Predicting Change of Vestibular Direction Detection Thresholds from Acceleration Profile Differences

In the absence of vision, the perceived direction of translational self motion is largely governed by signals originating from the otoliths. Although it has been shown that direction detection thresholds depend on the frequency of the motion stimulus, the influence of the actual time course of the motion has not been thoroughly investigated. The goal of our study was to measure, model and predict vestibular direction detection thresholds for different motion profiles in the horizontal plane. Detection thresholds for three acceleration profiles, one sinusoidal and two non-sinusoidal (Fig. 1A), with three different durations were measured for six human participants. An anthropomorphic robot arm, the Max Planck CyberMotion Simulator, was used to provide the motion stimuli. The experiment was designed as a four-alternative forced-choice task, where blindfolded participants judged the direction of motion from four possibilities: forward, backward, left or right. Stimulus intensity (peak acceleration of the motion profile) was varied based on a Bayesian adaptive method, and a psychometric function fit to the measurements determined the sensory threshold. For modeling, a 2nd order linear dynamical system with two poles and one zero, originally proposed by Young and Meiry (1968), was used to describe the data. The parameters of this model have been previously identified with sinusoidal motion stimuli over a broad frequency range for similar tasks, but predictions concerning perceptual thresholds for general motion profiles are unknown. In our study, the thresholds obtained from the three sinusoidal acceleration profiles were used to identify the static gain of the model by fitting the system gain to the inverted thresholds. The other parameters were derived from the literature. Predicting the thresholds for general motion profiles was based on the assumption that the output of the model can be interpreted as the signal intensity coming from the otoliths and that if this intensity overcomes a certain value the correct direction of motion can be perceived. In order to predict the threshold, the peak acceleration of the input profile must be selected so that that the corresponding maximum model output is equal to one (Fig. 1B). Predictions for the remaining six non-sinusoidal profiles showed that they were in good agreement with the measured data, with the average error being smaller than 20 of the average detection threshold. This is a promising result, as just the static gain of the model was identified from only three data points. Accepting the linear model as a method to predict thresholds, it is also possible to fit the model to the nonsinusoidal profile data and identify the whole parameter set. Instead of fitting the system gain to the inverted sinusoidal thresholds, we computed the predictions for all profiles given a certain set of model parameters and iteratively varied the parameters to minimize the error between measurements and predictions. Two of the three identified model parameters agreed with the values given in the literature, while the third was found to be different. This difference suggested a phase lead for lower frequencies, which corresponds to sensitivity to jerk (the time derivative of acceleration). Comparing threshold predictions between models with different jerk sensitivities reveal distinct differences between the predictions at low frequencies. The predictions for a model with higher jerk sensitivity appear more appropriate and could be tested in future experiments. To summarize, we have shown that a linear model approach is able to predict vestibular perceptual direction detection thresholds. This allows the model parameters to be identified while resorting to non-sinusoidal stimuli, and helps to better understand vestibular linear motion perception. Future studies will extend these measurements to lower frequencies and assess this modeling approach for rotational movements