# «Published in final edited form in: European Journal of Neuroscience. (2013) doi: dx.doi.org/10.1111/ejn.12324 Gaze direction affects linear ...»

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 Paradigm B, LED OFF (N=8): Same as paradigm A, except that the LED was turned off just before motion onset. Subjects were instructed to maintain the eccentric eye position during motion. There were 20 repetitions of the 8 conditions (4 trajectory deviations × 2 eccentric eye positions). To examine the residual eye movements during motion, the left eye of three subjects was monitored with the video-oculography system. Smooth eye movements after the guiding LED disappeared were smaller than 1°.

Paradigm C, Sustained Fixations (N=12): A single LED was constantly on for the duration of a block and subjects were instructed to not break fixation of the LED during this time. (1th & 3th block: left LED on, 2rd & 4th block: right LED on or vice versa). There were 20 repetitions of the 8 conditions (4 trajectory deviations × 2 eccentric eye positions).

Paradigm D, 3 LEDs (N=15): Of the four blocks of trials, two were exactly as in paradigm A, with fixations alternating randomly between left and right. In the other two blocks of trials, instead of an eccentric LED, the center LED was on in all trials. There were ten repetitions for each of the 8 conditions with eccentric fixations (4 trajectory deviations × 2 eccentric eye positions) and 20 repetitions of the four conditions with centric fixation (4 trajectory deviations × 1 eye position).

Paradigm with head-on-trunk eccentric 17 subjects completed this paradigm. The mask fixating the participant’s head to the back of the seat was made with the participant’s head deviating 16 degrees to the left from the trunk straight ahead (H= -16°, Figure 1) so that the head faced the left LED. A laser pointer at the level of the chin indicated when the head was facing the left LED. Trajectories were the same as in the head-centered paradigms, thus they were the same with respect to the trunk, but not with respect to the otoliths. The task remained the same: to report whether the trajectory was felt to the right or the left with respect to the trunk. During motion one of two LEDs was on, one facing the head so that it was fixated with eyes centered in the orbit (E = 0°, G = -16°), the other facing the trunk so that it required an eccentric eye in the orbit (E = 16°, G = 0°). The order of presentation of trajectory deviations and eye positions was randomized. There were 20 repetitions for each of the 8 conditions (4 trajectory deviations × 2 eye positions) giving a total of 160 trials that were divided in 4 blocks of 40 trials each. After the first two blocks the head was freed for a minimum of five minutes before resuming the experiment and completing the last two blocks.

Data Analysis Data were analyzed offline with customized scripts written in MATLAB (R2007b,The MathWorks, USA). For each recording, trials were sorted according to platform trajectory and LED direction, then the report of the participant was determined, this could be right, left or void if the subject failed to report during a given trial. Overall missed trials were rare but a few subjects did miss a considerable number of them as reported in the Results section. The calculations described below were performed taking into account the actual number of valid trials per condition.

Psychometric Curves The analysis was based on the psychometric curves, which represent the proportion of rightward responses as a function of trajectory deviation PR ( ) (Wichman & Hill, 2001). We Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 To characterize such curves we defined the bias, B, as the total proportion of rightward responses, so that B can only have values between 0 and 1. When B = 0.5, there is no preference of rightward over leftward reports.

R 4 B P5 ( ) ( 2 ( 5 / ( ) P2 P ) P) (5) R R R As a measure of sensitivity S we used the difference between the mean proportion of

**rightward reports for rightwards and leftwards trajectories:**

(6) This quantity is linearly related to the percentage correct measure defined above ( PC (1 S ) / 2 ).

Parametric versus Non-parametric Quantities describing the psychometric functions were calculated separately for each subject and each viewing condition. Only subjects with reliable parametric measures for all psychometric curves were included in analyses involving PSE and σ. Thus, either all psychometric curves in a dataset would contribute to both PSE and σ, or none of the psychometric curves would. Otherwise, all valid recordings contributed to the nonparametric measures (bias and sensitivity).

While PSE and σ are based on a cumulative Gaussian, non-parametric measures do not make any assumption about the form of the underlying psychometric function and describe ‘local’ properties of the psychometric curve at the sampled range of trajectory-in-trunk deviations θ = (-5, -2, 2, 5)°. In the case of a cumulative Gaussian psychometric function the two sets of parameters are nonlinearly related by equations (1) (5) and (6), and when PSE remains close to zero within the sampled range of trajectory deviations, there is a strong negative correlation between bias and PSE on the one hand, and sensitivity and σ on the other.

The two approaches, although not strictly equivalent, can be viewed as complementary;

while the parametric representation provides a direct interpretation and is easier to compare with results in the literature; the non-parametric representation allowed us to use all datasets and was particularly useful in adding power when comparing performance across paradigms.

Statistical analysis We established whether performance was above chance level for each psychometric curve separately. We considered percentage correct (defined in Equation 4) as the statistic of interest and estimated the distribution of this statistic under the null hypothesis that the psychometric curve PR ( ) was constant, that is: PR ( 5) PR ( 2 ) PR ( 2 ) PR ( 5) (where corresponds to the best maximum likelihood estimate to the data assuming a constant value for all deviations). We generated the distribution corresponding to the null hypothesis empirically by generating 2000 random draws (each random draw generates a synthetic psychometric curve) from the binomial distribution (with the number of valid trials for each direction of motion for each subject. From this synthetic data we calculated the corresponding percentage correct by using Equation 4 (obtaining 2000 percentage correct values, one for each synthetic psychometric curve derived from the null hypothesis). Percentage correct of the actual measured psychometric curve was deemed above chance level if it lied outside the 95 percentile of percentage correct values derived from the null hypothesis.

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 We followed a similar procedure to determine whether two psychometric curves from the same subject (each corresponding to a gaze direction) were significantly different. In this case we used as statistic ΔNR, the difference in the total number of rightward reports for the two curves (ΔNR=4ΔB with B defined in equation 5). We asked whether this value was consistent with the null hypothesis that there was no difference introduced by gaze direction. We calculated the psychometric function corresponding to the null hypothesis pooling all the trials independently of viewing Rn condition P, ull ( ) ≡ (PR,GAZE 1 (θ)+ PR,GAZE 2(θ))/2. We used the binomial distribution to empirically generate the distribution of N 0 expected from such P.null () values (10000 draws). The two curves R were deemed statistically different if ΔNR lied outside the 95 percentile of N 0.

Figure 1 Experimental setup. Paradigms had subjects with head either oriented along the trunk (A) or facing the left LED (B), which deviated 16 degrees from straight ahead (left panel). In all paradigms the actual direction of motion, represented in the diagrams by an arrow, was defined in relation to the trunk straightahead (there were four different trajectory deviations symmetric about the trunk straight-ahead). LEDs were mounted on the front railing of the motion platform. The drawings illustrate the situation in which the left LED is on and the participant fixates it either with eye-in-head eccentricity (left panel) or head-on-trunk eccentricity (right panel). H: head-on-trunk, E: eye-in-head, G = H+E, gaze.

Results The effect of eye-in-head direction With head centered on the trunk, three paradigms assessed the effect of eye-in-head direction (right vs. left, E = ±16°) on the point of subjective equivalence (PSE), and the fourth, which also included E = 0° trials, looked at the influence on precision by comparing σ in trials with E = ±16° and in trials with E = 0°.

There were a total of 46 valid recordings (13 in paradigm A, 7 in B, 11 in C and 15 in D), corresponding to 38 different subjects (6 subjects participated in more than one paradigm).

Sometimes participants failed to give a report (missed trial). From the total of 46 valid recordings, 33 had no missed trials and 8 had one missed trial. The number of missed trials in Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 the remaining 5 recordings was (8, 10, 13, 22 and 33) respectively. In all the expressions including the number of trials per condition (N), only the actual number of valid trials was used.

Most participants showed a significant modulation of reports with the direction of motion. This was assessed by looking at whether percentage correct was significantly different from chance for all psychometric curves belonging to the same subject. Figure 2 shows two sample pairs of psychometric curves, including an example of performance not above chance level (right panel, curve for E = 16°). Significant modulation with direction was found in 10/13 (paradigm A), 7/7 (paradigm B), 7/11 (paradigm C) and 14/15 (paradigm D). If a dataset contained a psychometric curve not above chance level, the whole dataset only contributed to the nonparametric measures (bias and sensitivity) and not to the parametric ones (PSE and σ).

Figure 2 Illustrative performance of two participants. Data fitted with cumulative Gaussians (grey and black continuous lines). Most participants, as that represented on the left, had significant modulation of proportion of rightward responses with trajectory deviation, and the parameters of the cumulative Gaussian fits were well determined. Some psychometric functions, as that on the right panel corresponding to E = 16°, did not differ significantly from a constant and the resulting Gaussian fits were not reliable. For such psychometric curves, the nonparametric measures (bias and sensitivity) were well defined.

Although the deviation of the trajectory with respect to the trunk was independent of eye direction, we found a clear effect of eye direction on the proportion of rightward reports.

Most recordings showed an effect of eye direction as measured by the difference in total count of rightward responses when fixating the right and left LEDs, 12/13 for alternating fixations (paradigm A), 6/7 for eccentric fixations in the dark, 10/11 for sustained eccentric fixations (paradigm C) and 14/15 for alternating fixations in paradigm D. From these, all but one showed a significantly higher number of rightward reports when looking right.

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 Figure 3 Changes in the psychometric curves elicited by eccentric eye positions characterized by the shift of the point of subjective equivalence (PSE, top left) obtained from the parametric fits, the change in average rightwards reports (non-parametric measure, top right). Overall measures of the detection thresholds (bottom left), and sensitivity (bottom right). The box plots represent median values and the first and third quartiles for each of the four experimental paradigms with centered head-on-trunk (See Methods for the description of the four paradigms: A-D).

Figure 3 summarizes the characterization of the psychometric curve pairs in paradigms A through D. It shows the shift in PSE: PSEL PSER, the change in Bias: BR BL, as well as RL and sensitivity: ( s R s L ) / 2. The distributions of PSEL PSER and

**measures of threshold:**

BR BL for different paradigms showed a big overlap, and medians had similar values (see Table 1).

A Kruskal-Wallis ANOVA test did not find significant differences among paradigms for PSEL PSER ( 3 = 1.09, n = (10, 7, 7, 14), P = 0.78) or BR BL ( 3 = 0.94, n = (13, 7, 11, 15), P