Absence of Nonlinear Coupling Between Electric Vestibular Stimulation and Evoked Forces During Standing Balance

Abstract

The vestibular system encodes motion and orientation of the head in space and is essential for negotiating in and interacting with the world. Recently, random waveform electric vestibular stimulation has become an increasingly common means of probing the vestibular system. However, many of the methods used to analyze the behavioral response to this type of stimulation assume a linear relationship between frequencies in the stimulus and its associated response. Here we examine this stimulus-response frequency linearity to determine the validity of this assumption. Forty-five university-aged subjects stood on a force-plate for 4 min while receiving vestibular stimulation. To determine the linearity of the stimulus-response relationship we calculated the cross-frequency power coupling between a 0 and 25 Hz bandwidth limited white noise stimulus and induced postural responses, as measured using the horizontal forces acting at the feet. Ultimately, we found that, on average, the postural response to a random stimulus is linear across stimulation frequencies. This result supports the use of analysis methods that depend on the assumption of stimulus-response frequency linearity, such as coherence and gain, which are commonly used to analyze the body's response to random waveform electric stimuli.

Keywords: coupling; cross-frequency coupling; electric vestibular stimulation; galvanic vestibular stimulation; linearity; random waveform; vestibular.

FIGURE 1

Experimental methods and setup. (A) Analysis example. In this study, we sought to examine co-variation in power between all stimulus and response frequencies to determine if a given frequency of stimulation resulted in a response at the same or a different frequency. The top row illustrates two simulated time-varying signals which are phase locked (co-modulated by the positive component of a 0.1 ± 0.06 Hz sinewave with negative values replaced by zeros) and vary in time at different frequencies (2 Hz stimulus inducing a 10 Hz response). The second row illustrates the modulation of signal power over time in these two time-series. Power amplitude is represented by the scale bar on the right of the figure. (B) In each subject, after alignment in time, we correlated the modulation in signal power over time between the stimulus and response (medio-lateral forces at the feet) for each combination of frequencies and represented these correlations as a response frequency by stimulus-frequency correlation matrix. In this simulated case, the stimulus contained 2 Hz power (see Figure 1A) and the response contained 10 Hz power, and therefore a correlation is observed at the intersection of these two frequencies. Correlation strength is represented by the scale bar on the right of the plot. (C) Schematic of the experimental set-up. Participants stood on the back force-plate of a two force-plate instrumented treadmill and held their gaze in an orientation meant to keep the head tilted 18° nose up. This head orientation focuses the postural response to the stimulus to the medio-lateral direction.

FIGURE 2

Experimental results. (A) Single subject responses (n = 1). These plots are the correlation matrices for three subjects. On the horizontal axes are stimulus frequencies and on the vertical axes are response frequencies. Correlation strength is represented by the color scale. Dark green indicates strong positive correlations, white indicates low correlations, and dark blue indicates strong negative correlations. In general, the strongest (positive) correlations were observed along the diagonal, indicating a linear frequency relationship between the stimulus and the induced responses. (B) Grand mean correlation matrix across all subjects. While there is high variance within each subject, on average (n = 45) responses induced by the stimulus were at the same frequency as the stimulus. Panel (B) uses the same scale bar as panel (A). (C) Statistical evaluation. The left plot illustrates responses significantly different from zero as defined by zero being outside of the bootstrapped 99% confidence interval for the mean (n = 45). The right plot illustrates responses significantly different from zero defined as zero being outside of the bootstrapped 99% confidence interval of the difference of means distribution between the responses and the pseudo-sham (n = 45). Both statistical tests reach similar outcomes, which was that responses to the stimulus predominantly occur at the same frequency as the stimulus. In these plots, white indicates significantly greater than zero (positive correlation), gray indicates non-significance, and black indicates significantly less than zero (negative correlation).

FIGURE 3

Off-diagonal axis coupling and the effect of time. We collected two additional subjects [one male, 42 years, 190 cm, 95 kg (Top row); and one female, 27 years, 163 cm, 55 kg, (Bottom row)] using the same methods as the other 45 except for the duration of stimulation. These two subjects completed two 1040-s trials to examine the influence of increasing collection duration on off-diagonal axis correlations. In these two subjects, the strength of off-diagonal axis correlations decrease with increasing collection duration, suggesting that the off-diagonal axis correlations observed in the 45 subjects are largely due to the limited collection duration.