Exp Brain Res (2006)
DOI 10.1007/s00221-006-0385-y
R ES E AR C H A RT I C L E
Simone B. Bortolami Æ Alberto Pierobon
Paul DiZio Æ James R. Lackner
Localization of the subjective vertical during roll, pitch, and recumbent
yaw body tilt
Received: 13 May 2005 / Accepted: 13 January 2006
Springer-Verlag 2006
Abstract Localization of the subjective vertical during
body tilt in pitch and in roll has been extensively studied
because of the relevance of these axes for aviation and
control of posture. Studies of yaw orientation relative to
gravity are lacking. Our goal was to perform the first
thorough evaluation of static orientation in recumbent
yaw and to collect as efficiently as possible roll and pitch
orientation data which would be consistent with the
literature, using the same technique as our yaw tests.
This would create the first comprehensive, coherent data
set for all three axes suitable for quantitative tridimensional modeling of spatial orientation. We tested
localization of the vertical for subjects tilted in pitch
(100 to +130), in roll (90 to +90), and in yaw
while recumbent (80 to +80). We had subjects point
a gravity-neutral probe to the gravitational vertical
(haptically indicated vertical) and report verbally their
perceived tilt. Subjects underestimated their body tilts in
recumbent yaw and pitch and overestimated their tilts in
roll. The haptic settings for pitch and roll were consistent with data in the literature obtained with haptic and
visual indications. Our data constitute the first tridimensional assessment of the subjective vertical using a
common measurement procedure and provide the basis
for the tri-axial modeling of vestibular function presented in the companion paper.
Keywords Spatial orientation Æ Otolith Æ
Somatosensation Æ Subjective vertical Æ Gravity Æ
Roll tilt Æ Pitch tilt Æ Recumbent yaw tilt Æ
Sensory illusions Æ Haptic vertical
S. B. Bortolami (&) Æ A. Pierobon Æ P. DiZio Æ J. R. Lackner
Ashton Graybiel Spatial Orientation Laboratory, MS 033,
Brandeis University, Waltham, MA 02454-9110, USA
E-mail: Simborto@brandeis.edu
Tel.: +1-781-7362033
Fax: +1-781-7362031
P. DiZio Æ J. R. Lackner
Volen Center for Complex Systems, Brandeis University,
Waltham, MA 02454-9110, USA
Introduction
Maintaining orientation to the upright is a key feature of
human and animal behavior. Many systems contribute
to this capacity including the auditory, visual, vestibular,
somatosensory, proprioceptive, and motor systems.
Considerable emphasis has been placed on understanding the contribution of the vestibular system to orientation because of its significance for aviation and space
flight, where unusual force levels and accelerations are
encountered. Illusions involving misperception of self
and vehicle orientation arise from transient (e.g. catapult
launches) or quasi-static (e.g. prolonged banked turns)
changes in gravitoinertial force. Most of the work on
orientation mechanisms has concentrated on the roll and
pitch axes relative to gravity because of their relevance
for aerospace flight and normal postural control on
Earth (e.g. Bourdon 1906; Clark and Graybiel 1962;
Colenbrander 1964; Correia et al. 1968; Curthoys et al.
1990; Mittelstaedt 1983, 1992; Mast and Jarchow 1996;
Glasauer and Mittelstaedt 1997; Bohmer and Mast
1999; Van Beuzekom and Van Gisbergen 2000; Clement
et al. 2003; Kaptein and Van Gisbergen 2004). Spatial
orientation dynamics with the head horizontal has been
studied during horizontal axis rotation (Benson and
Barnes 1970; Mast et al. 2002); however, static performance with the body horizontal and tilted about its
spinal axis relative to gravity, which we call recumbent
yaw, is virtually uncharted.
Many techniques have been used to assess apparent
orientation to gravity. Visual measurements usually
involve setting a luminous line or shape to what the
subject perceives to be the vertical or horizontal.
Haptic settings involve a blindfolded subject manually
aligning a gravity-neutral rod with the perceived
gravitational vertical. The latter approach has the
advantage of not being influenced by vestibulo-ocular
reflexes. For example, during roll body tilt, the eyes
counterroll in the opposite direction by approximately
10% of the tilt (Miller and Graybiel 1962). Both tilt
amplitude and background force level affect the magnitude of the counterrolling. During pitch tilt, there is
a doll’s eye reflex (Citek and Ebenholtz 1996) that
influences eye position.1 The presence of these reflexes
may affect orientation judgments that are made using
visual indicators. The interrelation of internal representations of gravity and visual perception is still an
object of active investigation (cf. Van Beuzekom and
Van Gisbergen 2000). Betts and Curthoys (1998) have
shown that during body tilt settings of the visually
perceived vertical and horizontal are not orthogonal to
one another. Consequently, care must be taken in
inferring the apparent orientation of the body from
visual settings.
Our ultimate objective is to develop an adequate
model of tri-dimensional mechanisms of spatial
orientation that will be applicable regardless of gravitoinertial force level. To develop and test a
tri-dimensional model of spatial orientation we needed
a comprehensive data set not influenced by ocular
reflexes for all three independent axes. To produce
such a data set, we tested blindfolded subjects at
different angles of tilt in roll and in pitch, and at
different yaw angles while they were recumbent. Subjects used two methods to indicate their perceived self
tilt with respect to gravity, a hand-manipulated rod
and verbal reports of self tilt. They were exposed to
roll and pitch angles that generally equaled or exceeded ones used in earlier studies of these axes. We
compared our data for the roll and pitch axes with
those available in the literature collected using visual
and haptic indication techniques to see which methods
gave similar results. There was no precedent for
recumbent yaw axis orientation judgments.
Materials and methods
Subjects
We tested 27 naı̈ve subjects. The subjects had been
screened using a medical history questionnaire to exclude any candidates with sensory-motor or balance
impairments that could have compromised their performance. They ranged from 20 to 60 years of age. The
experimental protocol was approved by the Brandeis
University Human Subjects Review Board, and each
subject gave written informed consent. Three subjects
participated in all three experimental conditions, others
in one or two. Table 1 shows the overlap of subjects in
the three conditions. A larger sample was tested in
recumbent yaw than in pitch and roll because there was
no precedent for the yaw data.
1
Unlike ocular counterrolling, the doll’s eye effect is eliminated by
visual fixation. The effect influences mainly the vertical axis, the
eyes pitch upward when the subject is pitched forward and downward during backward tilt.
Table 1 Overlap of subjects across the roll, pitch, and recumbent
yaw conditions
Pitch, N=7
Roll, N=6
Recumbent yaw,
N=25
1
2
3
4
5
6
7
1
1
2
6
7
8
9
10
4
5
6
7
8
9
11–27
Apparatus and experimental conditions
Two pieces of equipment were used to orient subjects
relative to the gravitational vertical, an upright pitch/
roll device and a bed-like yaw device. Figure 1a shows
the sign convention and frame of reference we adopted
for our experiments. Positive angles represent pitch
forward, roll right ear down and recumbent yaw left
ear down (right hand coordinate system). One device
provided roll (±90) and pitch (100 to +130) body
tilts, the other allowed for recumbent yaw (±80) tilts.
Figure 1b depicts the three axes tested in the experiments, the subjects’ body configuration, and the rod
(gravity-neutral probe) subjects used for indicating the
vertical (haptically indicated vertical). Both devices
were manually tilted to prescribed angles read off from
protractors graduated in 1 increments. The roll axis
corresponds to the subject’s naso-occipital axis; and,
the roll angles used were ±90, ±70, ±50, ±30,
0. The pitch/roll device could only be tilted backwards
in pitch from the vertical start position; therefore,
subjects were positioned face-out of the apparatus for
pitch back trials and face-in for pitch forward trials,
which were run in separate sessions. Forward pitch
angles of 0, 10, 30, 50, 80, 110 and 130 were
used. Pitch backward angles were limited to 10,
30, 60, 90, 100, because of limitations imposed by restraining subjects facing out of the apparatus. The pitch axis was about 85 cm posterior to the
body’s center of mass for pitch back and 85 cm
anterior for pitch forward. Subjects were held within
the body cradle of the pitch-roll device by means of a
four-prong head clamp, a form-fitting Velcro jacket,
pads, and straps. Each subject was secured in the test
apparatus with attention to avoiding protruding pressure points and ensuring comfort. The yaw axis
bed rotated recumbent subjects about their spinal axis
(cf. Fig. 1b). Recumbent yaw angles of ±80 in 20
divisions were used. Restraints in the recumbent device
included a breastplate, a form-fitting, hard-foam head
holder, and individually adjusted leg, hip, and shoulder
restraints.
A
Head alignment
+Yaw
+Pitch
+Roll
B
PITCH
BKW(-)
FWD(+)
For roll tilts, subjects fit into the device with their head
in a natural upright position, which we defined as 0 roll.
We did not attempt to measure the horizontality of the
inter-pupillary line. For tilts in recumbent yaw, the
Polhemus sensor signal value was offset to zero with the
bed in the nominal 0 or horizontal supine position. For
tilts in pitch, the subject was restrained in what felt like a
natural upright head posture. We then measured the
angle of the Frankfort plane (DeBeer 1947) between the
‘‘lower border of the eye socket and the meatus of the
ear’’ (Pozzo et al. 1990) with a protractor, for each
subject. We considered the head to be upright when the
Frankfort plane was pitched up 30 and we offset each
subject’s Polhemus readings so that 0 would signify this
definition of the upright. Head position fluctuations
were minimal, circa 1, in all axes.
Task
ROLL
RED(+)
LED(-)
RECUMBENT YAW
LED(+)
RED(-)
Fig. 1 a Sign convention and body-fixed reference frame used. b
The different tilt conditions tested. The subject used the illustrated
rod to point to the perceived gravitational vertical (haptically
indicated vertical). The crosses represent the body rotation axes; the
indicator rod always rotated about an axis through its center,
parallel to the body rotation axis. Forward pitch is positive, rightear-down roll is positive, and left-ear-down recumbent yaw is
positive. The abbreviations are as follows: backward (BKW),
forward (FWD), left ear down (LED), and right ear down (RED)
Each tested angle was presented three times in a
random order yielding three data points per tilt angle per
tested axis per subject. Although device orientations
were manually set according to protractor readings, the
subject’s head angles were the dependent variable of
interest. Orientation of the head and of the indicator rod
were measured relative to a room-fixed frame of reference with a Polhemus 3SPACE device. Sensors were
mounted on the head and indicator rod. Metallic objects
can distort the room-fixed reference magnetic field generated by the Polhemus device, but we used a protractor
to calibrate the Polhemus to within 0.5 accuracy. The
following procedures describe our conventions for
reporting head angle.
At each test orientation, the experimenter asked the
blindfolded subject to align (‘‘point to the vertical’’) the
pivoting instrumented rod (8·1·1/2 in., gravity-neutral
probe) with what he/she thought was the gravitational
vertical (haptically indicated vertical). The rod pivoted
about an axis parallel to the tilt axis of the device and
was symmetrically balanced to avoid gravitational torques being generated as a function of tilt position. The
rod was positioned so that the subject could manipulate
it using the tips of the fingers of both hands to make the
judgment. After reorientation to a new tilt position, the
subject was instructed to rotate the rod from side to side
(‘‘turn it side-to-side’’) before indicating the perceived
vertical. At least 20–30 s elapsed at each tilt position
before the subject performed the pointing task. This
interim was long enough for the transient response of
the semi-circular canals to decay substantially and for
the subject to make a definitive determination. After
recording the Polhemus measurement of rod orientation,
the experimenter asked the subject to report verbally his/
her perceived body orientation in degrees of tilt from the
vertical (verbal report of self tilt). This report was
manually recorded. Subjects did not have any difficulty
in performing the tasks. Each test period (roll, pitch, or
recumbent yaw) lasted approximately 40 min. The presentation order of the body tilts was randomized for
each of the test axes. The different axes were tested on
separate days.
Data reduction
We define haptically indicated body tilt as the difference
between head angle and rod angle when the subject was
indicating the vertical with the rod. Verbally reported tilt
was supplied directly by subjects. In addition, we define
the errors in haptically indicated tilts and in verbally
reported tilts as follows (see Fig. 2):
ERRORROD ¼ haptically indicated tilt
physical head tilt;
ð1Þ
ERRORVERBAL ¼ verbally reported tilt
physical head tilt:
ð2Þ
Figure 1 illustrates the sign conventions used in Eqs. 1
and 2. The interpretation of the calculated errors is as
follows: If the subject using the rod indicated the vertical on the opposite side of the gravity vector with
respect to the actual body orientation, we assumed that
he/she felt more tilted than actually was the case (cf.
also Howard and Templeton 1966). If the subject
indicated the vertical on the same side of his/her body
tilt with respect to gravity, we assumed that he/she felt
less tilted than was actually the case. Over-estimation of
tilt is signified by positive errors for positive tilts and
negative errors for negative tilts and vice versa for
under-estimation.
For the roll and yaw conditions, head angles were
equated to the Polhemus sensor readings and these
values were uniformly within 1 of the prescribed tilt
angles. For the pitch condition, small variations in the
A
Results
HAPTIC
g
error (+)
head
tilt (+)
indicated
vertical (-)
indicated
tilt (+)
B
VERBAL
g
head
tilt (+)
reported
tilt (+)
positions subjects chose their head to be constrained in
led to between-subjects variations in measured head
position relative to the goal orientations. (Such differences usually exist in experiments involving body tilt
with respect to gravity but are generally ignored during
data presentation and analysis.) Because we wanted to
compare subjects across precisely the same physical head
tilt angles, i.e. the Frankfort plane angles, we interpolated the haptic indications and verbal reports of the
subjects to the prescribed angles (100, 90, 60,
30, 0, 10, +10, +30, +50, +80, +110,
+130). Before this correction, the seven subjects in the
pitch conditions had discrepancies between prescribed
and actual angle of 1, 2, 0, 4, 0, 0, and 4 for pitch
back, and discrepancies of 1, 1, 1, 4, 1, 4, and 2 for
pitch forward. Thus, for example, if the desired physical
position of the subject’s head was 10 pitch forward with
respect to gravity (i.e. the desired Frankfort plane tilt
was 20 backward with respect to horizontal), but the
actual head orientation during testing resulted in 11
pitch forward (1 discrepancy), the subject’s haptic and
verbal reports were linearly interpolated to expected 10
values.
error (+)
Fig. 2 a Diagram, for the case of roll tilt, of quantities involved in
the calculation of the errors of the haptically indicated tilt. b
Diagram of quantities involved in the calculation of the errors of
the verbally reported self tilt. The interpretation of errors is as
follows: If the subject using the rod indicated the vertical on the
opposite side of the gravity vector with respect to the actual body
orientation, we assumed that he/she felt more tilted than actually
was the case. If the subject indicated the vertical on the same side of
his/her body tilt with respect to gravity, we assumed that he/she felt
less tilted than was actually the case. Over-estimation of tilt is
signified by positive errors for positive tilts and negative errors for
negative tilts and vice versa for under-estimation
The results for the three different axes are presented in
Fig. 3 plotted in terms of head tilt with respect to gravity
and the associated haptically indicated and verbally reported self tilts with respect to the upright. The haptically indicated tilt represents the angle between the
haptically indicated vertical and the subject’s z-axis (see
Fig. 2). Each point in Fig. 3 represents the average of
the three judgments each subject made at each head tilt.
Different symbols are used for different subjects in the
pitch and roll conditions. There were too many subjects
in the recumbent yaw condition to differentiate with
different symbols. For statistical analysis of our data, we
used median scores across subjects for each head tilt
angle in pitch, roll, and recumbent yaw, because it is a
conservative estimate of central tendency in relatively
small samples.
Table 2 reports the linear, bivariate relationships of
haptically indicated and verbally reported tilt (medians)
with the physical head tilt. The linear fits accounted for
most of the variance, with r2 values approximately unity.
The slopes of the regression lines are very close to but
nevertheless significantly different from unity, or ideal
performance (P<0.05). The slopes of the pitch and yaw
haptic and verbal tilt indications were significantly less
than ideal, and the slopes of the roll estimates were
greater than ideal. In each tilt axis condition, the slope
and y-intercept of the regression lines for the three
subjects who overlapped in all conditions were not significantly different from those of the other subjects in
that condition, however, the power of these tests was
low, less than 20%.
HAPTICALLY INDICATED TILT
N=7
PITCH [°]
100
VERBALLY REPORTED TILT
100
50
50
0
0
-50
-50
-100
-100
BKW -100
0
-50
100 FWD
50
BKW -100
-50
0
50
100 FWD
N=6
ROLL [°]
Fig. 3 Plots of haptically
estimated tilt and verbally
reported tilt of all subjects at
the tested head angles. Each
data point is the average of three
repetitions for one subject.
Different subjects are
discriminated by different
symbols in the pitch (N=7)
and roll (N=6) conditions, but
this was not practical for
recumbent yaw (N=25). Solid
lines represent the perfect
response. Figures 1 and 2
illustrate the definitions of the
angles plotted here
50
50
0
0
-50
-50
0
RECUMBENT YAW [°]
LED -50
50
RED
LED -50
0
50
RED
RED -50
0
50
LED
N=25
50
50
0
0
-50
-50
RED -50
0
50
LED
PHYSICAL HEAD TILT [°]
Table 2 also reports the RMS values of the median
haptic indication and verbal report errors with respect to
the perfect or ideal response. These values are small;
consequently, in order to make our analysis more
discriminative, we chose to work with error values (see
Eqs. 1, 2).
We attempted to fit the median error patterns for
each individual axis with linear and quadratic functions
of body tilt. The quadratic terms increased the variance
accounted for by a mere 1–6%, and the quadratic
coefficients were not significantly different from zero for
any axis. Therefore, we describe the median error patterns for each axis in terms of their linear relationship to
PHYSICAL HEAD TILT [°]
body tilt in that axis. The companion paper develops a
more complex, non-linear equation which is necessary to
fit the full tri-axial data set.
Pitch
Figure 4, upper panel shows the median error values of
haptically indicated tilts and of verbally reported self
tilts in pitch relative to actual tilt. The haptically indicated tilt errors show a trend for subjects to indicate
themselves as less tilted than they actually were. Within
the tested head range of 100 to +130, the magnitude
Table 2 Relationship of actual head tilt to median indicated tilt
Pitch
Roll
Recumbent yaw
Linear relationship with physical head tilt
Indicated tilt (haptic)
b=0.98 r2=1.00
Reported tilt (verbal)
b=1.08 r2=0.99
b=1.08 r2=1.00
b=1.06 r2=0.99
b=0.92 r2=0.99
b=0.93 r2=0.99
RMS error with respect to physical head tilt
Indicated tilt (haptic)
2.0
Reported tilt (verbal)
9.5
7.5
7.3
5.1
4.5
The first two rows report the slope (b) and the percent variance (r2) of perceived tilt accounted for by the linear relationship to actual tilt,
and the bottom two rows report the RMS errors of indicated tilts relative to actual tilt
of underestimation of pitch for haptic settings was a
linear function of head pitch (r2=0.45; F(1,7)=7.4,
P=0.024) with a shallow but negative slope, significantly different from zero (95% confidence interval=
-0.018±0.015). We performed a regression analysis on
the backward pitch and forward pitch error data separately and found statistically identical slopes. The pattern of errors for verbal reports differed from the haptic
indication errors, with small overestimates for forward
pitch in contrast to the underestimates produced by
haptic indications. For small pitch back angles, true
head tilt was verbally underestimated but overestimated
for angles more negative than about 30. A straight
line fit, across all head pitch angles, accounted for a
significant portion of the variance in verbal report errors
(r2=0.40; F(1,9)=5.9, P=0.04). A two-way, repeated
measures ANOVA showed an interaction between head
tilt and mode of indicating the vertical. Thus, the haptic
indication and verbal report errors differed significantly
(P<0.05) across tilt angles.
Roll
0
FWD
-20
INDICATED TILT
overestimation
MEDIAN ERROR [°]
ROLL
overestimation
20 BKW
20
MEDIAN ERROR [°]
PITCH
MEDIAN ERROR [°]
The error patterns for the haptic and verbal judgments
of roll tilt are plotted in Fig. 4, middle panel. The haptic
errors show overestimations of the magnitude of head
tilt across nearly all head tilt angles. The haptic overestimations increased as a linear function of head tilt
20
0
REPORTED TILT
Both the haptic indications and verbal reports exhibited
trends of underestimating recumbent yaw tilt relative to
gravity. The error patterns are plotted in Fig. 4, bottom
panel. The errors for the haptically indicated tilt were
well fit by a straight line (r2=0.86; F(1,7)=47.01,
P=0.0002) with a negative slope of 0.051±0.017
(95% confidence interval). The y-intercept of the line
was not significantly different from zero, indicating that
there was no overall bias in settings. The slopes of error
versus head tilt for right ear down tilts versus left ear
down tilts were not significantly different from each
other, indicating that the haptic indications of tilt were
symmetrical for left and right ear down tilts. By contrast, straight-line fits did not account for significant
variance in the verbal reports. Nevertheless, a two-way,
repeated measures ANOVA showed that the verbal report and the haptic indication patterns of errors were
not significantly different (P>0.05) as a function of head
tilt.
Discussion
LED
RED
overestimation
overestimation
0
RED
-20
Recumbent yaw
overestimation
-20
RECUMBENT
YAW
(r2=0.82; F(1,7)=30.8, P=0.001), with a positive slope
of 0.085±0.036 (95% confidence interval). The slopes
were not significantly different for left and right body
tilts. The y-intercept of the function fitting haptic error
versus
body
tilt
was
significantly
negative
(4.96±2.18, 95% confidence interval). The intercept
of the median value of the haptic errors at 0 of head tilt
was 4.3 with a 7.5 to 1.0 interquartile range.
Verbally, subjects tended to underestimate tilts up to
about ±60 and then overestimated for larger tilts.
Straight-line fits did not account for significant variance
in the verbal report errors. A two-way, repeated measurement ANOVA showed an interaction between head
tilt and method for indicating the vertical. This means
haptic errors and verbal report errors differed significantly (P<0.05) across tilt angles.
LED
overestimation
-100
-50
0
50
100
PHYSICAL HEAD TILT [°]
Fig. 4 Errors in haptic and verbal indications of self-tilt using
conventions of Fig. 2. Medians and inter-quartile ranges are
reported
Our objective was to collect the orientation data necessary for developing and validating a comprehensive, tridimensional model of static body orientation. The
present findings represent the first set of orientation
judgments of the vertical measured with the same techniques for body tilt about all three primary axes,
including for the first time systematic data on the
recumbent yaw axis.
We performed two types of comparisons of our data
with data sets from other investigators collected with
larger sample sizes and a variety of techniques for
indicating the vertical. All of the other investigators
published mean orientation values, so we computed
mean values across subjects for our data for comparisons to these data (see Figs. 5a, 6a, 8a and bottom
panels of Tables 3, 4). We also produced unbiased,
symmetrized versions of our roll and yaw (but not pitch)
error data. To do this, we added the y-intercept to the
data so it would pass through the origin at zero head tilt,
negated the error values associated with negative head
tilts and averaged them with the values of comparable
positive tilts, and then negated again the averages
associated with negative tilts. This process was done for
individual subjects, and, then we calculated median error values across subjects. We then compared our
unbiased, symmetrized medians to the unbiased symmetrized means of several other investigators (see
Figs. 5b, 6b, 8b and bottom panels of Tables 3, 4)
Comparison with earlier studies: roll
Bauermeister et al. (1964) had 60 subjects indicate the
subjective vertical with a rod (similar to ours) from
different roll tilt angles. Figure 5a plots the mean error
patterns of Bauermeister et al.’s (1964) subjects with that
of our subjects. The data in Fig. 5a are all means because Bauermeister et al.’s (1964) data are reported as
mean values. The correlation analysis between our data
and that of Bauermeister et al. (1964) yielded an r2 value
of 0.92 (significant, P<0.05) showing the compatibility
of the two data sets. In Fig. 5b, we have plotted Bauermeister et al.’s (1964) data in the form of symmetrized
A
ERROR [°]
20
Comparison with earlier studies: pitch
0
Figure 7 shows our haptic pitch error data plotted with
data from Schöne (1964) who employed a visual indicator. Schöne (1964) used a more limited range of pitch
angles compared to us but within that range, his mean
data are within the inter-quartile ranges of our median
data, and the two data sets are significantly correlated
(P<0.05), with a r2 value of 0.5. Schöne’s (1964) visual
indications also significantly correlate with our verbal
report data (r2 =0.5; P<0.05).
-20
Bauermeister, Means
B
Bortolami, Means
20
ERROR [°]
means together with our symmetrized, unbiased haptic
error data, which are medians across subjects. We correlated the two data sets and found an r2 value of 0.97
(significant, P<0.05).
We ran an equivalent comparison with roll data from
Miller et al. (1968) who had subjects indicate the vertical
using a line of light. Figure 6a presents the means of
errors of haptically indicated roll tilts for our data with
those from Miller et al. (1968). The correlation was
significant, r2=0.63. Figure 6b shows that the two
symmetrized data sets (means for Miller et al. (1968) and
medians for our data) virtually overlap for a ±70 range
of roll, and are correlated with an r2 value of 0.99 in that
range (significant, P<0.05). Beyond ±70 our error
data plateau and Miller et al.’s (1968) decline sharply
(the two traces are still significantly correlated over the
full ±90 range, P<0.05, r2=0.51). The data of Bauermeister et al. (1964) also plateaus beyond about ±70
(see Fig. 5). Miller et al. (1968) also measured the ocular
counterrolling exhibited by their subjects at the different
roll tilts. We were able to fit their ocular counterrolling
data with the function: 5.3 tan1(head tilt/22), with
head tilt specified in degrees. Figure 6b also presents
Miller et al.’s (1968) data ‘‘corrected’’ for the calculated
eye counterrolling magnitude for each head tilt angle2.
The correlation of our median data with their corrected
mean roll data is very poor, r2=0.16. These patterns
show that our haptic indications and Miller et al.’s
(1968) visual settings of the vertical are fully compatible
without any need to make a correction for ocular
counterrolling.
0
Comparison with earlier studies: recumbent yaw
-20
Bauemeister, Symmetrized means
Bortolami, Symmetrized medians
0
-100
-50
LED
PHYSICAL HEAD ROLL [°]
50
100
Only DiZio et al. (2001) had previously assessed
recumbent yaw orientation with respect to gravity. Their
study involved auditory localization judgments rather
than judgments of the vertical or self tilt. Subjects were
RED
Fig. 5 a Comparison of our measures of haptically indicated roll
tilt with those from Bauermeister et al. (1964), who tested 60
subjects with a comparable paradigm. Both data sets are expressed
as mean values. The error bars are standard deviations. b The same
data after being unbiased and symmetrized. The error bars are
interquartile ranges
2
Colenbrander (1964) experimentally compared visual settings and
counterrolling measurements during centrifugation and concluded
that both were correlated to otolith output over a range of at least
60 of tilt (cf. also Van Beuzekom and Van Gisbergen 2000; Bohmer and Mast 1999; Bucher et al. 1992; Curthoys et al. 1990).
A
A
20
ERROR [°]
ERROR [°]
20
0
0
-20
DiZio, Means
Bortolami, Means
-20
Miller, Means
Bortolami, Means
B
20
ERROR [°]
B
ERROR [°]
20
-20
0
DiZio, Symmetrized means
Bortolami, Symmetrized medians
-100
Miller, Symmetrized means
-20
RED
Miller, Corrected, symmetrized means
Bortolami, Symmetrized medians
-100
LED
0
-50
50
PHYSICAL HEAD ROLL [°]
100
RED
Fig. 6 a Comparison of errors in haptically indicated roll
orientation in our data with errors found using a visual indicator
by Miller et al. (1968). Both data sets are mean values. The error
bars are standard deviations. b Comparisons with Miller et al.
(1968) using unbiased, symmetrized data. The error bars are
interquartile ranges. The Miller et al. (1968) data are also presented
corrected for ocular counterrolling
asked to adjust a sound to the apparent midline of their
head.
Figure 8a plots the auditory error pattern for
recumbent yaw of DiZio et al. (2001) together with our
haptic indications of the vertical for recumbent yaw tilt.
The data in Fig. 8a are means. In Fig. 8b, we have
plotted symmetrized averages of the DiZio et al. (2001)
data and our symmetrized median haptic indications. A
20
ERROR [°]
0
0
Schöne, Means
Bortolami, Medians
-20
-100
BKW
-50
0
50
100
FWD
PHYSICAL HEAD PITCH [°]
Fig. 7 Plots of our haptic indication errors (medians and interquartile ranges) for pitch with those of Schöne (1964) obtained
using a visual indicator. The correlation is significant (P<0.05)
0
-50
50
PHYSICAL HEAD YAW [°]
100
LED
Fig. 8 a Errors in our haptic data for recumbent yaw are plotted
with those of the auditory data from DiZio et al. (2001) for
recumbent yaw. Both data sets are expressed in terms of mean
values. The error bars are standard deviations. b Comparison of
unbiased, symmetrized data. The error bars are interquartile
ranges. All correlations are significant (P<0.05)
correlation analysis of the untreated average data sets in
Fig. 8a yielded an r2 value of 0.94 (P<0.05). The symmetrization in Fig. 8b also yielded a significant correlation (P<0.05) with an r2 value of 0.91. The correlation
between our untreated data and unbiased, symmetrized
data were extremely high, r2=0.98 (P<0.05).
Cross-comparison of all data sets
To capsulize the relationships between data sets acquired with different techniques, we ran independent
correlation analyses between all pairs of untreated (nonsymmetrized means) data sets, for each tested axis. Tables 3 and 4, top panels, show the results for roll and
yaw, respectively. The same analysis was repeated using
our symmetrized median data (haptic-indication and
verbal report errors) and the symmetrized mean data
from the literature, see Tables 3 and 4, bottom panels.
The linear trends within our data and comparisons of
our data to data in the literature indicate that the roll
and yaw axis data have symmetrical natures, with equal
slopes in the positive and negative tilt directions, and
zero error at zero head tilt. Enough subjects were tested
in the yaw condition for a high level of statistical confidence in this pattern in the raw data. The artificially
unbiased, symmetrized yaw data were almost perfectly
correlated with the inherently unbiased, symmetrical
large sample of raw yaw data. Large roll data sets in the
literature (Bauermeister et al. 1964; Miller et al. 1968)
demonstrate the inherently unbiased, symmetrical nature of orientation for this axis. Our raw haptic estimates
Table 3 Top panel: correlation coefficients (r2) of the relationships between our data (cited as Bortolami et al. 2006) and other data sets
for the roll axis. Bottom panel: the same analysis using the unbiased, symmetrized versions of the data
Untreated error data
Bortolami et al. (2006), haptic
Bauermeister et al. (1964), haptic
Miller et al. (1968), visual
Bauermeister et al. (1964), haptic
r2=0.92
Miller et al. (1968), visuala
r2=0.63
r2=0.66
Bortolami et al. (2006), verbal
r2=0.10
r2=0.004
r2=0.15
Bauermeister et al. (1964), haptic
r2=0.97
Miller et al. (1968), visuala
r2=0.51
r2=0.68
Bortolami et al. (2006), verbal
r2=0.10
r2=0.04
r2=0.10
Symmetrized error data
Bortolami et al. (2006), haptic
Bauermeister et al. (1964), haptic
Miller et al. (1968), visual
All correlations among haptic and visual indications are significant (P<0.05, bold). All correlations between haptic indications and verbal
reports and between visual indications and verbal reports are not significant (P>0.05)
Not corrected for ocular counterrolling
a
Table 4 Top panel: correlation (r2) of data sets for the recumbent yaw axis. Bottom panel: the same analysis repeated using the unbiased,
symmetrized version of the data
Untreated error data
Bortolami et al. (2006), haptic
DiZio et al. (2001), auditory
DiZio et al. (2001), auditory
r2=0.94
Bortolami et al. (2006), verbal
r2=0.17
r2=0.32
DiZio et al. (2001), auditory
r2=0.91
Bortolami et al. (2006), verbal
r2=0.18
r2=0.27
Symmetrized error data
Bortolami et al. (2006), haptic
DiZio et al. (2001), auditory
All correlations among haptic and auditory indications are significant (P<0.05, bold). All correlations between haptic indication and
verbal reports and between auditory indications and verbal reports are not significant (P>0.05)
of roll tilt are in accord with this, except for a slight
rightward bias, which we attribute to sampling error
because the subject sample we tested was relatively
small. The process of unbiasing and symmetrizing our
data brought it into line with the large published data set
for haptic and visual indications of roll tilt. Asymmetries
and zero biases should be considered essential features
of pitch data, because during exposure to different pitch
body tilts across 1 g and hyper-g force backgrounds,
judgments of the subjective horizon reflect about a head
tilt of 30 (Correia et al. 1968; Schöne 1964), and zero
biases exist in judgments of pitch axis orientation
(MacDougall 1906). This may be related to the 30
pitched back orientation of the saccular and utricular
maculae relative to the head (Rosenhal 1972). Our untreated pitch data are not inconsistent with this, because
the confidence intervals about the regression line of
indicated tilt error versus head tilt include zero for head
pitch angles of 10 pitch back to 30 pitch forward.
Our verbal report data showed less association with
our physical indicator data, a pattern that has also
been seen by other investigators. Similar dissociations
of perceptual and manual performance occur when
subjects experience mislocalizations of visual targets
or distortions of their size, yet point or adjust grasp
reasonably accurately (Glover 2002; Goodale et al.
1986). Psychophysical measurements like the ones
discussed in this paper are influenced by many factors
and often have high spread.
Conclusion
Our data generated using haptic indication of the gravitational vertical correlated extremely well with data
obtained by other investigators using haptic, auditory,
and visual methods. This suggests that such settings
would be appropriate ‘‘system variables’’ for development of an orientation model, because they are reproducible across experiments and techniques. The
compatibility is optimized if we remove the zero bias and
symmetrize our roll and yaw data but leave our pitch
data untreated. Such axis-by-axis description of the
linear trends in the data does not obscure non-linearities
which are important for development of the full tri-axial
model of human vestibular-somatosensory static spatial
orientation mechanisms which is presented in the companion paper (Bortolami et al. 2006).
Acknowledgements This research has been supported by AFSOR
grant F49620110171 and NASA grant NAG9-1483. We thank Dr.
Simone Rocca and Dr. Sebastiano Daros for their contributions
and experimental help.
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