Transitions between discrete and rhythmic primitives in a unimanual task

Dagmar Sternad, Hamal Marino, Steven K Charles, Marcos Duarte, Laura Dipietro, Neville Hogan, Dagmar Sternad, Hamal Marino, Steven K Charles, Marcos Duarte, Laura Dipietro, Neville Hogan

Abstract

Given the vast complexity of human actions and interactions with objects, we proposed that control of sensorimotor behavior may utilize dynamic primitives. However, greater computational simplicity may come at the cost of reduced versatility. Evidence for primitives may be garnered by revealing such limitations. This study tested subjects performing a sequence of progressively faster discrete movements in order to "stress" the system. We hypothesized that the increasing pace would elicit a transition to rhythmic movements, assumed to be computationally and neurally more efficient. Abrupt transitions between the two types of movements would support the hypothesis that rhythmic and discrete movements are distinct primitives. Ten subjects performed planar point-to-point arm movements paced by a metronome: starting at 2 s, the metronome intervals decreased by 36 ms per cycle to 200 ms, stayed at 200 ms for several cycles, then increased by similar increments. Instructions emphasized to insert explicit stops between each movement with a duration that equaled the movement time. The experiment was performed with eyes open and closed, and with short and long metronome sounds, the latter explicitly specifying the dwell duration. Results showed that subjects matched instructed movement times but did not preserve the dwell times. Rather, they progressively reduced dwell time to zero, transitioning to continuous rhythmic movements before movement times reached their minimum. The acceleration profiles showed an abrupt change between discrete and rhythmic profiles. The loss of dwell time occurred earlier with long auditory specification, when subjects also showed evidence of predictive control. While evidence for hysteresis was weak, taken together, the results clearly indicated a transition between discrete and rhythmic movements, supporting the proposal that representation is based on primitives rather than on veridical internal models.

Keywords: arm movements; discrete; internal models; primitives; rhythmic.

Figures

Figure 1
Figure 1
Experimental set-up. Subject holds a handle with a magnetic sensor attached that measures and shows its position online on the monitor in front. Subject is instructed to perform discrete movements forward (away from his body) and backward (toward his body), sliding on the horizontal table surface. Movement amplitude is indicated by two large circles on the monitor.
Figure 2
Figure 2
Sequence of metronome intervals and their change in percent. (A) Intervals (blue) and their corresponding percent change (green) displayed as a function of real time. (B) Intervals (blue) and their corresponding percent change (green) as a function of metronome number.
Figure 3
Figure 3
Time series of continuous position over the entire trial of 194 s duration. Red vertical lines indicate the onset of the metronome sounds, the green circles mark the onset and offset of each movement (see methods).
Figure 4
Figure 4
Exemplary kinematic profiles to illustrate details of data analysis. The black line denotes position, the blue line denotes velocity. (A) Movement time, dwell time, and total movement time are demarcated by onset and offset times, shown by red dots. Onset asynchrony is the temporal difference between metronome onset and movement onset. (B) Exemplary profile where detected onset and offset are in close proximity and dwell time is greater than zero (first segment of profile); onset and offset are identical (second segment) and dwell time is zero. Linear regression at this point yields R2 greater than 0.99.
Figure 5
Figure 5
Exemplary trial of one subject to illustrate the landmark events that were used to evaluate the transition from discrete to rhythmic movements. The black solid line represents the instructed movement time; the green data show the dwell time, the blue data denote the movement time. The green line is the linear regression of dwell time between movement number 20 (end of initial steady state interval) and DT = 0Accel; in the decelerating portion between DT = 0Decel and movement number 140 (start of steady state interval).
Figure 6
Figure 6
(A) Simulated profile of a discrete movement to illustrate the definition of the discreteness index, DI: the interval between movement onset and time of first peak acceleration divided by the total movement time. (B) Simulated profile of a rhythmic movement; the discreteness index is zero as the interval between movement onset and peak acceleration is zero. (C) Data profile of a slow movement where the position signal was approximated by a quintic spline and the acceleration profile was the double-differentiated signal. The movement has clearly demarcated dwell times and is discrete. (D) Data profile for a fast movement that was determined to be continuously rhythmic.
Figure 7
Figure 7
Total movement time of all 10 subjects across trial 1 in condition V-short. The green band illustrates the instructed movement time with an envelope of ±350 ms that includes 99% of all data.
Figure 8
Figure 8
Movement time (blue), dwell time (green), and duty cycle (red) of one representative subject in all three conditions. The black line serves as reference denoting the instructed interval.
Figure 9
Figure 9
Movement time (blue), dwell time (green), and duty cycle (red) averaged over all subjects. The black line represents the instructed interval. The shaded areas around movement time, dwell time, and duty cycle denote ± one standard deviation around the mean of 10 subjects.
Figure 10
Figure 10
Discreteness index values of all subjects across metronome number. (A–C) All subjects' values in the three perceptual conditions. (D) A single subject's trial; the vertical lines show the trial segmentation delineated by the time when dwell time is zero. The discreteness indices DI calculated for the three segments are shown.
Figure 11
Figure 11
Onset asynchrony values of all subjects across metronome number. (A–C) All subjects' values in the three perceptual conditions. (D) A single subject's trial with line fits. The linear regressions regressions were performed over the intervals 0–40 and 120–160 of metronome numbers. The red lines are dashed after DT = 0Accel and before DT = 0Decel.

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