Fig 1.
Envelope statistics of self-motion signals experienced during everyday activities.
A: Schematic showing a sinusoidal trace whose amplitude also varies sinusoidally (blue trace, top left). The power spectrum is non-zero only at the carrier frequency Fc (top right). The envelope of the signal (red trace, bottom left) oscillates with a different frequency Fe than that of the full signal as confirmed by taking its power spectrum (bottom right). B: A MEMS module consisting of three gyroscopes and three linear accelerometers was mounted on the subject’s head and measured linear accelerations along the Fore-Aft, Inter-Aural and Vertical axis as well as rotations about the Pitch, Yaw, and Roll axes. C: Example signal (gray) recorded from the MEMS module and its time varying envelope (red). D,E,F,G,H,I: Example angular velocity or linear acceleration envelope signals recorded during everyday activities for Inter-Aural (D), Fore-Aft (E), Vertical (F), LARP (G), RALP (H), and YAW (I). In each case, shown are an example time series (left), the probability distributions plotted using logarithmic (middle left) and linear (middle right) scales, together with a Gaussian fit (dashed black), and the population-averaged excess Kurtosis (right). Gray bands show 1 STD.
Table 1.
Subject-averaged maximum value, mean, and kurtosis for passive everyday activities.
The maximum and mean values are expressed in mG for the Lateral, Fore-Aft and Vertical linear acceleration while they are expressed in deg/s for the LARP, RALP and Yaw angular velocity.
Table 2.
Subject-averaged maximum value, mean, and kurtosis for active everyday activities.
The maximum and mean values are expressed in mG for the Lateral, Fore-Aft and Vertical linear acceleration while they are expressed in deg/s for the LARP, RALP and Yaw angular velocity.
Fig 2.
Envelope signals deviate from scale invariance.
A: Subject-averaged power spectra (red lines) with best-fit power laws over the low and high frequency ranges (black lines) as well as best-fit single power law over the entire frequency range (blue lines). Also shown are the best-fit power law exponents with confidence interval as well as the transition frequency. The dashed gray lines show the “noise floor”, which is the spectrum of the noise in the measurement obtained when the sensor was not moving (see Methods). Gray bands show 1 STD. B: Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). “*” indicates statistical significance at the p = 0.01 level using a one-way ANOVA. C: Subject-averaged frequency at which the power spectrum starts decreasing more sharply for all six motion dimensions.
Fig 3.
Active motion introduces deviation from scale invariance in the envelopes of natural translational self-motion signals recorded along the Inter-Aural and Vertical axes.
A: Schematic showing a subject engaged in active self-motion (left) and in passive self-motion (right). B,C,D,E, F, G: Subject-averaged envelope power spectra for active (left panels) and passive (right panels) activities for inter aural (B), Fore-Aft (C), Vertical (D), LARP (E), RALP (F), and YAW (G). In each case, the power spectra were fitted using two power laws over the low and high frequency ranges (black lines) as well as by a single power law over the entire frequency range (blue lines). Also shown are the best-fit power law exponents with confidence interval as well as the transition frequency.
Fig 4.
Comparison between the spectral properties of envelope signals recorded during active and passive self-motion.
A: Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions for active self-motion. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). B: Subject-averaged best-fit power law exponents over the low (gray) and high (black) frequency ranges for all six motion dimensions for passive self-motion. Also shown for comparison are the subject-averaged best-fit power law exponents for a single power law over the entire frequency range (blue). “*” indicates statistical significance at the p = 0.01 level using a one-way ANOVA.
Fig 5.
Statistics of environmental signals obtained when the subject is absent.
A: Schematic showing the MEMS module (gold box) located on the subject’s head and placed on the seat during passive self-motion. B,C,D,E, F, G: Trial-averaged power spectra of signals in the external environment (green) during passive self-motion for inter aural (B), Fore-Aft (C), Vertical (D), LARP (E), RALP (F), and YAW (G). The power spectra were in general well fit by a single power law over the entire frequency range (blue lines).
Fig 6.
External envelope signals display scale invariance.
Subject-averaged best-fit power law exponents for the envelopes of external stimuli during passive self-motion when fitting a power law over the entire frequency range (blue) and when fitting two power laws over the low (gray) and high (black) frequency ranges.
Fig 7.
Well-established models of the vestibular periphery predict that irregular afferents have greater sensitivities to envelopes than their regular counterparts.
A: Schematic showing the vestibular end organs as well as regular and irregular vestibular afferents projecting to the vestibular nuclei. B: Sensitivity to the carrier for the regular (dashed black) and irregular (solid red) model afferents. C: Time series showing a segment of the envelope stimulus (solid black) and the responses of the model regular (dashed black) and irregular (solid red) afferents. D: Gain to the envelope as a function of frequency for the regular (dashed black) and irregular (solid red) model afferents. In both cases the gain is relatively independent of frequency but is about twice higher for the irregular model afferent.