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1Department of Neuroscience, University of Minnesota, Minneapolis, Minnesota 55455; and 2Department of Experimental Psychology, University of Nijmegen, Nijmegen, The Netherlands
Submitted 25 November 2002; accepted in final form 6 February 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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; Flash and Hogan 1985; Morasso 1981). In addition to these kinematic features, optimization of dynamic force production (kinetics) may dictate the use of energetically efficient patterns of joint rotation (Soechting et al. 1995; Uno et al. 1989). Whereas a great deal of research effort has been devoted to revealing the relative importance of these factors, few studies have gone beyond reaching to consider the kinematic and kinetic aspects of planning or performing sequences of arm movement.
The general problem of planning and executing movement sequences has been studied at various levels, ranging from cortical activity (e.g., Carpenter et al. 1999; Hikosaka et al. 1999; Tanji 2001) to movement kinematics (e.g., van Mier et al. 1993). In terms of the kinematics, the basic problem can be posed in the following way: is a movement sequence from a starting target (ST) to target 1 and then to target 2 (i.e., sequence ST-1–2) identical to a serial joining of the separate performances of movements from the starting target to target 1 (ST-1) and from target 1 to target 2 (1–2)? Alternatively, do these movements change when performed in combination? Experimentally, the most tractable way to address this issue is by testing for "coarticulation." In this case the question is the following: does the first segment of movement sequence ST-1–2 differ from the first segment of movement sequence ST-1–3? If so, one can go on to ask whether this difference somehow facilitates the performance of the second segments.
The term coarticulation is derived from studies of speech, where the analysis of speech sounds, or of movements of the articulatory apparatus, has revealed many cases of anticipatory modification of phoneme production in preparation for the following phoneme (e.g., Kent and Minifie 1977; MacNeilage 1980). Surprisingly, however, previous studies of hand and finger movements have revealed a much more modest amount of coarticulation for typing and playing the piano (Engel et al. 1997; Soechting and Flanders 1992), suggesting that the arm motor system may be more limited in this regard. This study sought to determine whether the drawing of angles and triangles would exhibit coarticulation, and if so, whether this would be manifested at the level of hand path kinematics or at the level of joint configurations (and therefore joint torques). Thus we studied the kinematics and kinetics of a point-to-point movement in cases where it was followed by various other movements. When coarticulation was observed, we went on to test the hypothesis that the anticipatory changes in the first movement facilitated the energetic efficiency of the following movement.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Six right-handed subjects (3 males and 3 females) participated in the experiment and began by signing the consent form approved by our human subjects committee. The ages ranged between 19 and 33 yr (mean age, 26 yr). All subjects had normal or corrected-to-normal vision and reported no history of neuromotor arm dysfunctions. Body mass ranged between 57 and 80 kg (mean body mass, 72 kg), and height ranged between 1.57 and 1.83 m (mean body height, 1.72 m).
Procedure
Subjects were seated in a comfortable chair and were asked to move a hand-held pen to targets. Targets consisted of balls with a radius of 2.25 cm that were either attached to the tip of a 6-joint robot arm (CRS, type 465) or hanging from the ceiling. In both cases, subjects were asked to stop just short of each target (i.e., not to actually touch it with the pen).
Three-dimensional positions of reflective markers were recorded at a rate of 60 Hz using a four-camera system from Motion Analysis. Markers were positioned at the shoulder, elbow, wrist, and on the tip of the hand-held pen. Wrist flexion/extension was prevented by a brace. A rod with markers at both ends was attached to the wrist brace perpendicular to the forearm to measure pronation.
Experimental conditions
Three different tasks were performed: single segments, double segments, and triangles. In all tasks, a central target position (T) was always the endpoint of the first segment (see Fig. 1 for target locations). There were two positions from which the first segment could start: starting target 1 (ST1) and starting target 2 (ST2). There were four final target positions that served as the endpoints of the second segment (A, B, C, and D). The third segment (only for the triangles) was back to the initial starting position (see Fig. 6). Thus there were two different first segments, eight different segment pairs, and eight different triangles. In the figures, the subject's shoulder is located at the origin. The length of the first and second segments was always 30 cm. The length of the third segment of the triangle varied.
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SINGLE SEGMENTS. All subjects started with the single-segment condition, followed by the double-segment condition, and then the triangles. In the single-segment condition, all targets were presented by the robot. The robot tip pointed at ST1 or ST2, and the subject moved the pen tip to a position in front of the ball attached to the robot tip. The robot tip moved to the central target position (T). As soon as the robot stopped moving, the subject moved the pen tip as fast as possible to the robot tip. Immediately after the subject's pen tip arrived at T, the robot tip quickly moved to a final target location (A, B, C, or D), followed by the subject's arm movement as soon as the robot stopped moving. Each of the eight possible segment pairs were presented in random order and repeated 10 times. Thus in the single segment condition, subjects performed the first movement segment without any information about which second movement segment would be required.
DOUBLE SEGMENTS. In contrast, in the double-segment condition, the second target position was known before the subject started making the first movement (to see if this would influence the first movement). Balls hanging from the ceiling indicated the starting target position and central target position, while the robot tip presented the final target. After a starting signal, the subject was to move to the starting position (ST1 or ST2), hold there while the robot moved to the final target position, and move first to the central target (T) and then to the final target (A, B, C, or D). We instructed subjects to use the same speed as in the single-segment condition. Because the experimenter had to physically place and remove the balls that indicated the starting positions (at ST1 or ST2), the double-segment movements were presented in eight alternating blocks, one-half with ST1 and one-half with ST2 as the starting positions. The final target positions were randomized within each block. Each segment pair was executed 15 times.
TRIANGLES. Finally, in the triangle condition, the robot tip drew the entire triangle: from the starting position to the central target (segment 1), to one of the second target positions (segment 2), and back to the initial starting position (segment 3). While the robot tip remained at the starting position, the subject was required to draw this triangle five times in a row with the pen tip. The subject then had a brief rest with the arm in a relaxed position. For all eight triangles, this sequence of five triangles was repeated four times consecutively, to see if there was any adaptation.
Data analysis
The position data of the shoulder, elbow, wrist, pen tip, and both markers on the wrist brace were low-pass filtered (3rd order; cut-off frequency, 10 Hz). The tangential velocity was calculated by differentiation of the pen-tip displacement, and acceleration was calculated by double differentiation. The beginning and end of a movement segment were determined as follows. First, the peak was detected in the velocity profile. The beginning was defined as the moment when the pen-tip velocity exceeded 5% of peak velocity, and the pen-tip acceleration exceeded 10% of peak acceleration. The end was defined as the moment when the velocity decreased below a threshold of 5% of peak velocity, and the deceleration was lower than 10% of peak acceleration.
We used the first movement segments of the single-segment, double-segment, and triangle conditions to compute kinematic parameters related to path shape and arm posture. For a measure of the overall path shape, we calculated the maximum deviation perpendicular to a straight line connecting the start and end of the movement. To focus on the end of the first movement segment, the final approach direction was calculated, defined as the angle between a line fitted to the final four position samples and a horizontal plane (Fig. 2, left). As a measure of arm posture, we calculated the angle between an earth vertical plane through the shoulder and pen tip and a plane through the shoulder, elbow, and pen tip. This parameter (the angle of the "arm plane") can be thought of more easily as how high the elbow is lifted to the side.
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= 0.0083 (i.e., = 0.05/6.00). Simulations
In the sections below, we will demonstrate that only one of the three parameters (hand path, approach angle, or arm posture) exhibited consistent coarticulation effects. We will show that as the hand approached the central target, T, the elbow was lifted higher when the next movement would be to the upper left target (D), rather than to the rightward targets (A, B, and C). Because this was a consistent result, we sought to determine whether this change in arm posture at T facilitated the movement from T to D, in terms of energetic efficiency. We had previously developed a computational model of the inertial characteristics of a human arm with four degrees of freedom (3 at the shoulder and 1 at the elbow), which allowed us to calculate the peak kinetic energy associated with a particular point-to-point arm movement between targets in 3D space (Flanders et al. 2003; Soechting et al. 1995). Kinetic energy (KE) was calculated as
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is the joint angular velocity vector, and I is the inertia tensor. In a movement with a bell-shaped velocity profile, peak kinetic energy occurs halfway through the movement.
In previous papers (Flanders et al. 2003; Soechting et al. 1995), we explained that for a particular hand path, the arm may follow a range of trajectories of whole arm postures, each of which is associated with a unique value of kinetic energy. Due to differences in arm inertia along the various rotation axes, for a given hand trajectory, some whole arm trajectories are more energetically efficient than others (i.e., they are "easier" and have lower kinetic energy).
In this study, we used the computer model described by Flanders et al. (2003). We simulated movements from target T to target D for comparison with movements to target B. We used a range of arm postures with the hand at the central target T and a range of arm postures with the hand at either target D or target B. We then simulated a movement with a smooth (cosine-shaped) speed profile by having the elbow and shoulder rotate in-phase with one another. We used a movement time of 500 ms. For these simulations, arm posture was defined by taking a vector normal to the plane of the shoulder, elbow, and pen markers, and then calculating the angle this vector made with the horizontal plane. This parameter differs only slightly from the measure of arm posture described above for the primary data analysis. In both cases, a vertical arm plane is 0°, and for a given hand location, the angle of the arm plane increases as the elbow is raised.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Hand paths for double segments
To give an idea of what the hand paths looked like, Fig. 1 presents all of the movements in the double-segment condition performed by subject 1. The top panels show all movements starting from ST1, with the left panel showing a view from behind (i.e., the subject's view), and the right panel showing a view from the subject's right. The bottom panels show the same views for movements starting at ST2. First and second segments of one movement sequence are shown in the same color. If there was significant coarticulation in this double-segment condition, the first segment would be different depending on the segment to follow. Focusing on the top right panel, one can distinguish a cluster of blue lines that seem to form a group slightly to the right of the other colors, near the end of the first segment. However, in other cases it is difficult to distinguish among the first segments that precede movements to different second targets (A, B, C, or D).
To test whether the hand path shapes of the first segments were different when the second segments went to different targets, we compared the path curvatures. Table 2 shows that no significant (NS) differences were found for any of the six subjects when the significance level was corrected for multiple comparisons (P > 0.05/6.00). Thus for the double-segment condition, we did not find an effect of the segment to follow on the overall path curvature. As mentioned above, we also examined the hand speed profile for each first segment. These profiles were similar to those presented below (in Fig. 7) for triangles and did not differ in shape (duration, peak velocity, or time to peak velocity) depending on the segment to follow.
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Approach angles for double segments
Since one might expect coarticulation to be most pronounced at the transition between segment 1 and segment 2, we next focused on the final part of the first segment. The left part of Fig. 2 shows (for subject 2) mean hand trajectories of first segments from ST1, with different segments to follow. The relative locations of the second targets are also indicated, with targets A, B, and C to the right and target D up and to the left. The bottom panel shows a close up of the final part of the path. It can be seen that, for this subject, the final part of the first segment curved toward the second segment: the first segments of A, B, and C curved to the right, where the final targets A, B, and C were located, whereas the first segment of D curved more to the left, with the approach angle for D being smaller. A smaller approach angle for second target D is consistent with a strategy of rounding the initial downward and leftward movement to turn the path horizontal before moving up and to the left. However this strategy was not seen in all subjects.
In the right part of Fig. 2, we summarize the approach angles of all subjects, with filled symbols for first segments starting at ST1 and open symbols for first segments starting at ST2. The two horizontal lines in each plot depict the approach angles when coming in a straight line from ST1 (top lines) or ST2 (bottom lines). The ANOVA test results are indicated in each plot and also given in Table 3; significant differences were found in one-half of the tests. However, in Fig. 2, one can see that the nature of this coarticulation was different for different subjects. For example, in some cases, the smallest approach angle was for the D sequence, while in other cases, the smallest approach angle was for the C sequence.
Arm postures for double segments
Thus far, we have concentrated on overall and local path shape. Since coarticulation might be aimed at joining or facilitating the entire arm movement and not just the movement of the pen tip, we also looked at arm posture, more specifically at the spatial orientation of the arm plane during the first movement segment. Using representative data (from all ST2 first segments of subject 6), Fig. 3 shows the spatial orientation of the whole arm (i.e., of the plane containing the shoulder, elbow, and pen tip) as it changed across time during the course of the first movement. The initial part of the arm plane trajectory was similar for all movement sequences, but the traces diverged about halfway through the normalized movement time. By the end of the movement, the arm plane for movement sequence D was significantly more elevated, i.e., the elbow was raised higher.
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Figure 4 summarizes this sequence effect on arm posture for all subjects by showing final arm plane angles for all first movement segments (see also Table 4). In contrast to the situation for approach angle, for arm posture, we found significant coarticulation in more than one-half of the cases. Moreover, for arm posture, the nature of this coarticulation was consistent across subjects. In each case where there was a significant difference (marked with asterisks in Fig. 4), the sequences ending on target D exhibited a more elevated arm plane at the end of the first segment. In only 4 of the 12 cases did the differences fail to reach statistical significance (marked as "NS" in Fig. 4), and in 3 of these 4, sequences ending on target D still exhibited a more elevated arm plane on average. This means that the elbow was almost always raised higher at the end of the first segment when the following segment went up and to the left than when the following segment went to the right or down.
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At what point during the first segment does this anticipatory modification begin? In the double-segment condition, the subject saw the second target before starting the first movement. Therefore the arm posture at the start of the first segment might have already been modified according to the second segment. Although the data in Fig. 3 suggest that this was not the case, we also examined this issue for all subjects and conditions by comparing the arm postures at various points in time across the conditions with different second segments (A, B, C, and D). For each subject, we did an ANOVA (with significance levels corrected for multiples comparisons) comparable with those presented in Tables 2, 3, 4 for the other parameters. At the beginning of the movement and at 25% of the movement time, we found a significant effect of the second segment in 0 of the 12 tests. At 50% of the movement time, we found a significant effect in 2 of the 12 tests (only for subjects 3 and 6). However, at 75% of the movement time, 5/12 tests were significant compared with the 8/12 significant differences in the final posture (see Fig. 4). Thus the difference was gradually manifested only after the first segment had begun and was most evident at the end of this segment (see Fig. 3).
Evaluation of kinetic energy for double segments
Since this effect on arm posture was consistent across subjects, it may be possible to propose an explanation for this phenomenon. Thus we sought to determine whether ending in a more elevated arm posture would energetically facilitate the movement to target D. We performed a simulation to estimate the peak kinetic energy of hypothetical reaching movements (500 ms duration) from central target T to target D, or for comparison, to target B. In the simulation, the hand was assumed to start and end on target, and the elbow and shoulder joint were assumed to rotate in phase with one another (see METHODS). In Fig. 5, we show the simulation results obtained using the biomechanical parameters (arm inertias) of the two subjects with the most pronounced coarticulation effects (subject 3 in the top row and subject 6 in the bottom row). Peak kinetic energy is plotted in gray scale (with lighter colors for lower energy). Peak kinetic energy is a function of the starting arm posture at T (vertical axis) and final arm posture at B or D (horizontal axis).
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Focusing first on the movements to target B (left column), a broad range of combinations of initial and final arm plane values (roughly along the diagonal) corresponds to equally low-energy movements. The actual arm postures (asterisk symbols) for these movements had relatively low values of arm plane angle (around 20–30°, with 0° corresponding to a vertical arm plane).
In contrast, for the movements to target D (right column), the simulations for both subjects showed an energy minimum for movements that began and ended at a relatively elevated arm plane. Thus for movements of a given duration, it would require substantially more energy to start a movement to target D from a more vertical arm plane (i.e., closer to 0°). For target D, the actual arm postures (asterisk symbols) showed arm plane values that were significantly higher than for target B (compare left and right columns and see Fig. 4 and Table 4). By raising the elbow at target T, subjects had brought the actual values for the T to D movement closer to a distinct low-energy zone: 0.75 J for subject 3 and 1.2 J for subject 6 (topright corners of the plots in the right column). Differences in energy values for the two subjects corresponded to the fact that subject 3 had a lower body mass than subject 6.
For subject 3, the first trial to D (marked with a circle and arrow) had a lower arm plane value (around 30°) than subsequent trials (around 50°). In terms of peak kinetic energy, this moved subject 3 from the 0.90 – 0.95 J range to the 0.85–0.90 J range. Subject 6 also showed a slight upward shift after the first movement (circle), with a modest savings of kinetic energy. In neither case did the actual values reach the lowest energy zone.
Drawing triangles
In contrast to the double segments, each of the eight different triangles was drawn repetitively, with only one of the three targets present during the drawing. As mentioned above, in the triangle condition, coarticulation effects were highly significant for all parameters (Tables 2, 3, 4). However, the type of anticipatory modification was different for different subjects. In terms of hand path curvature (Table 2), the first segments of triangles were most curved when they involved target D for one-half of the subjects and when they involved target A for the other half of the subjects (data not shown). Anticipatory changes in approach angles and arm postures were also idiosyncratic.
In Fig. 6, we show two examples of the triangle drawings. Hand paths are viewed from three perspectives (top, behind, right) for subject 2 (top row) and subject 6 (bottom row). All data are from the third series of five-triangle drawings (we did not notice any adaptation across the 4 series). It is apparent from the top and right views that subject 2 rotated the triangle toward the frontal plane instead of moving the hand in the more oblique plane specified by ST1 and the virtual target locations of T and A. One other subject, subject 4, exhibited the same phenomenon. Subject 2 drew the triangles more slowly than any of the other subjects (and more slowly than his own singles and doubles), but subject 4's triangle drawing was relatively fast (Table 1).
Figure 6 also shows examples of idiosyncratic final approach angles: some subjects tended to round the corners while others exhibited more acute angles, or even loops. An extreme case of loops is shown in the bottom of Fig. 6, for subject 6. In Fig. 7, we show the hand speed profiles for the 3 x 5 segments that correspond to the drawings in Fig. 6 (with subject 2 in the top panel and subject 6 in the bottom panel). Even for the slowest subject (subject 2), there was generally no pause between segments. Subject 6 sometimes paused, or perhaps made corrections, at the first (ST1) target (time points circled in Fig. 7), since this target was physically present during the drawing. However, she did not pause within each triangle.
The most consistent feature of the triangle drawing was a tendency to accumulate changes in arm posture across consecutive repetitions of the triangle (Fig. 8). Neither the initial nor the final arm plane was stable across repeated drawings of triangles. This was obviously true in at least one-half of our subjects. Although there were some individual differences, the magnitude of this phenomenon generally differed depending on which particular triangle was being drawn (e.g., ST1-T-A or ST1-T-D).
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In the triangle drawing condition, the subject rested (with the arm back at his or her side) at the end of each five-triangle drawing, and then (after being shown the targets again) repeated the same drawing. Thus each of the plots in the bottom of Fig. 8 is broken into four sets of five data points. In most cases the postural changes accumulated during the continuous drawing, i.e., the elbow started higher and higher for the second, third, fourth, and fifth triangle in each series. In some cases, this progressive change appeared to plateau at a high angle or to suddenly reset to a lower angle during a five-triangle sequence. In most cases, the arm returned to its normal initial position after the rest period.
We quantified this effect by fitting a regression line to each set of five consecutive initial arm planes. As shown in the top of Fig. 8, using grand means (±SD) across all subjects, the slopes were consistently positive for the triangles including targets B and C, both with the ST1 starting targets (left) and the ST2 starting targets (right). The S-T-B and S-T-C triangles were drawn in a counterclockwise direction when viewed from behind the subject (cf., Fig. 1). Interestingly, the S-T-D triangles were drawn in a clockwise direction and were not associated with a progressive elevation in initial arm plane (slope values near 0 in Fig. 8). However, although the ST1-T-A triangle and the ST2-T-A triangles were both drawn in the counterclockwise direction, one (ST1) was associated with a relatively large accumulation of changes in arm posture, while the other (ST2) was not. This suggests that the accumulation was a function of the geometry of the triangle and not just the direction of the drawing.
In summary, in the triangle condition, coarticulation effects were highly significant for all parameters, but the type of anticipatory modification was different for different subjects. This may be related to the fact that target locations T and A, B, C, or D were from memory, and the triangle drawings were repeated many times in succession. The most consistent feature of the triangle drawing was the tendency to accumulate changes in arm posture (i.e., to gradually raise the height of the elbow; Fig. 8).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Coarticulation was found in multiple aspects of drawing triangles but not double segments. For the double segments, when we evaluated the hand path curvature, we found a distinct lack of coarticulation. When we focused on the angle of approach at the corner between the first and second segments, we found idiosyncratic patterns of coarticulation in one-half of the cases. This represents an individualized joining of the two segments, limited to the transition point. The most robust coarticulation effect was an anticipatory modification in the whole arm posture, which occurred during the movement from the beginning to the end of the first segment.
Joining the segments of arm movement sequences
Because all three targets were visible during the double segments and because subjects were instructed to visit each target in succession, it is perhaps not surprising that there was so little coarticulation in the 3D hand paths. This result can be contrasted with other studies of arm movement sequences, where the second target replaced the first, after the subject began to move to the first. For example, Flash and Henis (1991) showed that their subjects' hand paths could be well fit with a model where a movement from the starting target to the first target was added with a movement from the starting target to the new, second target. However, Feldman and colleagues have emphasized that the control signal for the movement temporally precedes the movement itself (Ghafouri and Feldman 2001) and have shown that similar data can be modeled by assuming that the control signal switches to the new, second target, rather than summing with a continued command to reach the first target (Flanagan et al. 1993). This idea of a switch rather than a summation is also consistent with the interpretation of similar studies involving motor cortical or electromyographic recordings in addition to hand path data (Georgopoulos et al. 1983; Soechting and Lacquaniti 1983).
In this study, neither the hand path nor the hand speed profile of the first segment (to target T) was altered when the second segment was to target D rather than to targets A–C. In terms of final approach angle, in some cases the hand curved toward the next segment, a strategy that would tend to minimize the jerk of the entire hand path (Flash and Hogan 1985). However, in other cases, the hand curved away from the next segment, as if to use elastic energy to help reverse the direction, instead of gradually changing the direction (see Desbiez et al. 1996). Although this was not a consistent finding (Fig. 2, see also Fig. 6), this latter result would suggest a strategy based on optimizing the overall efficiency. This more global strategy can be contrasted to the sequential blending in the cases discussed above, where the second movement simply begins to be executed before the first one is over.
It is difficult to interpret the change in arm configuration during the first movement (Figs. 3, 4, 5) as an early beginning of the second movement. Since the hand path did not change, and the final arm plane at D (i.e., at the end of the second segment) was in fact lower than at the central target T (at the end of the first segment; see Fig. 5), we cannot assume that the elevated arm posture at T was due to an early initiation of the movement to D. Instead we can only report that this postural coarticulation was appropriate for improving the energetics of the second segment (as discussed in Optimizing kinetics).
Segmentation in drawing movements
The present observation of coarticulation of a segmented drawing movement (i.e., an angle) may seem opposite to previous reports of segmentation in smooth drawing movements (e.g., circles and figure eights). In several previous investigations (Morasso 1983; Soechting and Terzuolo 1987a,b; Sternad and Schaal 1999), subjects were asked to draw figure eights, stars, scribbles, and other smooth shapes in the air (by moving the hand in a 3D workspace). Even when the drawing was done under isometric conditions (using a joy stick and a 3D display; Pellizzer et al. 1992), the endpoint trajectory was segmented and each segment was confined to a plane. Although this is a controversial topic (see Richardson and Flash 2002), these results may suggest that motor control is facilitated by stringing together one discrete movement segment after another. However, the fact that the present study showed coarticulation in a segmented drawing, while others have focused on segmentation in smooth drawings may simply suggest that the motor system does both. Perhaps one should envision a hierarchical arrangement where, depending on the task, the cognitive planning and the sensorimotor execution impose various degrees of segmentation and overlap.
Based on a recent study of segmented drawing movements in monkeys (e.g., triangles and squares), Averbeck et al. (2002) suggested that, in consonance with the classical hypothesis of Lashley (1951), all segments are readied in preparation for a movement sequence. Averbeck et al's analysis of recordings from prefrontal cortical neurons showed a partial readiness of all segments that, for each segment, gradually increased and decreased around the time of execution. While this scenario shows temporal overlap of the neural representations of the segments, it does not necessarily suggest a mechanism for anticipatory modification of the kinematics. Since the temporal overlap is presumably at the sequence planning level, the sequence execution could conceivably be triggered in a strictly serial manner, with each segment preserving its own, stereotypical movement kinematics.
Optimizing kinetics
Although hand paths did not vary depending on the upcoming movement, we found substantial variation in the fourth degree of freedom (the spatial orientation of the plane formed by the shoulder, elbow, and hand). As subjects moved the hand from S to T, the series of arm postures differed in a consistent manner depending on whether the next segment was to target D (a movement up and to the left) or to targets A, B, or C (movements to the right). Since the series of arm postures generally followed a simple, nearly linear transition from the start to the end of each segment (Fig. 3), this result implies a more dramatic form of coarticulation than one aimed at rounding out a corner. Instead, this coarticulation united entire segments of the whole arm movement.
We sought an explanation for this phenomenon and found that the coarticulation of arm configuration facilitated the energetics of the second segment. Subjects modified the movement from S to T by ending in a more elevated arm posture at T only when S-T would be followed by T-D. Our simulations showed that the minimum-energy movement from T to D began and ended at an even more elevated arm posture than was observed experimentally (Fig. 5, right column). In contrast, depending on the subject, movements from T to B (Fig. 5, left column) were either of equally low energy for a range of elevations (subject 6) or of slightly lower energy for a lower elevation (i.e., a more vertical arm plane, subject 3).
Several issues should be emphasized with respect to this result. First, although our analysis was based on mechanical kinetic energy, previous studies have shown that a minimization of kinetic energy is similar to a minimization of dynamic muscle forces (Nishikawa et al. 1999; Soechting and Flanders 1998). Furthermore, this type of optimization is in the same spirit as minimization of change in motor commands (Wada et al. 2001) or minimization of variance (Harris and Wolpert 1998). In each case the system tends to avoid large changes in muscle activation.
Second, we would like to emphasize that subjects did not generally achieve the "minimum-energy" posture; in fact in Fig. 5 (right column), the two subjects both fell short by about 40°. Since the ideal was an extremely elevated arm posture (i.e., a very high elbow position), perhaps other constraints, such as anti-gravity torques or comfort, came into play. Thus as previously shown, minimum-energy appears to be a principle that influences the relative kinematics of various reaching movements, without dictating an exact solution (Soechting et al. 1995; Vetter et al. 2002).
A more subtle result of the simulation was to show that some point-to-point movements do not have a distinct low-energy arm configuration (e.g., bottom left panel of Fig. 5). Thus seeking a low-energy solution is more useful in some cases than in others. However, for a given hand path, changing arm configuration is the only way for subjects to alter arm inertia (Mussa Ivaldi et al. 1985). We recently reported that subjects sometimes seek a low-energy state in response to perturbations. For example, our subjects adopted a low-energy arm configuration in the course of adapting to the unusual dynamics of a hand-held gyroscope (Flanders et al. 2003). Surprisingly, however, subjects did not continue to use that low-energy arm trajectory. Instead, over the course of about 200 reaching movements to various targets, they returned to the arm configuration more typically used for each particular target pair. This unexpected reversion from the kinetic optimum to the kinematic norm suggests that there must be multiple constraints, both kinematic and kinetic, that influence the specification of particular arm postures.
Constraining kinematics
The planning and execution of movement sequences could conceivably be facilitated by a kinematic constraint dictating a unique arm posture for each 3D target (or hand) location. Such a constraint is described by Donders' law. This law was derived from studies of saccadic eye movement, where each 2D gaze location corresponds to a unique 3D eye posture (Donders 1848; see also Tweed and Vilis 1987). This has an obvious advantage for a system that produces movements by commanding a particular rotational velocity, with the current posture as the starting point: if the current eye posture is unique to the gaze target, errors (or unusual eye postures) will not accumulate across successive gaze transitions.
Donders' law is relatively robust for saccadic eye movement and is only rarely violated for head movements (Ceylan et al. 2000). However, the law does not hold as well for point-to-point arm movements (see, for example, Admiraal et al. 2002). In the present study, we found that Donders' law was violated when subjects drew five triangles in succession. An accumulation of past arm postures was therefore not prevented, and the height of the elbow often increased over the five successive repetitions of the triangle drawing (Fig. 8).
When subjects make saccadic eye movements or head movements directed to targets arranged on the perimeter of a square, eye torsion plateaus at slightly less than 1° for clockwise gaze paths, and the head torsion plateaus at slightly more that 1° for counterclockwise gaze paths (Desouza et al. 1997). In each case, this gradual accumulation of torsion (over about 3–5 cycles) is much less for tasks where gaze covers the targets in the opposite direction. In our study, the accumulated arm plane rotation was present for counterclockwise drawings but not for clockwise drawings (Fig. 8). For several of the counterclockwise triangles, the accumulation was, on average, about 5° (i.e., about 1° per triangle for 5 successive triangles). However, we may not have given this effect a chance to saturate, since subjects rested and started over after each set of five repetitions. In another recent study, the direction of the accumulation of arm torsion was opposite for series of pointing movements in opposite directions (C.C.A.M. Gielen, personal communication).
Due to the failure of Donders' law, the arm motor system cannot generally rely on a unique mapping from target location to arm posture. Instead, the sensorimotor system is obliged to predict and/or monitor initial arm posture as a starting point for commanding each movement, movement segment, or incremental velocity command for a smoothly changing path.
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ACKNOWLEDGMENTS |
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This work was supported by the National Institute of Neurological Disorders and Stroke Grant R01-NS-27484. M. D. Klein Breteler was also supported by the Dr. I.B.M. Frye Stipendium, a travel grant from the University of Nijmegen, The Netherlands.
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Address for reprint requests: M. Flanders, Dept. of Neuroscience, 6-145 Jackson Hall, University of Minnesota, Minneapolis, MN 55455 (E-mail: fland001{at}umn.edu).
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