E,Xl_'mental BrainResearch

Exp Brain Res (1987) 67:225-240

9 Springer-Verlag t987

Trajectory control in targeted force impulses I. Role of opposing muscles

C. Ghez and J. Gordon Center for Neurobiologyand Behavior, New York State PsychiatricInstitute, Collegeof Physiciansand Surgeons, ColumbiaUniversity,722 W. 168th Street, New York, NY 10032, USA

Summary. The functional role of opposing muscles in the production of isometric force trajectories was studied in six adult subjects producing impulses and steps of elbow flexor force, with different rise times and amplitudes. Rapidly rising forces were invariably associated with an alternating pattern of EMG activity in agonist and antagonist muscles: an agonist burst (AG1) initiated the development of force in the desired direction while a reciprocal burst in the antagonist (ANT-R) led to the deceleration of the force trajectory prior to the peak force. The temporal pattern of agonist and antagonist activation was dependent on force rise time. Force trajectories with long rise times (> 200 ms) were entirely controlled by the agonist, and EMG activity closely followed the contours of the rising force trajectory. For rise times of about 120 to 200ms, agonist activation formed a discrete EMG burst, and force continued to rise during the subsequent silent period. For brief force rise times (< 120ms), reciprocal activation of the antagonist muscle occurred at about the time of the peak dF/dt. The integrated magnitude of AG1 was dependent on peak force but was independent of force rise time. AG1 duration varied directly with both peak force and force rise time. The integrated value of ANT-R varied as an inverse function of force rise time and was minimally influenced by peak force. ANT-R was present with the same magnitude and timing in both force impulses and steps when rise times were equal; therefore it did not serve to return force to baseline. Rather it served to truncate the rising force when very brief rise times were required, thus compensating for the low-pass filter properties of the agonist muscle. Subjects were able to voluntarily suppress ANT-R in rapidly accelerated force trajectories, indicating that the linkage between the commands controlling agonist and antagonist is not Offprint requests to: C. Ghez (address see above)

obligatory; however AG1 findings emphasize that opposing muscles acting at constraints imposed by neuromuscular plant.

was then prolonged. Our neuronal commands to a joint must be adapted to the properties of the

Key words: Human subjects - Isometric - Trajectory control - Agonist-antagonist EMG pattern - Muscle properties

Introduction

The purpose of the series of studies introduced by this paper was to characterize the processes used by normal human subjects to control the amplitude and direction of limb trajectories aimed to a target. We have approached this problem by examining trajectory control in a simple motor response, the aimed isometric force impulse. The first group of papers of this series (Gordon and Ghez 1987a; Gordon and Ghez 1987b) defines a general control strategy used by subjects to accurately vary the size of targeted responses and assesses the influence of mechanisms acting concurrently to correct initial trajectory errors. The second group of papers (in preparation) examines how antecedent stimulus information from a target triggers the occurrence of a response and determines its trajectory (Hening et al. 1983; Hening and Ghez 1984; Favilla et al. 1985, 1986). We have studied the control of motor responses under isometric conditions in order to minimize several problems which complicate the experimental analysis of position control mechanisms. First, as the limb changes position during movement, there are complex shifts in internal and external forces acting on the joints. Second, stretch reflexes, evoked by changes in muscle length during movement, interact

226 with the central signals intended to control the trajectory. Third, during limb displacements, the relationship between myoelectric signals (EMG) and trajectory variables is complex and not uniquely determined. Although isometric responses minimize these problems, they share with displacements many of the same challenges to central control. For example, one major difficulty in controlling both force and position is the filtering action of the musculo-skeletal system, which distorts and delays the effects of central commands. Such delays increase the time required for feedback to affect the trajectory and make preprogramming necessary for achieving accurate control of rapid responses, whether isometric or not. In addition, since the control of limb position requires the central nervous system to grade the forces developed by muscles in order to overcome opposing loads, analyzing the strategies available to control force isometrically seems a necessary first step toward understanding the general principles underlying trajectory control. Because we wished to focus directly on the dynamic phase of force trajectories in these studies, the isometric responses we examined in detail were transient force impulses rather than sustained force steps. These studies have been guided by the consideration that the neural strategies responsible for trajectory control need to be adapted to the constraints imposed by individual elements in the overall system. Thus, we begin our analysis by examining how the control signals to opposing muscles acting at a joint are modulated in order to generate force trajectories of different sizes and rise times. In this study, we examine the relationships between the EMG signals recorded from opposing muscles at the elbow joint and the magnitude and time course of the changes in force produced under isometric conditions. Although a number of studies have quantified the relationship of EMG activity in a single muscle to force under both static and dynamic conditions (see Agarwal and Gottlieb 1982 for review), there is little systematic information available concerning the relationship between activity in opposing muscles and force trajectories. While it might be expected that the development of force in a single direction would require only the contraction of a single muscle group, this is not necessarily the case. It has recently been shown that rapidly rising force trajectories depend upon the precisely timed and coordinated action of sets of opposing muscles (Gordon and Ghez 1984; Sanes and Jennings 1984; Meinck et al. 1984). The observed EMG pattern is similar to the "triphasic" pattern seen in rapid voluntary limb displacements (Wachholder and Altenburger 1926; Hallett et al. 1975). The neural mechanisms underlying contrac-

tion of the antagonist during position adjustmer remain controversial (cf. Ghez and Martin 198 Sanes and Jennings 1984), as do the factors influe~ ing the relationship of the agonist-antagonist EM pattern to trajectory parameters and task conditio (cf. Lestienne 1979; Brown and Cooke 1981; Mat den et al. 1983). The experiments reported in this study addre three questions. First, what are the functional rol played by contraction of agonist and antagon: musTcles in controlling isometric force trajectorie We have addressed this question by examining tl patterns of EMG activity in opposing muscles assoq ated with force trajectories of different amplitud and rise times. Second, does activation of the antag nist muscle in rapid force impulses merely serve return the force to baseline, or does it control tl rising phase of the force trajectory? We have addrc sed this question by comparing the patterns of EM activity in opposing muscles during transie impulses and during sustained force changes. Thir is the sequential activation of agonist and antagon: muscles the result of an obligatory linkage betwe~ the signals driving the corresponding motor neur( pools? To address this question, we have designed task in which subjects attempt to produce a rapid rising trajectory without reciprocal activation of tl antagonist muscle. These questions were approached by examinil the parametric relationships between EMG activi and force trajectories in trained subjects performiJ a series of tracking tasks. Subjects were provid~ with visual and auditory feedback of various featur of their performance to help them master the diffe ent tasks. Analytic methods, including the selectk and matching of trials and multiple regression anal sis, were used to define the unique relationships. different EMG and trajectory variables to o~ another. Some of these results formed part of doctoral thesis (Gordon 1985). An abstract and shc communication describing some of the results ha' been previously published (Gordon and Ghez 198 Gordon and Ghez 1984).

Methods Subjects and general features of the task

Experiments were conducted in nine neurologicallynormal ad volunteers (S1-$9, ages25-45; 7 males, 2 females). In all subje, we first studied trajectory and EMG features of transient elbt flexion responses consisting of fast isometricforce impulses aim to targets of different amplitudes (see below: Tasks, Fast con, tion). We then used variants of this basic task in subgroups subjectsto answer specificquestions raised by the first set of da

227 Pilot studies carried out in two of the subjects indicated that the patterns of EMG activity in opposing muscles were similar for flexion and extension responses at the elbow.

Apparatus The experimental arrangement is illustrated schematically.~.:in Fig. 1. Subjects were tested in the sitting position with right ~ m abducted to approximately 70 ~ and the elbow flexed to ~;!)~ Adjustable metal restraints were used to immobilize the shoulder, upper arm, forearm and wrist. The forearm was secured in a neutral position between supination and pronation by a rigid wrist cuff lined with dense rubber padding (1 cm thick). The force transducer was coupled to this wrist cuff and consisted of four strain gauges arranged to be maximally sensitive to forces applied in the horizontal plane. Facing the subjects were two visual displays. First, a large (23 cm across) video monitor (Kikusui, model 5122A), located at eye level and set at a fast sweep speed (20 ms/screen), indicated the target level and the force produced by the subject. Second, a storage oscilloscope (Tektronix, model 511A), set at a slower sweep speed (1 s/screen) and located below the monitor, was used by the subject between trials to review trajectory variables, the target, and, in some experiments, EMGs. In one set of experiments, subjects listened through earphones to a frequency modulated (40-100 Hz) auditory display of target and response waveforms (see below: Tasks, Matched trajectory condition).

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Tasks All subjects were trained to produce a common response type consisting of an aimed isometric force impulse. The basic task was to generate a single force impulse whose peak amplitude matched that of a previously presented visual target step, and then to allow the force to return passively to baseline. Subjects were specifically instructed to refrain from correcting their responses once initiated. Additionally, subjects were urged not to respond to the target step "as soon as possible", but rather to respond "when ready" so as to optimally prepare their responses. Responses were initiated from a neutral force level. In order to characterize the relationships of specific features of the EMG activity to particular trajectory variables, different sets of instructions were added to those indicated above to form several task conditions:

Fast condition. Subjects (N = 9) were instructed to make the force rise as rapidly as possible (see Fig. 2A). Step condition. Subjects (N = 2) were instructed to produce a brief initial impulse and then hold the force at the new target level rather than allowing it to return to baseline. Subjects were also instructed to reach the target level with little or no overshoot. In order to facilitate the production of step responses with similar trajectories to those produced in force impulses, the following procedure was used during both practice and testing sessions. Subjects)~ere presented with a block of 20 trials with the same target amplitude, and they were instructed to respond with rapid step responses and to avoid overshooting. After each trial, the target, the force, and the first time derivative of force (dF/dt) were displayed on the oscilloscope screen; subjects were instructed to make the dF/dt peak rise consistently to the same level. After doing a block of step responses, the subjects were given another block with the same target amplitude and were instructed to produce impulse responses with a similar dF/dt as they had

Fig. 1. Schematic representation of subject and experimental apparatus. Subject was seated with right arm fixed in a system of rigid restraints. A force transducer (strain gauge) fixed to the wrist restraint measured isometric force produced by contraction of muscles at the elbow joint. Subject is shown facing a large oscilloscope on which target and force changes are displayed. A storage oscilloscope (not shown) was placed directly under the large oscilloscope, allowing subjects to review the results of a trial. In some experiments, subjects monitored target and response variables through earphones

produced in the step responses. The same procedure was then repeated for other target amplitudes.

Matched trajectory condition. Subjects (N = 4) were instructed to produce a force trajectory which replicated a previously presented waveform acting as a template. In this condition, instead of a step change in target level, the target was shifted to a different level gradually, with a one-half-cycle sinusoidal waveform and with rise times ranging from 80 to 400 ms. As illustrated in Fig. 2B, the subject's task was to match both the amplitude and the rise time of the target shift which thus served as a template. Performance of this task was greatly facilitated by presenting the subjects with a frequency-modulated audio signal indicating the target waveform and their own force response, along with the visual displays. The audio signal enabled subjects to produce force trajectories that were both smooth and matched to the contour of the previously presented waveform. The subjects were still to allow force to return passively to baseline.

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For all task conditions, training consisted of two to four sessions of 200--400 trials each, during which subjects viewed both force and dF/dt traces on the storage oscilloscope. Responses with more than one peak in the dF/dt were assumed to be corrected and were pointed out to the subjects. After practice, these constituted no more than 5% of subjects' responses and were excluded from analysis. Testing sessions consisted of 200-400 trials of 1.5-2.0 s duration. Inter-trial interval was varied randomly between 4 and 6 s. Trials under a specific task condition were organized as blocks of 20-30 trials with 1-2 rain rest periods allowed between blocks. In most sessions, 3 to 5 target amplitudes were presented, typically requiring peak forces from 20% to 60% of maximal voluntary flexion force. Within a block of trials, target amplitude was always the same. Testing sessions began with several practice trials during which the position of the subject's arm in the manipulandum was adjusted and EMG signals were monitored to produce initial conditions with no force being exerted when agonist and antagonist muscles were silent. At the end of a session, maximal voluntary flexion and extension forces produced at the elbow were recorded, along with the associated EMG.

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Fig. 2A, B. Single trials illustrating two of the task conditions. A Fast condition. Subject views visual display of target (required force) and actual force and is required to initially align target and force. After a variable interval, target line shifts upward and subject is required to produce an impulse of force with as brief a rise time as possible. B Matched trajectory condition. In addition to visual display, subject also hears an auditory display of target shift and actual force trajectory. Subject is required to match the amplitude and rise time of response to that of target (template). The actual auditory signal was modulated between 40 and 100 Hz, but is displayed here at a lower frequency for illustrative purposes. Calibration: 48 N, 58% maximum biceps EMG, 55% maximum triceps EMG

Matched force acceleration with antagonist suppression. In order to compare rapid force impulses with and without an antagonist burst, subjects (N = 3) were given the task of matching the peak d2F/dt z (force "acceleration") to a visual target. Instead of the usual force display, the dZF/dtz was displayed along with the target on the oscilloscope. Target levels were chosen to correspond to the mean peak d2F/dt2 produced in a preceding block of impulses

Presentation of targets and timing of trials were controlled by a PDP 11/23 computer (Digital Equipment Corporation), which was also used for on-line data acquisition. The computer has a 16 channel, 12 bit A/D converter (ADAC Corporation). All data were collected with a bin width of 2 ms. The output of the force transducer was amplified and low-pass filtered (cut off-100 Hz) before being displayed to the subject and sent to the computer. The first and second derivatives of force were computed off-line. Electromyograms were recorded from the biceps muscle and the lateral head of the triceps using surface electrodes with built-in FET preamplifiers and filters with optimal band pass of 40-500 Hz (Boston Elbow Myoelectrodes, Liberty Mutual). The EMG signal from these transducers was further amplified, then rectified and integrated. Following sampling of the integrated signal by the A/D converter at each bin, the computer reset the integrator to zero. Thus, the integrated signal received by the computer closely followed the contours of the rectified EMG without the temporal distortions introduced by long time constants of integration.

Data analysis The first stage of analysis was the computation of a set of "critical points" for each trial. These included the onset and peak of the force impulse, the first maxima and minima of the first and second derivatives of force, and the onsets and terminations of agonist and antagonist EMG bursts. Each of these points was determined in individual trials by means of automatic programs; they were then visually checked for errors. The algorithm for determining force onset used the first bin of a consistent rising trend of the first time derivative of the force. The onset and termination of EMG bursts were marked by a routine which computed the standard deviation of the EMG signal during the initial alignment and then used a threshold at three times the standard deviation to indicate the

229 onset and termination of the burst. The magnitude of an individual burst was then computed as the integrated value of the EMG between these points. All EMG data were calibrated as percent of maximum EMG. Maximum EMG for each muscle was measured during a set of trials at the end of each session. Subjects were requested to produce 5 trials in which they maintained maximal flexionforce on the lever, and then 5 trials with maximal extension force. Each of these maximum force trials was scanned using a computer algorithm to find the 100-ms interval with the highest integrated EMG magnitude for each muscle. The integrated value over this 100-ms interval was defined as maximum EMG and provided a standard for comparison of agonist and antagonist EMG within a subject and session. The choice of a 100-msinterval was arbitrary; actual EMG bursts observed in the experiments varied widely in duration (see Fig. 5). Because most of the dependent variables, especially EMG burst magnitudes, are difficult to compare across subjects and sessions, most statistical comparisons were limited to data for a single subject within a session. For certain of the figures, curves were fit to the data using a non-parametric least squares estimation procedure referred to as LOWESS (Cleveland 1979), or Locally Weighted Scatterplot Smoother. This procedure employs an algorithm which is conceptually similar to a quadratic movingaverage smooth performed on time series data. It also includes a "robustness" criterion which gives less weight to outlying data points.

Results

termination coincided both with the end of the agonist silent period and with the end of the negative phase of d2F/dt 2. As illustrated in Fig. 3A, the positive and negative peaks of d2F/dt 2 closely followed the peaks of AG1 and A N T - R respectively. The close temporal association between the derivatives of force and the burst pattern in agonist and antagonist is further illustrated in Fig. 3B, which represents the E M G patterns of single responses to targets of a range of amplitudes by the same subject. The E M G of individual trials in this figure are transformed into frequency-modulated pulse trains (Evarts 1974). In the center, the lengths of the horizontal lines represent the peak forces achieved in the individual trials. In this raster, trials are ordered by decreasing peak force (from top to bottom) and are aligned on the dF/dt peak. This figure shows that an alternating pattern of bursts is present over a wide range of peak forces. AG1 terminates at about the time of peak dF/dt, although in the largest force impulses it extends into the deceleration phase of the impulse. A N T - R has a relatively constant duration and begins just before the occurrence of the peak dF/ dt. The following sections will attempt to clarify the functional role of this alternating pattern of E M G bursts and to define the trajectory features upon which each of the bursts depend.

General features of EMG activity in opposing muscles during rapidly rising force trajectories In all subjects, the production of rapidly rising force trajectories was associated with a characteristic pattern of E M G activity in opposing muscles. As illustrated in Fig. 3A, which is an ensemble average of 16 trials to a single target, this pattern consisted of alternating bursts in agonist and antagonist. The timing of these bursts showed a consistent temporal relationship to the peaks and troughs of the first and second time derivatives of force (dF/dt and d2F/dt 2 respectively). When, as in the case illustrated here, the response occurred on a background of tonic agonist activity, the first sign of the impending response was a pause in the agonist EMG. The rising phase of force was produced by a well-defined E M G burst which preceded the onset of force development by 30-50ms. The first agonist burst (AG1) terminated abruptly at about the time of the peak dF/dt and was followed by a silent period. At the end of the silent period, there were often one or more late bursts in the agonist; these occurred after peak force had been reached. The antagonist muscle exhibited a small amount of coactive activity during the first agonist burst. However, just as agonist activity started to decline from its peak, a large reciprocal burst (ANT-R) occurred in the antagonist. A N T - R

Comparison of agonist and antagonist activity in impulse and step responses The first question we addressed was whether A N T - R functions to return force to baseline or to control the rising phase of the force trajectory itself. In order to resolve this question, we compared the E M G patterns producing impulsive responses with the E M G patterns producing sustained changes in steady state force (step responses). However, to make such a comparison meaningful, it was necessary that the initial trajectories be similar in the two conditions. This required specific training (see Methods); otherwise, step responses invariably had longer rise times than impulses. Once subjects learned to produce impulses and steps with equally brief rise times, a similar pattern of alternating reciprocal bursts was present in both types of response. This is demonstrated in Fig. 4A, showing average impulse and step responses of the same amplitudes and similar early dynamics. The averaged AG1 and A N T - R are virtually identical in the two conditions. The raster displays of single trial E M G ' s sorted by peak force, in Figs. 4B and 4C, show that an antagonist burst is present in both impulses and steps across all response amplitudes.

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B e c a u s e A N T - R is p r e s e n t in steps w i t h t h e s a m e timing a n d m a g n i t u d e as in i m p u l s e s , t h e a n t a g o n i s t b u r s t c a n n o t f u n c t i o n m e r e l y to r e t u r n f o r c e to b a s e l i n e after t h e p e a k . R a t h e r , a n t a g o n i s t c o n t r a c tion serves to c o n t r o l t h e t e r m i n a l p o r t i o n of t h e rising p h a s e o f t h e f o r c e t r a j e c t o r y itself. I m p u l s e a n d s t e p r e s p o n s e s differ, h o w e v e r , in

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