JOURNALOFNEUROPHYSIOLOGY Vol. 62, No. 2, August 1989. Printed

in U.S.A.

Organizing Principles for Single-Joint Movements II. A Speed-Sensitive Strategy DANIEL M. CORCOS, GERALD L. GOTTLIEB, AND GYAN C. AGARWAL Department of Physical Education, University of Illinois at Chicago, Chicago 60680; Department of Physiology, Rush Medical College, Chicago 60612; Department of Electrical Engineering and Computer Science, and Bioengineering, University of Illinois at Chicago, Chicago, Illinois 60680

factors of possible importance are how fast the movement I. Normal human subjects made discrete flexions of the elbow over a fixed distance in the horizontal plane from a stationary must be performed, how rapidly the limb must accelerate, initial position to a visually defined target. We measured joint or how accurately the target point must be approximated. angle, acceleration, and electromyograms (EMGs) from two agoThe experimental study of simple movements usually nist and two antagonist muscles. involves controlling many of these factors, fixing some, 2. Changes in movement speed were elicited either by explicit and manipulating one, to see what kinematic and myoelecinstruction to the subject or by adjusting the target width. Intric patterns emerge from the subjects’ behaviors. Even structions always required accurately stopping in the target zone. when restricted to studying discrete movements of single 3. Peak inertial torques and accelerations, movement times, and integrated EMGs were all highly correlated with speed. We joints, however, there remains a considerable richness to show that inertial torque can be used as a linking variable that is the exhibited behaviors that has produced a few points of almost sufficient to explain all correlations between the task, the agreement and a number of fundamental disagreements. EMG, and movement kinematics. It is generally agreed that a rapid self-terminating move4. When subjects perform tasks that require control of movement of a single joint, from one stationary position to anment speed, they adjust the rate at which torque is developed by other, ending in a visually defined target zone and opposed the muscles. This rate is modulated by the way in which the only by the inertia of the limb and any added apparatus, is muscles are activated. The rate at which joint torque develops is initiated by a burst of activity in agonist muscles, which correlated with the rate at which the agonist EMG rises as well as generate accelerating torque, and is arrested by a burst of with integrated EMG. activity in antagonist muscles, which generate most of the 5. The antagonist EMG shows two components. The latency decelerating torque. Beyond this, there are a variety of obof the first is 30-50 ms and independent of movement dynamics. servations concerning additional bursts of muscle activity The latency of the second component is proportional to movement time. The rate of rise and area of both components scale and the expected correlations to be found among the magwith torque. nitudes and durations of the electromyogram (EMG) 6. We propose organizing principles for the control of singlebursts, kinematic measures such as movement time and joint movements in which tasks are performed by one of two speed, and independently controlled task variables such strategies. These are called speed-insensitive and speed-sensitive as distance or load. Extensive discussions of these works strategies. will be found in Corcos et al. (1988) and Gottlieb et al. 7. A model is proposed in which movements made under a (1989a, b). speed-sensitive strategy are executed by controlling the intensity One reason for the diversity of both observation and of an excitation pulse delivered to the motoneuron pool. The conclusion is that different subjects do identically defined effect is to regulate the rate at which joint torque, and consetasks in different ways. A second reason is that different quently acceleration, increases. patterns of behavior emerge from different tasks. The first 8. Movements of variable distance, speed, accuracy, and load are shown to be controlled by one of two consistent sets of rules of these is the burden of all investigators who perform for muscle activation. These rules apply to the control of both the human studies; the second is the problem we wish to adagonist and antagonist muscles. Rules of activation lead to distindress here. If different behaviors do in fact emerge from guishable patterns of EMG and torque development. All observdifferent tasks, we would like rules to help us distinguish able changes in movement kinematics are explained as determinthose differences that are qualitative from those that are istic consequences of these effects.

quantitative. For example, movements that differ only in distance are quantitatively different. The same applies to movements which differ only in the size of the inertial load. In each case, a set of rules can be stated that describes how INTRODUCTION various measures will change according to the magnitude Simple observation reveals an enormous diversity in the of the manipulated variable. It is reasonable to ask the kinds of voluntary movements normal humans make. In following question: Do the sets of rules for these two differspecifying how any single movement will be performed, ent kinds of movement task also represent a simple quanmany different factors must be incorporated; for example, titative distinction between tasks, or is this a difference we external constraints, such as where the movement must should consider at another level of description? start and end and the load the limb must move. Other In a recent paper (Gottlieb et al. 1989a), we defined

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FIG. 1. A: time-series plots of averaged (of 10) angle, velocity, acceleration, inertial torque, and EMGs for 54” movements to a 9” target width at 4 subject-selected speeds. The EMGs from the flexors biceps and brachioradialis, and the extensors triceps lateral and triceps long, are shown after full-wave rectification and smoothing with a 25ms moving average digital filter. The arrows on the inertial torque plot indicate the torque generated during maximal voluntary contractions in each direction. (Angle origin is with the elbow at a right angle, flexion positive.) B: time-series plots of averaged (of 10) angle, velocity, acceleration, inertial torque, and EMGs for 54” movements to 3,6,9, and 12” target widths. The EMGs from the flexors biceps and brachioradialis, and the extensors triceps lateral and triceps long, are shown after full-wave rectification and smoothing with a 25-ms moving average digital filter.

“strategy” as: “a set of rules between a movement task and measured variables sufficient to perform the task” and argued that strategies can be determined from information concerning the task. In the preceding companion paper (Gottlieb 1989b), we described a “speed-insensitive” strategy (SI strategy) that subjects use to move to a visually defined target of fixed size over different distances or with different inertial loads under instructions to be “accurate and fast .” The term speed-insensitive indicates that tasks that induce a subject to use this strategy do not specify the control pattern according to either the speed or the movement time. The control was insensitive to these variables. For example, increases in load or distance had opposite effects on speed and movement time but similar effects on the agonist EMG and, by inference, on the neural control patterns underlying those observable measures. The above question concerning quantitative differences between patterns of movement control can be rephrased in terms of strategy. Are all single-joint movements controlled by an SI strategy? Are there classes of movements which

cannot be described by the rules of an SI strategy? Are there one or more sets of rules of these movements? The answers to these questions might provide a theoretical framework for explaining in a logical manner the experimental differences in behavior described in the literature. In the present paper, we consider movements in which there is some specific speed which is required to accomplish the instructed task. One way to elicit such movements is to instruct the subject to complete the movement within a time window of so many milliseconds. This procedure has been extensively used by Newell and colleagues ( 1979, 1980), Schmidt and colleagues (1979, 1988), and Shapiro and Walter (1986) as well as by Sherwood et al. (1988). A second procedure is to allow the subject to choose a speed and then ask that movements be made faster or slower than the reference movement (Hoffman and Strick 1986; Lestienne 1979). A third is to change the size of the visual target, which, as Fitts and others have shown (Corcos et al. 1988; Fitts et al. 1954, 1964; Soechting 1984), will often cause subjects to trade movement speed for end-point accuracy.

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FIG. 2. A: integrated agonist activity over the first 30 ms (- - -, Q& and over the acceleration phase of the movement C----9 Qacc)is plotted vs. peak accelerating inertial torque. These data are from an experiment in which 54” was moved at 4 speeds. They are from the same subject as in Fig. 1A. Standard error bars are drawn for both EMG and torque. B:integrated agonist activity over the first 30 ms (- - -, Q3J and over the acceleration phase of the movement (, Qacc)is plotted vs. peak accelerating inertial torque. The data are from the experiment in which the subject moved 54” to targets of 5 different widths. They are from the same subject as in Fig. 1B. Standard error bars are drawn for both EMG and torque.

In the experiments described here, we used the second and third of these methods. Under these task conditions, subjects control their muscles according to patterns that differ from those exhibited with an SI strategy. This different pattern of activation, manifested in the EMG, inertial torque, and kinematics, we will call a speed-sensitive (SS) strategy. METHODS

Experimental

procedures

The forearm was strapped in a rigid manipulandum which could rotate in the horizontal plane. The axis of rotation was alignedwith the elbowjoint, with the arm abductedto the sideat 90”. Joint angleand accelerationand four EMGs (from biceps and brachioradialis,and lateral and long headsof triceps) were digitized by a computer for subsequentanalysis.The origin for anglemeasurements waswith the elbow flexed 90°, corresponding to 0’ on the anglegraph, and flexion was positive. Inertial torque was computed from the product of accelerationand an estimateof the total moment of inertia (manipulandum,subject forearm, and any added load). Agonist EMG wasquantified by integrating the rectified envelope over the first 30 ms after the onset of the agonist activation (Q& and also over the interval from onsetto the first return to zero of the acceleration(Qacc).The antagonistEMG wasintegratedfrom agonistonsetto a projected secondzero-crossingof the acceleration(Q&. The details concerning thesemechanical and EMG measurementsand EMG normalization are describedin full in the precedingpaper (Gottlieb et al. 1989b).Figures 1 and 6 are time-seriesplots that have beennormalizedwith respectto a maximal voluntary contraction

accordingto Eq. I of that paper. In all plots of integratedEMG, valuesare in microvolts per second.

Task: d@erent speed experiments Four subjectswere askedto make 54” flexion movementsof the elbow at four speedsto a 9” target. They were first instructed to make the movement at their preferred speed.They werethen askedto move a little faster,their fastest,and finally slowerthan their first speed.This generated a wide variety of movement speedsboth within and betweensubjects.Thesesubjectsalsoparticipated in the secondprotocol (accuracy experiments).

Task: accuracy experiments Eight of ten subjectswere askedto perform 54” elbow flexion movementsaccurately and quickly to targetsof 4 or 5 different widths (1.5, 3, 6, 9, and 12”). Accuracy and speedwere equally stressed.Accuracy wasalwaysmentionedfirst in the instructions aswasthe casein Fitts’ experiment (1954). Unlike Fitts’ experiment, thesesubjectswerenot provided with feedbackduring the experiment from the experimenter about either the accuracy or the speedof their individual movements.The last two subjects were provided with knowledge after each movement about whetherthey hit the target or not. RESULTS

Four sets of flexion movements over 54” to a 9’ target at four different subject selected speeds are displayed in Fig. 1A. These are all averaged (of 10) records that were aligned on the onset of the biceps EMG. All subjects performed the

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task in a similar fashion, although the ranges of movement velocity differed among individuals. A series of 54O movements in which the target widths were 3, 6, 9, and 12” is shown in Fig. 1B. The movement times of this subject conformed to Fitts’ law. That is, the subject reduced movement speed and increased movement time as the target width diminished. Only two of our eight subjects who were not provided with knowledge of results altered movement speed in this way. The other six made virtually identical movements irrespective of target width. The failure of subjects to alter their movements was probablv due to the lack of knowledge of results nrovided. We

ran two more subjects and provided them on a trial-by-trial basis with information about whether their movements were accurate or not. Both these subjects slowed their movements for smaller targets. In both series of experiments, subjects performed movements of the same distance at different speeds. These different speeds were achieved by varying the pattern of muscle activation and, concomitantly, the resulting net torque. In both cases, the torques (and consequently accelerations) diverge from the earliest moments of the movement. Associated with this is a similar divergence of agonist and antagonist EMGs during their rising phases.

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AND G. C. AGARWAL

For movements that are sufficiently vigorous, identification of the onset of the antagonist burst is usually unambiguous (Mustard and Lee 1987). The latencies measured in the lateral head of triceps for the two sets of movements shown in Fig. 1, A and B, are plotted in Fig. 4. For the movements performed at different speeds shown in Fig. lA, we could always measure the latency of the first or early component because antagonist activity always rose above the baseline. The latency of the second or late component was not measured for the two slower movements because we could not identify a later major vertical deflection in the EMG after the initial rise above the base line. This is not surprising because little muscle activity is needed to decelerate and stabilize slow movements (Mustard and Lee 1987). Our inability to visually identify and therefore to measure the onset of the second component does not imply EMG silence in its interval. For the movements performed to different-size targets shown in Fig. 1B, visual inspection of the averaged data suggests that it is difficult to observe both the first sustained rise above the baseline and a subsequent major deflection. This distinction was easier to observe in the individual trials, and both early and late components are plotted in Fig. 4. Quantijkation

of the antagonist EMG

The strength of the combined antagonist bursts (Q& was quantified by integrating from the agonist onset to The agonist EMG has been quantified using two mea- approximately the time of the second zero-crossing on the sures. These are the time integrals for the first 30 ms (Q& acceleration trace (Gottlieb et al. 1989b). Figure 5 shows and to the switch from acceleration to deceleration (Qacc). Qdec as a function of peak inertial decelerating torque for These are plotted for the biceps as a function of peak iner- the two experiments. Note that Qdec is integrated from the tial torque in Fig. 2, A and B, for the two different tasks shown in Fig. 1, A and B. Both measures show a strong positive covariation with peak inertial torque. The differ50 Q decINTEGRATED ANTAGONISTEMG ence in their scales is a consequence of their different inter. vals of integration. Except for the fact that instructing the subject to vary movement speed usually elicits a wider range of forces and 40 therefore speeds than does changing target width, there ap. pears to be no basis in the data as analyzed for distinguishing between these two experiments. In both experiments peak velocity increased and with it, peak acceleration and deceleration and their rate of rise, as well as peak inertial accelerative and decelerative torques and their rate of rise. Movement time decreased. The relationships between velocity, movement time, and decelerative inertial torque as functions of peak accelerative inertial torque are illustrated in Fig. 3, A-C. Quantljication

of the agonist EMG

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Inspection of Fig. IA suggests that the antagonist can be partitioned into two components. The first has a short and relatively constant latency of ~50 ms. In Fig. 1A it is a distinct burst component, but it is often small or poorly defined, as in Fig. lB, and in some subjects not always noticeable. It is ended by the onset of a larger component at a latency which varies with movement time. This second component is what is usually termed “the antagonist burst. ’ ’

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onset of the agonist EMG, so evaluating the area of the antagonist burst does not rely upon identifying a burst onset.

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FIG. 7. Integrated agonist activity over the first 30 ms (0, l , Q& and over the acceleration phase of the movement (0, W,Qacc)plotted vs. peak accelerating inertial torque for the 2 sets of movements plotted in Fig. 6. Dashed lines are for 54” movements at 4 speeds with an SS strategy. Solid lines are 4 distances with an SI strategy. Standard error bars are drawn for both EMG and torque.

54’ movements to a 9’ target width at four different speeds as in Fig. 1A. The second required fast and accurate movements to 9’ target width to four distances of 18,36,54, and 72O (as in Fig. 1 of the preceding paper (Gottlieb et al. 1989b)). Collecting both sets of data in a single session allows direct comparison of both kinematics and EMGs a across experiment types. Figures 3 of this paper and 5 of the preceding paper (Gottlieb et al. 1989b) illustrate similar relationships between peak velocity, movement time, and peak decelerating torque and peak accelerating torque variables for both sets of movements. The fact that the two data sets in Fig. 3 appear to lie on partially overlapping ranges of 50 -+ the same curve is in part coincidence because the two experiments were performed in two different subjects with slightly different limb moments. However, were we to plot two experiments from the same subject, we would expect such overlap. Inspection of the figure reveals how in the distance experiment, inertial torques and agonist EMGs rise on the same trajectory. The movement time and magnitude of peak inertial torque increase together. By contrast, in the speed experiment, inertial torques and agonist EMGs both rise in a fan-like manner, and the movement time and -sol,,,,,,,,,,,, magnitude of peak torque vary inversely. This is a qualitative as well as a quantitative difference. 600 Time (ms) For these two sets of movements, EMG quantities (QjO FIG. 6. Time-series plots of averaged (of 10) biceps EMG, angle, and and Qacc) are plotted in Fig. 7 against peak accelerative inertial torque for 2 sets of movements performed by the same subject. inertial torque. Qacc scales with peak inertial torque for The movements drawn in thick lines represent movements of 18, 36, 54, both sets of movements, but QjO only scales for the set that and 72” to a 9” target width. The movements drawn in thin lines correspond to 54” movements to 9” target width at 4 subject-selected speeds. explicitly varied movement speed.

% P 32 z

The EMGs from the flexor (biceps) are shown after full-wave rectification and smoothing with a 25ms moving average digital filter. The arrows on the inertial torque plot correspond to the torque generated during maximal voluntary contractions in each direction. (Angle origin is with the elbow at a right angle, flexion positive.)

DISCUSSION

In the preceding paper (Gottlieb et al. 1989b), we interpreted the relations between task variables, torques, EMGs

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and kinematic measures based upon four organizing principles. The same logical scheme will be used to interpret the data presented here. The numbering of the principles is the same as the cited paper. IV. A4uscle torques interact with limb loads to generate kinematics (angle, its derivatives, and movement intervals). Because of the role of load in determining kinematics, no general correlations between EMG and purely kinematic measures are possible. In the experiments described in this paper, the subject was induced to alter movement speed. This was accomplished either explicitly by instruction (e.g., “go faster”) or implicitly by varying target width. Regardless of the subject’s motives for changing movement speeds, to move a given load over a fixed distance in a variable time, it was dynamically necessary to exert control over the accelerating torque. Subjects changed both the peak magnitude of applied torque and the rate at which it rose to that peak. The way in which the rate of rise of the torque is modulated according to the desired movement speed is evident in Fig. 1 but is best seen in contrast to movements which do not require this form of modulation in Fig. 6. In the experiment illustrated by this latter figure, even though velocity is not explicitly plotted, peak (and average) velocity do vary for different distances, and no distinction between the two sets of movements can be drawn from this fact. It is rather that initial torques (and therefore accelerations, velocities, and joint angles) rise uniformly and independently of final distance (and independently of peak velocity) in the distance series but rise at a correlated rate in the velocity series. ’ Other differences between the series can also be discerned, such as the relationship between the time of peak torque (or acceleration) and the magnitude of that peak. Such kinematic distinctions are, we suggest, secondary to the way the descending command controls the activation of the motoneuron pool and are effects rather than causes. III. Rulesfor must/e activation lead to patterns of muscle torques and EA4Gs. Well-chosen scalar measures of torque and EMG will be highly correlated irrespective of task because of their shared causal, neural activation. Agonist muscle In these experiments, the integrated EMG (Qacc) is highly correlated with peak inertial torque (Fig. 2) a feature it shares with other kinds of manipulations of task parameters such as distance (Fig. 7) and inertial load (Gottlieb et al. 1989b). Pari passu, there is also a correlation with measures of velocity. In distinguishing these movements from those performed with an SI strategy, we can look to measures of the EMG as well as of the torque and kinematics. The observed ’ In principle, the two sets of data we presented in Figs. 6 and 7 should intersect for the 54” movements. We believe that the reason for this not occurring is that the variable-speed data were collected first so that the subject had more recent practice when performing the distance experiment. (That is, the speed experiment was “practice” for the distance experiment.) Practice of even these simple movements leads to improvements of both speed and accuracy (Gottlieb et al. 1988). As a consequence, the movements in the distance set were performed relatively faster than in the speed set.

AND

G. C. AGARWAL

modulation of the rate at which torque rises is associated with a parallel change in the rise of motoneuron activity as revealed by the initial slope of the agonist EMG burst (QsO in Fig. 2). These changes in rate of agonist EMG rise are a consequence of the pattern of muscle activation necessary to increase the rate at which torque rises. Both QjO and Qacc are proportional to the peak accelerating inertial torque. Antagonist muscle The antagonist muscle obeys similar scaling rules. Qdec is proportional to peak decelerating inertial torque (Fig. 5). Inspection of Fig. 1 shows that the early antagonist component is also modulated, as are the rates of rise of both components. We have not attempted to demonstrate this proportionality rule (by means of a graph such as Fig. 5) for all the subintervals of antagonist activity to which we have referred. The observation is clear in Fig. 1 (clearer in Fig. IA, which shows the widest range of movement speeds) and provides a parsimonious summary of the data. The latency of the early antagonist component is independent of speed, whereas the second and larger component occurs later as speed diminishes (Fig. 4). For these experiments, the latency is simply proportional to movement time, but, as we have shown elsewhere (Gottlieb et al. 1989b), this is only a simplification of a more dynamically complex timing problem. II. Strategies consist of sets of rules that determine the patterns of muscle activation. In some classes of movements, such as those that vary only distance (Fig. 6) or inertial load while keeping target width fixed, the EMG bursts rise with a uniform slope. We suggested that for such movements, the initial excitation to the motoneuron pool, once chosen, was constant and insensitive to the speed at which the subject performed the movement. This strategy resulted in uniform rates of rise in inertial torque in spite of changes in the magnitude of the task variable, although peak and average velocities did change. We named this a speed-insensitive strategy (Gottlieb et al. 1989b). The data presented here for these movement tasks show diverging inertial torque records from the earliest moments of the movement. That and the accompanying modulation of the early EMG (Q3J differ from movements performed under an SI strategy. This requires us to define a different strategy and a new set of rules relating task variables to both kinematic and myoelectric measures. Control of muscle contraction One way to characterize tasks which cannot be performed with an SI strategy is that the tasks impose constraints, either on movement speed, movement time, or target width, that explicitly require the subject to modulate movement speed. This is different from tasks that permit the subject to change the speed by asserting no constraints. This occurs with many experimental manipulations that are not designed to prevent or control changes in speed. Instructing the subject to move a fixed distance faster (or to move a greater distance in a fixed time) demands faster

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rising accelerations; in the first case because movement time will shorten while acceleration amplitudes increase and in the second case because higher accelerations must be achieved in fixed intervals.2 By this logic, increasing the width of the target allows the subject to exploit the speedaccuracy trade-off to use higher speeds.3 This appears to be behaviorally indistinguishable from simply telling the subject to move faster. In all of these cases, dynamic constraints require that greater speeds be achieved by more steeply rising torques to produce faster accelerations. Control of muscle activation We can exploit the notion that the EMG is a low-pass filtered observation of a rectangular “excitation pulse” [N(t)] that activates the motoneuron pool to explain the way in which the EMG pattern is affected by changes in the task. A simple model with a single time-constant parameter (a) for this filter is given in Eq. 1 (Gottlieb et al. 1989b). The variable e(t) is defined as the mean depolarization of the motoneuron pool, and the EMG is proportional to it within upper and lower bounds. de(t) 1 T + - e(t) = N(t) a

Control

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’ Other kinematic regimes are dynamically possible that involve shortening the interval of deceleration and increasing its strength to shorten movement time when acceleration time remains constant or even lengthens. We have not yet found any movements which are performed in this way. 3 For this to be the case, target width must exert control over the subject’s behavior. Clearly this was not the case in six of our eight subjects who were not given knowledge of results during the experiment. In these six subjects, we would expect -and found-no difference in either torque or EMG patterns for movements to targets of different widths. The degree to which target width influences performance in these types of tasks is crucially dependent on: I) the instruction given and 2) the type of feedback provided (number of errors, movement time, etc.). For example, in Fitts’ ( 1954) paper, his (and our) instruction included the statement: “Emphasize accuracy rather than speed.” (p. 384). In his paper with Peterson ( 1964), the instructions were: “The subjects were instructed to make quick movements aimed at hitting one of. . . .” (p. 105). What is of interest is that, despite the fact that Fitts’ Law describes both sets of data well, there is a significant difference in the intercept between the two sets of data. One possibility is that this is because different tasks were used, and we believe that this is the most likely explanation for this set of data. Another possibility is that instructions can affect both the intercept and slope of the relationship. This can be seen in a comparison among the studies of Fitts (1954), Fitts and Peterson (1964), and Bailey and Presgrave (1958) presented by Keele ( 1985). Because experimental instructions affect the intercept and the slope of the relationship, a speed-sensitive strategy is only induced when the subject is forced to change movement velocity for different accuracy requirements. An additional point to note is that Fitts’ Law is always based on data pooled over subjects. We are not able to present our time-series plots (Figs. 1 and 6) as pooled data for the obvious reason that EMG times series can not be pooled across subjects. A previous study of 5 subjects (Corcos et al. 1988) showed averaged kinematic data in support of Fitts’ Law. This study also showed that pooled scalar EMG measures can be related to both distance and target width. Inspection of figures in that paper show agreement with the data discussed in the present study. An important distinction to be drawn between that paper and this one is that we have now shown that the control of distance and accuracy are done by two different mechanisms, distance by the SI strategy and width by the SS strategy (Gottlieb et al. 1989a).

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complished by modulation of the intensity with which the motoneuron pool is activated [i.e., by modulation of the amplitude of N(t)]. The model predicts that EMGs will have an initial slope that is similarly modulated and is illustrated in Fig. 1 1B of Gottlieb et al. ( 1989b). These predictions are consistent with measures of EMG, such as Q30 and Qacc,that both scale with the task variable as shown in Fig. 2. Our data are consistent with the notion that the rules governing antagonist burst intensity are identical to those for the agonist. The latency of the first component is constant and that of the second component proportional to movement time. I. Elements of a movement task lead to a strategy for governing its control. We have ident$ed two strategies to describe how single-joint movements are accomplished for a variety of tasks. Strategy A strategy is a set of rules that defines relations between task variables and measured variables sufficient for computing activation parameters to perform the task (Gottlieb et al. 1989a, b). We have examined the effects of changing movement velocity, either by explicit instruction or by presenting different-width targets, and observed the same patterns of muscle activation. These data describe behavior that can be characterized by a single strategy that is used to make accurate, fast movements to targets at different speeds. We call this a speed-sensitive (SS) strategy. An SS strategy causes the initial excitation to the motoneuron pool to be proportional to the speed at which the subject wishes to perform the movement. This appropriately scales the initial rise in contractile torque. The delay before applying a decelerating torque still is proportional to movement time, so this strategy makes the latency of the antagonist burst inversely proportional to speed or to peak inertial torque, as shown by Figs. 3 and 4. The SS strategy is implemented by modulating the amplitudes of excitation pulses to motoneurons and the latency of the antagonist pulse. It modulates the amplitude of the excitation pulse N(t) while keeping its duration constant. The choice of initial excitation intensity is not made in absolute terms of velocity but only in relative terms. The same intensity will produce different speeds for different inertial loads, and the subject must know how to account for this if a particular speed is required. This is easily learned in a few movements. If only a change in speed is what the subject is intending to accomplish, then an appropriate change in excitation intensity is sufficient. Evidence for variable excitation pulse intensity arises from the initial EMG slope. Evidence for an invariant excitation pulse duration would have to be found on the falling phase of the EMG burst, which is sensitive to both pulse duration and intensity. Rules The foregoing discussion can be summarized into a set of rules which describe how subjects make movements under an SS strategv.

366 SSRULEFOR

lated. Duration

D. M.

THEEXCITATIONPULSE.

CORCOS,

G. L. GOTTLIEB,

Intensity is modu-

is constant?

The initial rate of recruitment andJiring rates of the alpha motoneurons are adjusted to adapt to changes in the task. This results in changes in the initial slope of the EA4G and in the area of the agonist burst. The duration of the agonist burst will be nearly constant if the duration of the excitation pulse is constant.

EMG RULES.

KINEMATIC RULES. The slope of the initial rise in muscle force (or joint torque) will scale with the intensity of the excitation pulse. For constant inertia! loads, this implies that acceleration will be proportional to intensity. The first of these rules defines the way the nervous system implements an SS strategy at the level of the motoneuron pool. It does not specify how such an excitation pulse is generated (e.g., central programing or use of peripheral feedback) but only what parameters are modulated (see Gottlieb et al. 1989a, reply to commentaries for a discussion of this issue). The second rule is a consequence of the first, combined with the postulated low-pass filtering effects of the motoneuron pool. The third rule is also a consequence of the first, based on physiological considerations of muscle excitation-contraction coupling mechanisms.

Strategies and EMG patterns Invariances or regularities in muscle activation can give rise to visually recognizable EMG patterns. Such patterns have been described in terms of bursts of EMG, and the “triphasic” burst pattern has frequently been described as the pattern accompanying single-joint movements (Angel 1974; Brown and Cooke 198 1; Cheron and Godaux 1986; Hallett et al. 1975, 1979; Meinck et al. 1984; Sanes and Jennings 1984; Wachholder and Altenburger 1926; Wadman et al. 1979). The three bursts, first agonist, antagonist, and second agonist, have each been assigned a dynamic role in accelerating, decelerating, and clamping the limb at the target position (Hannaford and Stark 1985). Such simplifying descriptions are useful in summarizing the presumed causal relations between neural input and kinematic output. In this and the companion paper (Gottlieb et al. 1989b), we have described features of the EMG that remain invariant over specific changes in the task. The EMG patterns for the first agonist and antagonist bursts emerge from fundamental assumptions about the nature of the rules used for motor control and for generation of the signals that activate the motoneurons. We have not discussed the second ago4 In Gottlieb et al. ( 1989a) we have described a less restrictive rule for an SS strategy. The data presented in this paper fits a narrower formulation of the rule, but some data in the literature (Gielen et al. 1985, Mustard and Lee 1987; Sherwood et al. 1988; Wallace and Wright 1982) is incompatible with a fixed-duration excitation pulse. The reason for this inconsistency is unclear and will require further experimentation. Our model does not require constant pulse duration, only variable pulse intensity, but invariant duration is compatible with the data here, to the degree we have presently quantified it. For purposes of simplicity, we assume that the durations of those pulses are independent of changes in the task variables, although they clearly must be selected initially according to some consideration based upon the intended movement.

AND

G. C. AGARWAL

nist burst, and therefore the triphasic pattern, because it does not emerge from the principles of motor control that we have enunciated. Our theory is presently neutral as to the existence of a second agonist burst or its dependence on task or kinematic variables. The literature shows many examples of biphasic and triphasic patterns. Our own data (Gottlieb et al. 1989a) provide examples of both. The triphasic pattern, although both visually distinctive and occurring not infrequently, is clearly not an invariant pattern of muscle activation for discrete elbow flexions to visually defined targets. It is task, velocity, subject, and muscle dependent. Kinematic factors such as movement speed and terminal overshoot are plausible contributors to the presence or absence of a second agonist burst (Feldman 1986). Brown and Cooke (198 1) have shown some movements where its intensity correlated with that of the first burst. Asserting that the second agonist burst is peculiar only to fast movements is not very informative because in varying degrees all three EMG bursts depend upon movements of sufficient speed. More precise kinematic correlates remain undetermined, and to incorporate this burst into our theory will require further study. One issue that is not illuminated by our data is the latency of the antagonist burst. It makes physical sense to delay activation of the antagonist when movement time increases to delay the deceleration the antagonist produces. This delay is clear in movements performed with a speedinsensitive strategy (Gottlieb et al. 1989b, Fig 6). For the speed-sensitive movements reported on here, the delay of the later component of the antagonist burst with increasing movement time is far less clear. Increases for movements at different selected speeds are clear in Fig. 4, but this latency was measurable for only two of the five speeds used. Movements of different speeds produced by different-sized targets show a positive trend for the four points, but it is weak. There are important differences in the way the antagonist is used for speed-sensitive and speed-insensitive movements. In the speed-insensitive case (different distances or loads) increases in the task variable lead to increased movement time, antagonist latency, inertial torque, and duration of the excitation pulse. Thus, for the late antagonist component, latency and intensity are positively correlated. The early component is of constant intensity and small compared to the late. In the speed-sensitive case, for the late antagonist component, latency and intensity are negatively correlated. The intensity of the early component is positively correlated with that of the late and relatively larger, compared to the speed-insensitive case, which may reduce the accuracy with which the late component’s onset can be determined for an speed-sensitive strategy. Physical laws do not require that antagonist latency vary with movement time. The timing of deceleration is constrained by muscle contractile dynamics, but within those constraints, timing rules can be varied if the symmetry of the movement (ratio of acceleration to deceleration time) can change. Hence, although it seems reasonable (albeit perhaps oversimplified) to expect antagonist latency to covary with movement time, the data do not clearly support this conclusion across both strategies.

SPEED-SENSITIVE TABLE

1.

Directions

of covariation

among movement

MOVEMENT

367

STRATEGY

tasks, resultant kinematics,

EMG, and strategy

Measured Variables Acceleration

Torque Task Variable

Initial

Peak

Initial

Peak

Distance Load Speed

0 0 +

+ + +

0 +

+ +

EMG Movement time

Excitation Pulse

Peak velocity

Q30

Qact

Q dec

Strategy

Width

Height

-

0 0 +

+ + +

* + +

SI SI ss

+ + @t

0 0 +

-

A positive (negative) sign indicates that an increase in the task variable is associated with an increase (decrease) in the measured variable. Zero indicates that the measured variable does not vary with changes in the magnitude of the task variable. EMG, electrbmyogram; Q30, first 30 ms after agonist EMG onset; Qacc,onset to the first zero-crossing of the acceleration; Qdec,deceleration to zero from 50% of negative peak; SI, speed-insensitive; SS, speed-sensitive. *A positive correlation to this measured variable may require that correction be made for the effects bf changing muscle length (Gottlieb et al. 1989b). ?A nonzero correlation may exist for classes of movements not studied here.

Two strategies summarized Table 1 summarizes the relationships among movement tasks, torques associated with movement, selected kinematic parameters, and measures of EMG. The table shows that we cannot use any of the EMG measures as predictors of any specific kinematic variable across strategies. No simple kinematic measure (acceleration, movement time, or velocity) maintains a consistent positive correlation with either EMG or with the manipulated task variable across all three kinds of tasks. The only consistent positive correlation is with inertial torque. Those kinematically derived functions that are successful (such as proposed by Bouisset et al. ( 1968, 1973, 1974, 1977) and Karst and Hasan ( 1987) can also be derived from torque-based measures. The data suggest that we both can and must partition our movements into at least two groups, describable by different strategies. In examining myoelectric and kinematic measures to distinguish the two strategies, we must look at the onset of the movement. It is measures like Q30, the initial rise in torque and acceleration and similar measures, that will separate movements performed under the SI strategy from those which are speed-sensitive. -The movements studied in this paper were performed under what we have called a speed-sensitive strategy because they are initiated by control patterns that change with speed requirements specified by the task. This is contrasted with movements made under a SI strategy in which, although speed is affected by the task variable, the initiation of the movement is not (Gottlieb et al. 1989b). Here we have shown that the control of movement speed, when distance and load are constant, is accomplished by controlling the rate of torque rise in the agonist muscles as well as the actual level of torque used, with analogous rules for the antagonist. We have further shown that the rates of EMG rise for both the agonist and antagonist bursts are proportional to the torques which, in these experiments, are also proportional to accelerations and velocities. These rules are shown to hold across two different experimental methods of manipulating movement speed. They demonstrate the applicability of the notion of a speed-sensitive strategy to one class of single-joint movements. Taken with the results on movements using a speed-insensitive strategy presented in the preceding paper, our theory

provides a uniform way of describing how single-joint movements are controlled over a diverse set of conditions. We thank 0. Paul for programming support and J. Bhopatkar, B. Flaherty, and Y. Yamazaki for assistance in performing these experiments. We also thank S. Keele for valuable comments. This work was supported, in part, by National Institutes of Health Grants AR-33 189 and NS-23593. Address for reprint requests: D. M. Corcos, Dept. of Physical Education, University of Illinois at Chicago, P.O. Box 4348, Chicago, IL 60680 M-C194. Received 4 August 1988; accepted in final form 17 March 1989. REFERENCES

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