Exp Brain Res (2000) 131:111–120 Digital Object Identifier (DOI) 10.1007/s002219900294

R E S E A R C H A RT I C L E

N. Smyrnis · P. Gourtzelidis · I. Evdokimidis

A systematic directional error in 2-D arm movements increases with increasing delay between visual target presentation and movement execution Received: 5 August 1999 / Accepted: 3 November 1999 / Published online: 14 January 2000 © Springer-Verlag 2000

Abstract Forty-seven normal subjects performed twodimensional arm movements on a digitizer board using a mouse device. The movements were projected on a computer monitor. Subjects were instructed to move the mouse using the whole arm from a center position to a peripheral target so that the projected movement would pass over the target without stopping on the target. A large number of targets (360) were used to cover the entire directional continuum. The direction of the arm movement was the parameter of interest, which was measured at an initial position, at one third of the distance towards the target, and at the vicinity of the target. Four conditions of delay between target presentation and movement execution were used (0, 2, 4, 6 s). A systematic directional error was observed at the initial portion of the trajectory. This error resulted from a clustering of movement directions on an axis that was perpendicular to the axis of the resting forearm before movement onset. This pattern of errors can be explained by the initial inertial anisotropy of the arm. As the trajectory evolved, a different directional error emerged, resulting from a clustering of movement directions in two orthogonal axes. This pattern of directional error increased in amplitude as the delay increased, in contrast to the error at the initial portion of the trajectory which remained invariant with increasing delay. Finally, the information transmitted by the movement direction was shown to increase with the evolution of the trajectory. The increase in delay resulted in a decrease in directional-information transmission. It is proposed that the directional bias towards the end of the movement trajectory might reflect the action of “movement primitives”, that is patterns of muscle activation resulting from spinal interneuronal activation. It is further proposed that the directional bias observed at the vicinity of the target might reflect a loss of cortical N. Smyrnis (✉) · P. Gourtzelidis · I. Evdokimidis Cognition and Action Group, Neurology Department, National University of Athens, Eginition Hospital, 72 Vas. Sofias Ave., Athens 11528, Greece e-mail: [email protected] Tel.: +30-1-7289115, Fax: +30-1-7216474

directional information with increasing delay between target presentation and movement onset. Key words Direction of movement · Motor control · Frame of reference · Visuomotor transformation · Information transmission

Introduction The trajectory of an arm movement in space can be described by its direction relative to an initial point of reference and its amplitude. Direction and amplitude appear to be specified by different channels of the motor system ( et al. 1990; Soechting and Flanders 1989a; Gordon et al. 1994a). The direction of an upcoming movement in space is coded by neurons in the motor cortex (Georgopoulos et al. 1982, 1986), the premotor cortex (Caminiti et al. 1991), the parietal cortex (Kalaska et al. 1983), and the cerebellum (Fortier et al. 1989). Regarding the frame of reference used by the CNS to program movement execution (Soechting and Flanders 1992), three alternative hypotheses have emerged: (1) that of a body-centered frame of reference (Soechting and Flanders 1989b), (2) that of a frame of reference fixed to the moving arm (Gordon et al. 1994a, 1994b; Desmurget et al. 1997), and (3) that of a viewer-centered reference frame (McIntyre et al. 1997). When directional errors were analyzed in a wide directional continuum, a small, but systematic directional bias was observed for arm movements (Ghez et al. 1994) as well as for isometric force pulses (Massey et al. 1991). We were able to reproduce this pattern of directional bias by using a large number (360) of directions in a two-dimensional (2-D) arm-movement task in which visual-feedback corrections were not allowed. We hypothesize that this systematic error reflected a distortion of the motor representation of direction in cortical areas involved in motor planning. In order to gain more insight into this directional distortion of 2-D space, we introduced a delay between the target presentation (visual

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stimulus) and the movement (motor output). This method has already been used to study the error distributions of 3-D reaching movements (McIntyre et al. 1998), although that study did not demonstrate the directional bias, not having used a wide directional continuum. The use of different delay periods in the current study also gave us the opportunity to study the capacity of the motor system (measured as the information transmission by the direction of the movement) under conditions of increasing demand on information retention. It has been established that information about movement direction remains active for small delays of a few seconds in many areas involved in higher motor control (prefrontal cortex: Funahashi et al. 1989; parietal cortex: Gnadt and Andersen 1988; motor cortex: Smyrnis et al. 1992). The output accuracy of the motor system when the input information reached 6.64 bits was, at best, limited to approximately 4.5 bits of transmitted information for 2-D movements (Georgopoulos and Massey 1988). Thus, an input of 100 movement directions resulted in a perfect output of 22 movement directions. In a study of isometric force pulses (Massey et al. 1991), a maximum directional information input of 5.91 bits (60 movement directions) resulted in 3.8 bits of information transmitted (12 movement directions). We therefore used the study of information transmission (Shannon 1948; Sakitt et al. 1983; Georgopoulos and Massey 1988) to investigate the hypothesis that increases in retention time would result in a reduction in motor output accuracy. This reduction could be the result of a decay of the information conveyed by neuronal activity due to noise interference during the delay.

Materials and methods For the purposes of this study, we recruited 47 healthy volunteers (39 male and 8 female) from the personnel of our hospital. The mean age of the subjects was 25.88 years, and the standard deviation (SD) was 2.85 years. All subjects gave informed consent after we explained the experimental procedure and the purpose of this study. Experimental design The subjects were seated comfortably in front of a computer monitor placed on a table at a distance of 60 cm from the subject. On the same table was a digitizer board with a remotely controlled mouse. The subjects used their preferred hand to grasp the mouse and make horizontal movements on the digitizer board. In order to reduce the friction of the mouse with the surface of the digitizer board, we used a coating material attached to the bottom of the mouse. The original position of the arm was adjusted a few centimeters to the right of the body midline for all subjects. This was the most relaxed position for the arm while resting on a horizontal surface above waist level (the height of the table was 76 cm). The subjects viewed a cursor (white cross, 3.5×3.5 mm) on the computer monitor that indicated the position of the mouse tip on the digitizer. Using this cursor as visual feedback, the subjects performed drawing movements on the digitizer surface (working window of 160×122 mm), which corresponded to cursor movements on the computer monitor (working window of 245×173 mm). The ratio of arm movement to the cursor movement was 0.7.

Each trial started when a small white circle (6 mm diameter) appeared at the center of the screen. The subjects had to move their cursor inside this circle (the origin of the movement). After a variable period of 0–2 s, a second 6-mm diameter target circle appeared at the circumference of an imaginary circle of 6 cm radius from the origin and remained on for 0.3 s. After that period, the origin was either turned off immediately or remained on for 2 s, 4 s, or 6 s (= delay time). The extinction of the origin was the signal for the subjects to move their cursor as soon as possible and cross over the position of the target without stopping at that position. If the movement did not exceed the 6-cm radius, it was considered an error and a feedback tone was given to the subject. Most of the movement trajectories were in the order of 6–7 cm in amplitude. The experimenter continuously observed the subject and corrected him/her when movements of the wrist or finger movements were used. It was observed that subjects very rarely used wrist or finger movements to perform these movements. Thus, all subjects made fast elbow and/or shoulder movements on the digitizer board plane. Four delay periods were used, and they were randomly selected for each trial. The position of the target for each trial was also randomly selected from a set of 360 positions spaced at 1° intervals on the imaginary circle of 6 cm radius. Each subject performed 200 trials, but we started recording after the first 5–10 trials, which were used to familiarize the subject with the manipulandum and the task requirements. Three subjects did not complete the full set of trials.

Data collection and analysis The X-Y position of the mouse on the digitizer was measured at a sampling rate of 100 Hz for the duration of each trial and was stored at the computer disk for off-line analysis. The total number of trials that were recorded was 8961. We derived the velocity at each position by differentiation of the record of positional X-Y data. We also calculated the second derivative of the positional-data record, which was a measure of the acceleration at each position. The time from the extinction of the origin circle until the first change on the velocity record was the response latency for the particular trial. The X-Y position that was closest to the target marked the end of the movement, and the difference in time from that point to the end of the response latency was the movement time for the particular trial. The angular error was a measure of the angle, in degrees, that was formed by two lines, one connecting a particular point of the trajectory and the center of the origin circle and the other connecting the center of the target circle with the center of the origin circle. Three values of angular error across the trajectory were measured: (1) the angular error at an initial position of the movement trajectory, which was defined as the third point of the trajectory after the initiation of the movement; (2) the angular error at one third of the distance to the target, which was the closest point of the trajectory at this distance from the target; and (3) the angular error at the final position, which was defined as the point on the trajectory at the end of the movement time. By definition, the clockwise angular error was positive while the counterclockwise angular error was negative. Finally, the maximum value of acceleration was measured for the first part of the movement until the point at one-third distance from the target was reached. We excluded from further analysis all trials where the angular error at the final position was larger than ±45° (11.74% of trials). We used a two-way ANOVA to analyze the pooled data from all subjects for the three values of directional error, response latency, movement time, and maximum acceleration for the initial part of the trajectory. The stimulus direction was grouped in a dichotomous variable of zero and one (see results and Fig. 3). The three different error measures were transformed to absolute values, and all the dependent variables were log transformed to make the variances homogeneous (a requirement for using the ANOVA analysis). We used the ANOVA/MANOVA module of the STATISTICA software package (STATSOFT, 1995) for these analyses and for basic statistical analyses.

113 Information-transmission analysis The information transmitted was calculated for each one of three different positions on the trajectory. These positions where the same that we used to measure the angular error, meaning the final position, the initial position, and the 1/3 position. All subjects’ data were pooled together for each one of the three analyses. The data were separated according to the delay time. We divided the space of target directions into 120 discrete categories with a binwidth of 3° for each category (stimulus categories). In the same fashion, the directions of the position of the moving arm (initial, 1/3, final) were also divided in 120 categories (response categories). We then constructed a stimulus-response performance matrix for each one of the three positions of the moving arm, for every delay time, resulting in twelve 120×120 square matrices. Thus, if the stimulus direction was at the first category and the response direction was also at the first category, then the number 1 was added to the cell with 1×1 coordinates on the matrix. If the response category 2 corresponded to the stimulus category 1 (meaning an directional error of more than 3° and less than 6° for the particular response), then the number 1 was added to the cell with 1×2 coordinates. The correct responses (where the stimulus category was the same as the response category) laid in the diagonal of the square matrix. Using the stimulus-response performance matrix, we then computed the information transmitted for each delay as follows: H(S) = log 2 N − 1 / N × ∑ (nk × log 2 nk )

(1)

H(R) = log 2 N − 1 / N × ∑ (nl × log 2 nl )

(2)

H(S, R) = log 2 N − 1 / N × ∑ (nk , l × log 2 nk , l )

(3)

T=H(S)+H(R)–H(S,R)

(4)

k

l

k, l

The information in the stimulus totals of the matrix is given by H(S), the information in the response totals is given by H(R), while the joint information in the matrix is given by H(S,R). T is the information transmitted. The term nk is the number of times the stimulus k is given and nl is the number of times the response l is given while nk,l is the number of times the response l is given to the stimulus k. In our case, k and l took values from 1 to 120. The total number of trials is N (see Sakitt et al. 1983 and Georgopoulos and Massey 1988 for more details on this method).

Results The X-Y position data from 7909 movements that were selected from 47 subjects are plotted in Fig. 1. Each plot depicts the X-Y position data for all movements for a particular delay condition (Fig. 1A for 0 s delay, Fig. 1B for 2 s delay, etc.). The trajectories of the movements were not uniformly distributed around the imaginary circle of 6-cm radius where the targets appeared. A directional bias towards the 45, 225 axis and the orthogonal to it 135, 315 axis is evident. The trajectories were clustered at these axes and the clustering became more evident as the delay increased from 0 s (Fig. 1A) to 6 s (Fig. 1D).

Analysis of the directional error The mean of the mean directional error for all target directions was 3.47° (SD=37.69°) at the initial position,

–0.71° (SD=13.15°) at one-third distance to the target position, and –0.35° (SD=10.47°) at the final position. The first three columns of Fig. 2 show the variation of the three measures of mean directional error with target direction for the four delays. A clear decrease of the mean directional error was observed when the error was measured at the final position compared with the error at the initial position (compare columns A and C). Thus, the evolution of the trajectory resulted in a reduction of mean directional error. The mean directional error at the initial position was larger for the directions close to the axis of maximum initial inertia of the arm. This axis was defined as the extension over the entire working surface of the longitudinal axis of the forearm when the arm was resting at the initial position (Hogan 1985; see gray strip at the upper left plot of Fig. 2). The sign of the mean directional error showed the initial bias of the movement towards an axis perpendicular to the axis of maximum initial inertia of the arm (axis of minimum initial inertia of the arm). For example, the error was positive at the 135–180° directional segment, thus showing that the movements were biased clockwise towards the 45–90° directional segment. Similarly, movements at the 315–0° directional segment were biased clockwise towards the 225–270° directional segment. The distribution of the mean directional error at the final position is shown in Fig. 2C. A clear difference in the pattern of this directional error from the pattern of the directional error at the initial position is evident for all delays (compare columns A and C in Fig. 2). At zero delay, there was a small increase of the mean directional error between the directions of 0 and 45°, between the directions of 45 and 90°, etc. This small variation of mean error, which has the shape of a shamrock, became more pronounced with the increase of the delay (see column C of Fig. 2). The mean directional error at one-third distance to the target was a combination of the two different types described for the initial and final error. The analysis of variance confirmed these observations. The target direction for each movement was grouped in a dichotomous variable of 0 or 1. Two such groupings were used as depicted in Fig. 3. The first grouping (Fig. 3A) has eight directional segments, where the categorical variable is equal to 0, and these segments represent the areas of low absolute directional error. These segments alternate with another eight segments, where the categorical variable is equal to 1, and they represent areas of high absolute directional error. This grouping of target directions captures the variation of directional error at the final position (see Fig. 2C). The second grouping depicted in Fig. 3B has two segments where the categorical variable of direction equals 0 (low absolute directional error), alternating with two segments where the categorical variable of direction equals 1 (high absolute directional error). This grouping of target directions captures the variation of directional error at the initial position (see Fig. 2A). The category of target direction (0 or 1) using the one of the two groupings of direction described

114 Fig. 1A–D Movement trajectories. This figure presents the trajectories for all movements for all subjects for each delay time (A 0-s delay, B 2-s delay, C 4-s delay, and D 6-s delay). Each point represents one X-Y-position sampling of the tip of the mouse device on the digitizer tablet (see Methods for description of the apparatus). Targets lay on the circumference of the large circle of each plot, while the center target is marked by a small circle at the origin of the trajectories. The movement trajectories clustered along the 45, 135, 225, and 315° directions of movement (by convention, 0° is the direction horizontal to the right and increases counterclockwise). This bias of movement directions was evident early in the trajectory evolution, became more evident as the delay increased, and was clear as the target was reached (compare A and D)

Fig. 2A–C Directional error distributions. Each polar plot shows the mean directional error measured at the initial position of the movement trajectory (A), at one-third of the distance to the target (B), and at the final position on the trajectory closest to the target (C), for all target directions. Each row depicts the data for each of the four delays. The mean directional error was positive for clockwise and negative for counterclockwise directions. The spread of the directional error for each value of mean error is shown in the cloud of points surrounding the line of mean error. A clear change of the pattern of directional error can be observed with the evolution of the trajectory (compare A and C). The directional error at the initial position was larger on the axis of maximum limb inertia, which is depicted with the gray stripe on the first plot at the upper right corner of the figure. The directional error at the initial position was not affected by the increasing delay (compare the first and last row of A). On the other hand, the pattern of directional error at the final position of the trajectory cannot be predicted by arm inertial force and was modulated with delay (compare rows 1 and 4 of C). The error at one-third of the distance to the target appears to be a transition between the two above-mentioned patterns (B). A modulation of error with delay was observed, but it was less obvious than the modulation observed for the final position

▲

above was the first independent variable and the delay time (0, 2, 4, and 6 s) was the second independent variable. The ANOVA results for the initial position error using the first grouping of target direction showed: (1) a non-significant main effect for direction category, (2) a non-significant main effect for delay, and (3) a nonsignificant interaction effect of direction versus delay. The ANOVA results using the second grouping of target direction showed: (1) a significant main effect for direction category (F1=12.99, P<0.001), (2) a non-significant main effect for delay, and (3) a non-significant interaction effect of direction versus delay. The ANOVA results for the final error using the first grouping of target direction showed: (1) a significant main effect for direction category (F1=95.12, P<0.001), (2) a significant main effect for delay (F2=41.03, P<0.001), and (3) a significant interaction effect of direction versus delay (F1,2=4.88, P=0.002). This interaction was due to the fact that the directional error increased with delay only in the directional segments of high directional error (grouped as 1). This can be seen in Fig. 2C, where the increase of the mean directional error with delay only affected the high direc-

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Fig. 4 Effect of delay on response latency. This histogram depicts the reduction of response latency with increasing delay. An interesting observation is that the decrease in response latency was observed for every increase in delay, suggesting that the effect of delay on response latency was continuous

main effect for direction category (F1=41.63, P<0.001), (2) a significant main effect for delay (F2=13.87, P<0.001), and (3) a non-significant interaction effect of direction versus delay. Using the second grouping of target direction, there was: (1) a significant main effect for direction category (F1=29.94, P<0.001), (2) a significant main effect for delay (F2=13.11, P<0.001), and (3) a non-significant interaction effect of direction versus delay.

Fig. 3A, B Division of directions for ANOVA. The definition of the categorical variable of direction for the analysis of variance is depicted. Thus, the three measures of movement direction (at the initial position, at one-third of the total distance, and at the final position, see Methods) were categorized as 0 or 1, alternating according to the directional segment to which the particular movement direction belonged. A The division of movement directions followed the variation of absolute directional error at the final position of the trajectory (see Fig. 2). An increase in absolute directional error is expected at the 22.5° slices marked with 1. The categorical variable of direction was equal to 1 for these directional slices. The directional slices marked with 0 indicate the segments where the absolute directional error decreased and the categorical variable of direction was equal to 0. B The division of directions that followed the variation of directional error at the initial position on the trajectory (see Fig. 2). Two segments with an increase in directional error and two with a decrease in directional error are marked with 1 and 0, respectively, and the categorical variable of direction was equal to 1 or 0 according to the directional segment

tional error (the tips of the leaves of the shamrock), while the error still crossed the zero line in the areas of low error. The ANOVA results using the second grouping of target direction showed: (1) a non-significant main effect for direction category, (2) a significant main effect for delay (F2=39.22, P<0.001), and (3) a non-significant interaction effect of direction versus delay. Finally the ANOVA results for the error at the one-third distance position showed a mixed result, as expected. Using the first grouping of target direction, there was: (1) a significant

Analysis of response latency, movement time, and maximum acceleration The mean response latency for all movements was 397.61 ms (SD=104.3 ms), the mean movement time was 117.7 ms (SD=44.39 ms), and the mean maximum acceleration for the first 1/3 of the distance to the target was 8.94 cm/s2 (SD=6.27 cm/s2). The response latency was not affected by the target direction, but was strongly affected by the delay. Thus, a decrease in response latency was observed with increasing delay (see Fig. 4). The ANOVA using the first grouping of target direction showed a significant effect of delay (F2=67.31, P<0.001). The ANOVA using the second grouping of target direction again showed a significant effect only for delay (F2=67.37, P<0.001). The variation of the mean movement time with target direction followed the same pattern that we observed for the directional error at the initial position (Fig. 5). Thus, an increase in mean movement time was observed for the axis of maximum initial arm inertia. Furthermore, this variation did not seem to be affected by the delay. The variation of maximum acceleration with target direction followed an opposite pattern, where the lowest mean maximum acceleration was observed for the maximum initial arm-inertia axis. Thus, the increase in mean movement time for the directions that laid on the axis of maximum limb inertia was accompanied by a smaller

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mean maximum acceleration on that axis. The ANOVA results confirmed these observations. Thus, the ANOVA for movement time using the first grouping of target direction showed no significant effect for target direction. There was a significant effect of delay (F2=9.91, P<0.001), but the magnitude of this effect was very small. The difference in mean movement time between the 0 delay and the mean movement time for all other delays was 5–6 ms. The interaction of delay with target direction was not significant. The ANOVA using the second grouping showed a significant effect of target direction (F1=240.66, P<0.001) and delay (F2=10.03, P<0.001). The interaction was again not significant. The effect of delay, although significant, was very small (5–6 ms difference). The maximum acceleration analysis showed no significant effects of target direction and delay when the first grouping of target direction was used. The use of the second grouping resulted in a significant effect only for target direction (F1=73.03, P<0.001). Information-transmission analysis We measured the transmitted information (T) using the initial position, the one-third distance position, and the final position on the trajectory of each trial (see Methods). The data were separately processed for each delay. The input information corresponding to 120 target directions (see Methods) was 6.9 bits, and Table 1 presents the values of information transmission for the three different positions on the trajectory and the different delays. A clear increase in information transmission was observed with the evolution of the trajectory. Thus, comparing the information transmitted in the zero-delay case (first row of Table 1), it can be seen that, for the initial position, the information was 1.05 bits, corresponding to two directions of movement (each bit of information in this analysis corresponds to two choices of movement directions). The information transmitted when the information was measured at one-third distance from the target increased by 2.79 bits, reaching 3.80 bits which corresponds to 14 movement directions. There was a smaller increase of information as the final position close to the target was reached. The transmitted information reached 4.08 bits, which corresponds to 17 movement directions. Another interesting observation was the decrease in information transmission with the increasing delay. This decrease was observed for the information at the initial position and the information at the one-third distance position (decrease of 0.17 bits and 0.16 bits from 0 to 6 s

Fig. 5 Movement-time distributions. Each polar plot depicts the distribution of mean movement time for all target directions for each delay. The mean movement time is represented with a solid line, while the cloud that surrounds the line shows the spread of values for each value of mean movement time. The distribution of the mean movement time appears similar to the distribution of the directional error at the initial position and was not affected by an increase in delay

118 Table 1 Transmitted information. This table shows the values (in bits) that resulted from the analysis of information transmission (see Methods). Each column shows the values of transmitted information for a different measure of movement direction (at the initial position on the trajectory, at one-third of the distance to the target, and at the final position closest to the target). Each row shows the information transmitted for a particular delay. A clear increase in information transmission was evident with the evolution of the trajectory (compare the means for different columns). A gradual decrease of transmitted information was observed for the final position (0.1 bits for the transition between 0- and 2-s delay and 0.7 bits for every other transition). The total difference between the 0-s delay and the 6-s delay was 0.24 bits. A decrease of transmitted information with delay was also observed at the initial position (0.17 bit difference between 0- and 6-s delay) and at the one-third distance position (0.16 bit difference between 0- and 6-s delay). However, this decrease was not as large as the case for the final position, and it was not stepwise from 0- to 6-s delay Delay

Initial position

1/3 distance position

Final position

0s 2s 4s 6s Mean (all delays)

1.05 0.86 0.84 0.88 0.91

3.80 3.75 3.72 3.64 3.72

4.08 3.98 3.91 3.84 3.95

delay). The decrease, though, was more pronounced at the final position (decrease of 0.24 bits from 0 to 6 s delay) than at the initial position (decrease of 0.17 bits from 0 to 6 s delay) or the 1/3 position (decrease of 0.16 bits from 0 to 6 s delay). In conclusion, the transmitted information of the motor output increased with the evolution of the trajectory as the target was reached. The increase in delay resulted in a decrease of transmitted information, especially at the final position of the trajectory close to the target.

Discussion The salient findings from our study were the following: 1. A systematic directional error at the final portion of the trajectory of an arm movement was revealed when a large number of target directions was used. This error resulted from a tendency of movement directions to cluster into four directions in 2-D space. 2. This error increased with the increase in the delay between target presentation and movement execution. 3. A different pattern of directional error was present only at the initial portion of the trajectory and did not change with the increase in delay. This error resulted from a tendency of the initial portion of the trajectory to cluster into two directions in 2-D space. 4. The transmitted information measured at the final portion of the trajectory was larger than that measured at the initial portion of the trajectory, and it progressively decreased with delay. In our task, subjects moved on a digitizer tablet without control for inertial forces due to the weight of the moving arm (Hogan 1985). Gordon et al. (1994b) provided

evidence that the motor command does not correct in advance for differences in limb inertia, resulting in a lower maximum acceleration and larger movement time on the axis of maximum limb inertia. Our subjects performed small-amplitude arm movements in a 2-D plane. These movements involved the shoulder and forearm, and we observed similar initial inertia effects of the resting position of the forearm on movement time and maximum acceleration. The directional error at the initial portion of the trajectory was larger in the axis of the forearm, in which the limb inertia for arm movement would be expected to be large (Hogan 1985). Thus, the initial force pulse applied in the direction of the target interacts with the initial inertia of the arm, and the resulting movement direction is biased towards the axis of lower initial inertia. This directional bias, then, can be viewed as the result of a mechanical filtering of the motor command at the initial portion of the trajectory. The directional bias was corrected as the trajectory evolved in time. This online correction of the trajectory was reflected in the gradual change of the pattern of errors that was seen at onethird of the distance to the target and at the final position when the target was reached. The idea of an ongoing correction of the trajectory has received support from other studies (Goodale et al. 1986; Prablanc and Martin 1992). The information-transmission analysis showed that the direction at the initial portion of the trajectory can be effectively reduced to two directions (1 bit of transmitted information). This reduction of directional information at movement initiation probably resulted from the effects of anisotropic limb inertia, the stiffness, and the viscosity of the moving arm. We believe that this reduction of information was not the result of a measurement error because we used a conservative method of measuring the initial position (see Methods). As the trajectory evolved in time to reach one-third of the distance to the target, we observed the appearance of a new pattern of directional error. This pattern became more evident at the final portion of the trajectory as the target was reached and resulted from a clustering of movement directions in two axes (45–225° and 135–315°). A similar systematic directional error has been observed by Massey et al. (1991) using isometric force pulses and Ghez et al. (1994) using reaching movements. In addition, this error became larger with delay, as also confirmed by the information-transmission analysis, whereas the increase in delay did not affect the pattern of error observed for the initial portion of the trajectory. Thus, both the pattern of the error at the final portion of the trajectory and the effect on this error of delay confirmed our hypothesis that this systematic error was not related to the initial inertial anisotropy of the arm. Ghez et al. (1994) speculated that this pattern of directional error might be related to the initial selection of a set of agonist muscles that will produce the movement. Karst and Hasan (1991) found that a good predictor for this selection was the direction of the arm movement relative to the initial arm position. A small number of such

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directions defined the boundaries between the activation of one set and the activation of a different set. These boundaries could be reflected in the directional bias that we observed. The idea that muscle activation for the execution of a movement trajectory in space can be classified according to a set of principal muscle synergies has also been studied in the experiments of Bizzi et al. (1991) and Giszter et al. (1993) in the spinalized-frog preparation. When microstimulation was applied at different segments of the frog spinal-cord gray matter, the resulting muscle force fields showed a convergence to an equilibrium point (a point were the net force applied to the limb was zero). If the initial position of the resting limb was constant, the active force fields elicited by microstimulation could be classified in a small number of principal configurations. When the direction of the equilibrium point of these force fields was measured relative to the initial resting position, these directions clustered in two axes. This clustering of directions looks very similar to the clustering that we observed in the directions of 2-D movements in our task (see Fig. 1). The authors of that study proposed that these principal configurations of force fields can be viewed as movement primitives, and simulation studies (Mussa-Ivaldi et al. 1991a, 1991b) have shown that the vectorial summation of such primitives could account for a large repertoire of movements in different directions in space. Could it be, then, that the directional bias that we observed at the final portion of the trajectory reflects the action of such movement primitives to which the motor command is attracted? If this is the case, then why does this attraction becomes stronger with delay? Assuming that a cortical directional signal modulates the output from the spinal-cord interneuronal system (Bizzi et al. 1991), and that this signal might degenerate with increasing delay, then the interneuronal system, lacking cortical information, will tend to fall back towards the set of movement primitives that constitute its building blocks. Motor cortical neurons are directionally tuned to the direction of an upcoming movement in space relative to the initial arm position (Georgopoulos et al. 1982; Schwartz et al. 1988; Caminiti et al. 1990). The same directional signal can be found in the activity of neurons in the premotor cortex (Caminiti et al. 1991). The introduction of a delay period between target presentation and movement execution results in the holding of directional information by the motor cortex (Smyrnis et al. 1992). As the delay time increases, this directional signal might become less precise due to the lack of a continuous redefinition of the target in space, as supported by the loss of information transmission with increased delay seen in our study. Finally, the possibility that the directional bias at the final position might reflect a bias in the cortical directional signal per se cannot be excluded. However, Schwartz et al. (1988) have shown that the preferred directions of neurons in the motor cortex before reaching in 3-D space span the entire continuum of directions. Furthermore, neurons in the motor cortex do not change their preferred direction with increasing delay (Smyrnis et al. 1992).

The hypothesis of a set of preferred movement directions specified by the spinal interneuronal system also has interesting implications concerning the frame of reference for movement specification (Soechting and Flanders 1992). A reference frame based on the initial arm configuration supports this hypothesis (Gordon et al. 1994a; Desmurget et al. 1997). Furthermore, changing the initial arm configuration would result in a different set of movement primitives, which would, in turn, change the directional error distribution. We are currently investigating this hypothesis by manipulating the initial arm configuration. A completely different hypothesis concerning the origin of this systematic directional bias is related to the visual environment. The subjects were watching a computer screen while they were moving their arm on the digitizer. Thus, they used a visual representation of the tip of their moving arm, the cursor, to perform their movements. The rectangular shape of the computer screen might, then, be used as a reference frame for these movements, and the diagonal axes of the display (the four edges of the screen) might be used as guiding axes for movement performance, especially for the memorized movements. Thus, a reference frame in visual space could also explain the directional bias at the final arm position. A test of this hypothesis could be to introduce a specific coordinate transformation from visual display to motor output and observe if the pattern of directional error followed the visual display or the motor output. We are currently investigating this alternative hypothesis for the origin of the directional error. A final point concerns the response latency. Interestingly, the increase in delay resulted in a decrease in response latency. This effect has been previously observed regarding memorized reaching in the monkey (Smyrnis et al. 1992) and memorized flexion-extension movements in the monkey (Riehle and Raquin 1989). One explanation might be that the “precueing” of the target information enables pre-planning and, thus, the faster onset of a response (Georgopoulos 1991). However, this would imply a single pre-defined reduction in response latency related to the pre-planning of the movement, whereas we observed a gradual decrease of response latency with delay. We are not aware of other explanations for this phenomenon. In conclusion, this study provided evidence of a systematic directional bias when 2-D arm movements were performed in a large number of directions. This directional bias can not be explained on the basis of differences in inertial anisotropy of the moving arm, and it increases with increasing delay, possibly reflecting the action of a set of primitive force fields that define a motor space. If these primitives in fact define the movement reference frame, their direct visualization through the systematic directional bias observed in these experiments could provide a useful tool for the investigation of visuomotor transformations and insight into their neurophysiological substrates.

120 Acknowledgements This work was supported from the National University of Athens internal funding. We would like to thank Prof. M. Dalakas for his support of our group for the accomplishment of this project. We would also like to thank two anonymous reviewers for their useful comments on an earlier version of this manuscript.

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