## Abstract

We investigated in normal human subjects how semicircular canal and otolith signals interact in the estimation of the subjective visual vertical after constant velocity or constant acceleration roll tilt. In the constant velocity paradigm, subjects were rotated in darkness at ±60°/s for five complete cycles before being stopped in one of seven orientations ranging from 0 to ±90° (right/left ear down). In the constant acceleration paradigm, subjects were rotated with an acceleration of +30 or −30°/s^{2} to the same seven end positions between −90 and +90°, by way of passing once through the upside-down position. The subjective visual vertical was assessed by measuring the setting of a luminous line that appeared at different test delays after stop rotation in otherwise complete darkness. The data suggest that gravitational jerk signals generated by otolith–semicircular canal interactions and/or carried by phasic otolith signals are responsible for the observed transient bias in the estimation of the subjective visual vertical. This transient bias depended on both rotation and tilt direction after constant velocity rotations, but was almost abolished following constant acceleration rotations.

## INTRODUCTION

During motion, the brain relies on visual, vestibular, and somatosensory cues to constantly update a representation of the physical surround. The information from these different sensory modalities is centrally fit together to form a stable percept of the world, which includes a reliable and robust sense of verticality. How the information from the diverse sensory channels is eventually organized into a coherent scheme of verticality and incorporated in an internal model of space perception is largely unknown.

The perception of earth verticality has been studied extensively by examining the subjective visual vertical (Kaptein and Van Gisbergen 2004, 2005; Mast and Jarchow 1996; Merfeld et al. 2001; Mittelstaedt 1983, 1992). This particular estimate is known to become strongly biased by head and body tilts in the roll plane. Accordingly, a perfectly earth-vertically oriented luminous line in an otherwise dark environment appears tilted toward the subject at small head (and body) inclinations and away from the subject at larger inclinations, phenomena that have become known as the E- and the A-effects, respectively (Aubert 1861; Müller 1916). The E-effect is generally encountered at head and body tilts of less than 60°, whereas the A-effect invariably occurs at larger tilt angles (Udo de Haes and Schöne 1970; Van Beuzekom and Van Gisbergen 2000).

Several factors seem to influence the occurrence of the E- and the A-effects, of which some might betray a change in the reference frame related to a specific interaction of sensory signals. For example, fast velocity tilts, which activate both otoliths and semicircular canals, have been shown to reduce the overall error and also to qualitatively change the estimation pattern in the range of ±90° roll tilt (Jaggi-Schwarz and Hess 2003; Jaggi-Schwarz et al. 2003). This is in line with earlier studies reporting that vertical semicircular canal activity influences the subjective visual vertical (Stockwell and Guedry 1970; Udo de Haes and Schöne 1970; von Holst and Grisebach 1951) and that concordant semicircular canal and otolith stimulation during tilt improves the accuracy of estimates (Stockwell and Guedry 1970). Similar conclusions have been reached in a number of studies on roll tilt perception using a somatosensory paradigm (Merfeld et al. 2005a,b; Park et al. 2006). More recently, Pavlou et al. (2003) demonstrated that per- and postrotatory vertical semicircular canal activity during and following yaw rotation in different head pitch orientations bias the subjective visual vertical in opposite directions. Thus incongruent semicircular canal and otolith activity seems to constitute an important factor that disturbs the delicate mechanisms underlying the estimation of earth-vertical. Since our percept of verticality relies on multisensory mechanisms, including proprioceptive–somatosensory inputs, it is generally difficult to unmask the contributions of the different sensory cues. In this study we exploit a behavioral paradigm that challenges the brain's capacity to consistently update spatial orientation, by preventing vestibular cues that unambiguously determine head-in-space orientation. We compare the subjective visual vertical estimates in subjects that are stopped in different roll positions after rotations at constant velocity about the roll axis, with estimates obtained after rotations at constant acceleration. When the normally present vestibular information about instantaneous head orientation becomes ambiguous due to prolonged constant velocity rotation, extravestibular cues might gain a stronger weight at stop of rotation. The question is then whether it is still the semicircular canal and otolith signals alone that determine the estimation of earth vertical in a dynamic situation. To evaluate the contribution of vestibular and extravestibular cues, we compared the subjective visual vertical settings and their time evolution obtained after constant velocity and acceleration. Preliminary data were previously published in abstract form (Lorincz and Hess 2005).

## METHODS

### Subjects

Seven healthy subjects, all right handed, completed each of two separate experiments (ages ranging from 27 to 45). All subjects gave informed written consent according to an experimental protocol that had been approved by the Ethics Committee of the Canton of Zurich, Switzerland, in adherence to the Declaration of Helsinki for research with human subjects. Participants had no medical history of balance disorder and their vision was normal or corrected to normal. The potential nauseating effect of the experiment was brought up to their attention and they were instructed how to stop the experiment at any time. Two subjects could not complete the experiments because of nausea and were discarded from the study.

### Experimental setup

Subjects were comfortably seated in a chair, mounted on a three-dimensional human turntable, which could be rotated by means of three servo-controlled motor driven axes (Acutronic, Bubikon, Switzerland). They were secured with safety belts and vacuum pillows shaped around the torso. In the start-up position, participants were facing a white spherical screen (145 cm radius) providing a visual angle of 100°. Each subject's head, placed in the center of rotation, was restrained with individually molded thermoplastic masks (Sinmed BV, Reeuwijk, The Netherlands). A laser mounted on top of the chair provided fixation targets as well as a luminous line that was projected on the center of the screen in front of the subject.

### Recording of the subjective visual vertical

To estimate the subjective visual vertical (SVV), a dimmed red laser line subtending 20° of visual angle (line thickness: ∼2 mm) and announced by a beep, was projected on the spherical screen in front of the subject. In our paradigms, the amount of deviation of the visual line from the body axis did not significantly alter the outcome of the SVV setting in contrast to previous claims (Hoppenbrouwers et al. 2004). Therefore the line was presented centered at eye level, in random orientations within a range of ±5 to ±20° relative to the body axis. Participants were instructed to align the luminous line as fast and as accurately as possible with the perceived direction of earth vertical, using a rotary knob placed horizontally in front of the subject that remotely controlled the line. Knob rotation and line orientation were linearly related at a ratio of 3:1. Once satisfied with the line adjustment, subjects pressed a button to indicate the end of the setting, which was quitted by a beep. The SVV was estimated about 2 s (mean ± SD: 1.8 ± 0.8 s), 30 s (31.7 ± 0.1 s), and 60 s (59.4 ± 0.1 s) after the end of rotation. Participants adjusted the line to the subjective vertical in less than 3 s. The total time from appearance of the luminous line to the end of adjusting the line was on average 1.7 s (±0.5 SD) in the constant velocity paradigm and 2.2 s (±0.8 SD) in the constant acceleration paradigm. The test delay only influenced the duration of luminous line setting in the constant velocity paradigm, as shown by the one-way repeated measures ANOVA [constant velocity: F(1.577, 152.98) = 6.458, *P* = 0.004; Partial Eta Squared (η^{2}) = 0.062; observed power = 0.843; constant acceleration paradigm: F(1.979, 191.927) = 1.022, *P* = 0.36; partial η^{2} = 0.010; observed power = 0.226]. The first setting took significantly longer (mean duration: 1.9 s) than the two others (mean duration φ̂_{SV30} and φ̂_{SV60}: 1.7 s; Least Significant Difference test: φ̂_{SV2} − φ̂_{SV30}: *P* = 0.006; φ̂_{SV2} − φ̂_{SV60}: *P* = 0.042; for statistics see Data analyses). The potentiometer output that controlled the angular orientation of the laser line and the button press were digitized and stored together with the chair position signal on the hard drive of a PC for off-line analysis with Matlab software (The MathWorks, Boston, MA). The angular orientation of the luminous line was measured with an error of less than 1°.

### General procedure and vestibular stimulation protocols

All tests were performed under binocular vision. A test trial without actual rotation was performed to familiarize subjects with the apparatus and the time course of visual events. Each trial started with the subject in upright position and the room lights were turned off. Before rotation onset, a fixation target was switched on for 4 s.

In the *constant velocity paradigm* (Fig. 2A), subjects were rotated at ±60°/s through five complete cycles in the roll plane (i.e., about the *x-axis;* see Fig. 1), with on and off accelerations reaching 150°/s^{2}, before being stopped in one of seven orientations of ±0, ±30, ±60, and ±90° (clockwise tilt angles positive). Before the end of rotation, a dimmed fixation target acoustically indicated by a beep was switched on for 3 s at the beginning of the last rotation cycle. The remaining 3 s of the last cycle were again in complete darkness.

In the *constant acceleration paradigm* (Fig. 2B), subjects were rotated at 30°/s^{2} with symmetric acceleration and deceleration phases, through ±270° (“upright to left or right ear down”), ±300, ±330, ±360° (“upright to upright”), ±390, ±420, or ±450° (“upright to upright to either left or right ear down”). Thus in this paradigm subjects passed just once through the upside-down position.

Note that each of these end positions can be regarded as being approached either from below (e.g., final head orientations at −90, −60, −30, and 0° in Fig. 1*A*) or from above (e.g., final head orientations at −30, −60, and −90° in Fig. 1*B*) depending on the rotation direction. In both paradigms, the final orientation was maintained for about 60 s, after which delay the subject was rotated back to the upright position. Finally, a fixation target, accompanied by a beep, was switched on in front of the subject for 3 s to dump any left over postrotatory vestibular activity, before another beep indicated the end of the trial and the room lights were turned on for 10 to 60 s.

In total, each experiment consisted of 14 trials completed in one or two sessions. Clockwise (cw) and counterclockwise (ccw) rotations were alternated across trials, whereas the final head and body orientation was chosen randomly. Head position was expressed relative to space-fixed coordinates x_{E}, y_{E}, and z_{E} as illustrated in Fig. 1, i.e., positive angles correspond to right ear down stops and conversely for negative angles. A cw rotation designated a rotation of the subject from upright toward right ear down and a ccw rotation designated a rotation of the subject toward left ear down (subject's viewpoint).

### Data analyses

The angle of the luminous line setting (*φ̂*_{SV}), the overall luminous line setting duration (time between the appearance and the disappearance of the line, which includes cognitive decision and sensorimotor integration times) were recorded at 833 Hz. Data were first checked for normal distribution with Kolmogorov–Smirnov statistics. Two different three-way univariate repeated measures ANOVAs were performed on the three SVV settings recorded 2, 30, and 60 s after stop rotation, referred to as *φ̂*_{SV2}, *φ̂*_{SV30}, and *φ̂*_{SV60}. The first one encompassed all the trials and was carried out with direction of the rotations (cw/ccw), tilt angles (0, ±30, ±60, ±90) and test delays (*φ̂*_{SV2}, *φ̂*_{SV30}, *φ̂*_{SV60}) as main factors. The second took into account the direction by which the head approached the final angle, i.e., either from below (Fig. 1*A*) or from above (see Fig. 1*B*). This analysis was thus performed on the setting of six tilt angles only, since the zero tilt could not be classified as being approached from above or below. Within-subject statistics were all corrected for violation of sphericity with Huynh–Feldt epsilon. Partial η^{2} and observed power are also provided to obtain information about the proportion of variance accounted for and the probability of not rejecting the null hypothesis. Pairwise comparisons for main effects were executed with Least Significant Difference tests and significance was assumed for *P* < 0.05. All statistics were performed with SPSS software (SPSS, Chicago, IL).

### Gravity-inertial force vector model

To model the influence of a vestibular bias on the estimation of the SVV after stop of constant velocity roll rotation, we partially follow a model suggested by Mittelstaedt (1991) and consider the following three vectors (the superscript “*T*” stands for transpose): a central estimate of gravity *Ĝ* = [0 *ĝ _{y} ĝ_{z}*]

^{T}; a general force vector

*F̂*= [0

*F̂*]

_{y}F̂_{z}^{T}with the same physical dimension as that of gravity, i.e., acceleration per unit mass or specific force, and a jerk vector Ĵ, representing a central estimate of magnitude and direction of rate of change of gravity in a dynamic or in a quasi-dynamic postrotatory situation.

Regarding the central estimate of gravity *Ĝ*, we follow Mittelstaedt's approach in assuming that it slightly distorts depending on the head roll orientation. For this, one sets *ĝ _{y}* = (

*U*/

*N*) sin (φ) and

*ĝ*= (

_{z}*S*/

*N*) cos (φ) as a function of the roll angle (φ, Fig. 1), using a scaling factor , where the parameters

*U*and

*S*represent, respectively, the weights of the utricular and saccular inputs. Because the model specifies only the ratio

*S*/

*U*, the utricular weight can be set to

*U*= 1. For simplicity, we assume that [

*Ĝ*]

_{z}=

*ĝ*> 0 in upright. Note that this central estimate of gravity

_{z}*Ĝ*is modeled as a unity vector (length of

*Ĝ*= 1), specifying only a direction in space.

The jerk vector that we introduce to account for dynamic or quasi-dynamic influences refers to information about the time rate of change of gravity, i.e., mathematically, Ĵ = d*Ĝ*/d*t*. Geometrically, it is always perpendicular to the estimated direction of gravity because the length of *Ĝ* is assumed constant. Since it is only this geometric property that matters, the model specifies only the contribution of a normalized jerk vector. We define the normalized jerk by setting Ĵ_{ω} = Ĵ/ω, where ω is the magnitude of per- or postrotatory head angular velocity. The dimension of Ĵ_{ω} is: (specific force/s)/(1 rad/s), which is compatible with the dimension of gravity (specific force). Mathematically, the gravitational jerk Ĵ can be expressed as the cross-vector product of the head angular velocity measured by the semicircular canals (for roll rotation one can write ) and the estimated gravity (*Ĝ*). Thus we write and thus Ĵ_{ω} = Ĵ/ω = [0 *−ĝ _{z} ĝ_{y}*]

^{T}. Note that the normalized jerk vector Ĵ

_{ω}retains all the spatial properties of Ĵ. Its relative contribution (or magnitude) is measured by a weighting factor

*k̂*. Having defined the direction (Ĵ

_{ω}) and the relative magnitude (

*k̂*), we can write the jerk contribution as Ĵ =

*k̂Ĵ*. Physiologically, it implies that a centrally estimated rate of change of gravity in both direction and magnitude can have an impact on the estimation of the visual vertical.

_{ω}Finally, we like to stress that the general force vector *F̂* can also be considered as a weighted unity vector that points approximately toward the zenith. To see this, we write *F̂* = *ĥF̂ _{head}* with

*F̂*= [0 sin (

_{head}*ζ̂*) cos (ζ̂)]

^{T}, where

*ζ̂*describes the angle subtended by the

*z*-axis and the unity vector

*F̂*in the roll plane, and represents the weight of the general force vector. Note that , , and, consequently,

_{head}*ζ̂*= tan

^{−1}(

*F̂*/

_{y}*F̂*).

_{z}In the general case, the direction of the subjective visual vertical is determined by a linear interaction of these three unit vectors, which can be formally written as *V̂* = *Ĝ* + *ĥF̂ _{head}* +

*k̂Ĵ*. At this point two major differences to Mittelstaedt's original model should be noted. First, we conceive the force vector

_{ω}*F̂*as an extension of Mittelstaedt's concept of an idiotropic vector (Mittelstaedt 1983), in that we do not require that it is necessarily aligned to the

*z*-axis (Jaggi-Schwarz and Hess 2003). The component

*F̂*can be considered as the equivalent of Mittelstaedt's static idiotropic vector, whereas all the dynamic information is contained in the component

_{z}*F̂*(see results). Second, the here proposed jerk vector Ĵ is different from the velocity-dependent vector

_{y}*K̂*=

_{M}*v*[0

*−K*]

_{s}ĝ_{z}K_{c}ĝ_{y}^{T}that Mittelstaedt (1991) introduced to model the influence of an optic flow pattern on the estimation of the visual vertical (

*v*denotes here the rotation velocity of the random dot pattern).

Having defined the unity vectors *Ĝ*, *F̂ _{head}*, and Ĵ

_{ω}, we postulate that the angular orientation of the SVV (

*β̂*) reflects the ratio of the

*y*- and

*z*-components of a linear combination of these three vectors:

*V̂*=

*Ĝ*+

*ĥF̂*+

_{head}*k̂Ĵ*(in the following we use

_{ω}*F̂*instead of the equivalent description of the general force vector by

*ĥF̂*), that is (1) For Ĵ =

_{head}*ω*=0 the vector

_{Ĵω}*V̂*represents the influence of the interaction of graviceptive signals with a general force signal on the SVV. In the following we refer to this model as the gravitoinertial force vector model.

*Equation 1*has four free model parameters—

*S*,

*F*

_{y},

*F*

_{z}, and

*k*(the free parameters in Mittelstaedt's general model are S, F

_{z}, K

_{s}, K

_{c}). For zero postrotatory activity (ω = 0), the jerk vector disappears,

*Ĵ*= 0, which reduces the input vector to

*V̂*=

*Ĝ*+

*F̂*(2) This equation has three free parameters:

*S*,

*F*

_{y}, and

*F*

_{z}. It will be shown that in the steady state, the parameter

*F*

_{y}becomes negligible, in which case

*Eq. 2*becomes indistinguishable from Mittelstaedt's idiotropic vector model.

The model parameters were determined by nonlinear least-squares fitting of the response errors obtained from the SVV data. We fitted both the population means (±SD) and individual responses. To estimate the variability, we computed the covariance matrix of the four fitted parameters characterizing the population response (Press et al. 2002). For comparison, we also computed the means (±SD) of the parameters fitted to the response errors of each individual subject. We determined the coefficient of determination of these fits by computing the generalized *R*^{2} of the general model (*Eq. 1*) versus a reduced model with *k̂* = *F̂ _{y}* =

*F̂*= 0 and Ŝ = 1, by computing

_{z}*R*

^{2}= 1 − RSS (full model)/RSS (reduced model), where RSS stands for residual sum of squares (for details see Anderson-Sprecher 1994).

### Sensitivity analysis of model parameters

Subjective visual vertical data show typically tilt-dependent variability. In modeling these data, it is of interest to know how much each model parameter contributes to this variability as a function of tilt. In a one-parametric model, say M(X), the sensitivity to a change in the parameter X can be measured by computing the derivative dM/dX because, by Taylor series, if ΔX is a small variation of X, then M(X ± ΔX) = M(X) ± ΔX(dM/dX). Thus the change in M due to a change in X is proportional to dM/dX (whenever the second derivative d^{2}M/dX^{2} is bounded). In the following we show that the sensitivity of the general model (*Eq. 1*) to small variations of its parameters changes as a function of tilt, which allows a characterization of the parameters' influence in terms of the model's output symmetry. To derive the sensitivity of the output β of the general model to variations of each of the four model parameters *S*, *F*_{y}, *F*_{z}, and *k*, we first determine the model output β (*Eq. 1*) at two arbitrary points *P* = [*S F*_{y} *F*_{z} *k*]^{T} and *Q* = [*S*′ *F*_{y} *F*_{z} *k*′]^{T} in the four-dimensional parameter space, which we assume to be separated by a small increment Δ*P* (i.e., *Q* = *P* + Δ*P*). The difference of the model output, evaluated at *P* and *Q*, denoted Δβ is: . Second, we expand the function β in a Taylor series around the point *P* = [*S F*_{y} *F*_{z} *k*]^{T} to obtain (3) *A*, *B*, *C*, and *D* are coefficients indicating how much the model output changes when one moves from the input point *P* by a small step in the direction of the respective parameter (e.g., from *P* = [*S F*_{y} *F*_{z} *k*]^{T} to *Q* = [*S* + Δ*S F*_{y} *F*_{z} *k*]^{T}). More specifically, we obtain for the four coefficients (4) in terms of *V*_{y}, *V*_{z}, *g*_{y}, *g*_{z}, ∂*g*_{y}/∂*S* and ∂*g*_{z}/∂*S* (see *Eq. 1*). The interesting point is that these coefficients, which in general depend on the four parameters, are also functions of the tilt angle φ. Finally, with *A*, *B*, *C*, and *D* at hand, we evaluated the function Δβ at the experimentally estimated mean values (Ŝ, *F̂ _{y}*,

*F̂*,

_{z}*k̂*) and SDs of the four parameters (denoted as

*ΔŜ*,

*ΔF̂*,

_{y}*ΔF̂*,

_{z}*Δk̂*) to obtain

*Δβ̂*. Since the SD of any of the four parameters was much less than 0.5 (see results), it is apparent that higher-order terms (products of SDs of the four parameters) in the expansion (

*Eq. 3*) can be neglected. The relative contribution of each parameter was computed as (Â/

*Δβ̂*)·

*ΔŜ*, (

*B̂*/

*Δβ̂*)·

*ΔF̂*, (Ĉ/

_{y}*Δβ̂*)·

*ΔF̂*, and (

_{z}*D̂*/

*Δβ̂*)·

*Δk̂*, and plotted in Fig. 6. All these expressions are dimensionless.

## RESULTS

The seven participants performed a total of 98 trials with three settings of the luminous line estimating the angle of the SVV at test delays of about 2 s (*φ̂*_{SV2}), 30 s (*φ̂*_{SV30}), and 60 s (*φ̂*_{SV60}) after stop of rotation.

### Effect of rotation direction

A major finding of this study was the dependence of the error pattern of the SVV settings on rotation direction and test delay (Fig. 3, *A* and *B*). Complete statistics are presented in Table 1. First of all, the analysis of the SVV setting by the three-way repeated-measures ANOVA with rotation direction, tilt angles, and test delay as main factors showed, as expected, a significant main effect of tilt angles (Fig. 3, *A* and *B*). The partial η^{2} statistics indicated a very large effect size for both the constant velocity and acceleration paradigms. The post hoc analysis revealed the well known A-effect for the largest tilt angles only, which were significantly different from the settings made at the other stop angles (constant velocity paradigm: SVV at +90° = 11.2 ± 13.5°; SVV at −90° = −16.0 ± 12.7°; *P* < 0.05; constant acceleration paradigm: SVV at +90° = 17.1 ± 5.9°; SVV at −90° = −17.9 ± 9.9°; *P* < 0.01). No significant E-effect was seen for tilts between −60 and +60°.

Interestingly, the SVV settings were globally shifted in the rotation direction. This main effect was significant in the constant velocity paradigm (cw rotation: 0.93 ± 12°; ccw rotation: −4.6 ± 11.7°) and was much more pronounced than that in the constant acceleration paradigm, where it did not attain significance (cw rotation: −0.17 ± 11.1°; ccw rotation: −1.66 ± 11.4°; Fig. 3).

This rotation direction effect was also dependent on the test delay at which the settings were performed (significant interaction between rotation direction and test delay for both experiments). In the constant velocity paradigm, the shift toward the rotation direction was much more pronounced during the first setting (cw rotation: 3.8 ± 11.9°; ccw rotation: −7.8 ± 13.6°, i.e., a difference of 11.5°) and almost completely disappeared at the second (cw rotation: −0.04 ± 11.9°; ccw rotation: −3.4 ± 10.5°) and third settings (cw rotation: −0.95 ± 11.9°; ccw rotation: −2.6 ± 10.3°). A similar but milder pattern was observed for the constant acceleration paradigm (cw rotations: *φ̂*_{SV2} = 1.9 ± 10.9°, *φ̂*_{SV30} = −0.5 ± 11.1°, *φ̂*_{SV60} = −0.8 ± 11.3°; ccw rotations: *φ̂*_{SV2} = −3.0 ± 11.6°, *φ̂*_{SV30} = −1.4 ± 11.1°, *φ̂*_{SV60} = −0.6 ± 11.5°).

All the other main effects or interactions (*main effect*: test delay; *two-way interactions*: rotation direction × tilt angles; test delay × tilt angles; *three-way interaction*: test delay × rotation direction × tilt angles) were not significant.

### Role of the semicircular canals

To estimate the contribution of the semicircular canals, we fitted *Eq. 1*, which describes the response errors in estimating the visual vertical as the result of a central estimation of gravity plus a general force vector (*Ĝ* + *F̂*) and a vestibular born jerk vector (*Ĵ*). After stop from roll rotation, the postrotatory semicircular canal activity is modeled as an angular velocity vector directed along the previous axis of rotation, and thus perpendicularly to the direction of gravity. The jerk vector *Ĵ*, which is the cross-vector product of the angular velocity vector and the estimated direction of gravity, will, in our paradigms, always lie in the roll plane (no component along the *x*-axis). In terms of magnitude, the contribution of the jerk is measured by the parameter *k̂* that indicates the proportion of “specific gravitational force/s” per “1 rad/s postrotatory activity” that has contributed to the estimated subjective visual vertical (for details see methods). We fitted both the response errors averaged across all seven subjects (see Fig. 3) as well as the individual response errors for each of the three test delays (see Fig. 4 and Table 2). We found that Ŝ as well as the force component *F̂ _{z}* did not depend on the rotation direction [Kruskal–Wallis test comparing cw vs. ccw parameter values in the constant velocity paradigm:

*p*(Ŝ) = 0.65, 0.57, and 0.41;

*p*(

*F̂*) = 0.75, 0.57, and 0.85 for the three delays; constant acceleration paradigm:

_{z}*p*(Ŝ) = 0.48, 0.66, and 0.57;

*p*(

*F̂*) = 0.75, 0.95, and 0.95 for the three delays]. Interestingly, these parameters also changed insignificantly across the two paradigms (Fig. 4,

_{z}*top*). However, in the constant velocity paradigm, not only the postrotatory activity (

*k̂*) but also the force component

*F̂*depended strongly on the direction of rotation during the first setting [Kruskal–Wallis test comparing cw vs. ccw parameter values:

_{y}*p*(

*F̂*) = 0.012, 0.18, 0.57;

_{y}*p*(

*k̂*) = 0.004, 0.11, 0.41 for the three delays], in contrast to the constant acceleration paradigm, where only the postrotatory activity (

*k̂*) showed some dependence on the rotation direction [Kruskal–Wallis:

*p*(

*F̂*) = 0.41, 0.48, 0.18;

_{y}*p*(

*k̂*) = 0.06, 0.75, 0.23 for the three delays] (Fig. 4,

*A*and

*B*,

*top panels*). Statistics using the covariance matrix of the fitted parameters and the

*t*-test with or without an ad hoc approximation of the Behrens–Fisher distribution (Kim and Cohen 1998) yielded the same conclusions with similar significances. Furthermore, the sign of

*F̂*and of

_{y}*k̂*were the same: that is, positive for stop after cw rotation and negative for stop after ccw rotation in the constant velocity paradigm. Because the jerk vector in the model is conceived as the cross-vector product of the perceived head angular velocity and gravity at stop of rotation, the components

*Ĵ*and

_{y}*F̂*pointed mostly in opposite directions (see Fig. 8,

_{y}*A*and

*B*). This rule is broken in 90° right or left side down positions, where the jerk is directed along the

*z*-axis (see Fig. 8,

*C*and

*D*). Accordingly, the force vector

*F̂*tilted always toward the left ear after stop of cw rotation and toward the right ear after stop of ccw rotation (Fig. 4,

*bottom panels*). The best fit parameters Ŝ,

*F̂*,

_{y}*F̂*, and

_{z}*k̂*are summarized in Table 2 together with the

*R*

^{2}(coefficient of determination) values for cw and ccw rotations for the two paradigms.

### Dynamic response asymmetries

To obtain a better idea of the dynamic contribution in the constant velocity paradigm, we extrapolated the model fits across the full tilt range from −180 to +180° and compared the immediate response with the delayed response after 60 s for cw and ccw rotations (Fig. 5*A*). In this larger view, it is apparent that the dynamic span between the errors of immediate and delayed responses (compare area between gray curves and area between black curves in Fig. 5*A*) is much smaller when the final tilt angle was approached from above, i.e., for cw tilts (gray curves in Fig. 5*A*) toward right ear down, and ccw tilts (black curves in Fig. 5*A*) toward left ear down positions than the other way around. As a consequence, the span encompasses both A- and E-type errors in close to upside-down positions, when the final tilt angle was approached from below.

To further analyze the effect of rotation direction in the constant velocity paradigm, we computed the difference between the error profiles measured 2 and 60 s, respectively, after cw and ccw rotations (Fig. 3*A*, gray and black curves for stops after cw and ccw rotations, respectively, *top panel* at 2 s and *bottom panel* at 60 s). The resulting differences (*φ̂*_{SV2} − *φ̂*_{SV60}), plotted in Fig. 5*B* (gray and black curves for stops after cw and ccw rotations), represent the *dynamic error increment* (Δe), due to the preceding rotation, which is maximal immediately after stop of rotation. This dynamic effect depended asymmetrically on the tilt angle, for it was increased at left ear down positions and reduced at right ear down positions after cw rotations (Fig. 5*B*, gray curve). Conversely, it was reduced at left ear down positions and increased at right ear down positions after ccw rotations (Fig. 5*B*, black curve). This asymmetry suggests that the strong postrotatory semicircular canal activity at stop of rotation in the constant velocity paradigm might not be the only factor that contributes to the observed dynamic error increment. A similar asymmetry, albeit much smaller, was found early after stop in the constant acceleration paradigm.

To determine the relative importance of the four model parameters on the observed error profile, we computed their influence on the output in a linear approximation, as outlined in methods (*Eq. 3*). First of all, the result of this analysis confirmed that two of the parameters—*F*_{y} and *k*—are responsible for the rotation-direction dependent effects (in agreement with the results shown in Fig. 4), whereas apart from some variability, the parameters *S* and *F*_{z} are not rotation-direction dependent (Fig. 6). As expected, it is *F*_{y} that is responsible for the observed tilt-dependent asymmetry. To provide an overview of the average impact of selectively incrementing a model parameter on the output, we computed the relative contributions (Â/*Δβ̂*)·*ΔŜ*, (*B̂*/*Δβ̂*)·*ΔF̂ _{y}*, (Ĉ/

*Δβ̂*)·

*ΔF̂*, and (

_{z}*D̂*/

*Δβ̂*)·

*Δk̂*to the total change of the model output

*Δβ̂*across the tested tilt angles (Fig. 6). Several observations can be made from this analysis. First, the impact of Ŝ is the largest at about 30° tilt and, as expected, zero in upright and 90° right or left ear down (see effect of

*S*on scaling constant

*N*in methods). Second, the impact of

*F̂*is largest in 90° right or left ear down (where it is directed perpendicular to gravity), but zero in upright (where it is parallel to gravity). Third, the impact of

_{z}*F̂*is largest in upright (where it is directed perpendicular to gravity). It is near zero in left or right ear down after cw and ccw rotation, respectively (i.e., tilts reached from below). In contrast, when the same tilts are reached by ccw or cw rotation (i.e., tilts reached from above),

_{y}*F̂*has again a significant impact. A geometrical explanation for this more complicated effect of

_{y}*F̂*in ear down positions depending on the rotation direction is provided in the discussion (see Fig. 8). In the constant acceleration paradigm, variations of Ŝ and

_{y}*k̂*have an impact similar to that in the constant velocity paradigm. However, differences emerge for variations of

*F̂*, whose impact in 90° side down positions grows larger, and for

_{z}*F̂*, whose influence becomes now symmetric in 90° side down positions without losing its impact in upright position.

_{y}### Dependence of E- and A-effect on the direction of approaching the stop angle

Does it matter for the subjective visual vertical whether it is estimated after a final head orientation has been approached from upright or from upside down (see Fig. 1, *A* and *B*)? To investigate the influence of the direction of approach, we replotted the data in Fig. 3 by combining the errors at left ear-down stops for ccw rotations with those at right ear down stops for cw rotations, yielding the error curves for stops from upright (Fig. 7, *A* and *B*, black error curves). Similarly, we combined the errors at left ear-down stops for cw rotations with those at right ear down stops for ccw rotations, yielding error curves for stops from upside-down (Fig. 7, *A* and *B*, gray error curves). Note that this rearrangement of the errors combines responses that are associated with oppositely pointing jerk signals. More specifically, tilts toward right ear down correspond to cw roll and are associated with a positive jerk at stop of rotation, whereas tilts toward left ear down correspond to ccw roll and are associated with a negative jerk at stop of rotation. Because of the resulting discontinuity of jerk in upright position, it is not possible to fit these rearranged data with a single curve.

The three-way repeated measures ANOVA with direction of approach, tilt angles, and test delay as main factors was performed on a total of 84 trials (excluding zero tilt trials). Statistics are presented in Table 3. As in the previous ANOVA analyses, there was a large main effect of tilt angles. Conversely to the previous ANOVA, however, these analyses did not reveal any significant main effect of test delay or interaction of tilt angles and test delay. Specifically, the interaction of tilt angles and test delay yielded a *P* = 0.05 at a high power, indicating that it was not meaningful.

As we could expect from the analyses performed with rotation direction as factor, there was neither a main effect of direction of approach nor a significant interaction between direction of approach and test delay for any of the two paradigms. Instead, the error pattern in the constant velocity paradigm varied with the direction by which a particular tilt angle was approached, as shown by the significant interaction between direction of approach and tilt angles. This effect was meaningful, as indicated by the large partial η^{2}. For the largest tilt angles (±90°, but also for −60°), the A-effect was far more pronounced when the angle was approached from upright (Fig. 7*A*, *top*, black curve) than from upside down, where it was even inverted for the ±60° angles (Fig. 7*A*, *top*, gray curve). Similarly, the E-effect that can be generally seen at ±30° angles was more intense when approached from upside down. None of the above was true for the constant acceleration paradigm, as shown by the nonsignificant interaction between direction of approach and tilt angles.

However, for both the constant velocity and the constant acceleration paradigms, the statistic revealed a complex significant interaction between direction of approach, tilt angles, and test delay. For both paradigms, settings almost did not evolve with time when the tilt angle was approached from upright. There was a decrease of the A-effect between the first and the third settings, especially in the constant velocity paradigm, while the E-effect at ±30° angle, which was inexistent initially, tended to slightly increase with time. In contrast, in the constant velocity paradigm, the estimation of SVV changed dramatically over time in stop positions approached from upside down (Fig. 7*A*; compare curves in *top* and *bottom* panels). Just after stop rotation, not only no A-effect at all was present at ±90°, but even an E-effect can be seen at ±60°, in addition to the usual tendency at ±30°. After 30 and 60 s, the A-effect appeared at the largest tilt angles, while the E-effect completely disappeared at ±60° and remained at ±30°. For the constant acceleration paradigm, effects produced by an upside-down approach were not so dramatic. Just after stop rotation, the unusual tendency to overcompensate ±60° tilt angles was nonexistent. However, with time both the E-effect and the A-effect increased slightly.

## DISCUSSION

Estimation of the subjective visual vertical after a sudden stop following constant velocity roll rotations partly shifts the estimation errors in the direction of the previous rotation. This effect is transient and completely disappears after about 1 min. In the following, we will discuss the characteristics of this transient error component in the light of previous studies and speculate about their possible sensory origin based on theoretical modeling.

### General characteristics of the subjective visual vertical after roll rotation

Estimation of the visual vertical shows immediately after cessation of constant velocity rotation an angular shift in the direction of the preceding rotation direction, confirming earlier observations (Schöne 1964; Schöne and Lechner-Steinleitner 1978; Udo de Haes and Schöne 1970; Von Holst and Grisebach 1951). In agreement with previous reports the observed shift disappears about 1 min after stop of rotation (Udo de Haes and Schöne 1970; Von Holst and Grisebach 1951). In contrast, there was little shift of the estimated visual vertical after constant acceleration rotation. Postrotatory semicircular canal activity may well explain the angular shift of the estimated visual vertical at stop of rotation. It probably results from the vertical semicircular canal activity that is generated during deceleration. This activity is no longer appropriately counterbalanced by the activity generated at onset of rotation due to the subsequent long-lasting constant velocity rotation. Consistent with this interpretation is that the shift depends, at least in part, on the rotation direction, that it disappears after about three time constants of the semicircular canals, and that it is much smaller in the constant acceleration than in the constant velocity paradigm. Similar shifts of the subjective visual vertical have also been reported by Pavlou et al. (2003) during and after cessation of constant velocity yaw rotation about an earth vertical axis within the first 20 s. Similarly, large field optokinetic pattern motions about the subject's roll axis induce a shift of the perceived direction of gravity in the opposite direction of the pattern motion (Dichgans et al. 1972). Interestingly, these otolith–optokinetic interactions share the same head tilt dependency as the otolith–semicircular canal interactions described in the present experiments. If the head tilts opposite to the direction of the induced postrotatory canal activity (e.g., stop at right ear down after cw rotation; see Fig. 8) or the optokinetic flow field, then the observed shift is maximal (Dichgans et al. 1974; Young et al. 1975). In the following, we will further analyze the causes underlying this shift of the subjective visual vertical.

First of all, the estimates of the visual vertical following stop of rotation are only partly characterized by a shift of the error pattern. Our data also evidence a marked response asymmetry that disappears with time after stop (Fig. 3*A*). The question is then whether the unbalanced postrotatory vestibular activity can explain all the differences between early and late estimations. Since the postrotatory activity of the canals does not depend on the direction of static roll tilt, one would expect that it results in a symmetric, both tilt-direction and tilt-magnitude independent effect on the errors. This, however, is clearly not the case. First, after both cw and ccw rotations, estimation errors are similar in close to upright positions (Fig. 3*A*). Second, the difference between the transient and the steady-state error profiles, which represents the dynamically induced error increment (Δe) after stop of rotation, is tilt-direction dependent (Fig. 5). The origin of this asymmetry cannot be due to the postrotatory semicircular canal signals alone. Rather, we will argue that the dynamic error most likely reflects a nonlinear semicircular canal–otolith interaction and, in fact, largely excludes a relevant participation of proprioceptive signals from the somatosensory system.

### Differential contribution of otolith and semicircular canal signals

To estimate the contribution of different sensory signals, we used a model that was earlier proposed by Mittelstaedt (1991) with the following modifications. First, we extended Mittelstaedt's concept of an idiotropic vector (a hypothetically constant vector along the *z*-axis), by replacing it by a vector that is not invariably aligned with the head *z*-axis but may tilt away from it (Jaggi-Schwarz and Hess 2003). Second, we assumed that at stop of rotation, vestibular signals proportional to the time rate of change of gravity (also called gravitational jerk) also influence the estimation of the visual vertical (for a peripheral coding of such signals by the otolith organs, see Fernandez and Goldberg 1976a,b,c). These signals indicate the plane and direction of the previous rotation (Hess 1992). To implement this idea, we lump the two independent parameters K_{s} and K_{c} in Mittelstaedt's model together in the form of a single parameter *k* that characterizes the strength of the contribution of the gravitational jerk.

A close comparison of the fitted parameters in the constant velocity and constant acceleration paradigms leads to a number of interesting observations. First, the observed dynamic error increment can be attributed in part to the postrotatory semicircular canal activity (Fig. 5, *A* and *B*), which is reflected by the significant contribution of the parameter *k*. Remember that this parameter describes the fraction of angular velocity that contributes to a shift of the subjective visual vertical via jerk signals at stop of rotation. Second, this contribution does gradually disappear with increasing delay after rotation. Third, it is very small in the constant acceleration paradigm. If the semicircular canal postrotatory activity would be the only factor, the crucial question is why this effect does not shift the error profile evenly across all tilt angles (Fig. 3*A*, *top* and Fig. 5). The fact is that only a relatively small shift occurs in the tilt range of ±30° around upright, as reported by Pavlou et al. (2003). For larger tilt angles, this shift increases in line with previous reports (Pavlou et al. 2003; Udo de Haes and Schöne 1970).

A closer analysis of the possible contributing factors to the error profile suggests that the dynamic error increment results not directly from the postrotatory semicircular activity, but rather from the particular interaction of this activity with the graviceptive signals (*Ĝ* in the model) and a general force signal (vector *F̂* in the model; same physical dimension as *Ĝ*, i.e., acceleration per unit mass or specific force). Before interacting with graviceptive signals, angular velocity signals need to be spatially transformed, since they encode a rotation about an axis perpendicular to the roll plane, whereas graviceptive signals encode a particular head roll orientation in this plane with respect to gravity. The jerk vector—i.e., the cross-vector product of the angular velocity and the graviceptive signals (see methods)—captures the essential of the required spatial transformation. Similar transformations have been considered in this context by Glasauer (1992). The underlying computations involve rather complex nonlinear interactions between semicircular canal signals and signals encoding the direction of gravity. Due to their rather limited spatial tuning properties with respect to the direction of gravity, proprioceptive–somatosensory information can hardly play an important role in these computations. In contrast, tonic otolith afferent signals are perfectly suited to mediate this spatial transformation. In addition, phasic otolith signals that carry by themselves jerk-like properties, can easily contribute to the encoding of gravitational jerk, independent of semicircular canal signals (Fernandez and Goldberg 1976a,b,c; Hess 1992, 2006). The fan-like arrangement of utricular and saccular otolith receptors facilitates the encoding of the spatial aspects of gravitational jerk by population vector coding (Dayan and Abbot 2001; Hess 1992). Physically, the gravitational jerk is directed along the subjects' *y*-axis when stopping in upright, whereas it is directed along the *z*-axis when stopping in 90° left or right side down. In these cardinal tilt positions, the model predicts that the estimated gravity vector does not deviate from the true earth vertical direction because either the *y*- or the *z*-component of *Ĝ* is zero (see the Ŝ contribution in Fig. 6 and definition of *Ĝ* in methods). As a consequence, the estimated jerk (*Ĵ*), which invariably signals the previous rotation direction, does also not deviate from the true earth horizontal. In contrast, the *F̂*-vector must reflect a head tilt-independent signal by the very definition of the model. Its *z*-component, which is equivalent to Mittelstaed's idiotropic vector, is found to remain approximately invariant, whereas the *y*-component closely matches the induced jerk in magnitude (Fig. 4, *top*, triangles and circles).

How do these two hypothetical vectors, the jerk *Ĵ* and the *F̂*-vector, influence the subjects' estimation of earth vertical direction according to the proposed modifications of Mittelstaedt's static model? The *F̂*-vector influences the error curves in two ways. First, in final head orientations close to upright, it approximately cancels the jerk vector due to the close match of its *y*-component with the jerk vector in terms of direction and magnitude (*Ĵ _{z}* = 0,

*Ĵ*≈

_{y}*−F̂*; see Fig. 8,

_{y}*A*and

*B*). As a result, estimation of the visual vertical is close to veridical. Second, it leads to an A-effect in left or right side down positions under the condition that these orientations have been approached from upright (Fig. 8,

*C*and

*D, top half circle*). When these same positions are approached from upside down, the estimation of earth vertical is predicted to be close to veridical (Fig. 8,

*C*and

*D*,

*bottom half circle*). Both of these effects reflect the influence of the tilt-invariant

*F̂*-vector. After cw rotation, it tilts always toward the left ear (Fig. 8,

*A*and

*C*), whereas after ccw rotation it tilts toward the right ear (Fig. 8,

*B*and

*D*). Interestingly, the

*F*

_{z}-component does not change much its magnitude from immediately after stop to steady state. To sum up, it is the interaction of the body-referenced

*F̂*- and space-referenced

*Ĵ*-signals that produces the time- and tilt-dependent errors. The error asymmetry is mainly due to an asymmetric, rotation-direction dependent contribution of the

*F̂*-signal (Fig. 6).

_{y}What could be the physiological equivalent of the *F̂*-vector signal and, in particular, its transient *F̂ _{y}*-component? Based on the model structure, it does not directly reflect an inertial signal mediated by otolith or other sensory afferents because of its directional invariance across the tested tilt angles. In contrast to the graviceptive signals (modeled by

*Ĝ*) and their time rates of change (modeled by

*Ĵ*), the

*F̂*-vector signal is not space- but body-referenced. Although it most likely does not represent the action of a sensory input, its time evolution closely matches that of the postrotatory canal activity, suggesting that it is correlated to the jerk signal. Moreover, close to upright orientations, the transient

*F̂*-component always opposes the jerk vector

_{y}*Ĵ*. Furthermore, depending on the preceding rotation direction, it points in opposite directions at the same head down orientations (see Fig. 8,

*C*and

*D*). One possibility to reconcile all these findings is to consider

*F̂*as the correlate of an efference copy of a righting signal. Righting signals prevent the subject from falling after a sudden stop from rotation by opposing the head jerk. This sort of interaction appears to make perfect sense when the subject reaches the final tilt from upright. In these cases, the

_{y}*F̂*-signal seems to correspond to an efference copy of a righting command (Fig. 8,

_{y}*C*and

*D*,

*top half circles*), which points against both the previous direction of rotation and the direction of gravity. However, when the subject approaches the final tilt from upside down (Fig. 8,

*C*and

*D*,

*bottom half circles*), the

*F̂*-signal seems to point opposite to a righting reflex that helps to right up the head, since it points now along the pulling direction of gravity. However, it would still help to right up the head if the fixed point or pivot of the righting reflex has shifted now from the feet to the head. Interestingly, evidence for such a reference change from the feet to the head seems to have been indeed observed when subjects are rotated toward or through upside-down positions (Kaptein and Van Gisbergen 2005).

_{y}Traditionally, the *z*-component of the proposed general *F̂*-vector has been interpreted as an idiotropic bias directed invariably along the body longitudinal axis (Mittelstaedt 1983). In our analysis, the *F̂*-vector, although generally directed toward the top of the head, can tilt toward the right or left ear depending on the dynamic situation. In the framework of Bayesian modeling, the idiotropic bias could result from an orientation bias toward earth vertical, reflecting a higher likelihood to stay in upright or close to upright positions (De Vrijer et al. 2008; Eggert 1998; MacNeilage et al. 2007). Our results are in line with such a concept, except that it appears that the orientation bias cannot be modeled by a single fixed vector, but rather by a fan of normally upward directed vectors that describe an inverted cone with axes parallel to the *z*-axis in a body referenced frame.

### Hysteresis: errors differ for tilts from upright compared with tilts through upside-down position

The observed asymmetry of the dynamic increment errors in the constant velocity paradigm (Fig. 5) suggests an alternative way to look at the modulation of the error profile as a function of the roll tilt angle. When the final orientation is approached from upright, the error profile shows a significant A-effect only for the largest tilt angles, whereas the estimates are close to veridical at midrange tilts (Fig. 7*A*, *black curves*). In contrast, when approaching the final orientation from below after passing through an upside-down position, the error profile shows on average an E-effect for tilts between upright and 60° left or right ear down, whereas the estimates are close to veridical at 90° left and right ear down (Fig. 7*A*, *gray curves*). These differences are much less pronounced in the constant acceleration paradigm (Fig. 7*B*), probably due to the more consistent pattern of vestibular orientation cues in this paradigm.

The strong asymmetries of the SVV response errors, measured immediately after tilt, clearly depended on whether the final head position was approached from upright or from upside down (Figs. 5 and 6). This effect, called *hysteresis*, is explained in the model by a large jerk signal that accompanies the abrupt stop of the subjects after constant velocity rotation. In contrast, the observed hysteresis was relatively small in the constant acceleration paradigm and it largely disappeared in both paradigms about 30 to 60 s or more after the stop. Small differences seem to remain, however, as suggested by extrapolating the fitted curves to a tilt range including upside-down positions (see Fig. 5*A*). Since we restricted our study to a tilt range of ±90°, we cannot make any firm conclusion about the response characteristics beyond this range. However, it has been reported by Kaptein and van Gisbergen (2004, 2005) using a quasi-static paradigm (30°/s constant roll velocity to final tilt positions, delayed SVV measurements 30 s after stop) that responses in a zone around ±45° about the upside-down position (180°) show abrupt transitions from A-type to E-type errors whenever the final tilt exceeds 135°. These observations are compatible with the assumption of a reference shift in estimating the SVV from the feet to the head, as pointed out by these authors. Despite the fact that our paradigm did not involve final tilt positions beyond ±90°, the error characteristics observed immediately after stop from constant velocity rotation seems to result in a similar reference switch regarding the pivotal point of a postulated righting signal. It needs to be stressed, however, that our paradigm involved longer-lasting rotations and a much stronger vestibular stimulus at stop of rotation than in the experiments by Kaptein and van Gisbergen (2004, 2005). The postulated reference switch in our experiments was present only when approaching the final tilt angle from below (Fig. 8, *C* and *D*). This interpretation of our data is supported by a recent study of Vingerhoets et al. (2008), which reports a bimodal pattern in SVV responses that alternated between the A- and the E-effects on entering the range of near-inverse tilts in the course of constant velocity roll rotations. Finally, as reported by others (Kaptein and van Gisbergen 2005; Udo de Haes and Schöne 1970), the response errors clearly depended on the direction of the preceding roll rotation (Figs. 5 and 8, *C* and *D*), an effect that was small in the delayed responses in the limited tilt range of ±90°. Using a similar constant velocity paradigm restricted to roll tilts in the range of ±90°, we have earlier observed small hysteresis effects in SVV responses, which showed a significant correlation to the parameter *F*_{y} based on fits of *Eq. 2* (Jaggi-Schwarz and Hess 2003). A hysteresis has also been reported in the otolith–ocular reflexes during quasi-static roll motion (Palla et al. 2005). In this context, we cannot exclude that torsional eye position (ocular counter roll) contributed to the described perceptual errors (Wade and Curthoys 1997). Such an influence should gradually increase in an approximately symmetric manner to a peak around ±90° side down. The E-effects in our experimental data (Jaggi-Schwarz and Hess 2003; Jaggi-Schwarz et al. 2003) only partially follow such a pattern, suggesting that there must be additional factors shaping the error pattern in SVV responses. The role of postrotatory torsional eye velocity that appears to change orientation and approximately parallel the SVV responses in the constant velocity paradigm remains to be determined (Lorincz and Hess 2005).

This study has exposed complex interactions between vestibular cues that influence the perception of the visual vertical. We have provided evidence that the tilt-direction independent rotational shift of the subjective visual vertical can be explained by nonlinear interaction of sensory signals from the semicircular canals and otoliths (including gravitational jerk signals) and a general force signal that reflects an interaction with an efference copy of righting signals. We conclude that the perception of the visual vertical can be biased not only by the interaction of static and dynamic vestibular cues, but also by efference copy signals related to the ongoing motor control of balance.

## GRANTS

This work was supported by Swiss National Foundation Grant 31-100802/1 and a Betty and David Koetser Foundation for Brain Research grant.

## Acknowledgments

We thank E. Buffone, M. Dürsteler, U. Scheifele, and A. Züger for excellent technical assistance, and the anonymous referees for helpful comments.

## Footnotes

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

- Copyright © 2008 by the American Physiological Society