Orientation of Human Semicircular Canals Measured by ThreeDimensional Multiplanar CT Reconstruction
Authors
 First Online:
 Accepted:
DOI: 10.1007/s101620050003x
 Cite this article as:
 Della Santina, C.C., Potyagaylo, V., Migliaccio, A.A. et al. JARO (2005) 6: 191. doi:10.1007/s101620050003x
Abstract
Analysis of vestibuloocular reflex experiments requires knowledge of the absolute orientations (with respect to skull landmarks) of semicircular canals (SCC). Data relating SCC orientations to accessible skull landmarks in humans are sparse, apart from a classic study of 10 skulls, which concluded that the horizontal and anterior SCC are not mutually orthogonal (111 ± 7.6°). Multiple studies of isolated labyrinths have shown the interSCC angles are close to 90°. We hypothesized that a larger sample would yield mean absolute SCC orientations closer to the mutual orthogonality demonstrated for isolated labyrinths. We measured canal orientations with respect to accessible skull landmarks using 3D multiplanar reconstructions of computerized tomography scans of the temporal bones of 22 human subjects. Images were acquired with 0.5mm thickness and reconstructed with inplane resolution of 234 μm. There was no significant difference between the left and a mirror image of the right (p > 0.57 on multiway ANOVA of orientation vector coefficients), so data were pooled for the 44 labyrinths. The angle between the anterior and posterior SCC was 94.0 ± 4.0° (mean ± SD). The angle between the anterior and horizontal SCC was 90.6 ± 6.2°. The angle between the horizontal and posterior SCC was 90.4 ± 4.9°. The direction angles between a vector normal to the left horizontal SCC and the positive Reid's stereotaxic X (+nasal), Y (+left), and Z (+superior) axes were 108.7 ± 7.5°, 92.2 ± 5.7°, and 19.9 ± 7.0°, respectively. The angles between a vector normal to the left anterior SCC and the positive Reid's stereotaxic X, Y, and Z axes were 125.9 ± 5.2°, 38.4 ± 5.1°, and 100.1 ± 6.2°, respectively. The angles between a vector normal to the left posterior SCC and the positive Reid's stereotaxic X, Y, and Z axes were 133.6 ± 5.3°, 131.5 ± 5.1°, and 105.6 ± 6.6°, respectively. The mean anterior SCC–contralateral posterior SCC angle was 15.3 ± 7.2°. The absolute orientations of human SCC are more nearly orthogonal than previously reported.
Keywords
vestibular labyrinth semicircular canal orientation VOR CT computed tomographyIntroduction
The semicircular canals (SCC) of the vestibular labyrinth encode head rotational velocity and provide input to the vestibuloocular reflex (VOR), vestibulocollic reflex, vestibulospinal system, vestibuloreticular system, cerebellum, and cortex (Ewald 1892; Cohen et al. 1964; Suzuki and Cohen 1964; Wilson et al. 1995; Maeda et al. 1975; Shinoda et al. 1994, 1997; Peterson and Abzug 1975; Wilson et al. 1976; Ebata et al. 2004). Accurate knowledge of the absolute orientation (with respect to skull landmarks) and position of SCC is essential for design of experiments studying the vestibular system and for understanding exam findings during clinical evaluation of patients with vestibular disorders. Apart from a widely cited classic study of 10 human skulls by Blanks et al. (Blanks et al. 1975; Curthoys et al. 1977), few of the many studies of human labyrinth morphology have related SCC orientations to accessible skull landmarks that can guide an investigator in orienting a subject's head for canalplanespecific vestibular stimulation. Blanks et al. reported that the angles between ipsilateral SCC of one labyrinth depart significantly from mutual orthogonality, with the angle between the anterior SCC and horizontal SCC equal to 111.8 ± 7.6° (mean ± SD). Multiple studies of the interSCC angles of isolated human labyrinths using highresolution histologic or radiographic reconstructions suggest that SCC orientations are much more nearly orthogonal to one another (Archer et al. 1988; Harada et al. 1990; Hashimoto 2003; Ifediba et al. 2004; Takagi et al. 1989; Spoor and Zonneveld 1995, 1998). This disparity suggests that one or more of the absolute SCC orientations reported by Blanks et al. may have been up to ∼20° off of the true population mean, a deviation that would be significant for many experimental designs.
We hypothesized that the departure from canal orthogonality observed by Blanks et al. does not represent the true population mean, and that a larger sample would yield mean canal orientations that are closer to mutual orthogonality. To test our hypothesis, we measured SCC orientations with respect to accessible skull landmarks using threedimensional multiplanar reconstructions of highresolution computed tomography (CT) scans of 44 labyrinths in 22 human subjects.
Methods
Subjects
Computed tomography scans were acquired for both ears of 7 male and 15 female subjects aged 48 ± 15 years. CT scans were performed for accepted clinical indications in all patients. The indication for CT imaging was headache with disequilibrium in nine subjects; motion sickness, fatigue, lightheadedness, or anxiety associated with dizziness in six subjects; evaluation of middle ear or mastoid inflammatory disease in three subjects; conductive hearing loss in two subjects; benign paroxysmal positional vertigo (BPPV) in one subject; and sensorineural hearing loss in one subject. Diagnosis after 1.5 years of followup was migraine in 10 subjects; middle ear or mastoid inflammatory disease in three subjects; otosclerosis in two subjects; depression or anxiety in two subjects; and obstructive sleep apnea, enlarged vestibular aqueduct, orthostatic hypotension, BPPV, and Eustachian tube dysfunction in one subject each. No subject had a history of temporal bone fracture. Except for the one subject whose CT scan revealed mildly enlarged vestibular aqueducts without abnormal SCC configuration or significant deviation in SCC orientation from the rest of the dataset, no patient had cochlear or labyrinthine dysmorphism (abnormal location, patency, caliber, shape, size, or orientation) as judged by the neuroradiologists reading the CT for purposes of routine clinical care and by two of the authors (C.C.D.S., J.P.C.). This study was a review of existing clinical data with patient identifiers removed. The Joint Committee on Clinical Investigation of the Johns Hopkins University School of Medicine determined that the study was exempt from a protocol requirement and that it qualified for exemption from an institutional review board protocol based on Department of Health and Human Services criteria 45 CFR 46.101(b)(4).
Data acquisition
The CT scans were acquired on a 16detector Toshiba Aquilion CT scanner, using a bone algorithm. To avoid loss of inplane resolution that can occur in helical scanning modes, scans were performed in stepscan mode. Each axial slice was scanned with the subject stationary, and the table was axially stepped 0.5 mm before each subsequent acquisition. The xray beam was generated with a 300 mA/100 kVP source and collimated to 0.5mm slice thickness at fullwidth halfmaximum. Each temporal bone was separately encompassed by 120mm diameter region of interest using a 512 × 512 voxel matrix, creating voxels of 0.234 × 0.234 × 0.5 mm. Axial scans of the whole head were acquired using a 240mm region of interest, yielding 0.468 × 0.468 × 0.5 mm voxels. The 3D datasets were exported to a workstation for multiplanar analysis using Vitrea® 2.3.3.1 software (Vital Images, Inc., Plymouth, MN) and Matlab (Mathworks, Cambridge, MA). The higherresolution temporal bone reconstructions were used to measure distances and angles reported for the semicircular canals, and wholehead reconstructions were used to define Reid's planes with respect to skull landmarks (as defined below).
Measurement of head and SCC orientation using multiplanar slice reconstructions
The Vitrea® software system allows one to view a CT dataset simultaneously using a 3D rendered image and a set of three 2D images that represent mutually orthogonal “slices” through the dataset. We measured a SCC's orientation by optimally aligning one slice plane with the SCC, then extracting the coordinate transformation matrix Vitrea® used to reach that alignment from a spacefixed coordinate frame defined by the CT dataset volume's boundaries (Kuipers 1999). Measurements were made with 1voxel resolution (∼0.22° angular, 0.234 mm inplane translational).
We pooled SCC orientation and position data across subjects by translating each into a common coordinate system defined by Reid's planes (Stedman 1976). Reid's horizontal plane (Z _{ REID }) was defined as a plane passing through the center of each bony external auditory canal (at the lateral entrance of the tympanic bone) and the cephalic edge of the inferiormost aspect of each infraorbital rim. Although only three points are required to define a plane, we found in practice that all four of these points lie within 0.5 mm of a common plane. We defined the interaural axis as a line passing through the bony external auditory canal centers (and thus in Z _{ REID }). Reid's sagittal plane (Y _{ REID }) was defined as the plane that bisects and is perpendicular to the interaural axis. Reid's coronal plane (X _{ REID }) was defined as the plane containing the interaural axis and perpendicular to Z _{ REID }. We defined a coordinate system using unit normal vectors (X _{ REID }, Y _{ REID }, Z _{ REID }) perpendicular to each Reid plane, with the +X _{ REID } axis pointing anterior (perpendicular to X _{ REID }), +Y _{ REID } pointing left (along the interaural axis, perpendicular to Y _{ REID }), and +Z _{ REID } pointing superior (perpendicular to Z _{ REID }). Throughout this report, planes are denoted with bold characters, while the unit vector normal (perpendicular) to a plane is denoted by the same letters in italic characters.
To account for variations in head orientation within the CT scanner, CT datasets were mathematically rotated to align the (X _{ REID }, Y _{ REID }, Z _{ REID } ) coordinate frames for all subjects with an Earthfixed coordinate frame of reference (X _{ Earth }, Y _{ Earth }, Z _{ Earth }). We defined +Z _{ Earth } (the “yaw” or “horizontal rotation” axis) as an Earthvertical axis that points up; +X _{ Earth } (the “roll” axis) is perpendicular to +Y _{ Earth } and +Z _{ Earth } and points anteriorly, and +Y _{ Earth } (the “pitch” axis) is perpendicular to +X _{ Earth } and +Z _{ Earth } and points out the left ear.
Head and eye rotations in this report are described from the subject's perspective (not the examiner's), using the righthand rule and the coordinate systems described above. Thus, a leftward horizontal (positive yaw) rotation is a rotation about the +Z _{ REID } axis, moving the nose toward the left ear. A clockwise rotation (positive roll) is a clockwise (from the patient's perspective) rotation about the +X _{ REID } axis, moving the top of the head toward the right ear. A nosedown rotation (positive pitch) is a nosedownward rotation about the +Y _{ REID } axis, moving the top of the head toward the nose.
For each SCC plane and Reid plane measured by multiplanar reconstruction, a unit vector normal to that plane was extracted and used for computation of angles between planes and distances between points in space using Matlab® software. In addition to rotational orientations, the (X _{ REID }, Y _{ REID }, Z _{ REID }) Cartesian coordinate position of the center of each SCC was measured by placing a crosshair at the visually estimated centroid of the canal (as in Fig. 2).
Left and right canal plane unit normal vector coefficients (mean ± SD)

X _{ REID } 
Y_{ REID } 
Z_{ REID } 
LA 
LH 
LP 
RA 
RH 
RP 
Z _{ REIDR } 

X _{ REID } 
1 
0 
1 
−0.58954 
−0.31645 
−0.69611 
−0.58905 
−0.32891 
−0.69248 
0.00302 
± 0.06787 
± 0.12805 
± 0.06961 
± 0.07930 
± 0.11925 
± 0.06477 
± 0.00996  
Y _{ REID } 
0 
1 
0 
0.78750 
−0.04108 
−0.66820 
−0.78928 
0.03566 
0.66561 
0.00256 
± 0.04598 
± 0.09289 
± 0.06523 
± 0.06425 
± 0.10795 
± 0.06852 
± 0.00473  
Z _{ REID } 
0 
0 
1 
−0.17971 
0.94772 
−0.26257 
−0.17334 
0.94369 
−0.27826 
0.99999 
± 0.09830 
± 0.04707 
± 0.10917 
± 0.11482 
± 0.04393 
± 0.11218 
± 0.00007 
Pooled (left and mirrored right) canal plane unit normal vector coefficients (mean ± SD)

X _{ REID } 
Y_{ REID } 
Z_{ REID } 
LA 
LH 
LP 
RA 
RH 
RP 

X _{ REID } 
1 
0 
0 
−0.58930 
−0.32269 
−0.69432 
−0.58930 
−0.32269 
−0.69432 
± 0.07296 
± 0.12244 
± 0.06647 
± 0.07296 
± 0.12244 
± 0.06647  
Y _{ REID } 
0 
1 
0 
0.78839 
−0.03837 
−0.66693 
−0.78839 
0.03837 
0.66693 
± 0.05522 
± 0.09956 
± 0.06612 
± 0.05522 
± 0.09956 
± 0.06612  
Z _{ REID } 
0 
0 
1 
−0.17655 
0.94573 
−0.27042 
−0.17655 
0.94573 
−0.27042 
± 0.10568 
± 0.04505 
± 0.10967 
± 0.10568 
± 0.04505 
± 0.10967 
Direction angles versus Euler angles
Angles (mean ± SD, in degrees) between Reid's planes X _{ REID }, Y _{ REID }, and Z _{ REID } and semicircular canal planes

X _{ REID } 
Y_{ REID } 
Z_{ REID } 
LA 
LH 
LP 
RA 
RH 
RP 

X _{ REID } 
0 
90 
90 
125.9 ± 5.2 
108.7 ± 7.5 
133.6 ± 5.3 
125.9 ± 5.2 
108.7 ± 7.5 
133.6 ± 5.3 
Y _{ REID } 
90 
0 
90 
38.4 ± 5.1 
92.2 ± 5.7 
131.5 ± 5.1 
141.6 ± 5.1 
87.8 ± 5.7 
48.5 ± 5.1 
Z _{ REID } 
90 
90 
0 
100.1 ± 6.2 
19.9 ± 7.0 
105.6 ± 6.6 
100.1 ± 6.2 
19.9 ± 7.0 
105.6 ± 6.6 
LA 
125.9 ± 4.8 
38.4 ± 4.2 
100.3 ± 5.7 
0 
90.6 ± 
94.0 ± 
103.4 ± 9.5 
87.1 ± 10.0 
15.3 ± 7.2 
LH 
108.4 ± 7.8 
92.3 ± 5.3 
19.5 ± 7.4 
91.1 ± 6.3 
0 
90.4 ± 
87.1 ± 10.0 
11.3 ± 6.9 
93.1 ± 9.0 
LP 
133.8 ± 5.6 
131.6 ± 5.0 
105.2 ± 6.5 
93.9 ± 3.7 
90.1 ± 4.6 
0 
15.3 ± 7.2 
93.1 ± 9.0 
83.2 ± 9.7 
RA 
125.8 ± 5.7 
141.7 ± 5.9 
99.9 ± 6.8 
103.4 ± 9.5 
87.0 ± 10.5 
15.5 ± 7.4 
0 
90.6 ± 
94.0 ± 
RH 
109.1 ± 7.3 
88.0 ± 6.2 
20.4 ± 6.9 
87.2 ± 9.7 
11.3 ± 6.9 
92.2 ± 9.2 
90.2 ± 6.3 
0 
90.4 ± 
RP 
133.5 ± 5.2 
48.6 ± 5.3 
106.1 ± 6.8 
15.0 ± 7.1 
94.0 ± 9.0 
83.2 ± 9.7 
94.2 ± 4.3 
90.7 ± 5.2 
0 
Z _{REIDR} 
89.8 ± 0.6 
89.9 ± 0.3 
0.6 ± 0.4 
100.3 ± 5.6 
19.6 ± 7.4 
105.4 ± 6.4 
100.2 ± 6.5 
20.5 ± 6.8 
106.1 ± 6.9 
In contrast to the three direction angles that define a vector's direction, a triplet of Euler angles describes a reorientation of a threedimensional rigid body (such as the eye or head) as a sequence of rotations about the cardinal axes x, y, and z. The order of Euler angle rotations must be predetermined by some convention, because rotations of rigid bodies in 3space are not commutative. (Turning the nose 90° toward the left ear then 90° toward the top of the head results in a head orientation different from that reached by switching the order of the rotations.) By convention, the sense of each rotation about a cardinal axis is determined by the righthand rule, so that positive rotation about an axis +n is a rotation in the direction the fingers of one's right hand would curl when one's thumb is pointing along the direction of +n. Euler angles are therefore signed (or described qualitatively, e.g., “pitch nose up” and “pitch nose down”). The most commonly used Euler sequence in vestibular and oculomotor research is the Fick sequence, in which an object is first rotated about its H (horizontal) axis, then rotated about its newly reoriented V (pitch) axis, then finally rotated about its newly oriented T (torsion) axis (Haslwanter 1995); however, any convention can be chosen as long as it is consistently applied (Kuipers 1999). The sequential rotations in Table 4 are Euler rotations, with the sequences and axes chosen to simplify the process of positioning a subject for vestibular tests involving rotation about Earthvertical or Earthhorizontal axes.
Measurement of SCC Position
Statistical analysis
Statistical analysis was performed using Matlab® and PASS 2002® (NCSS, Inc., Kaysville, UT). Interplane angles, plane normal vector coefficients, and distances for each canal center point to the Reid planes were aggregated separately for the left and right labyrinths of all 22 subjects. A multiway analysis of variance with interaction was used to compare orientation vectors for left and right SCC, after reflecting the right side data through the Y _{ REID } plane. The same procedure was used to perform left–right comparison of SCC positions. Coefficients of unit normal vectors were renormalized after computation of their mean values, so as to yield a mean normal vector of unit length. Student's ttest with Bonferroni correction (twotailed, α = 0.05) was used to compare interSCC angles to the hypothesized mean interSCC angle of 90°.
Results
The individual and mean unit normal vectors for each SCC plane are displayed in Figure 4 and summarized in Table 1A. Figure 4A shows all measured unit SCC normal vectors for each of the 22 subjects, tailaligned at the Reid coordinate system origin and viewed along each cardinal axis (panels A–C) and from a high/left/posterior viewpoint (panel D). The skull insets may be compared to Figure 3 for orientation. The sphere shown in each image is of radius 0.5, centered on the Reid origin. In Figure 4A, each unit length vector represents the orientation of the axis of one SCC in one subject; the corresponding SCC plane would be perpendicular to the vector shown. Figure 4B shows the same data, reduced to mean vectors for each SCC and a circle of radius equivalent to 1 standard deviation of the direction angles measured for each SCC axis. Left SCC (blue) vectors represent the axis about which a righthand rule head rotation would be excitatory for that SCC, whereas righthand rule head rotations about the right SCC (red) vectors axes would inhibit the corresponding right SCC.
There was no significant difference in any canal plane orientation vector coefficient between the left side and a mirror image of the right (MANOVA, p > 0.57, power 80% to detect a 1 standard deviation difference), so data were pooled for the 44 labyrinths after reflecting rightside data through the Y _{REID} plane (Table 1B).
The planes corresponding to the pooled mean left labyrinth SCC planes are illustrated from several different angles in Figure 5, along with a 3D skull rendering of one subject's skull. The mean left labyrinth SCC planes (red = LH, blue = LA, green = LP) are shown from a different viewpoint in each panel, as are the Reid coordinate axes. Panels A, B, C, D show views from the +X _{ REID } (anterior), +Y _{ REID } (left), +Z _{ REID } (superior), and −X _{ REID } (posterior) axes, respectively. Panels E and F show high/left/anterior and high/left/posterior views, respectively. To simplify visual interpretation, the intersection of the SCC planes shown was translated to the center of the head [(X _{ REID }, Y _{ REID }, Z _{ REID } ) = (0, 0, 0)] for these images. The approximate mutually orthogonality of the SCC planes is clearly apparent.
The direction angles between a vector defining the axis of the left horizontal (LH) SCC and the +X _{ REID } (nasal), +Y _{ REID } (left), and +Z _{ REID } (superior) Reid's axes were 108.7 ±7.5°, 92.2 ± 5.7°, and 19.9 ± 7.0°, respectively. The direction angles between a vector defining the axis of the left anterior (LA) SCC and +X _{ REID }, +Y _{ REID }, and +Z _{ REID } were 125.9 ± 5.2°, 38.4 ± 5.1°, and 100.1 ± 6.2°, respectively. The direction angles between a vector defining the axis of the left posterior (LP) SCC and +X _{ REID }, +Y _{REID}, and +Z _{ REID } were 133.6 ± 5.3°, 131.5 ± 5.1°, and 105.6 ± 6.6°, respectively.
When measured separately for each individual, then pooled for left and mirroredright, and then averaged, the angle between the two horizontal SCC was 11.3 ± 6.9°. In contrast, the angle between the mean LH and right horizontal (RH) SCC axes was 4.5°. This occurs because the LH and RH SCC vectors have overlapping distributions. Thus, the angle between the mean horizontal SCC axes in Table 1B underestimates the expected angle between the horizontal SCCs in any single subject.
In contrast with the findings by Blanks et al., the horizontal SCC was within 2.2 ± 5.8° of being coplanar with the interaural axis and did not, on average, “droop” downward laterally. In fact, the mean horizontal SCC plane tilted slightly up laterally 2.2° above the interaural axis (and 18.8° upanteriorly above the +X _{ REID } axis).
When measured separately for each individual, pooled for left and mirroredright, and then averaged, the angle between an anterior SCC and the contralateral posterior SCC was 15.3 ± 7.2°. The angle between the mean anterior and contralateral posterior SCC axes was 10.7°, with the mean posterior SCC unit normal vector being posterior and inferior of that for the mean anterior canal.
Cartesian coordinates (mean ± SD, in mm) of the centroid of each semicircular canal (SCC) and external auditory canal (EAC) center point with respect to Reid's planes X _{ REID } (coronal through interaural axis), Y _{ REID } (midsagittal), and Z _{ REID } (horizontal through interaural axis)
Center of... 
Distance anterior to X _{ REID } plane (mm) 
Distance left of Y _{ REID } plane (mm) 
Distance left of Y _{ REID } plane, normalized to mean LEAC–REAC length (mm) 
Distance superior to Z _{ REID } plane (mm) 

Left EAC entrance 
0.0 ± 0.0 
49.8 ± 3.6 
49.8 ± 0.0 
0.0 ± 0.0 
LA SCC 
−4.9 ± 1.9 
38.5 ± 3.2 
38.4 ± 1.4 
11.2 ± 1.5 
LH SCC 
−5.1 ± 1.8 
40.9 ± 3.2 
40.9 ± 1.4 
7.4 ± 1.4 
LP SCC 
−8.5 ± 1.9 
38.9 ± 3.2 
38.9 ± 1.4 
6.5 ± 1.6 
Right EAC entrance 
0.2 ± 0.3 
−50.5 ± 3.6 
−50.6 ± 1.1 
0.3 ± 0.5 
RA SCC 
−4.9 ± 1.7 
−38.4 ± 3.3 
−38.4 ± 1.4 
11.6 ± 2.0 
RH SCC 
−5.0 ± 1.5 
−40.9 ± 3.2 
−40.9 ± 1.4 
8.0 ± 1.9 
RP SCC 
−8.3 ± 1.7 
−38.7 ± 3.2 
−38.7 ± 1.3 
7.2 ± 2.1 
Pooled left EAC entrance 
0.1 ± 0.2 
50.2 ± 3.6 
50.2 ± 0.8 
0.1 ± 0.4 
Pooled LA SCC 
−4.9 ± 1.8 
38.4 ± 3.2 
38.4 ± 1.4 
11.4 ± 1.8 
Pooled LH SCC 
−5.1 ± 1.7 
40.9 ± 3.2 
40.9 ± 1.4 
7.7 ± 1.6 
Pooled LP SCC 
−8.4 ± 1.8 
38.8 ± 3.2 
38.8 ± 1.4 
6.8 ± 1.9 
Discussion
The absolute orientations (with respect to accessible skull landmarks) of semicircular canals of the normal human labyrinth are more nearly orthogonal to each other than previously reported. Neither the mean anterior–horizontal nor the mean horizontal–posterior interSCC angle was significantly different from 90°. Although the mean anterior–posterior interSCC angle is different from 90° (94.0 ± 4.0°), all mean interSCC angles in the present data set are much closer to 90° than the 111° angle between the anterior and horizontal SCC found by Blanks et al. (1975).
For conceptual and computational simplicity, the six labyrinthine canals are commonly grouped into three approximately coplanar pairs—the left and right horizontal canals (LHRH); the right anterior and left posterior (RALP) canals; and the left anterior and right posterior (LARP) canals. Our data support the use of this approximation, because the intercanal angles for these pairs are small. Although the two SCC of each pair are not exactly coplanar, the difference in orientation is negligible, because head rotation stimulates canals to a degree dictated by the cosine of the angle between the axis of head rotation and the SCC axis. Rotation of the head about an axis midway between the mean LH and RH SCC axes (which are 5.7° from a compromise axis) would approximate maximally aligned rotation about each individual SCC's axis to within (1 − cos(11.3°/2)) < 0.5%. Rotation of the head about an axis midway between the mean LA and mean RP SCC axes (which are 7.7° from a compromise axis) would simulate rotation about each individual SCC's axis to within (1−cos(15.3°/2)) < 0.9%.
Tables 1A–3 permit calculation of the equivalent inplane stimulation of each SCC during head rotations about arbitrary axes. A noseleftward horizontal rotation of velocity 100°/s about Z _{ REID } is equivalent to an inSCCplane stimulus of 94, −18, and −26°/s, respectively for the LH, LA, and LP SCC. (Here, a negative sign denotes rotation in the direction inhibitory for a given canal.) A nosedownward 100°/s pitch about Y _{ REID } is equivalent to an inSCCplane stimulus of −4, 78, and −66°/s, respectively for the LH, LA, and LP SCC. A leftearupward roll of 100°/s about X _{ REID } is equivalent to an inSCCplane stimulus of −32, −58, and −69°/s for the LH, LA, and LP SCC, respectively. One can improve the specificity of canal stimulation by pitching the head 20° nose down to bring both horizontal SCC planes approximately into the Earthhorizontal plane Z _{ Earth }. A 100°/s noseleftward rotation about Z _{ REID } is then equivalent to an inSCCplane stimulus of 99.5, −1.0, and 0.2°/s, respectively, for the LH, LA, and LP SCC. A 100°/s LA excitatory rotation about the mean LARP axis yields an inSCCplane stimulus of −4.3, 97.4, and 2.0°/s for the LH, LA, and LP SCC, respectively, and −2.0, +15.3, and −97.2°/s, for the RH, RA, and RP SCC, respectively. A 100°/s LP excitatory rotation about the mean RALP axis yields an inSCCplane stimulus of 2.6, −15.3, and 97.1°/s for the LH, LA, and LP SCC, respectively, and 2.0, −97.0, and −2.0°/s for the RH, RA, and RP SCC, respectively.
Ideal head orientations for vestibular stimulation
Orienting angles for optimal alignment of a human subject's head for (A) rotary chair testing about an Earthvertical axis, (B) caloric stimulation, and (C) headonbody “head impulses” with the subject seated upright, for each SCC separately and for functional canal pairs
Rotary chair testing 
Explanation of orienting rotations 
Semicircular canal to align 
First orienting rotation 
Second orienting rotation  

Angle 
Axis 
Direction 
Angle 
Axis 
Direction  
Orient head to align axis of SCC being tested with chair rotation axis parallel to Z _{ Earth } axis. 
Starting in ReidEarth Aligned Starting Orientation (REASO, in which +X _{ REID }, +Y _{ REID }, +Z _{ REID } axes align with +X _{ Earth }, +Y _{ Earth }, +Z _{ Earth }, respectively), first rotation is a noseup (NU) or nosedown (ND) pitch about Y _{ Earth } axis. Second rotation is a lefteardown (LED) or righteardown (RED) roll about X _{ Earth } 
Left 
Horizontal 
18.8° 
Y _{ Earth } 
ND 
2.2° 
X _{ Earth } 
LED 
Anterior 
73.3° 
Y _{ Earth } 
NU 
52.0° 
X _{ Earth } 
LED  
Posterior 
68.7° 
Y _{ Earth } 
NU 
41.8° 
X _{ Earth } 
RED  
Right 
Horizontal 
18.8° 
Y _{ Earth } 
ND 
2.2° 
X _{ Earth } 
RED  
Anterior 
73.3° 
Y _{ Earth } 
NU 
52.0° 
X _{ Earth } 
RED  
Posterior 
68.7° 
Y _{ Earth } 
NU 
41.8° 
X _{ Earth } 
LED  
Best Fit Canal Pair 
LH RH 
18.8° 
Y _{ Earth } 
ND 
n/a 
n/a 
n/a  
LA RP 
70.8° 
Y _{ Earth } 
NU 
47.0° 
X _{ Earth } 
LED  
RA LP 
70.8° 
Y _{ Earth } 
NU 
47.0° 
X _{ Earth } 
RED 
Orienting angles for optimal alignment of a human subject's head for calorie stimulation
Caloric testing 
Explanation of orienting rotations 
Semicircular canal to align 
First orienting rotation 
Second orienting rotation  

Angle 
Axis 
Direction 
Angle 
Axis 
Direction  
Make both the axis of SCC being tested and the interaural axis (Y _{ REID }) Earthhorizontal to maximize thermal convection in SCC 
Starting in REASO, pitch head about the Y _{ Earth } axis. 
Both sides 
Horizontal 
71.2° 
Y _{ Earth } 
NU (or start supine on table then incline head end of table 18.8° up from floor)  
Anterior 
16.7° 
Y _{ Earth } 
ND 
n/a  
Posterior 
21.3° 
Y _{ Earth } 
ND 
n/a 
Orienting angles for optimal alignment of a human subject's head for headonbody “head impulses” with the subject seated upright, for each SSS separately and for functional canal pairs

Semicircular canal to stimulate 
Orienting rotations starting from REASO 
Stimulus Rotation should be about an axis that is... 
Excite SCC by turning head  

Headonbody rotational head acceleration impulses (“head thrusts”) with subject sitting erect 
Left 
Horizontal 
18.8° ND about Y _{ Earth } then 2.2° LED about X _{ Earth } 
Y _{ Earth } 
Leftward 
Subject sitting upright and visually fixating a target directly anterior of nose (along +X _{ REID }). 
Anterior 
16.7° ND about Y _{ Earth } 
In Earthhorizontal plane, 38.0° posterior to +Y _{ Earth } 38.0° anterior to −Y _{ Earth } 
CCW/ND  
For horizontal SCC, it is convenient to deliver head impulses about the Z _{ Earth } axis, just as for rotary chair test. 
Posterior 
21.3° ND about Y _{ Earth } 
In Earthhorizontal plane, 48.2° anterior to +Y _{ Earth } 48.2° posterior to −Y _{ Earth } 
CCW/NU  
For anterior and posterior SCC, limited neck range of motion prevents delivery of head thrust rotation stimuli when SCC axis is aligned with Z _{ Earth } and body is sitting upright. Instead, reorient head pitchnosedown to bring anterior or posterior SCC axis of interest into Earthhorizontal plane, then deliver rotational stimuli about that SCC axis. 
Right 
Horizontal 
18.8° ND about Y _{ Earth } then 2.2° RED about X _{ Earth } 
Z _{ Earth } 
Rightward 
Anterior 
16.7° ND about Y _{ Earth } 
In Earthhorizontal plane, 38.0° posterior to +Y _{ Earth } 38.0° anterior to −Y _{ Earth } 
CCW/ND  
Posterior 
21.3° ND about Y _{ Earth } 
In Earthhorizontal plane, 48.2° posterior to +Y _{ Earth } 48.2° anterior to −Y _{ Earth } 
CW/NU  
Rotation directions are from subject's point of view, so counterclockwise (CCW) and leftward (L) rotations move the forehead toward the left ear. ND = nose down. NU = nose up. LED = lefteardown. RED = righteardown. REASO defined in Table 4A. Axes illustrated in Figures 3 and 4. 
Canal Pair 
LH RH 
18.8° ND about Y _{ Earth } 
Z _{ Earth } 
See sidespecific directions above 
LA RP 
19.2° ND about Y _{ Earth } 
In Earthhorizontal plane, 43.0° posterior to +Y _{ Earth } 43.0° anterior to −Y _{ Earth }  
RA LP 
19.2° ND about Y _{ Earth } 
In Earthhorizontal plane, 43.0° anterior to +Y _{ Earth } 43.0° posterior to −Y _{ Earth } 
In rotary chair testing, the subject is typically seated in a chair that rotates about an Earthvertical axis, Z _{ Earth }. Although one could align a given SCC axis with +Z _{ Earth } using a single reorientation from the REASO, in practice it is easier to employ two rotations in sequence such as shown in Table 4A. For example, starting from the REASO, one may bring the mean LH SCC into alignment with +Z _{ Earth } by first rotating the head 18.8° pitchnosedown about the interaural axis +Y _{ REID }, then rolling the head 2.2° counterclockwise about the +X _{ Earth } axis (bringing the top of the head toward the left ear). This slight roll yields only a 0.07% change in the effective stimulus experienced by the mean LH SCC, so in practice it can be omitted, and a compromise axis midway between the two horizontal SCC can be used by simply rotating the head 18.8° pitchnosedown from the REASO. Table 4A describes similar sequences of reorienting rotations for all other SCC. Note that these sequential rotations are not the same as the direction angles listed in Table 2, because they represent a sequence of nested rotations about cardinal axes, rather than the single most direct rotation that would bring the SCC axis in line with +Z _{ Earth }.
For caloric testing, the head is oriented to maximize the thermal convection current generated in a SCC's endolymph by warm or cool water irrigation of the ipsilateral ear canal. This can be achieved by orienting the SCC in an Earthvertical plane while keeping the interaural axis (which approximates the thermal gradient vector during irrigation of the ear canal) Earthhorizontal (Minor and Goldberg 1990). Starting from the REASO, this can be achieved for either horizontal SCC with a 71.2° pitch noseup rotation about the interaural axis, or by lying supine semirecumbent on a table inclined 18.8° openposteriorly (Table 4B). Caloric stimulation of the anterior and posterior SCC of the test ear is minimal in this position, because the thermal gradient, gravitational vector, and the axes of these SCCs are all approximately coplanar.
Caloric stimulation is less effective for the anterior and posterior SCC's, because neither has an axis that is nearly perpendicular to the thermal gradient (Bohmer et al. 1996). However, the head may be oriented to maximize the caloric effect on the anterior and posterior SCCs. To maximize caloric stimulation of an anterior SCC, the head should be pitched 16.7° nosedown from the REASO. For a posterior SCC, the head should be pitched 21.3° nosedown from the REASO. In each case, the horizontal SCC plane is nearly Earthhorizontal, so its contribution to the caloric response nystagmus should be minimized, allowing a semiselective probing of “vertical SCC” (combined anterior and posterior SCC) function.
In performing the “head thrust test” (Halmagyi and Curthoys 1988; Aw et al. 1996; Della Santina et al. 2002), an examiner typically delivers headonbody impulsive rotation stimuli with the subject sitting erect and fixating a target directly anterior of the nose (i.e., along +X _{ REID }). As listed in Table 4C, optimal orientation of the head for stimulation of the horizontal SCCs with head rotation about Z _{ Earth } is the same as for chair rotations about Z _{ Earth }. Selective stimulation for the other SCCs can be achieved by orienting the head to bring the axis of the SCC into the Earthhorizontal plane, then delivering impulsive head rotations about that SCC axis. Given the lack of precision of manual positioning for head rotation, a reasonable approximation is to place the head 19° pitch nose down from the REASO and then deliver horizontal rotations (for the LH RH SCC pair) about +Z _{ Earth } and left anterior–right posterior (LARP) and right anterior–left posterior (RALP) head rotations about Earthhorizontal axes 45° off the midline. The resulting departure from the maximal effective stimulus for each SCC would only be 0.09%, 0.76%, and 0.24% for the horizontal, anterior, and posterior SCC, respectively.
Distinction between anatomic and physiologic canal planes
In using these data to design and analyze rotational tests of SCC function, one should note that anatomic SCC planes approximate but do not exactly equal the planes of maximum and minimum directional sensitivity for each SCC. Morphologically precise fluid dynamic models suggest that coupling of endolymph flow between SCCs alters each SCC's directional sensitivity. For example, head rotation purely about the mean axis of the anterior SCC causes some movement of posterior SCC endolymph via their communication in the common crus. The extent of this effect varies depending on labyrinthine morphology. In toadfish (Opsanus tau), the difference between anatomic and maximal sensitivity directions is ∼8.8°, ∼16.8°, and ∼3.8° for the horizontal, anterior, and posterior SCC, respectively (Rabbitt 1999). Similarly, in rhesus monkeys (Macaca mulatta), the difference between anatomic and maximal sensitivity directions is ∼3.1°, ∼9.9°, and ∼5.3° for the horizontal, anterior, and posterior SCC, respectively (Reisine et al. 1988). In humans, the difference between anatomic and maximal response planes is smaller, estimated to be 0.7°, 1.1°, and 5.7° for the horizontal, anterior, and posterior canals, respectively (Rajguru et al. 2004). These angles are equal to or less than the intersubject variation of anatomic SCC orientation angles we observed. Because of the cosine dependence of maximal response on misalignment angle, using anatomic SCC planes to approximate maximal response directions would lead to errors of ≤0.5%. Anatomic SCC planes are therefore a useful proxy for maximum directional sensitivity orientations.
In contrast to the case of maximum sensitivity directions, even small angle errors in estimates of SCC nullresponse directions or prime directions (rotations for which only one SCC of a labyrinth is stimulated, while others have no response (Rabbitt 1999)) can cause significant differences between expected and actual ampullary nerve activity. Prime directions align poorly with anatomic planes (Rajguru et al. 2004), and cosine dependence magnifies effects of misalignment in this case. Intersubject variability alone can also cause significant error. For example, during a head rotation expected to elicit no response for the mean LH SCC, an individual with that SCC misaligned 1 standard deviation (∼7.5° in Table 2) from the population mean would experience an LH SCC stimulus 13% of maximal. A 15° error would result in 26% of maximal response. Thus, one should exercise caution in relying upon mean anatomic planes to estimate SCC null directions and prime directions.
Acknowledgments
This work was supported by the National Institute on Deafness and Other Communication Disorders (grants K08DC06216 to C.C.D.S., K23DC00196 to J.P.C., and R01DC02390 to L.B.M.), and by Clinician Scientist Development Awards from the American Otological Society and the Johns Hopkins School of Medicine to C.D.S. The authors gratefully acknowledge Peter Elfert and Michael Kraut, M.D. (of the Johns Hopkins Department of Neuroradiology) and Tim Nicholson (Toshiba USA) for aid in obtaining CT images; Todd Deckard of Vital Images, Inc., for aid in adapting Vitrea 2 software to meet the aims of this study; and Richard Skolasky, MA, Johns Hopkins School of Medicine Department of Neurology for helpful comments regarding statistical analysis.