead to undershooting the initial position. As F&L describe, this deviation from equifinality has been used to question the validity of the IC concept. F&L argue, however, that instead of invalidating the EP hypothesis, these findings can point to limitations in holding control variables (e.g., lambda) constant. We quite agree with F&L's interpretation: any reasonable model of motor control should incorporate limits in stability to perturbations. However, we do not think that this limit would be solely in terms of the inability to hold "central" control variables constant. Instead, this limit could also arise within the global dynamical regime underlying the observed postures or movements, and can be explored through manipulation of system control parameters (e.g., Haken 1977). These control parameters could originate from within the system (F&L's "control variables" or CVs), but can also be drawn on the system externally. From this perspective, mass or perturbation magnitude could also act as a "control parameter," the manipulation of which can unravel different stability regimes (e.g., van Emmerik 1992). The breakdown of equifinality and phase-resetting has been observed in several experiments on rhythmic limb movements. The effects of perturbations in phase transitions between bimanual finger movements have been examined by Scholz et al. (1987) using tools from synergetics (Haken 1977). One of the predictions from synergetics is that phase transitions between different qualitative states, as expressed by the "order parameter" (here the relative phase between the fingers), can be induced by systematically scaling a control parameter. In this experiment a systematic increase in movement frequency resulted in an abrupt change from out-of-phase to in-phase movement. This abrupt transition was shown by critical fluctuations in the order parameter and increased relaxation times following perturbations. Scholz et al. (1987) showed that perturbations added to the fingers at low frequencies (stable out-of-phase mode) did not effect the relaxation time back to the original pattern. Close to the transition, however, similar perturbations resulted in large increases in relaxation time, demonstrating instability of the out-of-phase attractor. This relaxation time was again reduced when perturbed in the stable in-phase mode at higher frequencies. Winfree (1980) has modelled the effects of external perturbations and different types of phase-resetting in so-called time crystals. These structures represent the geometric properties of old phase versus new phase as a function of changes in a control parameter, such as the duration of a light pulse on activity patterns in biological organisms. Gradually increasing the pulse duration will change the resetting curve from phase-resetting to no phaseresetting. Such control parameter manipulations can distinguish regimes of stability from so-called bifurcation points, where oscillations can start, be extinguished or become "chaotic." That a




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Commentary/Feldman and Levin: Motor control systematic scaling of control parameters can unravel dynamical regimes with different stability characteristics is shown in the logistic population dynamics model by May (1976): ,,+ 1 = a x j l -

(1)

where x,, is the population at generation n, xT 0 or relaxed if C < 0 (target article, sect. 5; see sect. 7 for a more specific definition in which reflex intermuscular interaction is taken into account). In the first case, whether or not die muscles will be coactive depends on their interaction with the environment. For example, in Figure R2, when the EP lies outside the zone, no antagonist EMG is seen, as in the Gielen & van Bolhuis experiments. It is interesting that the C command facilitating, say, biceps and triceps motoneurons changes the distance between the thresholds of synergists (biceps and brachioradialis). As a consequence, the activity of the synergists in the final EP will be redistributed so that biceps activation will dominate, although triceps activity will be absent (Fig. R2). Without expecting it, we have a deeper understanding of the C command and its role in the control of intermuscular interaction: the C command directed to agonist and antagonist motoneurons may also change the coordination among synergist muscles. We can suggest two tests for the presence of a coactivation zone. First, one could measure the excitability of antagonist motoneurons at the final position (e.g., with the H-reflex), which should be different under isometric and isotonic conditions. Second, despite die absence of antagonist activity at the final EP, sudden unloading from the final position (instruction "do not intervene" or "do not correct") should bring the EP into the zone (Fig. R2) and antagonist activity will appear. The Cielen & van Bolhuis data and our explanation stimulate further questions, explanations, and tests. Why might muscle coordination be different at the same EP under isometric and isotonic conditions when the final combinations of net joint torque and position are identical? It may be that current muscular activity depends on the history of motor unit recruitment in those muscles (cf. Windhorst). Another answer is that even if the system arrives at the same EP, the stability requirements at this EP may be different. For example, under isometric conditions,




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Response/Levin and Feldman: Motor control the system limits changes in joint position in case of unforeseen changes in the load (Fig. R2). Cielen & van Bolhuis s data allow us to illustrate that unjustified rejections of the model actually obstruct a more profound understanding of specific aspects of motor control and interfere with the ability to test predictions related to these aspects (Hodgson, Loeb, Scott).

JC BB BR

Joint angle Figure R2. The C command directed to agonist and antagonist motoneurons may also change the coordination among synergist muscles in isometric (A) and isotonic (B) conditions with the same final combination of net joint torque and position (filled circles; response to Cielen & van Bolhuis). As in Figure 1, horizontal strips show the angular range in which flexor and extensor muscles may be active. A: Isometric flexor torque exertion at the elbow is produced by shifts of flexor and extensor invariant characteristics from the initial position i (open circle) to the final position / ' (shaded circle) by the R command. In this case, a small coactivation zone occurs around position/'. However, movement of the arm is blocked at the initial position so that the initial and final positions of the arm coincide (i = / ) . In the figure, only the final positions of the invariant characteristics for biceps brachii (BB), brachioradialis (BR), triceps bracii (TB) and for the total joint (JC) are shown. The final EP (the point of intersection of the total joint characteristic, JC, with the load characteristic, vertical dashed line) is shown by the filled circle. At the final position, both BB and BR, but not TB, contribute to the total joint torque. B: Isotonic flexor movement leading to the same final combination (filled circle) of total joint torque and position as in A. The C command is greater than in A and creates a coactivation zone for BB and TB • leading to a difference between the activation threshold for synergists (BB and BR). Compared to A, the contribution of BB to the total joint torque increases. Note that in the final position (/) of the joint, TB is not active in both A and B because/is outside of the zone of TB activity. The existence of the coactivation zone may be demonstrated by unloading the joint. This will bring the elbow to position (/') inside the zone and TB activity will appear.

the obstacle that the arm encounters contributes to its stability. In free movement, on the other hand, stability has to be provided by the motor system itself, leading to different muscle activation patterns. Why does the system control the activity of synergists (i.e., biceps vs. brachioradialis) differently? It may be due to the different stiffness characteristics (slope of the invariant characteristic, IC) for different muscles. By using a C command, the system may give preference to one synergist (e.g., biceps) or another (brachioradialis), depending on the motor task. Last, and perhaps most important, by using a C command

R3. Control variables and the environment. Point (1) of the definition given for CVs (target article, sect. 1) clearly precludes a continuous dependence of CVs on current biomechanical variables. The same point specifically indicates that CVs may undergo discontinuous (triggered, or in dynamical systems terminology, bifurcational) changes under the influence of environmental factors or because of changes in the internal state of the system. This reservation, however, did not deter several commentators from unjustly criticizing the A. model based on the incorrect view of CVs as absolutely independent variables or as ignoring environmental influences (Corcos & Pfann; Dean; Hamm & Han; Hatsopoulos & Warren; Scott). Indeed, CVs may be specified based on previously experienced, actual, or anticipated physical characteristics of the environment (Flanagan et al.). Bifurcations are indeed a rich area of the dynamical systems approach nicely outlined in commentaries by Fikes & Townsend, Sternad & Turvey, and van Emmerik & Wagenaar. Thus, discontinuous changes in CVs resulting, in particular, in nonequifinality of movements are welcome in the model. We pointed out (target article, Fig. 3) that findings of nonequifinality using the "do not intervene" paradigm were earlier reported in Russian by Feldman (Feldman 1979; see also Gottlieb & Agarwal 1988; Lackner & Dizio 1994). In other words, the possibility of nonequifinality of motor behavior was not an obstacle to the elaboration of the model. In fact, in naive subjects, sudden unloading - a procedure underlying the measurement of invariant characteristics - produces a change in arm position without any particular instruction. The instruction "do not intervene" is only intended to ensure that subjects do not change their natural behavior (see McClosky & Prochazka, 1994). However, even in this case, additional tests (target article, sect. 3) were made to confirm that subjects had not modified CVs. Since nonequifinality is a threshold phenomenon (van Emmerik & Wagenaar), training may enhance the threshold for triggered reactions to perturbation and thus produce equifinal behavior. On the other hand, equifinality may be less important when it is necessary to comply with different external and internal constraints imposed by the motor task. This may be relevant to the explanation of positional errors (nonequifinality) during arm pointing in the presence of velocitydependent Coriolis forces in a rotating room (Lackner & Dizio 1994). The subject's first priority may have been to diminish the arm deflections elicited by the Coriolis force, which may have been done by appropriately curving the endpoint equilibrium trajectory. This strategy gives rise to an endpoint positional error in the direction of the Coriolis force. In the process of adaptation from trial to trial, subjects could, first, increase the curvature of the equilibrium trajectory to further compensate the curvature of the actual trajectory and thus make it approximately straight, and, second, diminish the positional error by rotating the equilibrium trajectory as a whole in the direction opposite BEHAVIORAL AND BRAIN SCIENCES (1995) 18:4



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Response/Levin and Feldman: Motor control to the Coriolis force. This explanation can be extended to postrotatory adaptation, in which inversion of positional errors would be predicted. Thus, the model suggests only that the invariant and equifinal behaviors are observable in specific conditions. Claims that these are universal phenomena or that the model cannot deal with nonequifinality data from perturbation experiments (Scott) are incorrect. Scott expresses some reservations about the "do not intervene" paradigm. Indeed, use of this paradigm in primate experiments (target article, sect. 11.2) may help to determine whether neuronal population vectors characterizing activity in different brain structures (1) depend on biomechanical variables or (2) are independent of them, reflecting motion of the positional frames of reference used by the nervous system to accomplish the motor task (see sect. 4). Pribram's experiments demonstrate the feasibility of the second possibility. There is an interesting possibility (not mentioned in the target article or by commentators) that bifurcations produced by the nervous system or elicited by environmental factors may transform some CVs into subordinate, nonCVs. In this case, control functions are transferred to a higher level defined by the new CVs. This idea is in agreement with that of Bernstein (1967), who also suggested that control functions may be transferred from one neuronal level to another, such that the latter becomes the "leading level." He also assumed that this process is associated with a change in the type of leading sensory information required for functioning at the new level. A specific form of this process, the transfer of control functions from a joint-oriented frame of reference to a frame associated with external space for arm movements and locomotion, is presented in section R6, below. The \ model relieves the CNS of the weighty task of direct modification of biomechanical or, according to Windhorst, Newtonian variables by clearly distinguishing between CVs and non-CVs. Supporting this view, Alexandrov et al. elegantly explains how kinematic (trunk movement) and kinetic goals (stabilization of the center of gravity) are simultaneously reached during forward leaning. To call a combination of CVs and kinematic and kinetic variables a "mixed global control variable" as Windhorst suggests (following Hasan, 1991) may confuse CVs with physical variables that are controlled by the CNS but are also directly dependent on the environment. Windhorst raises several points concerning the regulation of stiffness and damping. In the physiological literature, damping is associated with regulation of force as a function of velocity. In contrast, the damping coefficient |x in the X. model characterizes the dependency of the threshold on velocity (cf. Hodgson). Both muscle intrinsic properties and proprioceptive feedback are velocity dependent and contribute nonlinearly to force-related damping. The component of force-related damping dependent on proprioceptive feedback, in a first approximation, is proportional to the product of muscle stiffness and damping coefficient (X (Feldman 1979). Stiffness is controlled by the C command and not less effectively by the R command. Even when these and other CVs are fixed, stiffness, according to the nonlinear shape of the IC, depends on the current joint angle (see also Fig. R2). It is because of this dependency that we cannot give the status of CV to stiffness and to

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force-related damping without compromising the logical basis of the model. Windhorst mistakenly assumes that the term "invariant characteristics" means the invariance of their shape. Actually, the term means that the system maintains invariant values of CVs for all EPs on the IC so that muscle force becomes a single-valued function of muscle length. Indeed, we were aware that our own and other data show that the shape of different ICs in the family is not the same (target article, sect. 3). In other words, the shape of the characteristic is a function of its position defined by K. Windhorst is right in pointing out that in our schematic diagrams (e.g., target article, Fig. 6) this aspect of ICs was not stressed. Note, however, that this simplification does not affect the aspects of the A. model illustrated by these diagrams. The fact that the slope is a function of X. does not change the status of stiffness from a non-Cv to a CV, nor does it require the introduction of a new CV into the model. The possibility of change in the shape of the force—length characteristic for an individual muscle regardless of the threshold is not supported by most data. Capaday (1994) recently observed an increase in the threshold of the tonic stretch reflex in decerebrated cats elicited by administering of baclofen, which facilitates presynaptic inhibition. Changes in the slope of the force-length characteristic were thereby related to the changes in the threshold. In light of the accumulated data on the absence of this independent control, we hesitate to introduce an additional CV responsible for setting individual muscle stiffness. R4. The measurement of control variables. In accord with Bernstein (1935), who emphasized that functional characteristics may be distributed rather than localized in specific brain structures (Pribram), we indicated that in principle, the same CNS structures may contribute to the generation of CVs and non-CVs. This did not preclude some commentators (e.g., Scott) from accusing us of a "centrist ideology." Perhaps it is more appropriate to regard a CV as a result of the transition of many neuronal structures from one steadystate to another. Each of these neurons can simultaneously participate in the generation of a CV while carrying sensory information, for example, from the periphery. This of course poses a problem for the experimentalist. How can we measure CVs and distinguish them from non-CVs at the neuronal level? Hodgson's theorem on the "fundamental unobservability of control variables" suggests that this is impossible. We are reminded of a quote from Jaroslav Hasek, who wrote that an educated man can always distinguish between a devil and a bull (from "The Good Soldier Schweik," 1921). Although the theorem may be correct to some extent, it may also be misleading. CVs or their effects can be studied in several ways. First, if applied properly, the "do not intervene" paradigm permits the identification of behaviors associated with invariant CVs from those elicited by changes in CVs. Second, the central component of the threshold, a CV, may be found when the body configuration matches the referent one (see sect. R7). A third method would be to measure the same CV when intermuscular interactions are pharmacologically blocked. Fourth, R and C commands may be distinguished at the suprasegmental level rather than at the level of motoneuronal membrane potentials. Finally, different methods of ensemble averaging of neuronal activity may be used to find CVs (Pribram).




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Response/Levin and Feldman: Motor control Concerning ensemble averaging, one may assume that despite individual peculiarities of each neuron in terms of its responsiveness to sensory inputs, all neurons from an anatomically defined area may participate to some extent in the transition from one steady-state of the system to another. Consequently, information about CVs may be obtained by some procedure of ensemble averaging of the activity of all neurons, or better, their postsynaptic potentials (PSPs). For example, Fortier et al. (1993) averaged the spike activity of cerebellar neurons during reaching movements in monkeys. As shown in Figure R3, this averaged activity could be interpreted as being independent of movement kinematics: a fast ramp increase in the activity before the movement onset, a steady-state level of activity during the movement and a gradual decline in the activity after the end of movement. Figure R3 can also be interpreted as a superposition of ramp-shaped R and C commands, where the C command declines after the end of the movement (target article, Fig. 14; Kay). The only reservation is that at the cerebellar level these commands start much earlier than at the motoneuronal level. In contrast, the population mean for motor cortical activity carries additional information probably related to the movement itself (Fig. R3). A finer analysis could reveal that there are two subpopulations of neurons differing in terms of their descending effects (reciprocal orcoactivation), in which case they could be associated with R and C commands.

CEREBELLUM

MOTOR CORTEX

500 msec

250 msec

Figure R3. A: Population histograms of cerebellar (solid) and motor cortex populations (outline) at the preferred direction of each cell oriented to the onset of movement (vertical dotted line). Horizontal calibration bar, 500 msec. Vertical calibration bar, 10 imp/sec. B: Same data with expanded time scale, and motor cortex histogram shifted so that premovement tonic activity is at same level as cerebellar cells, vertical calibration of 10 imp/sec only applied to cerebellar neurones. Horizontal calibration bar, 250 msec, (adapted from Fortier et al. 1993, Fig. 8).

R5. Arm movements. Many commentators (e.g., Alex-

androv et al., Fidelman, Goodman) appreciate the explanation of pointing movements in the model, which offers a solution for the redundancy problem and predicts kinematic and EMG patterns (target article, sects. 11.2 and 11.3). Goodman, for example, elegantly demonstrates that many models dealing with redundancy may be characterized in part by a general algorithm relating the velocity of change in a planned trajectory with the current planned position and the target. He includes our model in this class of models, but we would add the reservation that neither the trajectory nor the final position are preprogrammed. As Fidelman correctly interprets the \ model, intentional movements begin before their final destination is determined, and the final destination is defined during the movement by the duration of central commands. In other words, there are separate mechanisms for coding spatial and temporal aspects of movement. Our model conforms to Fidelmans model for hemispheric specialization. His data may provide some clues as to how this process is accomplished. Some commentators expressed a feeling of dissatisfaction with some aspects of the model (Dean, Desmurget et al., Fikes & Townsend, Haggard et al., Wright & States). For example, Desmurget et al. argue against the conservative control strategy, based on interesting data on grasping an object placed in different spatial orientations. Our response is that although the conservative control strategy may minimize the number of degrees of freedom of a movement, it does not mean that while performing the task, the system suppresses functionally significant degrees of freedom. In their example, the coordination of shoulder and wrist rotation is a key element in providing the appropriate orientation of the hand for grasping the cylinder. We consider this coupling as a minimal synergy (target article, sect. 11.3), a concept described in the framework of the conservative control strategy. In general, in agreement with Desmurget et al., we do not insist on the universality of the conservative control strategy (see sect. R6). At the same time, in contrast to Desmurget et al., we do not consider the minimum torque change and force minimization strategies as serious alternatives, because they comprise pseudocontrol models, which we strongly criticized (target article, sect. 2). We have also identified other problems with our solution for the control of arm movement. First, the assumption of the existence of the control velocity vector U as a CV for pointing has not been related to the main idea of the model (shifting the origin point of a positional frame of reference to produce movement). Second, although the model rejects the idea of inverse computations of muscle torques (Desmurget et al.), it still relies on some internal model of the limb geometry as well as on computations based on it for the transformation of the control velocity vector into R commands for individual joints. Although the idea that the nervous system uses internal physical and geometrical models for movement planning is popular (e.g., Flanagan et al., Haggard et al., Morasso & Sanguineti, in contrast, see Ostry et al.), the transformation may result from some dynamic process that does not rely on internal models (sect. R6). Concerning the first problem about the nature of the frame of reference for pointing, the available data are not




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Response/Levin and Feldman: Motor control very helpful. Lestienne et al. remind us that the origin of the frame of reference has been localized at different anatomical sites defined within the body architecture: head-, shoulder-, and trunk-centered (Blouin et al. 1993; Jeannerod 1988; Soechting & Flanders 1992). In our formulation, these sites do not form the origin point of the frame of reference for the control of pointing but may be considered fixed points of the body configuration preselected for a given task. For example, arm-pointing movements produced by a seated subject whose trunk is strapped to a back support will (if the subject is not asked to do otherwise) be produced with minimal displacements of the center of rotation of the shoulder. In this example, the physical conditions and explicit or implicit instruction ("do not move your back") compel the system to keep the center of shoulder rotation motionless. This may be one way that the system handles the diversity of task demands using a common control system (Haggard et al., Kay). To refer to this physically constrained point as the origin of a frame of reference for pointing conflicts with the basic idea of the X model, that motion is produced by shifting the origin point of the frame of reference. The best answer is that for pointing, the system uses a frame of reference whose origin does not depend on the center of shoulder rotation. Such a frame of reference may be associated with external space with its origin point outside of the body as in Figure R4A. Shifting the origin point of this frame of reference will result in a pointing movement, because in the X model the generation of EMG activity and muscle forces are framedependent. In other words, if the arm was initially in some equilibrium configuration, the shift of the origin point in a specific direction would elicit motion to another equilibrium configuration. This idea is more fully elaborated in the next section. R6. Key elements in the generation of frames of reference: A solution for a frame of reference associated with the external space. The ability of the model to integrate other sensorimotor systems (visual, vestibular, etc.) and their associated frames of reference is questioned by Bonnard & Pailhous. We understand this problem because in this respect the model has not yet gone far enough. At the same time, however, we would like to stress that the model contains key principles for the creation and integration of many frames of reference. Specifically, several components are essential for the generation of a positional frame of reference used for movement production. The first is the existence of threshold elements (neurons) projecting directly or indirectly to motoneurons. The second is the convergence of sensory information (visual, vestibular, auditory, proprioceptive, etc.) and independent control inputs on these common threshold elements. In order to relate the frame of reference to the physical world, afferent systems are necessarily sensitive to variables associated with the environment. Finally, and most important, the generation of activity and forces is frame-dependent. Shift the frame of reference and the system will be compelled to establish a new equilibrium position. It has recently been shown, for example, that vestibular and ocular systems cooperate in providing a frame of reference for postural stabilization of the body in the lamprey (Wallen et al. 1994). Destruction of the vestibular organ on one side of the head caused the animal to rotate

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B

ill

x3

E

o

n

Figure R4. Frames of reference associated with external space (described in sect. R6) may be used for the control of arm movement and locomotion. Xv X2, X3: Cartesian coordinates associated with coronal, sagittal, and vertical axes. A: Schema showing the shift in the origin of the frame of reference from E to E' (left arrow). The shift results in a change in the R command for the individual joints, bringing the arm to a new equilibrium configuration with displacement of the arm endpoint from position P to P' (right arrow). The direction of the shift in the origin point may be adjusted to produce movement of the endpoint toward the target. B: For locomotion, the origin of the frame of reference may be shifted sagittally to allow for progression of the body. C: Lifting and replacing the foot (arrows) may be accomplished by vertical shifts of the origin of the frame of reference. Locomotion over an obstacle (black square) may be viewed as a combination of the two shifts shown in B and C.

continuously. This asymmetry was reversed by visual stimulation nicely demonstrating that these two systems act as antagonists establishing an equilibrium point associated with the stable posture of the body. Thus, afferents from more than one system (visual and vestibular) may be combined in determining the external frame of reference. As another example, we consider how an extrapersonal frame of reference can be generated and used for limb movement and locomotion (see also sect. R8). Our main assumption is that proprioceptive information can be processed by a higher-order population of neurons such that these neurons will be sensitive to afferent inputs proportional to the orientation (coronal, sagittal, vertical, or mixed) of the body or limb in space. Control inputs to these neurons will define the origin point for this Cartesian frame of reference associated with some real point in external space (say, the corner of the table). Indeed, vestibular and visual information may also be integrated into the frame of reference, an aspect especially important for the control of locomotion (sect. R8). All that remains is for the system to




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Response/Levin and Feldman: Motor control use this frame of reference for the control of movement. The natural assumption is that neuronal elements produce R commands in this frame of reference as a function of the distance between the current orientation X( t) of the limb and the origin E of the frame: = s,d(X - E)/dt

(1)

The expression on the right-hand side is a scalar product of vectors X = (Xu X2, X3) is the vector of the coronal, sagittal, and vertical coordinates with respect to the body; E = (Ex, E2, E3) is the vector of the position of the origin point in these coordinates; s( = (s1(,s2,-,S3j)isadimensionless vector characteristic of commands for the i th joint in this coordinate system. We would like to stress several points of this, in many respects, interesting solution based on the Bernsteinian idea of the transfer of control functions to a higher level (sect. 3; Fig. 4). (1) The riming of the shifts in the equilibrium state of the system is now defined by the timing of the new CV, namely, E and not by the R commands (see definition of equilibrium state in the target article, sect. 1). (2) Changes in R commands continue even after the end of changes in the E command (clE/dt = 0), until a new steady state (dX/dt = 0) of the system associated with a new equilibrium configuration of the arm is established. (3) The direction of the movement of the endpoint will depend continuously on the direction of the shift in the origin point E and can be adjusted to reach the target (Fig. 4A). Unlike the former model, the shifts in the position of the arm endpoint by the R commands cannot be specified independently of external forces and cannot be considered as CVs. (4) The present solution gives more freedom to manipulate with joints participating in the common task (Wright & States): the system may keep the R commands independent of each other or coordinate them in synergies (called "primitives" by Giszter) or restrict the participation of other joints (Haggard et al.). (5) This solution does not seem to require an explicit representation of limb geometry for the computation of the R commands: they are generated as a result of the shift in the external frame. What is required for the generation of the R commands is specific sensory information showing the orientation of each joint relative to the sagittal, coronal, and transversal directions. (6) The solution predicts the existence of high-order proprioceptive neurons sensitive to the general orientation of the limb in Cartesian coordinates rather than to joint positions. Giszter suggests that we missed a set of CVs associated with arm endpoint force regulation. (Note that an endpoint force is only produced when the endpoint interacts with an obstacle.) The problem, however, is that we do not know what we missed: these studies give no information on CVs used in this motor task. Indeed, the phases of the wiping reflex in the frog, characterized in our previous studies (Berlcinblit et al. 1986), were not identified as CVs. Giszter s studies are concerned only with force and position variables (contained within force fields or "primitives"), which depend directly on external conditions and would not be classified as CVs (target article, sect. 1). For comparison, studies of invariant characteristics suggested variables (R and C commands and the central component of X) outside the habitual domain of non-CVs. It would be more helpful if Giszter could identify physiologically plausible CVs asso-

ciated with the control of the position and shape of the force field. Giszter and his colleagues have relied heavily on deafferentation experiments to support their point of view. This approach has been inspired by the a model and its erroneous views on the nature of CVs (see n. 1). Thus, in a sense, these studies could not go beyond the domain of non-CVs. Giszter's concern, however, may be reformulated in the form of the following question. Is the set of CVs that already exists in the X model sufficient to explain endpoint force regulation? We would argue that the answer is yes. To create an endpoint force against an obstacle, the subject may use the same CVs as in free arm-pointing movements. In other words, the subject may generate an endpoint force by specifying a control velocity vector (or, in the new interpretation, the vector that translates the origin E of the external frame of reference). Some may say that this strategy could fail because the directions of positional shifts of the frame of reference and the resulting endpoint force may be different. This only means that the subject should adjust the direction of the change in E until the desired direction of the endpoint force is reached. This theoretical framework may also assist in the interpretation of the neuronal population vectors in studies of directional endpoint force control in primates (Georgopoulos et al. 1992; Kalaska & Crammond 1992). If the population vector coincides with the direction of the force, it is most likely that these neurons are not related to control functions. If the vector differs essentially from the direction of force, there is a possibility that these neurons participate in the positional shift in the frame of reference. The X model predicts that in this case sudden removal of the load from the limb will produce motion in the direction coinciding with the direction of the population vector. R7. Control variables for multi-muscle coordination.

There is an expression of surprise by Ingvaldsen & Whiting and even the suggestion that we used circular logic when we indicated that not the total threshold length but only a component of it is a CV. The idea is in fact not new (see Feldman 1986, Fig. 16); in addition, it is based on experimental facts (see target article, sect. 3 and Fig. 5; Nichols). There is a central component of threshold regulation specified by descending systems (i.e., Dieter's nucleus, pyramidal tract, medial reticular formation; Feldman & Orlovsky 1972). At the same time, there is an additive component of the threshold dependent on reflex intermuscular interaction (not to mention that the dynamic threshold depends on the velocity of stretch of the homonymous muscle). Like the EP, X. is a key state variable and it is not surprising that both control and peripheral systems are involved in its regulation. The reason for confusion may be the use of the symbol 8X for the central component of the threshold, which may be understood as any change in the threshold. We would like to remove this terminological source of confusion. Here we describe a multi-muscle frame of reference formulated in terms of intrinsically consistent mathematics according to the recipes provided in the target article. This reinforces the arguments on the role of intermuscular interaction in providing biomechanical correspondence of CVs. Let us denote the total static threshold, as usual, X, its central component Xc, and its peripheral component de-




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Response/Levin and Feldman: Motor control pendent on reflex intermuscular interaction p. Thus, we may rewrite the equation for the total dynamic threshold length (k*j) for any muscle i as: n

\*i = \f + p,- where p, = 2 Py and plf = —jx£ dxjdt (2) where p,^ is a change in the threshold of muscle i mediated by proprioceptive afferents or Renshaw cells of muscle/ (cf. Smeets), |JL,- is centrally controlled damping (a timedimensional CV). The invariant characteristic is associated with an invariant value of the central component Kf but the additive component p; is not the same for different points of the IC. It has been illustrated that the reflex intermuscular interaction influences the shape and position of ICs (Feldman 1993; Nichols). The central component, \f, has two additive components depending on the vector command R = (R 1; . . . , Rn) and C = (Ct, . . . , C n ), where n is the number of joints:

the value of C. It is natural to suggest that this component of interaction is reduced to zero when C = 0: Pj(C)=OifC

= 0

(8)

In this case, the global minimum (5) is associated with the state when the reflex intermuscular interaction is reduced to zero, the total threshold (\f) coinciding with its central component (\ c ) and simultaneously with the actual muscle length: (9)

*t ~ K = 0

for all muscles of the body. In addition, in this state, threshold angles, R = (R1, . . . , Rn), coincide with actual joint angles R = Q — (0 X , . . . , 0 n ), and thus the relationship between the total threshold length or its central component and threshold angles mirror the dependencies of actual muscle lengths on actual joint angles. Mathematically, if function / f (O) describes the anatomical relationship between actual muscle length x, and joint angles:

*,=/,(e) As has been defined in the target article, the R command specifies the referent body configuration and the C command creates a spatial zone of muscle coactivation or relaxation (depending on the signs of components of C) in the vicinity of the referent configuration (cf. Hodgson). It has been suggested that changes in the C command preserve the EP if it exists. At the level of spinal interneurons and motoneurons, the borders of this zone are modified due to intermuscular interactions. It has been suggested that there are two independent subsystems of intermuscular interaction subserving R and C command systems (target article, sect. 7). Thus, symbol Pj may be represented as a sum of two components: p, =

P i (fl)

+

Pi (C)

(4)

When external forces are removed, a global minimum may be reached when the R component of intermuscular interaction is zero, whereas the R components of the thresholds coincide with the actual muscle length for all muscles of the body such that: x, - \ 0 and vice versa

(6)

External forces such as gravity will be compensated by the muscle forces at an equilibrium body configuration that is different from the referent one. These two states represent, in dynamical terminology (Sternad & Turvey), local and global minima of the sensorimotor interactions described here. Indeed, in any equilibrium state different from the referent one, S ^ f i and: 0 and also p,(fl) # 0 (7) x, The model thus admits the possibility of a strong intermuscular interaction in the equilibrium configuration. Concerning the C command, it has been suggested (target article, sect. 7) that the C component of intermuscular interaction, p,( C), tends to maximize itself according to

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then, for any referent configuration 0 = R, the same function describes the relationship between the total static threshold length or its central component and threshold angles: which resembles Equation 6 (of the target article) for the referent body configuration. In contrast to Ingvaldsen & Whiting, we see no logical problem in using the total threshold \ in Equation 6 of the target article: for any referent body configuration, the total threshold coincides with its independent central component. We would like to emphasize that the process of minimization of the intermuscular interaction according to Gelfand & Tsetlin's (1971) principle guides both the reaching of the equilibrium configuration and, if external forces are absent, the referent body configuration. A global minimum (zero intermuscular interaction) is only established when the referent configuration is reached. Remarkably, many commentators (Alexandrov et al., Bonnard & Pailhous, Lestienne et al., McDonald) expressed the idea that exploring different configurations of the body in the absence of gravity may be a good way of testing the hypothesis of biomechanical correspondence. Indeed, their results, though extremely interesting, are not conclusive; for example, they neither support nor reject the hypothesis, but may represent a necessary prerequisite for the elaboration of more specific experiments. They point out that the barycenter of mass and the lengths of body segments change in the microgravity environment. These facts may be used to test the hypothesis, also suggested by Maioli & Lacquaniti (1988), of the existence of a neurodynamical scheme of the body that functions to preserve some geometric invariants (target article, sect. 9; Lestienne et al.) We appreciate the effort Smeets has made to formulate an alternative hypothesis on intermuscular interaction. Nevertheless, his formulation does not answer the question of how the system should coordinate \ s to produce singlejoint movement in isolation or in combination with other joints. Second, in his formulation the specific role of intermuscular interaction in providing the correspondence between control functions and body architecture has been




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Response /Levin and Feldman: Motor control lost. We think that alternative hypotheses on intermuscular interaction should address these fundamental issues. Note that the specification of Xs in our approach does not rely on the use of an internal geometrical model for computations. Although specific details are not clear, it is likely that the principle of minimal interaction will produce a dynamical solution without an internal model. It is also intriguing that the principle can be applied to the analysis of muscle spindle behavior (Gutman 1994). The possibility of an alternative solution for multi-muscle coordination has been explored in terms of the \ model for the jaw-hyoid system (Ostry et al.). It has been shown that each degree of freedom in this system may be controlled by a specific linear combination of changes in Xs called the command vector. In addition, there is a command vector that specifies muscle coactivation without motion in the system. These vector commands can be applied in isolation or in combination to produce any desired jaw-hyoid configuration. Thus, the systems geometry may be represented indirectly in the CVs by specific invariants - coefficients defining the direction of vectors in X coordinates. It remains to be seen whether these interesting properties will persist if intermuscular interaction were to be included in the jaw-hyoid model. We would like to point out that the concepts associated with multi-muscle control and body configurations in the model require careful consideration. For example, addressing Kay's concern about the possible collapse of the body in the referent body configuration, it should be noted that this is not a state of complete relaxation of muscles in their whole physiological range (which in the model is produced by a negative C command). In the referent configuration, muscles become active in response to any deflection from the state by external forces. Constantly acting external forces such as gravity will finally be balanced at an equilibrium configuration (see Equation 4), which is different from the referent configuration (Equation 7). By the way, normal standing is usually associated with a low level of muscle activity of leg and trunk muscles such that the difference between the two configurations may be small. In addition, the C command may be applied in this and in many other cases of standing when enhanced stability is required. Smeets argues that his findings on the activation of shoulder muscles during fast elbow movements contradict the hypothesis on multi-muscle coordination (target article, Fig. 7) augmented in this Response (Equations 2-11). We believe that he came to this conclusion because he did not consider the role of the C command in the production of fast movements (target article, Figs. 6 and 14). Even if the R command is constrained to produce a fast movement in a single joint (e.g., elbow), the C command should be applied not only to muscles of the elbow but also to adjacent joints (wrist and shoulder). The obvious function of the C command at adjacent joints is to stabilize them against high inertial forces. For example, if we make a fast movement in the elbow without coactivation of wrist muscles, the hand will be slack and the high inertial deflections of the hand caused by the fast elbow movement may be painful. Thus, the C command is applied to stiffen the wrist joint to avoid injury. Even without our arguments concerning the C command, Smeets's approach to the hypothesis on multimuscle coordination has some drawbacks. He suggests that

Figure 7 postulates zero interaction of single-point muscles of one joint with muscles of other joints. This was not meant to be inferred from Figure 7. Our hypothesis states that intermuscular interaction is reduced to zero for the point describing the referent body configuration (the point of intersection between the muscle activation border lines in joint space). Any defection from this point elicited by an external load will evoke a nonzero intermuscular interaction (Equation 7). The same is true for active movements produced by a shift in the referent point. Generally, the greater the rate and the distance of the shift of the referent point, the larger the interaction. The hypothesis that movements are produced by shifts in the referent point implies that any movement, even one made at a single joint, may be associated with a nonlocal control process dealing with the whole body configuration rather than with individual joints. It is likely that most motor acts, for example, the activation of leg muscles prior to the initiation of a fast arm movement (Belen'kii et al. 1967; Bouisset & Zattara 1987; Flanagan et al.), may be consequences of such a process rather than of a specific anticipatory reaction. R8. Rhythmical movements and locomotion. Several commentators explored the possibility of using the X model for rhythmical movements and locomotion. Hatsopoulos & Warren think that the only way the X model can produce rhythmical movement is by rhythmical changes in the R command at a frequency independent of peripheral influences. Although this possibility is not excluded, the fact that in their example the frequency depends on stiffness and afferent feedback indicates that frequency could not be a CV (see sect. 3). Using this contradiction they conclude that CVs do not exist. Actually, the X model offers different solutions to their logic problems. First, R and C commands can be constant during rhythmical movements and consequently independent of the periphery. Another control parameter, u,, can be specified in such a way as to remove the stability of the limb leading to a limit cycle oscillation. The position of the limit cycle will be defined by the value of the R command. The frequency will be affected by the C command, which influences the stiffness of the system. At the same time, the frequency will depend on the interaction with the environment. Perturbing the limb will affect the phase of oscillation. Thus, all features of rhythmical generation described by Hatsopoulos & Warren are consistent with the idea of generation of movement by constant R, C, and [i commands. Second, as we explained above (see sect. R3), some CVs can be transformed into non-CVs when control functions are transferred to higher levels. In this case, for example, R commands will become dependent on the periphery but may also be associated with constant CVs specified by the higher levels (sect. R6). These CVs may be the ones that specify the extrapersonal frame of reference that orients rhythmical movements in this, rather than internal joint space (see also our response to Hamm & Han and Patla, below). Third, initiation of each cycle of a rhythmical movement may be produced by independent changes in the R commands for a specific time. For the remainder of the cycle, the R command may be influenced by peripheral feedback. This feedback restores the R command to its initial value,




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Response/Levin and Feldman: Motor control for example, when the limb reaches a specific position. At this point, the influence of peripheral feedback is suppressed and the R command starts the next cycle. This schema may be appropriate for the generation of locomotion, in which transition in activity from stance to swing is dependent on hip position (Grillner & Rossignol 1978; Hamm & Han). Hamm & Han focus on the problem of the interaction of the body with the environment during locomotion. They ask how X can help to solve this problem. It is unfortunate that higher-level CVs and the major emphasis of the model, namely, that active movements are produced by specification of CVs that shift positional frames of reference in space, escaped their attention. We think that especially fundamental for the understanding of how forward or backward progression of animals or humans is achieved is the idea that locomotion results from changes in CVs translating the extrapersonal frame of reference for the whole body in space (target article, sect. 9; sect. 6; Fig. 4). Note that the control of locomotion is usually associated with a nonspecific variable analogous to tonic electrical inputs to the locomotor area (Orlovsky & Shik 1976). In our approach, this nonspecific variable appears to be very specific and deals with a global orientation and progression of the body in space. Indeed, much should be done to make this idea an effective tool in studies of locomotion. Even a simplified mathematical model of locomotion based on this idea would be a step in this direction. There is a specific requirement for neuronal systems that translate the external frame of reference for locomotion. The translation is a continuous process and may be associated with monotonic changes in membrane potentials and firing frequencies of neurons. At the same time, the fact is that the ability of neurons to accumulate activity is limited and requires that this process be interrupted and quickly reversed in order to reset the system. The vestibulo-ocular nystagmus may be a manifestation of the existence of such a mechanism. Patla describes interesting data on how subjects step over obstacles of increasing heights during locomotion (see also Drew 1991) and asks whether the X model can walk. Our answer is that X has two legs, and with a little understanding it may not only walk but may even run and jump over obstacles. The more complex tangential velocity profiles of the toe when negotiating obstacles compared to simple locomotion may be explained by the superposition of two control patterns. One pattern would produce unperturbed locomotion and the other would lift the limb to reach the height of the obstacle while standing and then return the foot to the support surface (Fig. 4 B-C). In terms of the X model, the limb steps over the obstacle by vertically shifting the local external frame of reference for the leg. A simple test of this schema would be to subtract the trajectory of the unperturbed locomotion from the combined trajectory and compare the result with the trajectory of the vertical lifting movement during standing (cf. Adamovich et al. 1993). R9. The X model and the dynamical systems approach.

The relationship between the X model and the dynamical systems approach to biological phenomena is elegantly explored by Sternad & Turvey, Thelen, and van Emmerik & Wagenaar. Others who subscribe to the dynamical approach are Dean, Fikes & Townsend, Ingvaldsen

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& Whiting, and Pagano & Bingham. Indeed, dynamical systems theory was a natural prerequisite for the formulation of both the X model and the dynamical approach. We agree with Stemad & Turvey that the problem of the environment-CV interaction is more elaborated in the dynamical approach. On the other hand, the question of the generation of positional frames of reference and their use in movement production has not, to our knowledge, been sufficiently advanced in this approach. In addition, in many respects the X model is more closely related to real physiological phenomena than the dynamical systems approach, which uses more abstract language. We agree with Sternad & Turvey that the X model and the dynamical approach should be integrated and that the benefits would be mutual. In contrast to Sternad & Turvey, Fikes & Townsend see only one side of the integration: they think that the X model should be reformulated in terms of the dynamical approach, and they do not consider the opposite. Although we generally appreciate any attempt to initiate the process of integration, we do not think that Fikes & Townsends specific illustrations are particularly helpful in advancing our knowledge of the system's behavior. In particular, their solution for the redundancy problem seems equivalent to that presented by Berkinblit et al. (1986), in which joints may produce relatively independent motions to reach a common goal. Fikes & Townsend mistakenly think that the minimal synergy assumes a unique relationship between the joint angles. In fact, the X model assumes quite the opposite: it is a unit of action constrained to produce shifts of the endpoint in any desired direction. The solution of Fikes & Townsend is stated in kinematic terms with all the associated problems of such models (target article, sect. 2). Their example illustrates a problem typical to the dynamic systems approach: the use of physical analogies and phenomenological equations not directly related to physiological substrates to illustrate biological phenomena. Sternad & Turvey correctly emphasize that the dynamical analogy - the mass-spring system - was taken literally. The idea that the X hypothesis was not tied to the morphology of muscle but rather to the neuromuscular system as a whole was lost (cf. Alexander and Partridge). The massspring analogy was initially helpful in illustrating some aspects of the model but later became a source of confusion. Even now we could not predict that the use of the car analogy to illustrate the concept of CVs would be hypertrophied to the point where we were accused of placing a homunculus (driver) in the brain (Ingvaldsen & Whiting). The sad story of the mass-spring analogy shows that analogies may not be the best way to advance scientific knowledge, especially if we wish to elaborate on physiologically plausible and testable models explaining taskspecific behavior. In contrast to Fikes & Townsend, we think one should proceed with a mathematization of the model with caution. Because our current knowledge is insufficient, the dynamical equations for important components of the system may be oversimplified. For example, the suggestion (by Fikes & Townsend and in our target article) that muscle activation is monotonically related to muscle force is indeed a simplification (Loeb). Some may also say that we did not take into account the sliding-filament theory (see, however, Feldman 1979) or other properties of neuronal components. It, therefore, makes more sense to focus on the basic




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Response /Levin and Feldman: Motor control principles or postulates underlying the model that do not require elaborate mathematics (sects. 6 and 7). These principles should be understood and tested first in terms of their physiological feasibility before further mathematical elaboration. Variability in behavior is considered to be an essential characteristic of dynamical systems. Perhaps with this in mind Latash argues against the idea of deterministic mechanisms in motor control. The fact that we discussed reproducible behavior without focusing on the variability of control patterns or other general system properties does not necessarily imply a deterministic approach. Indeed, the model has potential to consider aspects of variability (Wright & States). Latash (1993) himself demonstrated nicely that the model is able to explain probabilistic phenomena such as movement errors. Because so many have labored to provide physiological explanations for complicated phenomena in motor control (Loeb), we are surprised that Latash suggests that we give up our attempts to relate X. to real physiological properties and call X. a "metaphoric abstraction." In fact, we consider our reformulation of the size principle (target article, sect. 4) an example of how the abstract language of the model may be related to the properties of neuronal networks. R10. Movement corrections and other errors. Movement correction in saccadic eye and arm-pointing movements is discussed by Desmurget et al. They mistakenly equate the control velocity vector with the derivative of the motor error. Most of their criticism (e.g., the suggestion that the model requires knowledge of the initial arm position) is associated with this misconception. In fact, the control velocity vector represents a control variable that produces shifts in the equilibrium configuration of the arm such that the end point moves to the target (with a possible error). Movement distance is defined by temporal coding of the command. In other words, the system does not predetermine the final position at the beginning of the movement; consequently, the movement may be performed with a positional error. Support for this strategy comes from experiments in which the arm suddenly encounters an opposing load during the course of a fast movement (Levin et al. 1992). The arm will undershoot the target. This demonstrates that the final position of the movement is not predetermined and the error is not used to correct movement distance if subjects are not specifically instructed to make corrections (see our response to Gottlieb below). Indeed, in eye movement, the positional error is essential but the regular occurrence of secondary saccades is indicative of the same strategy. Aside from the addition of a secondary movement or saccade, the \ model also suggests an on-line correction strategy. When the error is detected at an early stage of movement, the correction is achieved by changing the time of the shift in the EP. In this case, the kinematics of the corrected movement will be indistinguishable from those of correct movements made to the shifted target from the very beginning (Flanagan et al. 1993; Jeannerod 1988; Prablanc & Martin 1992). This strategy can also be applied to cases when eye movements compensate the loss of gaze shift due to the blockage of head movement (Fuller et al. 1983; Guitton & Voile 1987; Desmurget et al.). In Gottliebs experiment, the springlike load with or without a viscous component shifted the EP of the system

(target article, sect. 1), but the instruction obliged the subject to reach the same final position regardless of the load. According to the model, the same position with different final loads can only be reached if different R commands are applied. In other words, the subject modified the R command during the movement leading to EMG changes that were load-dependent. In addition, to diminish the effects of perturbations and comply with the instruction, the subject specified, for all trials, a C command leading to strong coactivation of the agonist and antagonist muscles from the very beginning of movement. The two factors - a strong C command and modifications of the R command (movement corrections) - allowed the subject to do what, in essence, was required by the instruction: to compensate any changes in kinematics elicited by changes in the load. No corrections were obvious from the averaged EMG and kinematic records. We argue that the averaged records may hide the true behavior of the subjects. It would have been more appropriate for Gottlieb to present individual recordings instead of averages, so that both early and late corrections could be seen (Crago et al. 1976). In addition, corrections could be seen if these data were compared to those obtained in the same experiments but executed following instructions to move as fast as possible without correction. R11. Motor development and skillful actions: First steps.

The question of maturation of motor systems was considered in the model only in terms of development of the system of intermuscular interaction. Although the acquisition of skilled behaviors (Pagano & Bingham; Winters) has not been addressed, the model does have this potential, a fact recognized and appreciated by Thelen. We are not ready to discuss her interesting data on the development of skilled "behavior in infants in terms of the model, but one hypothesis may be useful. The rapid improvement of movements at a certain age may reflect a specific phase in the formation of the united frame of reference for all muscles of the body. The ability to perform purposeful movement or to stand and walk may be realized after the formation has been completed. No description of the control of skilled actions (Pagano & Bingham; Winters) can be elaborated without integrating the basic dynamic principles underlying the model, especially the idea of the generation and use of positional frames of reference for motor control. To clarify our view, we discuss briefly the problems associated with throwing a ball to a target (Pagano & Bingham). In practical terms, the goal of the task is to convey the velocity of the arm to the ball at a particular angle of release relative to gravity. One may think that no particular EP is required for this action (Pagano & Bingham). Similarly, Bonnard & Pailhous are of the opinion that expressive actions, such as dancing, do * not have real endpoints. On the contrary, look, for example, at your arm and body right after throwing. They must reach an equilibrium position at the end of the throw. This may provide some clues as to how the system performs the task: by means of a fast transformation of the equilibrium body configuration, including the endpoint of the arm. The high velocity of the arm movement resulting from such a transformation was used to throw the ball. The system benefits from this strategy: the movement is made and the probability of negative consequences for the body (falling or injury) is minimized as a result of the transition to a new




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References/Feldman & Levin: Motor control equilibrium body configuration. Thus, the X model may provide an initial framework within which we can understand skilled actions. The same idea can be applied to other skilled actions, such as piano playing or typing (Winters). The production of optimal finger motion in the workspace in either of these tasks requires specific wrist, arm, and body postural adjustments. Hence the use of an external frame of reference as defined above (sect. R6) may be especially necessary in skilled movements. NOTES 1. Bernstein (1935; 1947) emphasized that the relationship between central impulses to motoneurons and the motor output cannot be unambiguous. To illustrate this idea, Bernstein used a hypothetical family of muscle-force characteristics, each associated with afixedmeasure of muscle activation. These relationships were described as early as 1847 (by Weber), as Partridge points out, and are similar to those used later in the formulation of the a model. Let us assume, argued Bernstein, that the nervous system tries to select a single muscle curve of the family by issuing appropriate descending signals to motoneurons. Thus, by anticipating, in addition, a specific external force, the system may predetermine a desired combination of muscle force and length. Bernstein indicated that this strategy is unreliable: sensory feedback depending on muscle length and velocity may modify the measure of muscle activation and the anticipated value of external force. As a result, the muscle curve and the desirable values of muscle force and length will be changed unpredictably. In this way, Bernstein in essence dismissed a models long before their formulation. In this analysis, Bernstein implicitly posed the following question: If the system cannot predetermine the level of muscle activation - force and length -~ which variable may be reliably specified? The \ model originates from this Bernsteinian question. 2. Feldman s (1979) book was translated in 1980, by one of Feldman's former colleagues, Mike Mirsky, who was well acquainted with the subject. The English translation required some editing. Although qualified persons offered to do this job, the publisher, MIT press, declined, leaving, to our knowledge, one copy available at MIT.

References Letters a and r appearing before authors' initials refer to target article and response respectively. Abdusamatov, R. M., Adamovich, S. V, Berkinblit, M. B., Chemavsky, A. V. & Feldman, A. G. (1988) Rapid one-joint movements: A qualitative model and its experimental verification. In: Stance and motion: Facts and concepts, ed. V. S. Gurflnkel, M. E. Ioffe, ]. Massion & J. P. Roll. Plenum. [aAGF] Abdusamatov, R. M., Adamovich, S. V. & Feldman, A. G. (1987) A model for one-joint motor control in man. In: Motor control, ed. G. N. Gatchev, B. Dimitrov & P. Catev. Plenum. [aAGF, SRG] Abend, W., Bizzi, E. & Morasso, P. (1982) Human arm trajectory formation. Brain 105:331-48. [SRG] Abraham, R. H. & Shaw, C. D. (1992) Dynamics: The geometry of behavior. Addison-Wesley. [TGF] Ackermann, E. (1990) Circular reactions and sensori-motor intelligence: When Piaget's theory meets cognitive models. Archives de Psychologie 58:6578. [PM] Adamovich, S. V. (1992) How does the nervous system control the equilibrium trajectory? Behavioral and Brain Sciences 15:704-5. [aAGF] Adamovich, S. V, Burlachkova, N. I. & Feldman, A. G. (1984) Wave nature of the central process of formation of the trajectories of change in the joint angle in man. Biophysics 29:130-34. [aAGF] Adamovich, S. V, Levin, M. F. & Feldman, A. G. (1993) Merging different motor patterns: Coordination between rhythmical and discrete single-joint movements. Exjjerimental Brain Research 99:325-37. [rAGF] Agarwal, G. C. (1992) Movement control hypothesis: A lesson from history. Behavioral and Brain Sciences 15:705-6. [aAGF]

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Akamatsu, N., Hannaford, B. & Stark, L. (1986) An intrinsic mechanism for the oscillatory contraction of muscle. Biological Cybernetics 52:21927. [REAvE] Alexander, G. E., DeLong, M. R. & Crutcher, M. D. (1992) Do cortical and basal ganglionic motor areas use "motor programs" to control movement? Behavioral and Brain Sciences 15:656-65. [aAGF, SS] Alexandrov, A., Frolov, A. & Massion, J. (1994) Voluntary forward bending in humans: A principal component analysis of axial synergies. In: Vestibular and neural front, ed. K. Taguchi, M. Igarashi & S. Mori. Elsevier. [AA] Amis, A., Prochazka, A., Short, D., Trend, P. StJ. & Ward, A. (1987) Relative displacements in muscle and tendon during human arm movements. Journal of Physiology 389:37-44. [RMcNA] An, K. N., Hui, F. C , Morrey, B. F., Linsscheid, R. L. & Chao, E. Y. (1981) Muscles across the elbow joint: A biomechanical analysis. Journal of Biomechanics 14:659-69. [RMcNA] Andersson, O. & Grillner, S. (1981). Peripheral control of the cat's step cycle: 2. Phase-dependent effects of the ramp-movements of the hip during "fictive locomotion." Ada Physiologica Scandinavica 113:89-101. [TMH] (1983) Peripheral control of the cat's step cycle: 2. Entrainment of the central pattern generators for locomotion by sinusoidal hip movements during •fictive locomotion." Ada Physiologica Scandinavica 118:229-39. [NGH] Andersson, O., Grillner, S., Lindquist, M. & Zomlefer, M. (1978) Peripheral control of the spinal pattern generators for locomotion in cat. Brain Research 150:625-30. [TMH] Andronov, A. A., Witt, A. A. & Haiken, S. E. (1959) Theory of oscillations. Moscow: Physmat (in Russian). [aAGF] Angel, R. W. (1973) Spasticity and tremor. Effects on the silent period and the after-volley. In: New developments in electromyography and clinical neurophysiology, vol. 3, ed. J. E. Desmedt. Karger. [aAGF] Appelberg, B., Johansson, H. & Sojka, P. (1986) Fusimotor reflexes in triceps surae muscle elicited by stretch of muscles in the contralateral hind limb of the cat. Journal of Physiology (London) 373:419-41. [aAGF] Arshavsky, Y. I., Gelfand, I. M. & Orlovsky, G. N. (1985) The cerebellum and control of rhythmical movements. In: The motor system in neurobiology, ed. E. V. Evarts, S. P. Wise & D. Bousfield. Elsevier. [aAGF] Asatryan, D. G. & Feldman, A. G. (1965) Functional tuning of the nervous system with control of movement or maintenance of a steady posture: 1. Mechanographic analysis of the work of the limb on execution of a postural task. Biophysics 10:925-35. [arAGF] Atkeson, C. G. & Hollerbach, J. M. (1985) Kinematic features of unrestrained vertical arm movements. Journal of Neurosdence 5:2318-30. [PH] Babinski, J. (1899) De 1'asynergie cerebelleuse. Revue Neurologique 7:80616. [AA] Bayev, K. V. (1978) Central locomotor program, for the cat's hindlimb. Neurosdence 3:1081-92. [TMH] Becker, W. & Jurgens, R. (1979) An analysis of the saccadic system by means of double step stimuli. Vision Research 19:967-83. [MD] Beek, P. J. & Van Wieringen, P. C. W. (1994) Introduction. Human Movement Science 3/4:297-300. [RI] Belen'ku, V. E., Curfinkel, V. S. & Pal'tsev, E. I. (1967) On the elements of control of voluntary movement. Biofizica 12:135-41 (in Russian). [JRF] Bennett, D. J., Hollerbach, J. M., Xu, Y. & Hunter, I. W. (1992) Time-varying stiffness of human elbow joint during cyclic voluntary movement. Experimental Brain Research 88:433-42. [aAGF, PM] Bennett, M. B., Ker, R. F., Dimery, N. J. & Alexander, R. McN. (1986) Mechanical properties of various mammalian tendons. Journal of Zoology A 209:537-48. [RMcNA] Berkinblit, M. B., Feldman, A. G. & Fukson, O. I. (1986) Adaptability of innate motor patterns and motor control mechanisms. Behavioral and Brain Sciences 9:585-638. [arAGF, SG, MLL] Berkinblit, M. B., Gelfand, I. M. & Feldman, A. G. (1986) A model for the control of multi-joint movements. Bioflzika 31:728-38. [SRG] Bernstein, N. A. (1935) The problem of interrelation between coordination and localization. Archives of Biological Science 38:1-35 (in Russian). [arACF, MLL, KHP] (1947) On the construction of movements. Moscow: Medgiz (in Russian). [rAGF] (1967) The coordination and regulation of movements. Pergamon. [arAGF] Bilodeau, M., Arsenault, A. B., Gravel, D. & Bourbonnais, D. (1990) The influence of an increase in the level of force on the EMG power spectrum of elbow extensors. European Journal of Applied Physiology 61:46166. [aAGF] Bingham, G. P., Schmidt, R. C. & Rosenblum, L. D. (1989) Hefting for a maximum distance throw: A smart perceptual mechanism. Journal of Experimental Psychology: Human Perception and Performance 15:507-28. [CCP] Bizzi, E., Accomero, N., Chappie, W. & Hogan, N. (1984) Posture control and trajectory formation during arm movements. Journal of Neurosdence 4:2738-44. [aAGF]




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Ke/erences/Feldman & Levin: Motor control Bizzi, E., Dev, P., Morasso, P. & Polit, A. (1978) Effect of load disturbances during centrally initiated movements. Journal of Neuroj>hysiology 39:43544. [LDP] Bizzi, E., Hogan, N., Miissa-Ivaldi, F. A. & Gistzer, S. (1992) Does the nervous system use equalibrium-point control to guide single and multiple joint movements? Bcluwioral ami Brain Sciences 15:603-13. [aAGF, MD, TGF, LDP] Bizzi, E., Mussa-Ivaldi, F. A. & Giszter, S. F. (1991) Computations underlying the execution of movement: A novel biological perspective. Science 253:287-91. [SG] Bloedel, J. R. (1992) Functional heterogeneity with structural homogeneity: How does the cerebellum operate? Behavioral and Brain Sciences 15:66678. [aAGF] Blouin, J., Bard, C , Teasdale, N., Puillard, J., Fleury, M., Forget, R. & Lamare, Y. (1993) Reference systems for coding spatial information in normal subject and a deafferented patient. Experimental Brain Research 93:32431. [arAGF, FL] Bock, O. (1990) Load compensation in human goal-directed arm movements. Behavioural 6 Brain Research 41:167-77. [aAGF] Bock, 0 . & Arnold, K. (1993) Error accumulation and error correction in sequential pointing movements. Exj)erimental Brain Research 95:11117. [iiACF) Boff, K. R. fir Lincoln, J. E. (1988) Vibration and display perception. Engineering Data Compendium: Human Percejition and Performance 20642133. [PVMcD] Bouisset, S. & Zattara, M. (1987) Biomechanicu) study of the programming of anticipatory postural adjustments associated with voluntary movement. journal of Biomechanics 20:735-42. [JRF] Boyd, I. A., Gladden, M. II., McWilliam, P. N. & Ward, J. (1977) Control of dynamic and static nuclear bag fibres and nuclear chain fibres by gammaand beta-axons in isolated cat muscle spindles. Journal of Physiology (London) 265:133-62. [aACF] Brooks, V. B., Horvath, F, Atkin, A., Kozlovskaya, 1. & Uno, M. (1969) Reversible changes in voluntary movement during cooling of sub-cerebellar nucleus. Federation Proceedings 28:396. [KHP] Brown, T. G. (1911) The intrinsic factors in the act of progression in the mammal. Proceedings of the Royal Society, London, Series B 84:30819. [TMH, rAGF] (1914) On the nature of the fundamental activity of the nervous centres: Together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system. Journal of Physiology (London) 48:18-46. [aAGF] Bruce, E. N. & Ackerson, L. M. (1986) High-frequency oscillations in human electromyograms during voluntary contractions. Journal of Neurophysiology 56:542-53. [TMH] Brunn, D. E. & Dean, J. (1994) lntersegmental and local intemeurons in the metathorax of the stick insect Carausius morosus which monitor middle leg position. Journal of Neurophysiology 72:1208-19. [JD] Bullock, D. & Grossberg, S. (1988) Neural dynamics of planned arm movements: Emergent invariants and speed-accuracy properties during trajectory formation. Psychological Reviews 95:49-90. [aAGF] Burgess, P. R. (1992) Equilibrium points and sensory templates. Behavioral and Brain Sciences 15:720-22. [aAGF] Burstriim, L. & Lundstrbm, R. (1994) Absorption of vibration energy in the human hand and arm. Ergonomics 37:879-90. [PVMcD] Busemeyer, J. R. & Townsend, J. T. (1993) Decision field theory: A dynamiccognitive approach to decision making in an uncertain environment. Psychological Review 100:432-59. [TGF] Caminiti, R., Johnson, P. B. & Urbano, A. (1990) Making arm movements within different parts of space: Dynamic aspects in the primate motor cortex. Journal of Neuroscience 10:2039-58. [aAGF] Capaday, C. (1994) The effects of a tonic increase of presynaptic inhibition of muscle spindle afferents on the stretch reflex parameters of the cat. Society for Neuroscience Abstracts 20:1583. [rAGF] Capaday, C. & Stein, R. B. (1986) Amplitude modulation of the soleus H-reflex in the human during walking and standing. Journal of Neuroscience 6:130813. [aAGF] Cavalleri, P. & Caty, R. (1989) Pattern of projections of group la afferents from forearm muscles to motoneurones supplying biceps and triceps muscles in man. Experimental Brain Research 78:465-78. [JBJS] Cheney, P. D. & Fetz, E. E. (1984) Corticomotoneuronal cells contribute to long-latency stretch reflexes in the rhesus monkey. Journal of Physiology 349:249-72. [SS] Christakos, C. N., Cohen, M. I., Bamhardt, R. & Shaw, C.-F. (1991) Fast rhythms in phrenic motoneuron and nerve discharges. Journal of Ncurophysiology 66:674-87. [TMH] Clement, G., Curfinkel, V. S., Lestienne, F. G., Lipshits, M. 1. & Popov, K. E. (1984) Adaptation of postural control to weightlessness. Exjierimental Brain Research 57:61-72. [FL]

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