Experimental procedure.

The experiments were organized into several blocks of trials. The order in which these blocks were delivered was randomized for each participant. Control experiments were done in three blocks with a single stimulus presented: surge (fore-aft motion), sway (left-right motion), or yaw (rotation about an earth vertical axis). During each of these blocks, there were two independent staircases that were randomly interleaved: one staircase began with the largest (7 cm or 7°) leftward stimulus, and the other began with the largest rightward stimulus. Subjects were always able to identify reliably this largest stimulus correctly. After each response, the subsequent stimulus was shifted in the direction opposite the response. Thus after a 7-cm rightward stimulus, which was identified as right, the next stimulus was delivered, 1.6 cm more leftward (i.e., 5.4 cm to the right). The initial step size was 1.6 cm or 1.6°. Within each staircase, the step size was decreased by one-half when the direction of responses reversed to a minimum of 0.1 cm or 0.1°. The validity of these methods is well established (Green 1993; Leek 2001; Levitt 1971; Treutwein 1995). Furthermore, if the response was in the same direction three times in a row, then the step size doubled to a maximum of 1.6 cm or 1.6°. Each staircase could move through zero so that later in the staircase, stimuli could be delivered in either direction. This method tended to focus stimuli near the point of subjective equality (PSE) but also delivered enough stimuli away from the PSE that threshold could be determined. It was thought to be a reasonable method of the current study, because both the PSE (i.e., mean of the psychometric function or bias) and threshold (i.e., width of the psychometric function) were of interest. Each staircase included 25 stimulus presentations (50 total within the trial block).

The influence of multiple stimuli was assessed in blocks of trials with combined translation and rotation (Fig. 1). In these experiments, there was a fixed, distracting stimulus delivered simultaneously with the test stimulus, although the subject was asked to report only the test stimulus direction. Blocks of trials included randomly interleaved sets of staircases with distracting stimuli in opposite directions. There were four blocks of trials of this type that are named as test distractor: surge-yaw, sway-yaw, yaw-surge, and yaw-sway. The distracting stimulus was always 7 cm or 7° (14 cm/s or 7°/s peak velocity). Each distracting stimulus had two staircases that started with test stimuli in opposite directions. Thus each block of trials, which included a distracting stimulus, had a total of 4 randomly interleaved staircases for a total of 100 stimulus presentations (Fig. 2). It is recognized that more stimulus presentations may have allowed the parameters of the psychometric function to be fit with narrower confidence intervals, but this length was chosen to improve subject alertness by keeping trial blocks to an appropriate length. This is in the same range of trials used in other human vestibular perception studies. Although some studies have used 150 stimulus presentations per trial block (Soyka et al. 2015) or 110 per trial block (Roditi and Crane 2012a), others have used 100, as done in the current series (Yi and Merfeld 2016). Many other trials have had fewer: 70–80 (Valko et al. 2012), 50 (Benson et al. 1989), or <50, on average (Grabherr et al. 2008).

Trial blocks, including combined rotation and translation. Each condition included both rotation and translation with subjects asked to judge left-right sway (top), forward-back surge (middle), or left-right rotation (bottom).

Sample date from an individual subject (#5, a 23-yr-old woman) for the sway-yaw condition. During the stimulus presentations, there was a 7° (14°/s peak velocity) leftward rotation (A and B) and similar rightward rotation (C and D). The subject was asked to report the amount of left-right sway translation. A and C: the circles represent this subject's responses and are drawn in proportion to the number of stimuli presented for a given combination. The smaller circles represent a single stimulus presentation, whereas the larger circles represent 4 stimuli. The solid lines represent the best fit of a cumulative Gaussian function to the responses. The values in parentheses represent the 95% confidence interval (CI). The same data are shown in the time domain (B and D). Four randomly interleaved staircases are shown. Each panel includes 2 staircases: 1 that began with a 14-cm/s translation (light) and another that began with a −14 cm/s translation (dark). The direction of each response is shown by the orientation of the triangles.

The influence of combined rotation and translation was also examined in a block of trials in which the axis of rotation was varied (sway-axis and surge-axis). These trials were, in some ways, similar to the surge-yaw and sway-yaw condition in that both translation and rotation occurred simultaneously, and subjects were asked to report the direction of translation. However, they differed from the surge-yaw and sway-yaw conditions in that the translation occurred about a curved trajectory. Attempts were also made to correlate these results with the surge-yaw and sway-yaw condition. In these trials, the distracting stimulus was ±7° (14°/s peak velocity) yaw rotation. In the sway-axis trial block, the axis was varied in the fore-aft direction (Fig. 1), and subjects were asked to report the perceived direction of left-right translation (sway). In the surge-axis block of trials, the axis was varied in the left-right direction (Fig. 1), and subjects reported if they perceived they were moving forward or backward (surge). Similar to the combined translation-rotation trials, there were independent pairs of staircases that started with the rotation axis located 100 cm away from center in either direction. The initial step size was 16 cm, which could be decreased to 1 cm with reverses in the perceived direction.