Balancing out dwelling and moving: optimal sensorimotor synchronization

Abstract

Sensorimotor synchronization is a fundamental skill involved in the performance of many artistic activities (e.g., music, dance). After a century of research, the manner in which the nervous system produces synchronized movements remains poorly understood. Typical rhythmic movements involve a motion and a motionless phase (dwell). The dwell phase represents a sizable fraction of the rhythm period, and scales with it. The rationale for this organization remains unexplained and is the object of this study. Twelve participants, four drummers (D) and eight nondrummers (ND), performed tapping movements paced at 0.5-2.5 Hz by a metronome. The participants organized their tapping behavior into dwell and movement phases according to two strategies: 1) Eight participants (1 D, 7 ND) maintained an almost constant ratio of movement time (MT) and dwell time (DT) irrespective of the metronome period. 2) Four participants increased the proportion of DT as the period increased. The temporal variabilities of both the dwell and movement phases were consistent with Weber's law, i.e., their variability increased with their durations, and the longest phase always exhibited the smallest variability. We developed an optimal statistical model that formalized the distribution of time into dwell and movement intervals as a function of their temporal variability. The model accurately predicted the participants' dwell and movement durations irrespective of their strategy and musical skill, strongly suggesting that the distribution of DT and MT results from an optimization process, dependent on each participant's skill to predict time during rest and movement.

Keywords: motor control; optimality; psychophysics; rhythmic movements; synchronization.

Fig. 1.

A: task apparatus, showing a subject seated at the table tapping on a hard rubber band. B: time course of a typical preferred frequency (PF, top), and fixed frequency (FF, bottom) trial. T, metronome period; ITI, intertrial interval. C: definitions of kinematic landmarks: contact (open circle), movement onset (filled circle), peak amplitude (gray circle), and position of peak upswing (up triangle) and downswing (down triangle) velocity. Definition of time intervals: cycle time (CT) is the time between 2 successive contacts; dwell time (DT) is the time between preceding contact and onset; movement time (MT) is the time between onset and contact; asynchrony (AS) is the time between acoustic cue (vertical dashed line) and contact (measured negative when contact occurs before the cue). D: 2 sample trajectories at a small (SA) and a preferred (PA) amplitude for 2 typical subjects. Note that the subjects follow different motor strategies to synchronize, by dwelling in contact with the rubber band (zero elevation) (subject S9) or by making overall slower movements (subject S5).

Fig. 2.

A: asynchrony (temporal synchronization error) as a function of interval duration [in s: 0.4 (purple), 0.5 (blue), 0.67 (green), 1 (yellow), 2 (red)] for 2 subjects. Dashed line, diamond, SA; solid line, circle, PA, dashed line, square, larger than free amplitude (LA). Note the very small SE bars plotted at each dot. B: same as A, averaged across subjects. C: comparative analysis of the asynchrony for drummers (open symbols) and nondrummers (filled symbols) as a function of the metronome period for SA (left), PA (center), and LA (right) trials. Kolmogorov-Smirnov (KS) test: **P < 10⁻¹⁰.

Fig. 3.

A: peak movement amplitude as a function of interval duration for a single subject. Colors and symbols as in Fig. 2. Solid line, PA; dashed lines, SA and LA. Filled black symbols correspond to PF conditions. B: average amplitude across subjects. Distributions across trials and subjects are shown as Gaussian curves (using mean and SD of pooled data). Open symbols correspond to PF data (amplitude vs. actual period).

Fig. 4.

A: upswing (left) and downswing (right) peak velocities as a function of interval duration averaged across subjects. Same format as Fig. 3B. B: comparison between upswing and downswing peak velocity. Black symbols correspond to the PF data. C: comparative analysis of peak upswing (top) and downswing (bottom) velocity for drummers vs. nondrummers for each amplitude condition. KS test: *P < 0.01, **P < 10⁻¹⁰. Note that the period in the PF condition (black symbols) is not in general the same for drummers and nondrummers.

Fig. 5.

A: time to upswing and downswing peak velocities as % of upswing and downswing duration, respectively, as a function of metronome period, for 3 subjects. Color codes are as in Fig. 2. Black symbols correspond to PF data. B: average velocity profiles during MT for each metronome period, normalized to fit the same time interval.

Fig. 6.

A: MT and DT as a function of interval duration for 3 subjects, with regression lines. Numbers at top are R² coefficients. Color codes are as in Fig. 2. Black symbols correspond to PF data. B: MT and DT expressed as % of CT for the same 3 subjects. C: MT and DT expressed as % of CT for each subject. Unlike in A, colors indicate individual subjects.

Fig. 7.

A: MT and DT standard deviation (std) for 3 subjects as a function of MT and DT, respectively, with regression lines. Numbers at top are R² coefficients. Color codes are as in Fig. 2. B: same as Fig. 6A and model predictions (black for MT, gray for DT).

Fig. 8.

A: accurate model fit for 2 subjects with MT >> DT. Same format as Fig. 7A. B: accurate model fit for 2 subjects with MT ≈ DT. C: loose model fit for 2 subjects. D: efficiency metric (black, MT; gray, DT) for each subject and amplitude (from top to bottom). Dashed line indicates the 90% efficiency threshold. Results from the qualitative analysis are indicated by the category (1, MT >> DT; 2, MT ≈ DT; +, accurate; −, nonaccurate; *, missing data). Negative efficiencies are omitted.

Fig. 9.

Summary of reaction time (RT) control task results. A: peak movement amplitude as a function of interval duration for both subjects and related MTs as a function of interval duration (black, 1 s; gray, 2 s). Note that SE bars at each dot are very small. Diamond, SA; circle, PA; square, LA. B: MT (filled symbols) and DT (open symbols) expressed as % of CT for PA amplitude as a function of metronome period for both subjects. C: average velocity profiles during MT for both metronome periods (amplitude PA), normalized to fit the same time interval. D: time to upswing (open symbols) and downswing (filled symbols) peak velocities for PA amplitude as a function of metronome period for both subjects.