Proximal-distal differences in movement smoothness reflect differences in biomechanics

Abstract

Smoothness is a hallmark of healthy movement. Past research indicates that smoothness may be a side product of a control strategy that minimizes error. However, this is not the only reason for smooth movements. Our musculoskeletal system itself contributes to movement smoothness: the mechanical impedance (inertia, damping, and stiffness) of our limbs and joints resists sudden change, resulting in a natural smoothing effect. How the biomechanics and neural control interact to result in an observed level of smoothness is not clear. The purpose of this study is to 1) characterize the smoothness of wrist rotations, 2) compare it with the smoothness of planar shoulder-elbow (reaching) movements, and 3) determine the cause of observed differences in smoothness. Ten healthy subjects performed wrist and reaching movements involving different targets, directions, and speeds. We found wrist movements to be significantly less smooth than reaching movements and to vary in smoothness with movement direction. To identify the causes underlying these observations, we tested a number of hypotheses involving differences in bandwidth, signal-dependent noise, speed, impedance anisotropy, and movement duration. Our simulations revealed that proximal-distal differences in smoothness reflect proximal-distal differences in biomechanics: the greater impedance of the shoulder-elbow filters neural noise more than the wrist. In contrast, differences in signal-dependent noise and speed were not sufficiently large to recreate the observed differences in smoothness. We also found that the variation in wrist movement smoothness with direction appear to be caused by, or at least correlated with, differences in movement duration, not impedance anisotropy.NEW & NOTEWORTHY This article presents the first thorough characterization of the smoothness of wrist rotations (flexion-extension and radial-ulnar deviation) and comparison with the smoothness of reaching (shoulder-elbow) movements. We found wrist rotations to be significantly less smooth than reaching movements and determined that this difference reflects proximal-distal differences in biomechanics: the greater impedance (inertia, damping, stiffness) of the shoulder-elbow filters noise in the command signal more than the impedance of the wrist.

Keywords: filter; impedance; jerk; kinematics; smoothness.

Fig. 1.

Experimental setup for wrist movements (A) and reaching movements (B). A. Subjects rotated their wrist in combinations of flexion-extension (FE) and radial-ulnar deviation (RUD) to point to targets on a screen. Each movement required 15° of wrist rotation. B: subjects also made planar shoulder-elbow (reaching) movements toward targets. Each movement required 14 cm of displacement of the hand. Both wrist and reaching movements included fast, medium, and slow movements (durations of 300, 550, and 900 ms, respectively).

Fig. 2.

To understand the effect of signal-dependent noise on movement smoothness, we modeled wrist and reaching movements using feedforward and feedback control according to (Tee et al. 2004). Variables q_u and q represent the desired and actual joint trajectories, with error e representing the difference. The feedforward torque τ_FF, feedback torque τ_FB, and signal-dependent noise torque τ_N sum to the control torque τ_C.

Fig. 3.

Examples of fast, medium, and slow wrist and reaching movements. Shown are the magnitude of the displacement, velocity, acceleration, and jerk vectors. The difference in smoothness is most easily seen in the speed profiles. All movements are outbound movements to target 1 (Fig. 1) made by the same subject. The circles in the top row indicate the start and stop of the movement based on 10% of maximum speed. To allow for better comparison of fast, medium, and slow acceleration and jerk, we added vertically offset versions as insets (each triad was scaled together).

Fig. 4.

Direct comparison of wrist (thick solid line) and reaching (dashed line), with equivalent minimum-jerk trajectories (thin solid line) for reference. Wrist and reaching movements are scaled in magnitude to have matching equivalent minimum-jerk trajectories. All movements are outbound movements to target 1 (Fig. 1) made by the same subject (same movements as in Fig. 3). The circles in the top row indicate the start and stop of the movement based on 10% of maximum speed.

Fig. 5.

Measures of movement smoothness: Jerk ratio (left) and NumMax (right). Row at top: both measures showed that reaching movements were smoother than wrist movements, and that fast movements were smoother than slow movements. Row at bottom: the smoothness of wrist rotations varied with target and whether the movement was outbound (center-out) or inbound (out-center). Target numbers are explained in Fig. 1.

Fig. 6.

Magnitude ratio (measure of how much different frequencies in the torque input appear in the displacement output) of wrist and reaching movements of 300, 550, and 900 ms durations (top, middle, and bottom row, respectively). The range in frequencies over which the magnitude ratio stays high (bandwidth) is larger for the wrist (red lines in left column) than for the shoulder-elbow (red in right column), allowing more high-frequency noise (>2–3 Hz) to pass from the wrist torque to wrist displacement, resulting in jerkier wrist movements. Shown for comparison in gray are the power spectra of actual movements (solid) and equivalent minimum-jerk trajectories (dashed). The power spectra of actual movements show that wrist movements contained more power at higher frequencies (another indicator of greater jerkiness) than reaching movements even though the minimum power required to complete the task (shown by the power spectra of the minimum-jerk trajectories) was similar for wrist and reaching movements.

Fig. 7.

A: simulated 900-ms wrist and reaching movements with signal-dependent noise (SDN), compared with the equivalent minimum-jerk trajectory. The displacement and speed of simulated wrist (thick solid line), reaching (dashed), and minimum-jerk (thin solid) trajectories are indistinguishable, indicating that SDN is not sufficiently large to produce the jerkiness observed experimentally (compare with Fig. 4). Wrist and reaching trajectories were scaled so their minimum-jerk trajectories matched, as in Fig. 4. The acceleration and jerk profiles are offset for a clearer view. B: to compare the smoothness of wrist and reaching movements as a function of movement speed instead of duration (Fig. 5), we plotted jerk ratio vs. mean angular speed for wrist movements (filled triangles) and reaching movements (solid and empty circles). Light gray, black, and dark gray markers represent 300-, 550-, and 900-ms movements, respectively. The mean angular speed for wrist movements within a duration category (300, 550, 900 ms) were very similar because amplitude and duration were constant, but for reaching movements, angular speed depended on target and relative vs. absolute speed (filled and empty circles, respectively). C: simulated 900-ms wrist movements with SDN, plotted as a function of target (explained in Fig. 1). This and other simulations of wrist rotations with SDN did produce differences in smoothness between targets, but the smoothness of outbound and inbound movements were in phase, unlike what we observed experimentally (compare with bottom-left subplot in Fig. 5), suggesting that factors not included in our model must be responsible for the observed differences in smoothness between targets.

Fig. 8.

Differences in wrist movement smoothness (jerk ratio, left column) with target (1–8) and direction (outbound vs. inbound) match the differences in duration (right column) with target and direction, indicating that the observed differences in smoothness between targets are likely caused by—or at least correlated with—differences in movement duration (which are known to cause differences in smoothness). Outbound and inbound values are plotted in black and gray, respectively.