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The Journal of Neuroscience, September 1, 2002, 22(17):7721-7729
A Real-Time State Predictor in Motor Control: Study of Saccadic Eye Movements during Unseen Reaching Movements
Gregory Ariff, Opher Donchin, Thrishantha Nanayakkara, and Reza Shadmehr Laboratory for Computational Motor Control, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Theoretical motor control predicts that because of delays in sensorimotor pathways, a neural system should exist in the brain that uses efferent copy of commands to the arm, sensory feedback, and an internal model of the dynamics of the arm to predict the future state of the hand (i.e., a forward model). We tested this theory under the hypothesis that saccadic eye movements, tracking an unseen reaching movement, would reflect the output of this state predictor. We found that in unperturbed reaching movements, saccade occurrence at any time t consistently provided an unbiased estimate of hand position at t + 196 msec. To investigate the behavior of this predictor during feedback error control, we applied 50 msec random-force perturbations to the moving hand. Saccades showed a sharp inhibition at 100 msec after perturbation. At ~170 msec, there was a sharp increase in saccade probabilities. These postperturbation saccades were an unbiased estimator of hand position at saccade time t + 150 msec. The ability of the brain to guide saccades to the future position of the hand failed when a force field unexpectedly changed the dynamics of the hand immediately after perturbation. The behavior of the eyes suggested that during reaching movements, the brain computes an estimate of future hand position based on an internal model that relies on real-time proprioceptive feedback. When an error occurs in reaching movements, the estimate of future hand position is recomputed. The saccade inhibition period that follows the hand perturbation may indicate the length of time it takes for this computation to take place.
Key words: forward models; reaching movements; eye movements; saccades; oculomanual control; feedback delay; sensory delay
INTRODUCTION
When a reaching movement starts, the neural commands to the arm are "feedforward" in the sense that they rely on an internal model that predicts forces necessary to initiate the movement (Shadmehr and Mussa-Ivaldi, 1994
; Thoroughman and Shadmehr, 1999
Theory suggests that the brain may cope with sensory feedback delays by relying on an internal, neural model that predicts the effects of motor commands on the arm (Miall et al., 1993
A crucial component of this theory is the idea that the brain can use feedback and efferent copy to compute the future state of the limb. To test this idea, experiments have been designed that ask subjects to program motor commands to one arm as a function of their estimate of the state of the other arm (Blakemore et al., 1998
MATERIALS AND METHODS
Subjects (n = 6) held the handle of a robotic arm (Shadmehr and Brashers-Krug, 1997
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Figure 1. Experimental setup. A, Subjects used a bite bar and were instructed to try to track their unseen hand during reaching movement. They were prevented from viewing their hands and arms, because both arms were covered under a heavy cloth (data not shown). The right hand held the handle of a robotic arm and moved it in the horizontal plane. The handle housed a high-intensity LED at its center and a force transducer at its base. The hand was below an opaque screen. An LCD projector, held from the ceiling, painted this screen. B, The task began with the robot bringing the hand to a random starting position, where a start target (green square) was displayed. The subject fixated the handle LED. The LED was turned off, and a movement target was displayed (yellow square). The subject saccaded to the target. The movement target was turned off, the handle LED was turned on, and the movement target was redisplayed. The subject fixated the LED. A stationary random-dot pattern was displayed and the start target was removed, signaling the subject to start the reaching movement. As soon as movement was detected, the handle LED was turned off. At the completion of the reach, the handle LED was turned on, the random-dot pattern was removed, and the target square was repainted, providing feedback to the subject. C, Two example trials. The component of eye and hand position parallel to the direction of target is plotted with green and black lines, respectively. Saccade origin is marked with a red dot, and saccade end point is marked with a blue dot. disp., Displacement.
A trial began with the handle LED on. A start target was displayed in a randomly selected start position, and the robot moved the handle (and the subject's hand) to it. After the subject fixated the start location, the handle LED and start target were extinguished, and a final target appeared at a randomly selected direction. The subject was required to fixate the final target for 0.5 sec (while maintaining the handle in the start position), after which the target was extinguished and the start target and the handle LED reappeared. The subject returned fixation to the start target, after which a stationary random-dot pattern filled the entire screen (~35 dots/in2). Each dot was 0.25 mm2 in size, and its position was randomly selected for each trial. After subjects fixated the start target for 0.5 sec, the target was extinguished so that only the random-dot pattern and the LED were visible. This signaled to the subject to begin movement to the remembered location of the target. As soon as movement initiation was detected (encoder resolution of handle position was better than 0.05 mm, and movement initiation was detected using a fixed 0.02 m/sec threshold), the handle LED was extinguished. Therefore, during the movement, the handle LED was off and the target was not displayed. The only visible information was the pattern of random dots. After completion of movement, the random dots disappeared, the handle LED was turned on, and the target reappeared. The target color provided feedback regarding the timing of the movement, and the position of the LED with respect to the target provided feedback regarding the accuracy of the movement. If the hand reached the target in 0.9 ± 0.05 sec, the target exploded and made a pleasing sound. It turned red if the hand arrived at the target too soon and blue if it arrived too late.
After ~150 unperturbed trials, on pseudorandomly selected trials (probability of 58%), a 50 msec, 25 N force pulse pushed the hand in one of two directions perpendicular to the target direction at either 200, 250, 300, or 350 msec after movement initiation. Force-pulse latency was determined pseudorandomly. As before, no auditory or visual cues were available in these trials.
We recorded eye position at 100 Hz using an infrared camera and light source (iView system; SMI Corp., Berlin, Germany) mounted on a helmet that was itself tracked using a Polhemus tracker (Polhemus Corp., Colchester, VT). To stabilize the recordings, subjects used a bite bar anchored to the floor. We performed a two-part calibration procedure. Each block of ~40 trials began with saccades to 24 points painted on the plane immediately above the hand. For each trial within the block, we checked on the calibration of the eye system with the hand position (as reported by the robot) by using the fixation period when the LED at the handle was on and the fixation period when the target was painted. Trials were aborted if eyes were not within 7.5 mm of the presented target. False starts also resulted in the rejection of that trial.
Subjects received training before experiments to familiarize them with the setup. In the pre-experiment session, robot motors were always off, and subjects were asked to try to look at the perceived position of their hand during unseen reaching movements. A typical subject's performance began with a single saccade to the remembered location of the target as the reach took place. With additional practice, they produced multiple saccades during the reach. Subjects never received feedback regarding the accuracy of their saccades during the reach. We began the experiments once the subjects were able to consistently make at least two saccades per reaching movement. Once the experimental session began, however, we did not exclude any trials other than those with false starts or poor calibration.
RESULTS
We instructed the participants to look at their hand to the best of their ability without vision of their hand or the target as they reached to the remembered location of a target (Fig. 1).
We begin by presenting the results of the unperturbed trials. The reach took place in 0.78 ± 0.18 sec and was accompanied by a sequence of 3.50 ± 1.1 saccades (mean ± SD). The trajectory of the hand was usually straight, but it varied in speed from movement to movement. An example of two trials that differed in speed is shown in Figure 1C. The timing and placement of saccades appear to correspond to the trajectory of the hand in each trial. However, the timing and placement properties of saccades varied greatly across the movements, resulting in a broad distribution in the probability of saccades during the reach (Fig. 2A) and a wide scattering of saccade origins and end points (Fig. 2B).
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Figure 2. Saccades during reaching movements in unperturbed trials. A, Probability (prob.) of saccade occurrence calculated in 10 msec time bins as a function of hand movement time. Each bin indicates the probability that in a single trial, a saccade would occur at that time bin. Reaches were to various target directions. B, Mean trajectory of the reach (± 1 SD; yellow line) is shown by the black line and is represented along directions parallel or perpendicular to the target direction. Saccades are represented by vectors of eye position change: this vector has an origin (red dots) and an end point (blue dots). C, Average timing, origins, and end points of the first three saccades (red and blue lines; ± 1 SD). The SD on timing of saccade end points is identical to the SD of saccade origin and is not shown for clarity. The green line is the average eye position across all trials and corresponds to the continuous representation of the discrete saccade data. Black lines show average hand position. A saccade end point is occasionally not equal to the origin of the subsequent saccade because of small amounts of smooth pursuit. Dir., Direction.
Because there were, on average, approximately three saccades during the reach, we began our analysis by considering the position of these saccades with respect to the hand. On average, saccades were initiated shortly after the hand passed the point of eye fixation and were made to a point that led the hand position (Fig. 2C). The end point of the first saccade was, on average, ahead of the hand toward the target (Fig. 2C). This eye position was maintained (although there were sometimes very small amounts of smooth pursuit, usually <4 mm) until the hand passed the point of fixation by ~7 mm, at which point a second saccade was generated. Note that the hand is not visible during the movement. After hand position progressed beyond the current eye position, a third saccade was generated. The data in Figure 2C describe the temporal and spatial distribution of all first, second, and third saccades, regardless of the number of saccades that there might have been in a given reaching movement. However, there were many trials with only two saccades and other trials with four saccades (the probability that a trial would have a given number of saccades is shown in Fig. 3A). It is not clear whether the second saccade in a two-saccade trial should be combined with the second saccade in a four-saccade trial. This variability in the number of saccades per trial results in the counterintuitive observation that in Figure 2C, the average origin of the third saccade is actually slightly less than the average end point of the second saccade. Indeed, the broad distribution of saccade timings (170-220 msec in Fig. 2C) suggests that they were not generated in a rigid temporal pattern. To investigate this further, we examined saccade generation probability as a function of time for trials with two, three, and four saccades separately. In each type of trial, we found a broadly distributed probability function peaking at ~280 msec, with little evidence of periodicity (Fig. 3B), reinforcing the idea that saccade timing is highly variable and saccades are not generated with rigid temporal structure.
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Figure 3. Saccades during reaching movements in unperturbed trials. A, Percentage of reaching movements that accompanied a given number of saccades. B, Probability (prob.) of saccade occurrence calculated in 10 msec time bins for reaching movements that had two, three, or four saccades.
Because our objective here is to compare the behavior of the eyes with that of the hand, we thought that rather than averaging all first, second, etc., saccades, a better approach might be to divide reaching movements into small temporal bins and analyze the behavior of saccades that began in each bin. For instance, we analyzed the end point, with respect to the hand, of saccades generated at different times into the movement.
We considered all saccades that took place in a given 10 msec time bin. For each of these saccades, we compared the eye position e(t) with the hand position h(t) in the corresponding reaching movement. We represented these positions as displacements toward the target (i.e., scalar quantities). The result is an error measure e(t)
h(t) for each saccade. In principle, the measure could be positive or negative depending on values of e(t) and h(t) in a given trial. We averaged this error across all saccades in each 10 msec time bin. When all time bins were considered, the result was a measure of error between saccade end points and hand positions as a function of time into the movement. We extended this analysis by considering the possibility that the saccade was related not to the current position of the hand (current meaning the time bin in which the saccade occurred) but perhaps to where the hand was in the past or would be in the future. This measure is described by the formula e(t)
). We considered
For a given 10 msec time bin, we found the value of
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Figure 4. Saccades during reaching movements in unperturbed trials. A, Eye position at saccade end point and hand position are represented as scalar quantities e(t) and h(t), indicating position along the direction of the target. The figure illustrates the distribution of the time delays, 196 msec. B, The SD of the error measure e(t)
Although there were saccades that took place after 600 msec, there were no values of
Figure 4A displays the time
Another way to estimate
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Figure 5. Saccades during reaching movements in unperturbed trials. Eye position at saccade end point and hand position are represented as scalar quantities e(t) and h(t), indicating position along the direction of the target. The figure illustrates R2 between eye position at saccade end point e(t) and hand position at time of saccade t +
The method of comparison of eye and hand data used to generate Figure 4 weighs equally the
For each saccade that took place during the interval
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Figure 6. Saccades during reaching movements in unperturbed trials. Eye position at saccade end point and hand position were represented as two-dimensional quantities indicating position in a Cartesian coordinate system with respect to origin of the reaching movement. The figure illustrates the position of the end point of a saccade and hand position in the corresponding reaching movement at saccade time + 196 msec for all saccades in all trials. Time of saccade refers to the time at which the saccade ended. There is a cluster of points at zero because a number of reaching movements were vertical or horizontal and had no x- or y-components. h, Hand position; e, eye position; m, slope of the line; b, crossing point.
The above data were all collected in conditions in which the hand freely performed a reaching movement. We subsequently quantified the behavior of the eye when the hand was suddenly perturbed. As before, subjects made reaching movements to targets, but now on randomly selected trials (probability of 58%), a 50 msec 25 N force pulse pushed the hand in one of two directions perpendicular to the intended movement direction at one of four possible times into the movement. Two perturbed trials are shown in Figure 7. In both cases, the first saccade leads the hand and has an end point that is along the direction of the target. However, the perturbation significantly alters the expected trajectory of the hand. Remarkably, the second saccade is not to a point where the hand was when it was perturbed, but rather to a point that the hand will visit in the future. The eyes fixate that location until the hand passes it; then a third saccade is generated to a location that again leads the hand.
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Figure 7. Two representative trials during which the hand was perturbed with a force pulse. The gray and black lines represent the trajectories of eye and hand, respectively. Gray dots locate the end point of each saccade. Black dots indicate hand position at the time of origination of that saccade. For example, e1 is the end point of the first saccade and h1 is the position of the hand at the start time of that saccade. pos., Position; sac, saccade.
The combination of movement directions and force pulses produced a wide range of hand displacements (the mean of the maximum hand displacement across movements was 40.2 mm). The probabilities of saccades during perturbed and unperturbed trials are shown in Figure 8A. We found that a force pulse at 200 msec was followed by a sharp dip in saccade probability, reaching a minimum at 320 msec. When the hand was not perturbed, there was a peak in probabilities at ~230 msec (Fig. 2A). The time between the pulse onset and the dip was similar regardless of pulse timing. Pulses at 200, 250, 300, and 350 msec produced a probability minimum at latencies of 120, 90, 90, and 120 msec. A peak in saccade probability immediately followed the minimum. The pulses produced a peak in saccade probabilities at latencies of 180, 170, 160, and 180 msec after pulse onset. Therefore, it appeared that the perturbation to the hand caused a significant inhibition of saccades at 100 msec, followed by an increased probability of saccades at ~170 msec after perturbation onset.
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Figure 8. Trials in which movements were perturbed with a force pulse. A, Saccade probability as a function of movement time. The first gray bar indicates the period (50 msec) during which the reach was perturbed with a force pulse. In all subplots, the second bar is positioned at perturbation (pert.) onset + 150 msec and is 50 msec wide. This period consistently coincides with a peak in postperturbation saccade probabilities. B, Eye positions at the saccade end point for saccades that occurred 150-200 msec after onset of the pulse were represented as two-dimensional variables and were multiplied by a matrix [a , of the saccade vector was needed to estimate hand position at all delays except at
We compared these postperturbation saccades (saccades that occurred at 150-200 msec after the pulse onset) with hand positions in the same movement. Unlike our analysis in Figures 4 and 5, in which eye and hand positions were viewed as one-dimensional quantities (displacement toward the target), because of the perturbation, here the eye and hand positions were represented as two-dimensional quantities (position parallel and perpendicular to the direction of target). For all saccades during the interval 150-200 msec after perturbation, we compared e(t) with the corresponding h(t +
] and rotation [arctan(b/a)] of the eye position vector (Fig. 8B). However, at However, considerable movement-to-movement variations existed for error that was caused by the pulse in the trajectory of the hand. Depending on the direction of motion of the hand and its speed, force pulses, which were perpendicular to the direction of motion, produced a large range of perpendicular displacements (
It seems reasonable that the brain programmed these postpulse saccades on the basis of feedback that it had received from the perturbed arm and an internal model that predicted where the hand would be in the future. If, indeed, the prediction was based on an internal model, then changing the dynamics of the arm unexpectedly after the perturbation should make the saccades inaccurate. For example, a resistive (or assistive) field introduced after the 50 msec pulse should cause a saccade that takes place 150-200 msec after pulse onset to overestimate (or underestimate) future hand position.
We performed two separate experiments in which we introduced a viscous force field that either assisted or resisted the subject's hand. As before, the pulse was present in only some of the trials (50%), and the field was engaged after the pulse in only a fraction of these pulsed trials (25%). We observed a postpulse minimum in saccade probability at 120 msec, followed by a peak at 150-200 msec (Fig. 9A). For each postpulse saccade, we compared its end point with hand position at 150 msec after the saccade. In trials in which a field was present after the pulse, these saccades were inaccurate. A resistive field caused saccade overestimation of the effect of the pulse (Fig. 9B). An assistive field caused underestimation of the effect of the pulse.
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Figure 9. In these trials, a viscous force field that either assisted or resisted the movement of the hand was introduced immediately after the offset of the force pulse to the hand. A, Saccade probabilities. The first gray bar indicates pulse period (50 msec). The second gray bar indicates a perturbation (pert.) period 150-200 msec after pulse onset. B, The end points of saccades that occurred 150-200 msec after the pulse are plotted versus hand position in the same movement at saccade time + 150 msec. Saccades overestimated hand position in resistive trials and underestimated hand position in assistive trials. perp. dir, Perpendicular direction.
DISCUSSION
Cortical motor commands that are generated in response to a perturbation reach the arm muscles 100-150 msec after perturbation onset (Petersen et al., 1998
Our rationale for this conjecture was the wealth of data suggesting that smooth-pursuit eye movements are influenced by commands to the arm. For one-dimensional arm movements, it has been demonstrated that when the eyes track a visual target attached to the hand, the smooth-pursuit eye movements that result are more closely linked to the motion of the target (Steinbach, 1969
Given these data, we reasoned that subjects might be able to express an estimate of the state of their arm through programming of their eye movements. However, in smooth pursuit, visual information regarding the state of the limb is always present. We eliminated this information so that the behavior of the state estimator could be observed when the only feedback was through proprioception. Preventing viewing of the moving hand prevents generation of smooth pursuit and results in saccadic eye movements. If the target of the movement is visible, the eyes saccade to the target and maintain fixation until the end of the reaching movement (Neggers and Bekkering, 2001
Some characteristics of reaching movements were stereotypical: the trajectory of the hand was straight, with a bell-shaped speed profile (Morasso, 1981
Although the estimator was unbiased for this particular
For the eyes to be able to estimate future hand position in real time as a reaching movement takes place, one theory suggests that the brain may use an internal model that relies on sensory feedback and efferent copy (Scarchilli and Vercher, 1999
In randomly selected trials and at random times during the selected trials, we applied a 50 msec force pulse to the hand. The direction of the pulse was always perpendicular to the direction of the target, but it could be either clockwise or counterclockwise (randomly selected). Because of the anisotropy of the inertia and stiffness of the arm, the pulses produced a very large range of hand displacements. The range of perpendicular displacements was ~140% of the distance traveled in the unperturbed movement, and the distribution within this range was fairly uniform (Fig. 8C). Therefore, the perturbations produced a large variance in the trajectory of the hand.
In response to the perturbation, we observed saccadic inhibition at a latency of ~100 msec. Choi and Guitton (2002)
At ~150-200 msec after perturbation onset, the probability of saccades increased from its low by approximately eightfold (Fig. 8A). The error caused the ongoing or planned saccades to be inhibited and a new saccade to be computed. The computation did not result in a saccade to the position where the hand was when it was perturbed. Rather, the resulting saccade was to where the hand would go in the near future. The analysis of the relationship between the postperturbation saccades and hand positions in the same movement found a remarkable correlation between saccade end point and hand position at saccade time + 150 msec. Thus, the postperturbation depression is interpreted as the point at which the proprioceptive information regarding the perturbation is integrated into the state estimator. The time between the perturbation onset and saccade generation ~170 msec later is a period during which we speculate that the behavior of the eyes is most influenced by a forward model of the arm. Because the saccades that responded to the perturbation predicted hand state 150 msec after the saccade, the brain appears to compute the future state of the hand for a time interval that is nearly equal to the delays in sensorimotor pathways.
In summary, we found that saccades were unbiased, real-time estimators of the future position of the hand. Immediately after a brief perturbation, the brain appears to be able to predict where the limb will be in the near future. It seems plausible that the long-latency motor commands that are computed in response to an error take into account such an estimator. As subjects learn to control their arms in novel dynamics, these estimators are thought to adapt (Shadmehr and Brashers-Krug, 1997
FOOTNOTES Received March 28, 2002; revised June 10, 2002; accepted June 12, 2002.
G.A. was supported by a Bozelle Fellowship. This work was also supported by a postdoctoral fellowship from the National Institutes of Health (NIH) to O.D., a Distinguished Postdoctoral Fellowship from the Johns Hopkins University Department of Biomedical Engineering to O.D., and grants from the NIH (NS37422) and the Office of Naval Research (N000140110534) to R.S. This work is part of a Masters Thesis submitted by G.A. to the Johns Hopkins University Department of Biomedical Engineering.
Correspondence should be addressed to Reza Shadmehr, Johns Hopkins School of Medicine, 419 Traylor Building, 720 Rutland Avenue, Baltimore, MD 21205. E-mail: reza{at}bme.jhu.edu.
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L. Ren, A. Z. Khan, G. Blohm, D.Y.P. Henriques, L. E. Sergio, and J. D. Crawford
Proprioceptive Guidance of Saccades in Eye-Hand Coordination
J Neurophysiol, September 1, 2006; 96(3): 1464 - 1477.
[Abstract] [Full Text] [PDF]
M. Synofzik, P. Thier, and A. Lindner
Internalizing Agency of Self-Action: Perception of One's Own Hand Movements Depends on an Adaptable Prediction About the Sensory Action Outcome
J Neurophysiol, September 1, 2006; 96(3): 1592 - 1601.
[Abstract] [Full Text] [PDF]
H. Gomi, N. Abekawa, and S. Nishida
Spatiotemporal tuning of rapid interactions between visual-motion analysis and reaching movement.
J. Neurosci., May 17, 2006; 26(20): 5301 - 5308.
[Abstract] [Full Text] [PDF]
S. Vaziri, J. Diedrichsen, and R. Shadmehr
Why does the brain predict sensory consequences of oculomotor commands? Optimal integration of the predicted and the actual sensory feedback.
J. Neurosci., April 19, 2006; 26(16): 4188 - 4197.
[Abstract] [Full Text] [PDF]
