Romero DH & Teulings HL (2003). In HL Teulings & AWA Van Gemmert (Eds.), Proceedings of the 11th Conference of the International Graphonomics Society, pp. 103-106, Scottsdale, Arizona: IGS.

Submovement Analysis in Goal-Directed Pen Movements

1. Introduction

Woodworth (1899) long ago noted that the execution of a manual goal-directed movement could be parsed into two smaller subsections: the primary and secondary submovements. The primary submovement is a rapid, ballistic movement that brings the limb into the vicinity of the target. It is considered to be planned prior to movement onset, and is error-prone. The secondary submovement is a corrective movement that acts as a homing-in of the limb to the target. The secondary submovement is based on feedback at the expense of time. Meyer’s (1988) Optimized Submovement Model proposed that goal-directed movements are planned on a combination of primary and secondary submovements that minimize total movement duration. Numerous studies have measured the kinematics of primary and secondary submovements for a more detailed analysis of the movement structure. The cumulative results support the contention that submovement parsing provides an indication of the integrity of the motor system, such that aging and neurological disease negatively affect the relative distance and duration of the preplanned portion of the movement, namely, the primary submovement (Romero et al., 2003; Seidler-Dobrin et al., 1998).

2. Experiment

Participants. Eight right-hand dominant, healthy adults between 21 – 38 years of age participated in the experiment after informed consent.

Equipment. Stimuli were presented on a ViewSonic VX2000 50.8-cm LCD display set at 1600x1200 pixels and 60 Hz vertical refresh rate. The display was positioned in front of the participant at a distance of 50 cm. Writing movements were recorded using a Wacom Intuos2, XD-0608-U display with an active area of 20.32 cm x 15.24 cm. The sampling rate was 102 Hz. The resolution was 0.001 cm and the RMS error <0.1 cm. Data were collected on a 3.0 GHz Intel4 PC with Windows XP. The recording and analysis of pen movements were done using MovAlyzeR (Teulings, 2003).

Stimuli. The stimulus was presented in real-size on the computer monitor. The stimuli consisted of square targets either 0.3 cm (“small”) or 2.5 cm (“large”) in size for a center-to-center distance of 3 cm (see Figure 1). The target sizes and distance corresponded to an Index of Difficulty (Fitts, 1954) of 1.26 for the large targets and 4.32 for the small targets. Targets were positioned in four directions around a home target, so that a center-to-center straight line corresponded to angles of 45°, 135°, 225°, and 315°. Movements in the 45° and 225° directions were produced by extension and flexion, respectively, of the wrist. Movements in the 135° and 315° directions were produced by extension and flexion, respectively, of the fingers. The home target was a filled-in square, 0.3 cm in size, and did not change position. The independent variables thus resulted in a 2 (size) x 4 (direction) experimental design.

Figure 1. Experimental conditions. Participants initially were presented with the home target (center, filled-in black square) and one target (outlined square), depicted as the Pre-cue. Depicted are three targets in the small size, and one in the large size. Targets were either small or large, and positioned in one of four locations around the home target. Target directions corresponded to 45° - upper right, 135° - upper left, 225° - lower left, and 315° - lower right. Targets in the 45° and 225° directions were performed by a wrist movement; targets in the 135° and 315° directions were performed using finger movement. Targets turned green (Imperative Stimulus) to signal the participant to begin the movement.

Procedure. Participants were seated comfortably in a chair in front of the digitizer tablet, on which they had to make fast and accurate strokes with the digitizer pen from the home position to the target, which were displayed on the computer monitor. Participants held the digitizer pen in a normal pen grip with their dominant hand. A trial began with the presentation of both the home target, and the target to be pointed to, as the precue. The participants were instructed to place the pen on the home position during this precue period. The target initially appeared in outline form for the 2 s precue period, after which it turned into a filled-in green square as the imperative stimulus which indicated “go”, and at which point recording of the trial began. Upon the color change, the participant drew a line from the home position to the target, which turned black when the pen entered the target. After a 2 s recording period, a beep was emitted indicating the end of the trial and the participant moved the pen back to the home position. Participants initially performed three practice trials of each of the eight experimental conditions. The actual experiment consisted of 15 trials of each condition, which were presented in a randomized order. Participants were instructed to execute the movement to the target as quickly and accurately as possible. The entire experiment took approximately 15 minutes per participant to complete.

Analysis. The pen movements were low-pass filtered at 12 Hz (transition band 5 Hz to 16 Hz), differentiated, and velocity and acceleration curves were estimated. Stroke segmentation was at points where the vertical velocity passed through zero. Subsequent zero crossings within 0.04 seconds were discarded. A stroke was further segmented into primary and secondary submovements by the first negative-to-positive zero crossing after absolute peak velocity, in the acceleration profile. Duration and distance were estimated for the entire stroke and for each submovement. Distance of the movement was considered the vector length from the start to end positions. The relative duration and size of the primary submovement were defined as T1/T and S1/S, respectively, where T1 and S1 are the duration and size of the primary submovement and S and T the duration and size of the entire stroke, respectively.
Trials were automatically discarded if the number of strokes was greater than one or if the participant moved prior to the imperative stimulus. In total, less than 5% of trials were eliminated from analysis. Statistical analyses were performed using SPSS for Windows, with significance set at a = 0.05.

3. Results

Effects of size
Duration of the overall movement was significantly influenced by size (F1,7 = 47.8, p < 0.001), with increased duration to small targets compared to large (see Figure 2). When parsed into primary and secondary submovements, both exhibited prolonged durations in the small targets relative to the large targets (F1,7 = 15.8, p = 0.005, and F1,7 = 44.9, p < 0.001, respectively).

Figure 2. Movement duration for the primary submovement (Submovement 1), secondary submovement (Submovement 2), and the overall movement (Submovement 3). Conditions for all graphs are as follows: 1 and 5 = 45°, 2 and 6 = 135°, 3 and 7 = 225°, and 3 and 8 = 315°. Conditions 1 - 4 were movements executed to large targets, conditions 5 - 8 were executed to small targets.

In contrast to the duration results, overall movement distance was not significantly affected by target size (p > 0.05; See Figure 3). This is important as it confirms that the subjects were producing movements of the same distance regardless of target size. Distance of the primary submovement, however, was different depending on target size (F1,7 = 17.2, p < 0.01), with an increased distance to large targets. Correspondingly, a longer distance was covered in the secondary submovement to small targets compared to large targets (F1,7 = 33.8, p < 0.001).

Figure 3. Movement distance for the total movement, primary and secondary submovements. Distances were computed as the vector between the start and end pen positions.

Peak acceleration was much greater with movements executed to large targets, and occurred during the primary submovement (F1,7 = 36.8, p < 0.001; see Figure 4). The relative time-to-peak velocity was significantly shorter for movements to small targets, occurring at 29% of the overall movement duration, compared to 40% for the large targets (F1,7 = 79.8, p < 0.001).

Effects of direction
Duration was influenced by direction (F3,21 = 8.4, p < 0.001), with finger movements prolonged compared to wrist movements (see Figure 2). Pair-wise comparisons showed that the finger extension movement (135°) was significantly prolonged compared to both directions utilizing wrist movements (i.e., 45° and 215°, p < 0.05).

Primary and secondary submovements demonstrated similar results, with main effects of direction (F3,21 = 4.34, p < 0.05, and F3,21 = 4.06, p < 0.05, respectively). Bonferroni-corrected pair-wise comparisons did not yield significant differences for the primary submovement, however, duration of the secondary submovement was significantly increased in the finger extension (135°) condition compared to the wrist flexion (215°) condition (p < 0.05).

Movement distance did not exhibit a main effect of direction (p > 0.05). Distance of the primary submovement differed depending on direction (F3,21 = 3.07, p < 0.05), although pair wise comparisons did not yield significant differences. A marginal trend for an effect of direction was evident for the distance of the secondary submovement (F3,21 = 2.75, 0.05 < p <0.1).

Peak acceleration was decreased in the 135º finger extension direction (F3,21 = 7.9, p < 0.001), with pair wise comparisons indicating reduced acceleration compared to the wrist extension (45º) and finger flexion (315º) conditions (p < 0.05 and p < 0.01, respectively). A size by direction interaction was also significant (F3,21 = 10.2, p < 0.001; see Figure 4).

Figure 4. Peak acceleration for each of the experimental conditions. A size by direction interaction was due to a reduced peak acceleration in the finger extension to a large target (Condition 2).

The relative time-to-peak velocity exhibited a main effect of direction (F3,21 = 10.4, p < 0.001), with pair wise comparisons indicating that it occurred earlier in the 315° finger flexion condition (31% of the overall movement duration) compared to the 135° finger extension condition (36%; p < 0.05) and wrist flexion condition (38%; p < 0.01).

4. Discussion
The results of the current experiment reproduce the well-established speed-accuracy trade-off, such that high-accuracy movements took longer to execute than those requiring low-accuracy. The results further demonstrated that short movements executed with the fingers were prolonged in duration compared to those produced with the wrist. Parsing the movement into primary and secondary submovements provides a more detailed analysis of the movement kinematics. In the current example, the parsing results indicated that the kinematic structure of the movement changed depending on target size and the effector executing the movement. The primary submovement, considered to be planned prior to movement onset, decreased in duration with an increase in distance, in both the low accuracy and wrist movement conditions. Thus, participants were able to cover a longer portion of the movement in a shorter amount of time. The current results support those of Dounskaia et al. (2000) and Teulings et al. (1988), in that wrist-only movements exhibit higher performance levels than finger-only movements. This result may be attributed to increased complexity in fingers-only movements, which entail an increased number of degrees of freedom compared to wrist-only movements. The results of the current experiment provide evidence that submovement analysis is an effective tool for processing of goal-directed movements.

5. References
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