The individual and mean unit normal vectors for each SCC plane are displayed in Figure and summarized in Table A. Figure A shows all measured unit SCC normal vectors for each of the 22 subjects, tail-aligned 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 for orientation. The sphere shown in each image is of radius 0.5, centered on the Reid origin. In Figure A, 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 B 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 right-hand rule head rotation would be excitatory for that SCC, whereas right-hand rule head rotations about the right SCC (red) vectors axes would inhibit the corresponding right SCC.
Fig. 4 (A) Unit length vectors normal to semicircular canals of left (blue, L) and right (red, R) horizontal (H), anterior (A), and posterior (P) semicircular canals of 22 human subjects, shown as viewed from each cardinal axis (A, B, C views from − (more ...)
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 right-side data through the YREID plane (Table B).
The planes corresponding to the pooled mean left labyrinth SCC planes are illustrated from several different angles in Figure , along with a 3-D 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 +XREID (anterior), +YREID (left), +ZREID (superior), and −XREID (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 [(XREID, YREID, ZREID ) = (0, 0, 0)] for these images. The approximate mutually orthogonality of the SCC planes is clearly apparent.
Inter-SCC angles are summarized in Figure and Table . When inter-SCC angles were computed separately for each individual and then left labyrinth and mirror-imaged right labyrinth data were pooled, the angle between the anterior and horizontal SCC was 90.6 ± 6.2° (mean ± SD), not significantly different from 90° (p > 0.4, power 80% for true difference of 2.7°). The angle between the horizontal and posterior SCC was 90.4 ± 4.9°, not significantly different from 90° (p > 0.4, power 80% for true difference of 2.1°). The angle between the anterior and posterior SCC was 94.0 ± 4.0°. This mean anterior–posterior inter-SCC angle was close to, but significantly different from, 90° (p < 0.0001, 95% confidence interval 92.8–95.3). Computing inter-SCC angles using the population mean SCC normal vectors yielded similar inter-SCC angles of 90.4°, 90.4°, and 94.0° for ipsilateral anterior–horizontal, horizontal–posterior, and anterior–posterior SCC combinations, respectively.
Fig. 6 Inter-SCC angles for left (red), right (blue), and pooled (black) canal pairs. Box plots show median (waist), estimated range of median (notch), first and third quartiles (box ends), expected data range (whiskers) and outliers (+). All are close to 90°, (more ...)
The direction angles between a vector defining the axis of the left horizontal (LH) SCC and the +XREID (nasal), +YREID (left), and +ZREID (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 +XREID, +YREID, and +ZREID 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 +XREID, +YREID, and +ZREID 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 mirrored-right, 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 B 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° up-anteriorly above the +XREID axis).
When measured separately for each individual, pooled for left and mirrored-right, 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.
The mean distances from each of Reid's stereotaxic planes to the center of each canal and the center points of the tympanic bone entrances are summarized in Table . There was no significant difference in any SCC center position between the left side and a mirror image of the right (MANOVA, p > 0.44, power 80% to detect a 1.5 standard deviation difference). The right external auditory canal entrance center point was within 0.3 ± 0.5 mm of the ZREID plane defined using the left external auditory canal entrance. The center points of the three SCC in a labyrinth lie approximately 38–41 mm off the midline. Variance in SCC center position along the interaural axis (distance from YREID) was largely a result of the difference in head size. Normalizing these distances to the distance from midline to left external auditory canal entrance markedly reduced this variance between subjects (Table ).
Table 3 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 XREID (coronal through interaural axis), YREID (midsagittal), and ZREID (horizontal (more ...)