Exp Brain Res (2001) 139:59–69 DOI 10.1007/s002210100767

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

P. Gourtzelidis · N. Smyrnis · I. Evdokimidis A. Balogh

Systematic errors of planar arm movements provide evidence for space categorization effects and interaction of multiple frames of reference Received: 8 November 2000 / Accepted: 23 March 2001 / Published online: 16 May 2001 © Springer-Verlag 2001

Abstract Healthy humans performed arm movements in a horizontal plane, from an initial position toward remembered targets, while the movement and the targets were projected on a vertical computer monitor. We analyzed the mean error of movement endpoints and we observed two distinct systematic error patterns. The first pattern resulted in the clustering of movement endpoints toward the diagonals of the four quadrants of an imaginary circular area encompassing all target locations (oblique effect). The second pattern resulted in a tendency of movement endpoints to be closer to the body or equivalently lower than the actual target positions on the computer monitor (y-effect). Both these patterns of systematic error increased in magnitude when a time delay was imposed between target presentation and initiation of movement. In addition, the presence of a stable visual cue in the vicinity of some targets imposed a novel pattern of systematic errors, including minimal errors near the cue and a tendency for other movement endpoints within the cue quadrant to err away from the cue location. A pattern of systematic errors similar to the oblique effect has already been reported in the literature and is attributed to the subject’s conceptual categorization of space. Given the properties of the errors in the present work, we discuss the possibility that such conceptual effects could be reflected in a broad variety of visuomotor tasks. Our results also provide insight into the problem of reference frames used in the execution of these aiming movements. Thus, the oblique effect could reflect a hand-centered reference frame while the y-effect could P. Gourtzelidis (✉) · N. Smyrnis · I. Evdokimidis Cognition and Action Group, Neurology Department, National University of Athens, Aeginition Hospital, Greece e-mail: [email protected] Tel.: +30-1-7494439, Fax: +30-1-7494095 P. Gourtzelidis 401 Army General Hospital, Neurophysiology Department, 138 Mesogeion and Katehaki, Athens, 11525, Greece N. Smyrnis · A. Balogh University Mental Health Research Institute, National University of Athens, Athens, Greece

reflect a body or eye-centered reference frame. The presence of the stable visual cue may impose an additional cue-centered (allocentric) reference frame. Keywords Motor control · Visuomotor transformation · Frame of reference · Space perception · Category · Human

Introduction In a previous study, we reported the presence of a systematic directional error when planar arm movements were performed toward remembered targets in two-dimensional (2-D) space (Smyrnis et al. 2000). Specifically, we observed that the movement directions measured in the vicinity of the target showed a systematic error that could be summarized as a tendency of directions to cluster toward two orthogonal axes crossing at the initial hand position. These two axes were on the diagonals between the vertical and horizontal axes that divided the horizontal plane and the vertical monitor where the targets where projected. In addition, the directional error increased with increasing delay. A similar pattern of systematic directional errors has been reported for various visuomotor tasks. Massey et al. (1991) have observed this pattern of errors in the production of 2-D isometric forces toward locations in 2-D space. Ghez et al. (1994) and Ghilardi et al. (1995) have observed the same pattern of directional errors when subjects performed planar reaching movements without visual feedback of arm position. Recent findings in the literature show that movement of the arm toward a visual target is specified by two components, direction and distance, that are processed separately (Flanders and Soechting 1990; Gordon et al. 1994a, 1994b). In addition, multiple frames of reference have been proposed as crucial for the specification of arm movement trajectories by the CNS. Soechting and Flanders (1989a, 1989b) have shown that the endpoint errors of arm movements are represented in a shoulder-

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centered reference frame. On the other hand, Ghez et al. (1994) and Gordon et al. (1994a, 1994b) have shown a vectorial representation of movement with respect to a hand-centered reference frame. In more recent studies, McIntyre et al. (1997, 1998) show that the representation of the target is carried out in a viewer-centered frame of reference. Finally, other studies have supported a gradual transformation of the visual target coordinates from an eye-centered reference frame used by subjects to locate the target, to a shoulder-centered reference frame most appropriate for organizing the movement of the effector arm (Flanders et al. 1992; Carrozzo et al. 1999; McIntyre et al. 1998). In previous experiments where a pattern of systematic directional errors toward the diagonals was observed (Ghez et al. 1994; Ghilardi et al. 1995; Massey et al. 1991; Smyrnis et al. 2000), only the directional component of the movement or the isometric force was studied. Thus, the present study was designed to investigate both directional and distance errors when subjects perform 2D pointing movements employing a full directional continuum. To address the principal aim, the authors’ previous study was modified to use three different target distances, employing 0-s and 6-s delay conditions. In addition, to investigate the frame of reference that any pattern of systematic errors may imply, in a separate experiment we introduced a stable visual cue that was always present during task execution. Our hypothesis was that subjects might use the visual cue as the basis for an allocentric frame of reference (Colby 1998; Gentilucci et al. 1996).

Materials and methods Subjects Thirty-two right-handed, healthy volunteers (17 men and 15 women, age 24 years (SD 5 years of age) participated in the study. The participants were recruited from Aeginition Hospital personnel and students of the Medical School of the National Athens University. All subjects gave informed consent and the experimental protocol was approved by the Aeginition Hospital Scientific and Ethics Committee. To avoid range effects (Poulton 1975), each subject participated in only one of the two experimental conditions. Apparatus and experimental setup We used the same experimental conditions as described by Smyrnis et al. (2000). Subjects were seated in an illuminated room on a 46-cm-high, straight-back chair at a table (120×75×76 cm) facing a computer monitor (27×21 cm) placed at the subjects’ midline approximately 60 cm from the subjects’ eyes. Subjects used the right hand to move a mouse-type manipulandum on a digitizing tablet. The manipulandum’s position was sampled at 100 Hz and displayed on the computer monitor as a cross-hair cursor. The ratio of the manipulandum movement to cursor movement on the computer monitor was 0.7. Subjects were instructed to maintain head and trunk in an upright position during the trials and to use only shoulder and elbow movements to move the manipulandum (not wrist or finger movements). No special equipment was used for stabilizing the trunk or head, but one of the authors was standing behind the subject giving instructions when he or she tended to change posture or use wrist or finger movements to perform the task.

Fig. 1A, B Arrangement of target locations on the computer monitor. Targets were arranged on the circumferences of three concentric circles of radii 2 cm, 4 cm, and 6 cm. Targets were positioned every 15°, with eight positions omitted on the smallest circle: 30°, 60°, 120°, 150°, 210°, 240°, 300°, and 330°. Note that only 1 of the 64 targets was flashed for each trial. The cursor is shown as a cross-hair inside the central circle (initial position). A Experiment 1. Arabic numbers indicate directions in polar coordinates. Roman numbers (I–IV) correspond to the four quadrants defined. B Experiment 2. The addition of the stable visual cue, a 6-mm-diameter solid circle at 70° and 4.7 cm from the origin Twenty-two of the thirty-two subjects participated in experiment 1, which was defined as follows: Each subject performed 200 trials. At the beginning of each trial, the subject moved the cursor into a 6-mm-diameter circle displayed at the center of the computer monitor (the origin of the movement). After a variable interval of 0–2 s, a 3-mm-diameter circle (the target) appeared at a peripheral position and remained on for 300 ms. The central circle was then either extinguished immediately (No delay condition) or after a 6-s-delay period (Delay condition). The extinction of the central circle indicated to the subject to move the cursor to the previously displayed target as quickly and accurately as possible and to maintain this position until the reappearance of the central circle (at least 1 s). This position was defined as the endpoint of the movement. No other feedback was given to subjects except from the cursor that remained visible during the task. At the beginning of the experiment, each subject performed some trials (mean of 3.8 trials per subject) that were not analyzed until he/she would get familiar with the task. Target positions were located along the circumferences of three imaginary circles, with a common center at the initial position of the hand (central circle) and radii of 2 cm (proximal), 4 cm (intermediate), and 6 cm (distal). Targets were positioned every 15° beginning from 0° (being toward the right) in a standard polar reference frame (increasing counterclockwise). For purposes of data description, the four standard polar quadrants were used: I=0–90°, II=90–180°, III=180–270° and IV=270–360° (Fig. 1A). In a pilot study using 24 positions for all circles, we noticed that the subjects understood after the first few trials that the targets were arranged in concentric circles. To avoid estimation biases and give the impression of a uniform target distribution in a plane, eight positions on the smallest circle were omitted (30°, 60°, 120°, 150°, 210°, 240°, 300°, and 330°). This arrangement resulted in a total of 64 positions on the computer monitor (Fig. 1A). Ten of the thirty-two subjects participated in experiment 2, which was defined as previously, with the following exception: A 6-mm-diameter solid circle was always present in the upper-right quadrant of the screen, 4.7 cm from the center at 70° (Fig. 1B). Subjects were instructed to ignore this “spot.” Data analysis The cursor trajectory was obtained from the digitizing tablet in Cartesian (x-y) space with the origin at the initial position in the central circle. By convention, the x-coordinate corresponds to the

61

Fig. 2A–D Experimental configuration. Subject position relative to the computer screen and digitizer. The two coordinate systems used in the analysis are shown with respect to the horizontal plane. A Cartesian (x-y) coordinates (positive errors right and forward, respectively). B Polar coordinates, with direction in degrees and distance in centimeters (positive errors counterclockwise and away from center). C Definition of endpoints in polar coordinates. O indicates the origin of the movement, while the horizontal line corresponds to direction 0°. The position of the movement endpoint E is then determined by direction d and distance OE. D Vectorial presentation of the directional error: O indicates the origin of the movement, while the small empty circle T represents the target of the movement. The free edge E of the line adjusted to the target shows the mean endpoint position for movements performed toward the target T. The mean directional error for this target corresponds to the angle e

Fig. 3A, B Experiment 1: Movement endpoint positions. A Each dot represents the endpoint of a single trial (left, No delay; right, Delay). B The circles represent target positions and the free edge of each line shows the mean endpoint position for movements performed toward the corresponded target, as shown in Fig. 2D. (left, No delay; right, Delay)

Results left-right component of movement, both on the digitizer tablet and on the monitor, while the y-coordinate corresponds to a down-up movement of the cursor on the screen or equivalently to a backward-forward direction of arm movement on the digitizer surface (Fig. 2A). Using this coordinate system, we calculated two types of error for each trial: the “x-error” was defined as the x-component difference between movement endpoint and target, and the “y-error” as the y-component difference between movement endpoint and target. Thus, positive x-error corresponds to rightward deviation of the cursor or arm, while positive y-error corresponds to upward deviation of the cursor or deviation of the arm away from the subject’s body. Cursor position was also transformed to conventional polar coordinates, again with the origin located at the initial position at the central circle (Fig. 2B, C). We again calculated two types of errors: the “directional error” was defined as the difference between cursor endpoint and target directions and the “distance error” as the difference between cursor endpoint and target distances from the origin. Thus, a counterclockwise deviation from the target was a positive directional error and overshoot of the target was a positive distance error. For visualization we used a “vectorial” representation of the error as defined in Fig. 2D. A total of 6,137 complete trials were obtained. Movements with absolute directional error greater than 45° or absolute distance error greater than 2.0 cm were excluded from analyses. These cases represented 1% of the data set. For statistical analyses, we used standard techniques (t-test, linear regression, analysis of variance). In certain cases, in order to test whether the individual regression slopes within different groups were differing, we used the test described by Armitage and Berry (1987).

Experiment 1 Final cursor positions for all targets are plotted in Fig. 3A (left, No delay; right, Delay). Each point represents the endpoint of one movement (one trial). Mean endpoint positions for each target location are superimposed on the actual targets in the vectorial plot in Fig. 3B (left, No delay; right, Delay). In general, the movement endpoints seemed to cluster toward the diagonals of each quadrant, an effect much more prominent in the Delay condition. The data were analyzed by separating the directional and distance components of the final cursor positions. In Fig. 4, the mean directional error is plotted versus the corresponding target direction. Directional error changed systematically in each quadrant. Taking into account that positive errors represent counterclockwise deviations, there was an apparent tendency of the movement endpoints to err toward the diagonals (45°, 135°, 225°, and 315°). In addition, this error increased in each quadrant as the target location deviated from the diagonals toward the quadrant borders, as indicated by the large errors near the horizontal and vertical positions. However, there was nearly no error for targets located on the vertical and horizontal axes (90°, 180°, 270°, and 360°). Linear regression was performed within each quadrant and for each target distance separately as shown in Fig. 5, with slopes presented in Table 1. For this analysis

62 Fig. 4 Experiment 1: Directional error versus target direction. Mean directional error in movement endpoint (degrees) is plotted versus target direction (degrees) for each target distance (dotted line 2 cm, dashed line 4 cm, solid line 6 cm). A systematic periodic directional error is present within each quadrant. Left, No delay; right, Delay

sponding to targets at horizontal as well as vertical axes (90°, 180°, 270°, and 360°) were not taken into account (see Results). Left, No delay; right, Delay. The slope and the zero crossings of each line are shown numerically in Tables 1 and 2, respectively

Fig. 5 Experiment 1: Linear regression models of directional errors within each quadrant: Each line represents a linear regression of the data in the corresponding quadrant. A separate regression model was used for each target distance. Note that data corre-

Table 1 Experiment 1: Linear regression model slopes. The slopes (β-coefficients) of the linear regressions, using directional errors as the dependent and target directions as the independent variables. Results are presented for both No delay and Delay conditions, for each quadrant and for each target distance (TD) separately

Table 2 Experiment 1: Zero crossing values for the directional error regression lines. The values of target direction at which the predicted directional error is zero. According to the conventions about the polarity of the directional error, these are the directions at which the movement endpoints gravitate

Quadrant

I (15°–75°) II (105°–165°) III (195°–255°) IV (285°–345°)

No delay

Delay

TD 2 cm

TD 4 cm

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

–0.059*** –0.095*** –0.120*** –0.150***

–0.076*** –0.048** –0.056** –0.092***

–0.052*** –0.076*** –0.083*** –0.065***

–0.300*** –0.243*** –0.328*** –0.297***

–0.245*** –0.274*** –0.308*** –0.271***

–0.148*** –0.176*** –0.272*** –0.195***

***P<0.000; **P<0.01; *P<0.05

Quadrant

I (15°–75°) II (105°–165°) III (195°–255°) IV (285°–345°)

No delay

Delay

TD 2 cm

TD 4 cm

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

35.2° 148.0° 239.2° 317.3°

48.0° 156.8° 262.1° 311.7°

38.1° 140.2° 255.4° 306.4°

37.8° 147.0° 222.0° 321.9°

32.2° 144.9° 229.8° 314.4°

34.6° 145.5° 234.2° 310.5°

we did not take into account data from targets at the edges of quadrants, i.e., on the horizontal and vertical axes. In all cases, there was a statistically significant fit of the linear model. Thus, within each quadrant the absolute mean directional error increased linearly as the target location deviated from the oblique axes. The slope (β-coefficient) of each regression line indicated the rate of increase in the error. The ANOVA for the slopes of the regression lines in the two delay conditions demonstrated a

significant difference between Delay and No delay (F1, 3,396=361.115, P<0.000). Thus, the directional error increased more abruptly as the target location deviated from the oblique axes in the Delay condition compared with the No delay condition, indicating an effect of memory on the oblique pattern of error. These results are in agreement with the findings reported in our previous study (Smyrnis et al. 2000). In addition, the directional error increased more steeply for targets located proximal

63 Table 3 Experiment 1: Mean x-and y-errors. Mean movement endpoint errors as calculated from Cartesian coordinates are presented (TD target distance)

No delay

x-Error (cm) y-Error (cm)

Delay

TD 2 cm

TD 4 cm

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

0.013n.s. –0.040**

0.010n.s. –0.098***

0.020n.s. –0.178***

–0.006n.s. –0.067**

0.046n.s. –0.154***

0.017n.s. –0.207***

P-values correspond to one sample t-test for difference from zero: ***P<0.000; **P<0.01; *P<0.05

Fig. 6 Experiment 1: Distance error (centimeters) versus target distance (centimeters). Mean distance error is plotted versus target distance. Systematic errors are present in both Delay and No delay conditions

(2 cm) to the origin of movement than for those located distally (6 cm). The ANOVA showed a significant difference of regression slopes among the three target distances, both in the No delay (F2, 1,742=5.79, P<0.003) and Delay conditions (F2, 1,650=13.00, P<0.000). In addition to information provided by slope analysis, the x-intercept values represent the target directions at which the directional error was zero or the directions toward which the movement endpoints gravitated. Table 2 shows that these points of minimal error, so to speak, were not exactly on the diagonals but lower with respect to the computer screen or toward the body with respect to the horizontal plane. In Fig. 6, the distance error of the movement endpoints is plotted versus target distance. In the No delay condition, subjects undershot the intermediate and distal targets (4 cm and 6 cm, respectively). In the Delay condition as well, subjects undershot the distal targets (6 cm); however, they overshot the proximal targets (2 cm). A linear regression analysis was performed using target distance as the independent variable and distance error as the dependent variable for the two conditions. There was a significant effect of target distance on distance error (No delay: slope=–0.031, P<0.000; Delay: slope=–0.123, P<0.000). There was a significant effect of delay on the slopes of the regression lines (F1, 4,183= 50.78, P<0.000). Thus, systematic biases in distance error were linearly dependent on target distance and were more evident in the delay condition. As stated previously, the directional error resulted in the clustering of movement endpoints not exactly toward the diagonals but downward with respect to the computer screen or toward the body with respect to the effector

Fig. 7 Experiment 1: Effect of delay and target distance on yerror. Because of pooling data from the full directional continuum, it is not possible to plot y-error versus its corresponding y-coordinate as this was done for directional error versus target direction and distance error versus target distance. Both effects, time delay and target distance, resulted in an increasing of absolute value of y-error

hand. This pattern was further investigated by analyzing the endpoint errors in a Cartesian coordinate system, since in this coordinate system possible downward or toward-the-body biases correspond to y-errors. The problem that arises using two coordinate systems (polar and Cartesian) for describing the same data is that errors already described in the one system might also emerge in the second system. Specifically, as can be seen in Figs. 1A, 2A, the y-error in 90° corresponded to the distance error, while the y-error in 270° corresponded to the inverse of the distance error. In order to isolate the yerror, the analysis in the Cartesian coordinate system was performed after pooling the data from the full directional continuum for each target distance. Note that using this analysis we could not study the possible influence on the y-error of its corresponding y-coordinate (as this was done for directional error versus target direction and distance error versus target distance). Mean x- and y-errors are shown in Table 3. The values of the y-error were negative and a t-test showed that they were significantly different from zero for each target distance, thus indicating that there was a significant tendency of movement endpoints to err downward with respect to the computer screen or toward the body with respect to the effector hand. We further investigated possible factors that might affect this bias. In Fig. 7, the y-error was plotted for each delay condition and target distance. An ANOVA with yerror as the dependent variable and delay and target distance as independent variables demonstrated a significant influence of delay (F1, 4,181= 4.690, P<0.030) as

64 Table 4 Experiment 2: Linear regression model slopes. The slopes (β-coefficients) of the linear regressions, using directional errors as the dependent and target directions as the independent variables. Results are presented for both No delay and Delay conQuadrant

I (15°–75°) I (45°–90°) II (105°–165°) III (195°–255°) IV (285°–345°)

ditions, for each quadrant and for each target distance separately. Analysis for quadrant I was repeated using a different set of data (target directions: 45°, 60°, 75°, and 90°). (TD Target distance)

No delay

Delay

TD 2 cm

TD 4 cm

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

–0.034n.s. 0.015n.s. –0.086** –0.099* –0.174***

–0.012n.s. 0.059** –0.048* –0.088*** –0.100***

0.012n.s. 0.007n.s. –0.011n.s. –0.074*** –0.108***

–0.090* 0.036n.s. –0.269*** –0.429*** –0.467***

0.009n.s. 0.139*** –0.124** –0.289*** –0.187**

0.022n.s. 0.018n.s. –0.128** –0.288*** –0.224***

***P<0.000; **P<0.01; *P<0.05

well as target distance from the origin of the movement (F2, 4,181= 20.936, P<0.000) on the y-error. As can be seen in Fig. 7, the absolute value of y-error was greater in the Delay condition and was maximal for movements toward the distal (6-cm) targets. In summary, two patterns of systematic errors of movement endpoints were observed in experiment 1, one when data were represented in the polar coordinate system and one when data were represented in the Cartesian coordinate system. The representation of data in the polar coordinate system enabled the observation of directional and distance errors. The majority of movement directions showed a tendency to err toward the two diagonals, with larger errors in the Delay than the No delay condition. In addition, there was a tendency for movement endpoints to err toward proximal distances in the No delay condition and toward intermediate distances in the Delay condition. The combination of both the directional and the distance errors resulted in a tendency for the majority of movement endpoints to err toward specific areas in the 2-D plane. These areas were located in the vicinity of the geometric center of each quadrant, namely at diagonal directions and intermediate or proximal distances. This pattern of systematic error (conventionally called “oblique”) was more pronounced in the Delay condition and also affected mostly the movements toward proximal targets. The second pattern of systematic error was an overall tendency for movements to err downward with respect to the computer screen or toward the body with respect to the horizontal plane in which the arm movements were executed. This y-effect was also dependent on delay as well as on target distance. Errors were larger in the Delay versus the No delay condition and larger at more distal targets. Experiment 2 As stated previously, experiment 2 was identical to experiment 1 except that a stable visual cue was always present in quadrant I. Figure 8 presents the endpoint errors for all target locations in experiment 2 (left, No delay, right, Delay). Systematic errors in the quadrant of the cue were much smaller than corresponding errors for

Fig. 8 Experiment 2: Vectorial representation of mean movement endpoint errors. Mean movement endpoint positions corresponding to each target location as in Fig. 3B. The filled circle in quadrant I represents the stable visual cue that was present during each trial. Left, No delay; right, Delay

similar target locations in experiment 1, particularly for the Delay condition (see Fig. 3B). As for experiment 1, the data were analyzed by separating the directional and distance components of the final cursor positions. In Fig. 9, the directional error is plotted versus the corresponding target direction. Initially, linear regressions were performed as in experiment 1 by clustering the data into four quadrants and three target distances, omitting data from targets at the edges of quadrants (90°, 180°, 270°, and 360°). As expected from Fig. 9, the data within quadrant I where the visual cue was located did not show a good linear fit (Table 4). Specifically, only in the Delay condition at target distance 2 cm was there a significant linear fit between target direction and directional error. Subsequently, the linear model in quadrant I was modified to include only directions located in the vicinity of the visual cue (targets corresponding to directions 45°, 60°, 75°, and 90°). For the remaining quadrants, we used the same model as in experiment 1. Significant fits are shown in Fig. 10. Within quadrant I, linear regression revealed a significant effect of target direction on directional error only for targets located 4 cm from the initial cursor position in both the No delay and the Delay conditions (Table 4). Interestingly, the 4-cm target distance was closest to the position of the visual cue (4.7 cm). In addition, the regression lines in quadrant I had positive

65 Fig. 9 Experiment 2: Directional error versus target direction. Mean directional error in movement endpoint (degrees) is plotted versus target direction (degrees) for each target distance (dotted line 2 cm, dashed line 4 cm, solid line 6 cm). The vertical line at 70° represents the position of the visual cue. Left, No delay; right, Delay

Fig. 10 Experiment 2: Linear regression models of directional errors within each quadrant. Each line represents a linear regression of the data in the corresponding quadrant. Only the statistical significant lines are shown. A separate regression model was used for each target distance. But in contrast to Experiment 1 (Fig. 5), in

the model that is represented here, we used data from targets corresponding to 45°, 60°, 75°, 90° for quadrant I. For the remaining quadrants, we used the same model as in experiment 1. Left, No delay; right, Delay

Table 5 Experiment 2: Zero crossing values for the directional error regression lines. The values of target direction at which the predicted directional error is zero. Only values corresponded to

statistical significant regression lines (Table 4) were calculated. Analysis for quadrant I was repeated using a different set of data (target directions: 45°, 60°, 75°, and 90°)

Quadrant

I (15°–75°) I (45°–90°) II (105°–165°) III (195°–255°) IV (285°–345°)

No delay

Delay

TD 2 cm

TD 4 cm

163.0° 242.5° 314.3°

79.4° 142.4° 251.5° 301.7°

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

68.6° 154.5° 226.8° 313.5°

141.3° 233.8° 309.8°

55.0° 263.7° 294.8°

slopes with x-intercepts near the visual cue (Table 5). Taking into account the definitions about the polarity of the directional error, the above results indicated a tendency for movement endpoints to err away from the visual cue. We confirmed that the70° location of the visual cue was the point from which the movement endpoints tended to err away, by calculating the 95% confidence interval for the prediction of the directional error at target direction 70° (No delay condition, target distance 4 cm: –0.122 to 1.232, Delay condition, target distance 4 cm: –1.477 to 1.076). In both cases, the intervals contained the zero value, thus indicating that the directional error at the position of the visual cue did not differ from zero. The possible effect of time delay within quadrant I was studied using ANOVA for the slopes of the regres-

150.3° 224.5° 319.1°

sion lines between the two delay conditions. There was no significant effect of delay (F1, 112=3.324, P<0.070). Thus, the presence of the visual cue in quadrant I drastically changed the pattern of systematic errors that was observed in experiment 1. Movement endpoints for targets near the cue tended to err away from the cue, and the effect of memory was eliminated. Concerning quadrants II–IV, the data were well fit by linear models except from one case (Tables 4, 5, Fig. 10). The ANOVA confirmed that the directional errors were delay dependent, that is the slopes of the regression lines were different between the two delay conditions (F1, 1,131=107.554, P<0.000). Also, as in experiment 1, the systematic directional error was maximal for the more proximal targets (ANOVA of regression slopes between target distances: No delay, F2, 570=2.993,

66 Table 6 Experiment 2: Mean x- and y-errors. Mean movement endpoint errors as calculated from Cartesian coordinates are presented (TD target distance)

No delay

x-Error (cm) y-Error (cm)

Delay

TD 2 cm

TD 4 cm

TD 6 cm

TD 2 cm

TD 4 cm

TD 6 cm

0.000n.s. –0.002n.s.

0.020n.s. –0.090***

0.013n.s. –0.228***

–0.037n.s. –0.068**

0.006n.s. –0.125***

0.029n.s. –0.107***

P-values correspond to one sample t-test for difference from zero: ***P<0.000; **P<0.01; *P<0.05

for movement endpoints for the whole directional continuum. In conclusion, the presence of a stable visual cue within quadrant I changed the pattern of systematic directional error of movement endpoints, particularly near the visual cue. Endpoints in this area tended to err away from the visual cue. This effect was present only within quadrant I, while, for targets within quadrants II–IV, the pattern of systematic directional error was very similar to that found in experiment 1. Fig. 11 Experiment 2: Distance error (centimeters) versus target distance (centimeters). Mean distance error is plotted versus target distance. Systematic errors are present in both Delay and No delay conditions

Fig. 12 Experiment 2: Effect of delay and target distance on yerror

P<0.050; Delay, F2, 557=17.220, P<0.000). Thus, we conclude that the systematic directional error that emerged in quadrants II–IV could be described with a similar model of linear regression as in experiment 1and was similarly affected by time delay and target distance. Concerning the distance error (Fig. 11), linear regression showed a significant effect of target distance versus distance error only in the Delay condition (No delay: slope=–0.014, P<0.160; Delay: slope=–0.072, P<0.000). For estimating the x- and y-errors, we pooled the data from all the target directions as in experiment 1. Again, only the mean value of the y-error was significantly different from zero (Table 6, Fig. 12). We could not investigate the effect that the visual cue might have on the distance error and the y-error. This is because the influence was restricted in a small area around it, while the estimation of the distance and y-errors required pooling of data

Discussion We studied systematic errors made by subjects when they performed 2-D aiming movements from a common starting position to remembered targets. The pattern of these systematic errors can be described as a combination of two kinds of effects. First, the oblique effect concerned a tendency for most of the movement endpoints to err approximately toward the diagonals of each of the four quadrants containing the targets. Second, the y-effect was evident as a tendency of movement endpoints to err toward the subjects’ bodies with respect to the effector hand or downward with respect to the computer monitor. The oblique effect was more prominent for movements to targets located near the initial cursor position, while the y-effect was more prominent for movements to more distal targets. Both effects became more evident by increasing the time delay between the appearance of the target and the initiation of the movement. Finally, in an additional experiment, we introduced a stable visual cue (a filled circle) in the vicinity of some targets. The pattern of the systematic error changed for these targets. Specifically a new pattern of systematic error emerged that involved a tendency for some movement endpoints to err away from the visual cue. Space categorization effects A hypothesis for the explanation of the above biases might come from the work of Ghez et al. (1994). These authors showed that the axis of maximum inertia of the upper limb is close to the axis of the forearm, while the axis of minimum inertia is perpendicular to it. These two axes correspond to the two diagonals at which the errors cluster in our analysis and could be a possible cause for the biases. Also the same authors suggest that systematic directional errors might reflect errors in the selection of

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elbow and shoulder muscle activation patterns (Karst and Hasan 1991a, 1991b). It is worth noting that Worringham and Beringer (1989) showed the significance of the forearm as a referent direction. Although the above explanations could be directly tested (for example performing the same task with different orientations of the arm), it is difficult to explain why the systematic error becomes greater in the delay condition or altered with the presence of a visual cue near the targets. In our previous work (Smyrnis et al. 2000), we suggested that the directional systematic error could reflect movement primitives, that is, the force fields proposed to be the principal control modules for the spinal specification of voluntary movement (Bizzi and Mussa-Ivaldi 1994; Bizzi et al. 1991; Giszter et al. 1993; Mussa-Ivaldi et al. 1990, 1991). Specifically, Bizzi et al. (1991) and Giszter et al. (1993) have suggested that movements are planed in an extrinsic coordinate system that represents the motion of the hand in space. The above authors have proposed that the CNS organizes motor tasks using a set of principal configuration of force fields for each limb. Mussa-Ivaldi et al. (1990, 1991) have shown that the combination of these primitive force fields could account for a large repertoire of movements toward different directions in space. In our previous work, we have suggested that when information about target location is impaired due to the memory delay, the motor output tends to rely more on intrinsic properties of the motor apparatus, among which could be a set of movement primitives. Thus, the systematic directional errors could reflect the action of such movement primitives. Again, this hypothesis is not fully satisfactory given the properties of the systematic error revealed in the present work. In experiment 2, the stable visual cue altered the pattern of systematic error. If this pattern of systematic errors is defined by movement primitives, then it should not be altered by the presence of a sensory stimulus such as the visual cue. A different explanation for the pattern of systematic directional and distance errors might come from the fact that these effects have been reported in perceptual tasks of estimation of spatial locations. In their study, Huttenlocher et al. (1991) instructed subjects to remember the position of a dot in a 15-cm circle printed on the center of a 22×28 cm white sheet of paper. The authors found that the reports of subjects were biased in direction as well as in amplitude with respect to the center of the circle. The directional systematic error was toward the diagonals, while the amplitude error was inward for locations near the circumference of the circle and outward for locations near the center of the circle. The combination of those effects suggested a tendency for estimations to cluster toward the “center of mass” of each of the four quadrants of the circle. The authors explained this pattern of systematic errors as a conceptual effect, emerging from space categorization. According to their model, subjects subconsciously imposed imaginary horizontal and vertical axes that divided the circle into four quadrants. These quadrants were used as categories of target

locations, while the imaginary axes served as the boundaries, and the geometrical center (center of mass) of each quadrant as the prototype of the corresponding category. The authors claimed that this effect served to improve the accuracy of the estimation, so that when the information about target location became inaccurate due to the time delay, subjects combined the remembered location with the prototype of the category. This combination of information about target location produced a bias toward the prototype (diagonal) and away from the borders of the corresponding category (quadrant). Huttenlocher et al. (1991) have discussed the application of this model in a broad range of stimulus-encoding situations. According to their conclusions, when information about a stimulus is inaccurate, estimation of stimulus magnitude tends to regress to a central value corresponding to the prototype (or “adaptation level”). Phenomena that could be explained within this frame have also been observed in a variety of perceptual estimation experiments. Tversky and Schiano (1989) asked subjects to reproduce an angle, drawn on a sheet of paper within an L-shaped frame. These authors noticed that the responses from subjects showed systematic errors toward particular angles. Engebretson and Huttenlocher (1996) have provided evidence that the above biases could also be interpreted within the model of space categorization described above. Lánský et al. (1989) asked subjects to estimate the orientation of dot patterns. The authors showed that the estimations of the subjects were systematically biased toward the nearest 45° oblique meridian. Also, a spatial diagonal bias has been reported in the neglect of the contralateral space for patients with neglect syndrome (Mark and Heilman 1998). Finally, an interesting aspect about these estimation biases is that they develop late in life, specifically at the age of 9 years (Sandberg et al. 1996). Thus, converging evidence regarding systematic directional and distance errors points to the fact that these biases might reflect a cognitive mechanism of categorizing a stimulus parameter such as location in space. These categorization effects might emerge when there is insufficient or degraded information about the stimulus, as when performing memorized movements, and might represent an aid in retaining information about the stimulus. Other situations might also be the cause of these effects, for example the restriction of the vision of the moving arm that again results in less information about the movement trajectory and its endpoint (Ghez et al. 1994). The same effects have also been observed in an isometric force production task, when again feedback information about force is manipulated (Massey et al. 1991). Concerning the second pattern of systematic error that we observed, the y-effect, it shared common properties with the oblique effect (increase with increasing delay, uneven distribution in the plane). However, we could not study the detailed distribution of this effect in plane because of the need to pool data across the whole set of target directions. A new pattern of systematic errors was

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observed when we introduced a visual cue in the task. This pattern concerned a tendency of movement endpoints to err away from the visual cue, a bias that possibly could be related again to space categorization effects. For example, this spot might represent a boundary for categories of space, resulting in movement endpoints erring away from it. Multiple frames of reference Regardless of the nature of these patterns of systematic errors, the fact that loss of information about an external stimulus resulted in a bias toward a default value can be used for identifying different frames of reference. Concerning the motor tasks, if there are separate information-carrying channels in the CNS, each one representing different attributes of the position of the target in space, then it is possible to express different attributes of systematic errors (for example different points of attraction or repulsion). Conclusions extracted from analysis of movement errors have already been presented in the literature regarding the split between directional and distance error (Flanders et al. 1992; Ghez et al. 1994). Similar distinctions between directional and distance errors were also observed in our data, but moreover we noticed the pattern of attraction toward four distinct points in the plane described above (oblique effect). Given the distribution of the attraction points around the origin of the movement, we can state that this systematic error provides evidence for a coordinate system located at the initial cursor position, which corresponds to a hand-centered frame of reference (Ghez et al. 1994). The y-effect was not centered on the origin of the movement, although the distance of the target from the initial point seemed to have an effect on this error. We could not distinguish whether this effect was based on a downward deviation on the computer monitor or a deviation of the hand toward the body and, thus, there are two possibilities regarding the frame of reference used. The first concerns a vertical frame of reference possibly related to the eyes or the environment. The second concerns a body-centered frame of reference, similar to that reported by Soechting and Flanders (1989a, 1989b) and McIntyre et al. (1998). The presence of a visual cue (circular spot) revealed a new pattern of systematic errors centered at the cue. Thus, we propose that in the second experiment a novel frame of reference emerged, related to the visual cue. According to this hypothesis, the CNS used additional information from this frame (direction and distance from the cue) to perform the movement. Such external (allocentric) frames of reference have already been reported in the literature (Colby 1998; Gentilucci et al. 1996). Summarizing the above, we propose that subjects organize the space near the initial arm position using a hand-centered reference frame (oblique effect), whereas, for the more distal targets, a body- or environmentalcentered reference frame is used (y-effect). These

frames of reference appear to be used simultaneously within the same movement and their influence gradually shifts from one to another with respect to the position of the corresponding target in plane. These frames of reference could be regarded as egocentric. When a visual cue was presented on the computer monitor, a novel frame reference emerged, centered on this particular cue. This frame was an allocentric frame of reference and it was used for movements toward targets located in its vicinity. According to our hypothesis, all the reference frames (egocentric and allocentric) were used simultaneously within the same motor task, and there was a gradual shift from one to another, depending on the position of target in space. Evidence regarding the existence of multiple frames of reference has been previously reported (Paillard 1991). Interesting results were also demonstrated recently in experiments where subjects performed movements corresponding to different target positions indicated by a vertical line on a monitor, or different amplitudes indicated by the length of a horizontal line (Heuer and Sangals 1999). The main conclusion was that visuomotor transformations could be executed using combinations of different reference frames, with the relative weights of the reference frames in the combination being taskdependent. Such multiple representations of space were proposed in behavioral studies of patients with hemispatial neglect (Behrmann and Tipper 1999). The authors demonstrated that patients with unilateral neglect, following a hemispheric lesion, expressed neglect with respect not only to an egocentric but also to an objectbased frame of reference simultaneously. Conclusions A distinct pattern of systematic errors emerged when human subjects made aiming movements to remembered targets displayed on a computer monitor, both with and without a stable visual cue present. The systematic errors became larger with increasing delay to movement execution, suggesting an effect of memory. Similar patterns of systematic errors have also been reported in a variety of tasks concerning estimation of location in space and they have been interpreted as conceptual effects. These effects were viewed as optimization phenomena. Thus, the categorization of space was a way to retain information when the information about the location of the target became inaccurate. In addition, by analyzing the systematic errors using both Cartesian and polar coordinate systems, we identified multiple frames of reference that can be present simultaneously and that appear to contribute to the localization of the target in space. These frames could refer to the origin of the movement, the stable visual cue, and possibly the body or the eyes of the subjects. We hypothesize that multiple reference frames coexist in the specification of the movement endpoint and they are weighted by their contribution to movement, so that the best performance can be achieved.

69 Acknowledgements This work was supported by internal funds from the Neurology Department of the National University of Athens. We would like to thank Professor M. Dalakas for his ongoing support to our group. Dr. Balogh is supported by the 97/HELLINOPHONO/125 fund from the Greek General Secretary of Research and Technology.

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