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1Centre de Recherche en Sciences Neurologiques, Département de Physiologie, Université de Montréal, Montreal, Quebec; and 2Department of Kinesiology and Health Sciences, Bethune College, York University, Toronto, Ontario, Canada
Submitted 21 September 2004; accepted in final form 8 May 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Cabel et al. 2001; Cheney and Fetz 1980; Evarts 1968, 1969; Humphrey et al. 1970; Thach 1978), or by the whole arm (Ashe 1997; Georgopoulos et al. 1992; Kalaska et al. 1989; Li et al. 2001; Sergio and Kalaska 1997, 2003; Taira et al. 1996), and during precision-pinch tasks (Hepp-Reymond et al. 1999; Maier et al. 1993; Smith et al. 1975). Other studies have reported correlations between neuronal discharge and muscle activity (Bennet and Lemon 1994, 1996; Cheney et al. 1985; Fetz and Cheney 1980; Holdefer and Miller 2002; Lemon and Mantel 1989; Morrow and Miller 2003; Park et al. 2004; Poliakov and Scheiber 1999). These findings suggest that M1 functions at a level near the final motor output to muscles.
In contrast, other studies have described relationships between M1 activity and various kinematic parameters of motor output such as the direction and distance of targets relative to the hand, and the direction, speed, and spatial path of hand displacement (Ashe and Georgopoulos 1994; Caminiti et al. 1990, 1991; Georgopoulos et al. 1982, 1983, 1988; Kalaska et al. 1989; Fu et al. 1993, 1995; Moran and Schwartz 1999a,b; Reina et al. 2001; Schwartz 1992, 1993, 1994; Schwartz and Moran 1999; Schwartz et al. 1988, 2004). These results suggest that M1 functions at a higher level in the putative motor control hierarchy further removed from the motor periphery and generates a descending motor command that defines the spatiotemporal form of the action to perform (its kinematics) rather than how it should be performed (its kinetics).
A related controversy concerns the parameter spaces and coordinate frameworks in which motor output is encoded in M1. This debate focuses on the degree to which activity is related to extrinsic spatial attributes of motor output or to intrinsic limb-, joint-, or muscle-centered parameters (Caminiti et al. 1990, 1991; Kakei et al. 1999, 2001, 2003; Scott and Kalaska 1997; Sergio and Kalaska 1997, 2003) and whether the reference frame is centered on the hand or on other parts of the limb (Cabel et al. 2001; Caminiti et al. 1990, 1991; Moran and Schwartz 1999a,b; Reina et al. 2001; Schwartz 1992, 1993, 1994; Scott and Kalaska 1997; Sergio and Kalaska 1997, 2003). Other findings suggest that the nature and point of origin of the framework may even vary with time during the planning and execution of a motor action (Fu et al. 1993, 1995; Scott and Kalaska 1996, 1997; Sergio and Kalaska 2003; Shen and Alexander 1997a,b; Zhang et al. 1997).
The interpretation of neurophysiological findings is further confounded by the continuing theoretical controversy over the computational architecture of the motor system, in particular whether it uses force control or position control to produce desired motor outputs. Force-control schemes assume that after defining the kinematics of the desired motor output but before emitting any control signals that specify the necessary muscle activity patterns, the motor system generates an intervening representation of the required causal forces or joint-centered torques (Bhushan and Shadmehr 1999; Haruno et al. 2001; Hollerbach 1982; Nakano et al. 1999; Schweighofer et al. 1998; Todorov 2000; Uno et al. 1989; Wolpert and Kawato 1998). A force-control architecture requires the motor system to possess implicit or explicit knowledge of the laws of motion and the dynamical properties of the limb and the environment, and to perform a neuronal equivalent of the notorious "inverse-dynamics" transformation in Newtonian mechanics. In contrast, position control schemes (e.g., Bizzi et al. 1984; Feldman 1986; Feldman and Levin 1995; Polit and Bizzi 1979) do not require the supraspinal motor system to generate an explicit representation of task dynamics or descending motor commands that explictly signal output forces or muscle contractile activity patterns. For instance, the "
" (lambda) model of "equilibrium-point" control (Feldman 1986; Feldman and Levin 1995; Feldman et al. 1990; Gribble and Ostry 1999, 2000; Ostry and Feldman 2003) achieves the inverse transformation between desired kinematics and causal muscle activity indirectly by descending control of spinal motoneuron recruitment thresholds, to drive the arm to a new posture at which internal and external viscoelastic forces are at equilibrium.
Beyond their theoretical significance, these issues have taken on added practical importance because of rapid advances in neuroprosthetic technologies that use the recorded activity of M1 neurons to control robotic devices (Carmena et al. 2003; Serruya et al. 2002; Taylor et al. 2002). These controllers typically use decoding algorithms that extract signals about desired kinematics (e.g., position, direction, velocity) (Paninski et al. 2004a,b), and do not cope readily with abrupt changes in the dynamics of motor tasks (Carmena et al. 2003). The performance of neuroprosthetic controllers could be improved by a deeper understanding of the motor representation in M1.
The present study examines the degree to which M1 activity reflects the kinematics or kinetics of whole-arm motor tasks. Monkeys alternately performed either a whole-arm isometric force task or a reaching task to displace a cursor between targets on a monitor screen. The cursor motions reflected the direction of motor outputs measured at the hand and imposed the identical global behavioral constraint on performance in both tasks. However, the output parameter used to control cursor motion differed between tasks. In the isometric task, the monkeys used their arm to generate force ramps at the hand in eight directions in a horizontal plane, and the cursor provided feedback of hand-centered forces. The direction and time course of the behavioral constraint (cursor motion) and of the causal forces at the hand were co-linear and isomorphic at all times. In the movement task, the monkeys made ramp displacements of the hand in the same eight horizontal directions to move a weighted pendular handle, and the cursor provided hand position feedback. The monkeys had to generate complex patterns of horizontal output forces at the hand to compensate for the inertial load imposed by the pendulum. Unlike the isometric task, however, the causal horizontal forces were not the output variable controlled by the task, they were not displayed on the monitor, and their directionality was transiently dissociated from hand displacement and cursor motion as the hand approached the targets.
The activity of many single neurons and the net population signal in the caudal part of M1 reflected the large differences in the time course and directionality of output dynamics between the two tasks to a much greater extent than they did the large differences in the output kinematics or the similarity in the global behavioral constraints of the two tasks. Preliminary results have been reported previously (Sergio and Kalaska 1998).
Note that terms borrowed here from mechanics (e.g., kinematics, kinetics, dynamics) have specific and at times variable meanings in that field. They are used here only as convenient descriptors to express the degree to which neuronal activity covaries with the externally observable spatiotemporal form of motor outputs (task "kinematics"), or to their underlying causal forces, torques, and muscle activity (task "kinetics"), while the system is in equilibrium (task "statics") and especially while in transition between static states (task "dynamics"). These terms clearly have implications for the nature of the motor representation in M1, but their use here should not be interpreted as support for the explicit coding of any particular Newtonian mechanical parameter by the activity of M1 neurons.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Two juvenile male rhesus monkeys (Macaca mulatta; 3.4–7.0 kg, 3.4–6.1 kg) were trained to perform isometric-force and arm-movement tasks. In the isometric task, the monkeys grasped a 20-mm-diameter ball on the end of a 65-mm vertical rod that was attached to a 6df (degree-of-freedom) force/torque transducer (Gamma F3/T10; Assurance Technologies) placed in a fixed position in front of them (Sergio and Kalaska 1997, 2003). They used their whole arm to exert forces against the rigid rod. The rod passed freely through a small hole in a thin metal plate that was attached by hinges to the top edge, furthest away from the monkey, of a box that housed the transducer. The free end of the plate sat on a microswitch. If the monkey rested its hand on the plate or applied forces to it, the switch would close and halt the task. This ensured that all force outputs at the hand were applied only to the rod and were sensed by the transducer.
In the movement task, an identical rod/transducer/housing assembly was attached to the end of a 1.6-m-long pendulum. The complete assembly weighed 1.3 kg (see Behavioral tasks below), and the pendulum plus transducer was 2.6 kg. This imposed a large inertial load during movement, unlike other studies in our lab (Cisek et al. 2003; Crammond and Kalaska 1996, 2000; Kalaska et al. 1989; Scott and Kalaska 1997). A sonic digitizer (GP-9; Science Accessories) measured the X–Y position of the pendulum base at 55 Hz with a resolution of 0.1 mm.
A computer monitor was positioned at eye level 60 cm in front of the monkeys. In the isometric task, a cursor on the monitor gave continuous feedback of the current force level applied to the force transducer in the X–Y (horizontal) plane, sampled at 200 Hz. The X-axis was aligned to the 0–180° (right–left) direction in front of the monkeys, and the Y-axis to the 90–270° direction (Fig. 1). In the movement task, the cursor gave position feedback about the current spatial location of the pendulum. The X–Y forces applied to the handle were also sampled at 200 Hz but were not displayed. In both tasks, the monkeys' starting hand location was at the midline, 20 cm in front of the sternum, approximately level to the zyphoid process.
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At the start of each trial of the isometric task, a circle appeared at the center of the monitor (Fig. 1). The monkeys had to generate a small static bias force (0.3 N) away from the body to position the cursor within the central force target for a variable (1–3 s) hold period. The central target then disappeared and a peripheral force target (diameter: 0.28 N) appeared at one of eight locations arrayed in a circle around the central target. The separation of the centers of the central and peripheral targets corresponded to a 1.5 N change of force. The monkeys generated a force ramp in the indicated direction in the horizontal plane to move the cursor into the peripheral target, and held it there for 2 s to receive a liquid reward (Fig. 2 A). The animals generated force ramps aimed at each target from their onset, and did not initially relax the bias force. Targets were spaced at 45° intervals, starting from 0° (to the right) and progressing counterclockwise. The eight targets were repeated five times in a randomized-block design. The same event sequence was followed in movement-task trials, but the cursor provided pendulum position feedback. The monkeys had to generate a bias force to push the pendulum from its suspended rest position away from the body by 2 cm to place the cursor in the central target. Movements of 8 cm were required to displace the cursor from the central to the peripheral targets. Extra weights were added empirically to the transducer assembly to ensure similar ranges of static and dynamic forces in the two tasks (Fig. 2). The mean change in static force relative to the central target exerted by the monkeys to hold the pendulum at the peripheral targets (about 1.0 N) was less than the static forces in the isometric task. However, increasing the pendulum's mass to require final static forces of 1.5 N increased the inertial load to such a degree that the dynamic accelerative and braking forces became far larger than any forces in the isometric task. It also made it very difficult for the monkeys to respect the behavioral constraints of movement timing, endpoint accuracy, and vertical forces (see following text) to ensure reliable and willing performance of the movement task. However, exact duplication of the range of dynamic and static forces in the two tasks was not essential in this study because its objective was not to make a quantitative comparison of the parametric coding of specific output force levels in the two tasks.
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Data collection
The animals were trained to >80% success rates in both tasks. They were then prepared for neuronal recordings in M1 using standard aseptic surgical techniques (Kalaska et al. 1989).
Conventional techniques were used to record the activity of single M1 neurons (Kalaska et al. 1989). During each recording session, a microelectrode was advanced through the cortex while the animal performed the tasks. When a neuron was isolated, its task-related responses were tested initially by performing a few trials in several directions. Its passive responses were tested by manipulating the arm joints, brushing the skin, and palpating muscles. The arm was also observed for signs of movements or muscle contractions during low-threshold intracortical microstimulation (ICMS) of the cortex. A neuron was selected for further study if this evidence indicated that it was related to movements of the contralateral shoulder and/or elbow but not to more distal joints, and it displayed directional tuning in at least one of the tasks. Attempts were made to record neurons from all cortical layers but the need for stable isolation over long periods of time (Sergio and Kalaska 1997, 1998, 2003) led to a bias toward neurons with large-amplitude extracellular spike waveforms recorded in intermediate cortical layers.
The monkeys performed data files of 40 trials first in one task and then the other. The order in which the tasks were performed varied from neuron to neuron, and duplicate sets of data files were sometimes collected from the same neuron to ensure repeatability of results.
In both monkeys, activity was recorded from 16 proximal-arm muscles in separate recording sessions. Muscles were implanted percutaneously with pairs of Teflon-insulated 50-µm single-stranded stainless steel wire electrodes. Implantations were verified by stimulation through the wires to evoke muscle contractions (<1.0 mA, 30 Hz, 300-ms train). Multiunit EMG activity was amplified, band-pass filtered (100–3,000 Hz), half-wave rectified, integrated (5-ms bins), and digitized at 200 Hz. The muscles studied were the biceps brachii, brachialis, anterior deltoid, middle deltoid, posterior deltoid, dorsoepitrochlearis, infraspinatus, latissimus dorsi, pectoralis, subscapularis, supraspinatus, teres major, rostral trapezius, caudal trapezius, triceps longus, and triceps medialis. These recordings were done only to assess the behavior of the muscles in the two tasks, to provide a benchmark against which to compare cell activity. They were not intended as a definitive quantitative study of the response properties of each muscle.
Near the end of recordings in each cylinder, small electrolytic lesions were made (5–10 µA, 5 s) in selected penetrations. At the conclusion of the experiment, the monkeys were deeply anesthetized with barbiturates and perfused with buffered saline and formalin (monkey A) or saline and 4% paraformaldehyde (monkey B). Pins were inserted into the cortex at known grid coordinates to delimit the area from which cell recordings were made and the cortex was sectioned to permit localization of the marked penetrations.
Data analysis
Four behavioral epochs were defined in both tasks. Center hold time (CHT) ended when the peripheral target appeared. Reaction time (RT) was the interval between the appearance of the peripheral target and the first detectable change in force measured by the transducer in both tasks. Movement time (MT, movement task) or the equivalent dynamic force time (DFT, isometric task) ended when the controlled motor output stabilized at either a constant spatial position (movement task) or static force level (isometric task) within the peripheral target. Target hold time (THT) was the remaining period of static hold in the target. Single-trial spike rates were calculated for each epoch using the whole and partial spike intervals that fell within the epoch, rather than simple spike counts (Georgopoulos et al. 1982, 1988; Sergio and Kalaska 2003; Taira et al. 1996). A leading partial spike interval is defined as the fraction of the whole spike interval between the first spike in the epoch and the last spike that occurred before the epoch started that falls within the epoch. A trailing partial spike interval is the fraction of the whole spike interval between the last spike in the epoch and the first spike occurring after the epoch that is contained within the epoch. If no spikes occur in an epoch, the partial spike interval is the duration of the epoch divided by the interval between the last spike before and the first spike after the epoch. The epoch spike rate (s/s) is the sum of the leading and trailing partial spike intervals and the whole intervals between consecutive spikes within the epoch itself, normalized for the epoch duration. This approach yields a more continuous distribution of spike rates than spike counts and provides a more accurate measure of activity by accounting for the entire time period of interest in the spike train within which it is embedded (Taira et al. 1996).
An unbalanced repeated-measures ANOVA was used to test for a significant main effect of direction and task, and for direction-task interactions (P < 0.01, 5V program, BMDP Statistical Software, University of California, Los Angeles, CA) in all epochs.
The electromyographic (EMG) activity recorded from proximal-arm muscles was subjected to the same analyses as the cells. Whenever analyses required the pooling of results from different cells or muscles, all data collected while the monkeys performed the task with the left arm were subjected to a mirror-image transformation about the 90–270° (Y) axis.
TIME COURSE OF CHANGES IN DIRECTIONAL TUNING. A temporal analysis was made of the evolution of each neuron's directional tuning during the trials. Spike data were aligned to the moment of force onset in each trial in both tasks. A 50-ms sliding window was advanced in 10-ms steps, from 400 ms before force onset to 1,200 ms after force onset, and tests were performed on the directional tuning of the windowed activity at each step, as follows.
The discharge rate was calculated within the 50-ms window at a given time step t in each trial, using whole and partial spike intervals. Discharge rates were not transformed further. The 40 samples of windowed activity in each task were tested for a significant relation to direction (ANOVA, P < 0.01), and the preferred direction (PD) of the windowed activity at time t was calculated for the movement (PDmt) and isometric (PDit) tasks. The data were also tested using a bootstrap method with random shuffling of data across directions to assess whether the directional tuning could have occurred by chance (Georgopoulos et al. 1988; Sergio and Kalaska 1998, 2003).
Next, the angular difference (
PDt) between PDmt and PDit was calculated for all cases of significant directional tuning in a given time window for both tasks. A second bootstrap procedure was used to assess whether the observed PDt was significant or could have occurred by chance. This test assumed that if the tuning function of a neuron is the same in the two tasks, then the distribution of PDt calculated from multiple samples of neuronal activity in the two tasks will be centered on 0° angular difference. To implement this test, we generated an estimate of the directional tuning curve of the cell in the movement task by random selection, with replacement, of five values of the discharge rate of the cell from the sample of five single trials at each of the eight directions. Data were not shuffled across directions for this test. The PD of this bootstrapped sample of data (PDmtb) was calculated by standard methods. This was repeated for the data in the isometric task to calculate a PDitb. The signed difference PDtb between PDmtb and PDitb was calculated. This was repeated 1,000 times to generate a distribution of PDtb values, which were rank ordered. The limits of the 95% confidence interval (CI) were defined as the 25th and 975th largest PDtb values (two-tailed test). A neuron was considered to have a significant difference in PD between the two tasks in a given time window if it was: 1) significantly directionally tuned in both tasks and 2) the value of 0° fell outside of the 95% CI of the distribution of bootstrapped PDt (i.e., the null hypothesis that the observed value for PDt was not significantly different from 0° can be rejected at P < 0.05, two-tailed test). This test was also used to compare the directional tuning of each neuron at different times in the same task.
POPULATION-VECTOR ANALYSIS.
To examine the directional correspondence between overall M1 activity and the motor output as a function of time, a population-vector analysis was performed on neuronal activity in nonoverlapping 20-ms bins, aligned to force onset in each trial, from 400 ms before force onset to 1,200 ms after force onset. The population vector P for a given direction of motor output d at a given moment in time t, was calculated in standard fashion as
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Each population vector is the sum of the vectorial contribution of all neurons along their own PD. However, the calculated PD of a neuron can change between windows, in part because the stochastic nature of its activity is accentuated when examined in short time windows from small data samples (40 trials). Furthermore, the windowed activity of muscles and neurons often showed large changes in apparent PD during the MT epoch of the movement task (Sergio and Kalaska 1998; see RESULTS). This raises the question of how to define the directional influence of a given neuron at a given moment in time, and thus its contribution to the population signal.
To address this question, we assumed that the directional influence exerted by each neuron on motor output remains stationary, at least over the time frame of single trials and single data files. The directional tuning of single muscles and M1 neurons was generally similar in the two tasks for the mean activity during the RT and especially the THT epochs. Therefore we calculated the PD of the M1 neurons using their mean activity during the THT epoch in each task, and used it as the canonical PD of the neuron for each 20-ms window of that task. Using the PD during the RT epoch did not fundamentally alter the basic findings of this analysis.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Task-related activity was recorded from 132 cells in both tasks during 134 penetrations in the primary motor cortex (M1) of three hemispheres from two monkeys (71 and 17 cells from the left and right hemispheres of monkey A, 44 cells from the right hemisphere of monkey B). These monkeys were also used to study the effects of changes in arm posture on isometric force–related M1 activity (Sergio and Kalaska 1997, 2003), and most of the neurons in that study form part of the present data set. Almost all neurons were recorded from the most caudal part of M1 in the anterior bank of the central sulcus. To be included in the data sample, a neuron had to be related to movements of the proximal arm and directionally tuned during at least one trial epoch in one of the tasks. As in previous studies (Crammond and Kalaska 1996; Kalaska et al. 1989; Scott and Kalaska 1997; Sergio and Kalaska 2003), the sample was biased toward neurons related to movements of the shoulder and shoulder girdle. Some neurons were related primarily to the elbow. Any neurons related to wrist or hand movements were not retained. All sampled neurons were active in both tasks. This was also true for the many neurons that met the inclusion criteria for the study but were lost before data collection was completed. There was no evidence of significant populations of neurons that were selectively activated in only one of the two tasks.
Task performance
The monkeys produced similar smooth ramplike X–Y trajectories of the experimentally controlled variable in each task, hand-centered forces in the isometric task, and hand positions in the movement task, to displace the cursor from the central to the peripheral targets (Fig. 2).
In contrast, the temporal profile of the forces measured at the hand differed between tasks. A temporal force profile was calculated as the moment-to-moment change in length of the vector component of the measured force output vector that was aligned along the axis of target direction, averaged across all trials in that direction, relative to the mean bias–force vector during CHT in both tasks. In the isometric task, the force profile was a monotonic ramp increase in the direction of the target (Fig. 2A). The force profile in the movement task was more complex, including an initial accelerating pulse in the desired direction of motion, a smaller decelerating force in the opposite direction, and a final static force to hold the pendulum over the peripheral target (Fig. 2B). The measured deceleration force was smaller than the acceleration force, attributed in part to the decelerating effect of gravity on pendulum motion. The MT epoch of the movement task was typically about twice as long as the corresponding DFT of the isometric task. This compromise was necessary to ensure comparable ranges of measured dynamic output forces in the two tasks and reliable performance of the movement task.
Muscle activity: general description
The differences in force profile were paralleled by task-related changes in muscle activity. In the isometric task, muscles showed a ramp increase in activity, beginning about 50 ms before force onset, across a range of force directions centered on its preferred direction and a decrease or complete suppression of activity in the opposite directions (Figs. 2A and 4A).
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), consistent with the smaller measured decelerating forces. The antagonist burst was more prominent for muscles whose preferred direction was along the lateral (0–180°) axis, such as the deltoids and pectoralis, and less prominent for muscles oriented along the 90–270° axis, such as elbow flexors and extensors. In both tasks, performance was characterized by reciprocal activation of muscles whose preferred directions were oppositely oriented. There was little evidence of extensive cocontraction of antagonist muscles in these highly practiced monkeys.
Neuronal activity: general description
Neurons showed a broad continuum of responses at their preferred direction in the isometric task, which could be subjectively divided into two patterns. Most (91/132; 69%) showed a large increase in tonic discharge (Fig. 3, A and C), often with a strong phasic burst of activity at the leading edge of the tonic increase before force onset (Fig. 4 C). Other neurons emitted mainly a phasic burst, with little or no change in tonic activity after completion of the force ramp (30/132, 23%). Eleven neurons were unclassifiable. Typically, neurons showed a reciprocal suppression of activity during isometric force production in the opposite direction (Figs. 3C and 4C).
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Although the details and timing of the responses varied between neurons, the task-related changes in activity typically paralleled and led in time the differences in force profiles between tasks (Figs. 3 and 6; see later sections).
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). Such strong antagonist bursts were never observed in the muscle activity, which were always much weaker than the muscle's agonist burst in its preferred movement direction (Figs. 2B and 4B). ANOVA of activity in different trial epochs
A repeated-measures ANOVA was performed on mean discharge rates during different trial epochs to assess the overall effect of task and direction on neuron and muscle activity (Table 1). Significant main effects of task and direction were prominent in all post-GO trial epochs, but were less common in RT than in later epochs. Most notably, however, the number of neurons that showed a significant task-direction interaction increased sharply from 23% in RT to 88% in MT/DFT and 79% during THT. Muscle activity showed similar trends (Table 1).
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). The depth of a neuron's directional tuning curve could change between tasks. Alternatively, the preferred direction could change between tasks. The following analyses evaluated both possible interaction effects. The effect of task on dynamic range of activity in different behavioral epochs
To test for task-dependent changes in the depth of a neuron's directional tuning curve independent of any directional shift, we calculated the neuron's dynamic range (DR) of activity in both tasks. The DR was defined as the difference in activity between the two directions of motor output that evoked the maximum and minimum mean discharge rates in a given task.
Figure 5, A–C shows scatter plots of single-neuron DRs between tasks for each trial epoch. The DR distribution was shifted toward significantly smaller values during the MT epoch of the movement task than during the DFT period of the isometric task (mean DR: 24.4 vs. 31.7 imp/s, respectively; paired t-test, P < 0.01). In contrast, there were no significant differences in DR distributions between the movement and isometric tasks during the RT (18.4 vs. 18.4 imp/s) and THT (20.8 vs. 19.5 imp/s) epochs. Furthermore, the correlation between the DR of neurons in the two tasks was much weaker during the MT/DFT epoch (R2 = 0.11) than during the RT (R2 = 0.46) and THT (R2 = 0.41) epochs, respectively. Both of these effects on DR during the MT/DFT epoch were likely a result, in part, of averaging the complex changes of neuronal activity across the duration of the MT epoch in each direction of the movement task. This could account for part of the increase in incidence of significant interaction effects between the RT and MT/DFT epochs but not for the continued high incidence in the THT epoch.
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Neurons were broadly tuned for the direction of motor output in both tasks (Figs. 3 and 4). The distributions of PDs were statistically uniform in all three trial epochs of both tasks (Rayleigh test, Rao's spacing test, P > 0.05; data not shown; Batschelet 1981).
A significant interaction effect could result from a shift in directional tuning between tasks independent of changes in DR. Figure 5, D–F shows the distribution of PD differences (PD) for those neurons that were significantly tuned in the two tasks in a given trial epoch. During RT and THT, PDs were similar between the two tasks, as indicated by the strong clustering of data near zero degrees difference (Fig. 5, D and F). During MT/DFT, in contrast (Fig. 5E), there was greater scatter in the distribution of PD. This was once again attributed in part to averaging the complex temporal profile of activity in the movement task across the entire MT epoch. For instance, if a neuron showed a strong delayed antagonist burst in directions of the movement task that were opposite to their PD in the isometric task, this would bias the calculated PD toward that direction and cause a large apparent PD between the two tasks. A bootstrap test was used to assess whether the observed PD between tasks was statistically significant (see METHODS). The incidence of significant PD increased sharply from RT (12/79; 15%) to MT/DFT (68/103; 66%) and then decreased in THT (60/117; 51%) (Fig. 5, D–F). This increase in PD also likely accounted for much of the change in incidence of significant ANOVA interaction effects across epochs.
Changes in directional tuning over time within and between tasks
The preceding epoch-based analyses treated neuronal responses as quasi-tonic signals, by averaging the activity of each neuron over several hundred milliseconds in each trial epoch. This masked any finer detail in the temporal pattern of activity.
To study the evolution of directional tuning in greater temporal resolution, we performed directional tests on a sliding 50-ms window of activity, incremented in 10-ms steps, aligned to force onset in each trial (see METHODS). The instantaneous PDit of single neurons often remained relatively constant throughout the trial in the isometric task (Fig. 6A). For instance, the neuron in Fig. 6A became directional about 100 ms before force onset with a PDit near 195°, and retained that directional tuning with minor fluctuations for the rest of the trial (confidence interval of 6.7° for the range of windowed PDit from 100 ms before to 1,000 ms after force onset). In contrast, the time course of instantaneous PDmt was often very complex in the movement task (Fig. 6B). The neuron became directionally tuned shortly before force onset in the movement task, with a windowed PDmt near 195°. Shortly after force onset, the PDmt began to change progressively in each successive window, to a momentary PDmt of 5–20° near the peak of movement velocity at 300 ms after force onset (Fig. 6B), as the sliding window spanned the period corresponding to a pause in activity for movements to the left and a delayed burst for movements to the right. The PDmt then rapidly rotated back to about 195° near the end of movement, although for much of the return rotation, the windowed activity was not significantly unimodally tuned (Fig. 6B).
To summarize the behavior of the entire population, a cumulative distribution was generated of the difference between a neuron's PD in a given 50-ms window at different times in a trial and its PD during a single fixed 100-ms "baseline" window spanning the time period ±50 ms relative to force onset in that task (Fig. 6C). A neuron had to be significantly directionally tuned both in the baseline window and in the 50-ms window to be included in the cumulative distribution for that particular time step. Figure 6C shows the cumulative distributions of PD differences for three different times in both tasks. In the 50-ms window, beginning 60 ms after force onset (Fig. 6C, left), 65% (movement task) and 75% (isometric task) of the neurons had a window PD that differed from their baseline PD by <20°, and 90% changed their PD by 
60° in both tasks. This is not unexpected because that 50-ms window was adjacent to the baseline window. The cumulative distribution of windowed PD changes relative to baseline shifted systematically and gradually to larger values as time progressed in the trial in the isometric task (Fig. 6C), but 53% of the neurons were still within 20° of their baseline PD and 82% within 90° for the 50-ms window 620 ms after force onset (Fig. 6C, right). During the MT of the movement task, in contrast, neurons rapidly began to show a wide range of windowed PD differences from their baseline PD. Almost 45% of the cells had windowed PD changes of 
90° 250 ms after force onset (Fig. 6C, middle; the distribution of PD changes in the movement task was nearly uniform at that time, deviating only slightly from a diagonal line). Near the end of the MT epoch, the windowed PD of many neurons was once again similar to that during the baseline window at force onset, and the distributions of PD changes were again very similar between the two tasks (Fig. 6C, right). Differences between tasks were significant at all time steps between 140 and 560 ms after to force onset (D <0.01; Kuipers test; Batschelet 1981).
The preceding analysis assessed the stability of directional tuning of each neuron at different times in a trial within a given task. We next compared the directional tuning of neurons at the same relative point in time in the two tasks. Each neuron was subjected to two bootstrap tests (see METHODS). The first determined whether a neuron was significantly tuned within a task at each 50-ms time window. In the isometric task, the number of directionally tuned neurons increased rapidly during the RT epoch before force onset, and remained steady at between 74 and 81% of the neurons for the remainder of the trial (Fig. 7 A). The incidence of directional tuning showed a very similar time course in the movement task (Fig. 7A).
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PDt). For this analysis, a neuron had to be directionally tuned in the same time window in both tasks. From 400 to 200 ms before force onset, the few neurons that happened to be significantly directionally tuned in both tasks showed nearly random PDt (Fig. 7B, mean PDt near 90°). This early part of the graph reflected the random nature of windowed tonic activity before and shortly after the appearance of the targets. As the sliding window began to encroach on the onset of the task-related response of each neuron, more neurons became directionally tuned in both tasks (Fig. 7A), and the mean PDt decreased rapidly, so that during the period ±100 ms relative to force onset in each task, the directional tuning of the single neurons was very similar between tasks (Fig. 7B). The mean PDt then began to rise rapidly, peaking at 93° about 320 ms after force onset, and then declined again, returning to low values for the remainder of the trial. Unlike the results from 400 to 200 ms before force onset, these large differences in PD reflected the strong task-related responses of many task-related neurons (see Fig. 7, A and C). A corresponding analysis on muscle activity showed a similar pattern, shifted to slightly later times. A second bootstrapping procedure tested whether the change in directional tuning between tasks was significant for each single neuron at each time step (Fig. 7C). The incidence of significant PDt began to rise about 180 ms before force onset, peaked at 50–58% between 200 and 400 ms after force onset, and decreased to a fairly steady value around 35% beginning 700 ms after force onset (Fig. 7C). The time course and mean magnitude of PDt did not change substantially when only those neurons having a significant PDt between the two tasks at a given time step were used (Fig. 7B).
The MT epoch was about twice as long as the DFT epoch (Figs. 2 and 3), so the peak of the PDt distribution from 200 to 400 ms after force onset occurred in the middle of the MT but near the end of DFT as the monkeys were about to begin a period of static isometric force. However, the large PDt values were not an artifact of comparison of disparate functional phases in the two tasks. The trend began 100 ms after force onset, early in both the MT and DFT. The instantaneous PDit remained fairly stable at all times during DFT and THT of the isometric task (Fig. 6). Finally, equally large PDt values were obtained when we compared the data in the time window from 250 to 300 ms after force onset in the movement task to the data in the middle of the DFT period of the isometric task from 150 to 200 ms after force onset (data not shown).
Population activity
Population histograms were generated by aligning the activity of all neurons that were directionally tuned in a given trial epoch of a task to their PD in that epoch (Fig. 8).
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The population response for neurons that were directionally tuned in the RT epoch of the movement task showed a triphasic time course like that seen in single neurons (Fig. 8A, thick black line). An initial phasic burst at the PD began about 150 ms before force onset, peaked at force onset, and then began to decline rapidly. Activity reached a momentary minimum between 300 and 400 ms after force onset, followed by a second burst that peaked about 650 ms after force onset, and then a sustained tonic discharge for the rest of the trial. In the opposite direction, population activity showed an initial brief decrease before force onset, followed by a brisk burst of activity peaking 300–400 ms after force onset, and then a low tonic discharge for the rest of the trial. The major components of the population responses led the corresponding components of the force profiles (Fig. 8A, thin black line) by about 150 ms.
The population histograms for the neurons that were directionally tuned during the THT epoch (Fig. 8C) were similar to those using the RT tuning. The most notable differences were that the initial phasic response at the PD was slightly weaker in both tasks and late tonic activity a little stronger compared with RT-aligned data, and that the suppression in the opposite direction is not evident before force onset. These response differences reflect differences in directional tuning at different times in the task (Fig. 6C; Crammond and Kalaska 1996, 2000).
The population histograms of activity aligned to the PD from the MT of the movement task showed a marked reduction in the depth of the transient decrease in activity during movement in the PD and in the amplitude of the delayed burst in the opposite direction. These changes resulted from the tendency for the calculated PD during the MT epoch to be biased toward the direction of movements in which the delayed burst occurred.
The population activity in the two tasks reflected to a first approximation the time course of measured force outputs. One discrepancy was the large initial activity overshoot at the PD of the isometric task. A corresponding overshoot may exist in the movement task, but was obscured by its complex temporal profile. An overshoot was evident, however, after the transient response suppression at the PD. Furthermore, the static force output at the hand was about 0.5 N greater during THT in the isometric task than in the movement task (Fig. 8, thin lines). However, the population activity converged on similar discharge levels in both tasks (Fig. 8, thick lines).
The population response profiles showed a gradual evolution across different directions of motor output in each task (Fig. 9) like that seen for single muscles (Figs. 2 and 4). The response profiles seen ±45° relative to each neuron's PD were similar to that at the PD in both tasks. Responses in the orthogonal directions were clearly transitional, and response profiles that were essentially reciprocal to that at the PD were seen for outputs ±135 and 180° away from the PD.
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Population vector analysis
This prediction was tested by a vectorial reconstruction of activity within a time sequence of nonoverlapping 20-ms windows, which provides a rich description of the moment-to-moment directional bias of population activity in different tasks (Georgopoulos et al. 1988, 1992; Moran and Schwartz 1999b; Schwartz 1993, 1994; Wise et al. 1996).
Figure 10 shows the results from the entire sample of 132 neurons for 0 and 180° motor outputs. In the isometric task, the direction of the change in output forces relative to the force offset bias during CHT pointed in the target direction (Fig. 10A, open circles). The length of the force vectors began to increase at force onset, reached a peak of about 1.5 N within 400 ms after force onset, and remained at that length throughout THT. The 20-ms population vectors likewise varied systematically with force direction (Fig. 10A, filled circles). They began to grow in the direction of force output 160–140 ms before force onset and showed little variation in direction throughout the trial. The length of the population vectors grew rapidly before force onset and peaked near force onset, then decreased to a shorter length (cf. Fig. 8, cell histograms).
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The neural population vectors in the movement task displayed similar patterns (Fig. 10B, filled circles). There was an initial increase in vector length in a direction corresponding fairly closely to that of the target, beginning about 160–140 ms before force onset and peaking in length at about the time of force onset. The population vectors then began to decrease in length and reversed direction at about 200 ms after force onset. The vectors later reversed direction again, pointing toward the targets for the remainder of the trial.
Figure 10 was generated using the PD of neurons during the THT epoch. Repetition using the PDs from the RT epoch did not substantially alter the basic findings (not shown).
Figures 11 and 12 display the time course of the direction of the force and population vectors for the other output directions in a polar-plot format (cf. Fig. 10, bottom). In the isometric task, the force vectors pointed in the target directions from the time of force onset to the end of the trial (Fig. 11). The population vectors also maintained a fairly constant direction from the onset of force to the end of the trial. There was, however, a systematic bias in the direction of the population vectors toward the lateral (0–180°) directions, especially for the diagonal force output directions, that was sustained during the final static-force period of THT (Fig. 11).
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