Balancing with Vibration: A Prelude for “Drift and Act” Balance Control

Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001 m, 15–50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed “drift and act” control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex time–dependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces

Vibration–induced enhancement of stick balancing skill as a function of vibration-induced amplitude lowering.

<p>a) and b) show the same data plotted in two different ways. Data is obtained from three subjects using three different vibration frequencies (15 Hz, 25 Hz, 50 Hz) on three different days. Relative survival is the same as defined in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007427#pone-0007427-g003" target="_blank">Figure 3</a>. The ‘% decrease amplitude’ is calculated from the standard deviation of in the presence and absence of vibration, where is defined in the legend to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007427#pone-0007427-g007" target="_blank">Figure 7</a>.</p

Effects of parametric excitation on the dynamics of a simple “drift and act” controller.

<p>a) Graphical representation of a simple realization of the feedback function that produces a limit cycle oscillation in (2) in the absence of parametric excitation and noisy perturbations, where and , , , and . The displacement from the upright position, , grows when and decreases when . b) Periodic parametric excitation is turned on at the . The effect is to decrease the amplitude of the limit cycle oscillation. Parameters are and .</p

Effect of vibration on neural latency for stick balancing skill.

<p>The cross–correlation function, for stick balancing is measured in the absence of vibration (top panels) and in the presence of vibration (bottom panels). Data is shown for two subjects having different skill levels: in the absence of vibration s for the subject on the left (33.2 s in presence of vibration) and 23.2 s for the subject on the right (45.5 s in presence of vibration).</p

Effect of vibration on the distribution of the changes in speed made by the fingertip during stick balancing.

<p>High speed motion capture cameras were used to measure the distribution, , of the changes in speed, , of the movements of the fingertip in the presence (red •) and absence (black •) of vibration, where is the standard deviation. Data is shown for the same subject: the 50 Hz vibration experiment was done 2 days after the 25 Hz vibration experiment. The broadening of is consistent with the increase in stick balancing skill that the subject experienced: s in the absence of 25 Hz vibration and s in the absence of 50 Hz vibration. The sampling frequency was 500 Hz.</p

Effect of vibration amplitude and frequency on the mean stick balancing time.

<p>a) shows the effect of 0.001 m vertical vibration at the fingertip on relative survival and b) shows the effects of whole body vibration on relative survival using a vibrating platform which vibrated the body in a way that did not produce detectable vertical vibrations at the fingertip. The relative survival is the mean stick survival time, , measured for stick balancing in the presence of vibration divided by that obtained in the absence of vibration. In a) the shape of the symbol indicates the vibration frequency; 15 Hz (), 25 Hz () and 50 Hz (), and filled symbols indicate a statistically significant enhancement in stick balancing skill (). In b) the relative survival of subjects () was not significantly enhanced by whole body vibration ( in all cases).</p

Effects of vibration on the vertical displacement angle and the amplitude of oscillatory relationship between the controlled variable and controller for stick balancing.

<p>a) and c) compare, respectively, the movements in the fingertip during stick balancing in the anterior–posterior (AP) and medial–lateral (ML) plane when the platform vibration is off and on (Physioplate vibrated at 50 Hz). These two–dimensional histograms are each determined from a single stick balancing time series of approximately equal length (39.96 s in the absence of vibration and 42.14 s in the presence of vibration). b) plots the normalized distribution of the amplitude d) plots the normalized distribution of the vertical displacement angle, in the absence (black) and presence (red) of vibration. The subscripts refer, respectively, to the coordinates of the tip of the stick and the fingertip. The distributions shown in b) and d) are determined for a total of min accumulated stick balancing time in the absence of vibration and min accumulated stick balancing time in the presence of vibration (sampling frequency 500 Hz in both cases).</p

Vibration enhances stick balancing skill.

<p>The survival fraction represents the fraction of stick balancing trials for which the stick was still balanced at time (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007427#s4" target="_blank">METHODS</a> for more details): ‘’ means no vibration and ‘’ means with vibration. The survival fraction is determined using stick balancing trials and the mean survival time, , is used as a measure of stick balancing skill. Here a 50 Hz, 0.001 m peak–to–peak amplitude vibration at the fingertip approximately doubles the mean survival time (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007427#pone-0007427-g003" target="_blank">Figure 3</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0007427#pone-0007427-t001" target="_blank">Table 1</a> for summary of results).</p