Functional Implications of Ubiquitous Semicircular Canal Non-Orthogonality in Mammals

The ‘canonical model’ of semicircular canal orientation in mammals assumes that 1) the three ipsilateral canals of an inner ear exist in orthogonal planes (i.e., orthogonality), 2) corresponding left and right canal pairs have equivalent angles (i.e., angle symmetry), and 3) contralateral synergistic canals occupy parallel planes (i.e., coplanarity). However, descriptions of vestibular anatomy that quantify semicircular canal orientation in single species often diverge substantially from this model. Data for primates further suggest that semicircular canal orthogonality varies predictably with the angular head velocities encountered in locomotion. These observations raise the possibility that orthogonality, symmetry, and coplanarity are misleading descriptors of semicircular canal orientation in mammals, and that deviations from these norms could have significant functional consequences. Here we critically assess the canonical model of semicircular canal orientation using high-resolution X-ray computed tomography scans of 39 mammal species. We find that substantial deviations from orthogonality, angle symmetry, and coplanarity are the rule for the mammals in our comparative sample. Furthermore, the degree to which the semicircular canals of a given species deviate from orthogonality is negatively correlated with estimated vestibular sensitivity. We conclude that the available comparative morphometric data do not support the canonical model and that its overemphasis as a heuristic generalization obscures a large amount of functionally relevant variation in semicircular canal orientation between species.


Introduction
Detection of angular head accelerations is mediated by the semicircular canals of the inner ear. Each semicircular canal consists of a toroidal bony passage within the petrous portion of the temporal bone and contains an endolymph-filled duct. When the head rotates, inertial drag of endolymph within the duct acts upon sensory hair cells that modulate the firing rates of primary vestibular afferent neurons. Firing rates are either increased or decreased depending on the direction of head rotation [1]. The excitatory and inhibitory signals from all six semicircular canals are combined in the brain to generate reflexive movements that help to stabilize the eyes and head when the body is in motion [2].
In contrast with more readily accessible peripheral sense organs like the eye, the fact that the inner ear is encased within dense bone has hampered the comparative study of semicircular canal anatomy. This limitation, combined with the assumption that the three canals in each inner ear evolved to optimally detect rotations in each of the three orthogonal spatial dimensions, led researchers to rely on a series of simplifying assumptions about semicircular canal anatomy that are seldom critically examined. According to this ''canonical model'' of semicircular canal morphology, the plane of each canal is orthogonal to the planes of the other two ipsilateral canals so that all three canals in a single inner ear intersect at 90u angles [3][4][5][6][7][8][9]. Furthermore, contralateral semicircular canals are assumed to be essentially identical in dimension and orientation [4,10]. As a result, corresponding left and right canal pairs are expected to have equivalent angles and contralateral synergistic canals are expected to occupy parallel planes ( Figure 1). These three basic components of the model, including orthogonality, angle symmetry, and coplanarity, are stated explicitly or implicitly in nearly every textbook or academic review covering the vestibular system [11][12][13][14][15][16]. Nonetheless, some empirical studies that measured semicircular canal orientation in a limited range of species reported results that are considerably divergent from the canonical model [e.g. 17,[18][19][20][21][22][23]. Humans, for example, are reported to have ipsilateral canal pairs that differ by as much as 22u from orthogonality [17].
The comparative morphology of semicircular canals is important because canal orientation ostensibly influences vestibular function [24][25][26]. However, most comparative analyses have examined the relationship between semicircular canal radius of curvature and locomotor agility [27][28][29][30][31]. Although radius of curvature is a major determinant of the sensitivity in each canal, the orientations of all six canals also help determine the relative sensitivity of the vestibular system to angular accelerations in three dimensions [15,[24][25][26]32].
As a result, some authors have incorporated canal orientation in their calculations of vestibular sensitivity to angular accelerations [25,33,34]. To date, the largest comparative analysis of three-dimensional vestibular sensitivity focused on semicircular canal morphology and locomotor kinetics in 11 species of strepsirrhine primates [35]. This study found substantial variation between species in the homogeneity of three dimensional sensitivity maps, and demonstrated that strepsirrhines with more orthogonal canals tend to encounter higher angular head velocities during locomotion. More broadly, this analysis also provided evidence that deviations from canal orthogonality have important consequences for vestibular function.
In contrast to early studies of vestibular anatomy that relied on gross dissection or histology (11,12,19,22,(28)(29)(30), computed tomography is now the standard for studies of semicircular canal morphology because it is nondestructive, quantitative, and can provide excellent resolution of internal cranial spaces [36,37]. We used high-resolution x-ray computed tomography scans of bilateral inner ear labyrinths to quantify semicircular canal size and orientation in 39 extant species from 11 mammalian orders (Table 1). For each taxon in our sample, these data were used to quantify mean deviations of ipsilateral semicircular canal pairs from orthogonality (90 var ), the degree to which corresponding contralateral canal pair angles differ (Angle Symmetry dev ), and the degree to which synergistic canal pairs deviate from coplanarity (Coplanarity dev ). The term 90 var was introduced by Malinzak et al. as the sum of the absolute value of the difference between each of three unilateral ipsilateral canal pair angle and 90u [35]. Here we calculate 90 var by summing the absolute value of the difference between all six ipsilateral semicircular canal pair angles and 90u, and taking the mean (see below).
We also used bilateral measurements of the size and orientation of all six semicircular canals to estimate the maximum (Sensitivity max ) and average (Sensitivity ave ) sensitivity of the vestibular system to angular accelerations in three dimensions. These data for a large and taxonomically diverse sample allowed us to examine the degree to which orthogonality, symmetry, and coplanarity are characteristic of mammalian semicircular canals and to determine whether deviations from these norms are correlated with interspecific differences in estimated vestibular sensitivity.

Materials and Methods
The crania of 39 extant mammals, each representing a different genus, were scanned at the University of Texas High-Resolution X-ray Computed Tomography Facility (Austin, Texas). This facility maintains an archive of all scans used in this analysis. Taxon, museum specimen number, and scan parameters for each cranium used in this study are listed in Table 1. With the   Table 1. Taxa, museum specimen number, High Resolution X-ray Computed Tomography image slices used for skull images, spacing between image slices in image stack, Field of Reconstruction, and image slice pixel size. exception of Chinchilla, for which a preexisting scan was made available by Dr. Timothy Hullar, all cranial specimens used in this analysis were scanned with the permission of the museums listed in Table 1. All crania were scanned bilaterally, ensuring that both the right and left semicircular canals were scanned in situ. This bilateral scanning protocol allowed measurements of contralateral canal pairs, a parameter that is rarely measured. Bilateral scanning also permitted the calculation of the vestibular sensitivity of each specimen to head rotations in three dimensions. The resulting image stacks were imported into VGStudioMaxß (Versions 1.2 and 2.0; Volume Graphics GmbH, 2004 and 2007) for 3D imaging and analysis. For the present study, canal angle comparisons required stable head-centered reference planes, especially for angle comparison of contralateral canals. Three reference planes were determined and segmented into the 3D digital images before any other analysis was undertaken. The terminology follows that of vestibular researchers [e.g., 22,24,26]. Approximately eight small reference segments along the median sutures of the skull images (e.g., nasals, nasion, bregma, and medial palatine sutures) were aligned in a best-fit plane to define the vertical sagittal (XZ) plane. Numerous previous authors assumed that the LSC represents the horizontal plane of a live animal's head orientation, thus the alternative designation of the canal as the horizontal semicircular canal [e.g., 26,38,39], but that also assumed that both the left and right lateral canals lie within the same horizontal plane. Because this assumption is not correct (see below), we used bilateral measurements of Reid's line (the line extending from the lower edge of the orbit to the center of the aperture of the external auditory canal [40] to define the horizontal/frontal plane (XY). The axial (YZ) plane contained the line connecting the two external auditory meatuses (interaural line) perpendicular to the frontal and sagittal reference planes. The positive X axis of the resultant head-centered reference system passed through the rostrum, the positive Y axis passed through the left meatus, and the positive Z axis passed dorsally through the skull. Such a coordinate system was fitted successfully to all specimens except a Thylacinus, which was discarded for phylogenetic purposes.
Images were thresholded in VGStudioMax based on the density of the petrosal using the VGStudio density averaging tool. The selected region of the bony labyrinth was subsequently outlined for each CT slice image in VGStudioMax and added together to produce segments representing endocasts of both bony labyrinths in each specimen. A resulting file of the reference planes and bony labyrinth endocasts for Petauroides volans is shown in Figure 1. For our determination of canal orientations with regard to the reference planes in VGStudioMax, we used a measurement tool to select an array of points (,60-100 per canal) representing the lumen centers of a canal from the end of the ampulla, around the canal and including the common crus. A circle circumference for each canal was calculated by a linear regression best-fit of the selected lumen points. The radius to the semicircular canal circumference (R, in mm) was recorded for use in sensitivity calculations. The fitpoints were imported into a VGStudioMax best-fit calculation to obtain the plane containing that semicircular canal [19], defined by coordinates of the unit normal axis perpendicular to that plane. A plane's normal line has no polarity, but each semicircular canal can be rotated in a direction that provides an increase in afferent neuron firing rate (excitatory direction) or it may be rotated in the opposite direction to produce a decrease in afferent neuron firing rate (inhibitory direction). To express this additional information, the normal line, serving as an axis of rotation, was polarized to give a vector (V) showing excitatory sensitivity direction according to the right-hand rule as described by Ezure and Graf [19] and utilized by Calabrese and Hullar [22]. Mathematical calculation of angles between all canals was performed in VGStudioMax, with corrections to ensure all angles are internal (in lateral direction of skull) [see 19,41]. Naming convention of the angles closely follows that of Spoor and Zonneveld [42]. For example, LASC]LLSC refers to the angle between the left anterior semicircular canal and the left lateral semicircular canal. All angles measured for each species are listed in Table 2, and summary data for ipsilateral canal angles and synergistic contralateral canals are provided in Table 3. The summary angular data in Table 3 includes both arithmetic means with standard deviations, as well as mean directions with circular standard deviations calculated by treating our data as vectors [43]. The arithmetic mean and mean direction for these data demonstrated negligible differences (i.e., !0.02u), while the circular standard deviation is less than the arithmetic standard deviation (Table 3). In all analyses, our angular measurements were quantified as the absolute value of the deviation from an expected value (either 90u or 180u; see below). Although these measurements are expressed in degrees, the data used in all analyses are scalar and do not require the use of circular statistics.

Orthogonality, Symmetry, and Coplanarity Calculations
We quantified semicircular canal orientation by comparing the deviations of canal pair angles from the expected normative values. Deviation from orthogonality (90 var ) [35] was calculated by taking the absolute value of the difference between each canal pair angle and 90u, adding those difference for all six ipsilateral canal pairs, and dividing by six. Deviation from side to side semicircular canal angle symmetry (Angle Symmetry dev ) was calculated as the absolute value of the difference between the left canal pair angle and the corresponding right canal pair angle. To quantify deviation from coplanarity (Coplanarity dev ) we first subtracted the angle between each synergistic contralateral canal pair from 180u. We then summed the absolute value of this difference for each of the three synergistic canal pairs and divided by 3. Values for these variables are given in Table 4.

Sensitivity Calculations
A rotation of the head in the plane of a given semicircular canal (i.e. around V) increases the firing rate of the vestibular nerve cells in that canal above a resting rate (in spikes ? sec 21 ), or decreases the firing rate (axis opposite to V). The rate of nerve cell firing change is proportional to R and the speed of rotation (in degrees ? sec 21 ), and is referred to as the sensitivity of the canal to rotation (in spikes ? sec 21 /degrees ? sec 21 ) [16,24,25,32]. A head rotation around an axis with orientation X changes the sensitivity of the canal nerve responses in proportion to the cosine of the angle between X and V. The responses of all six individual semicircular canals to rotation along X can be determined with R and V for each canal, and the orientation of X. Therefore, for a head rotation along any head-centered axis X, the sensitivities of all six canals can be summed to provide a global sensitivity to the rotation (S, in spikes ? sec 21 /degrees ? sec 21 ). By calculating such global sensitivities for a high number of rotational axes, an axis of rotation resulting in the maximum summed sensitivity of all six canals can be determined (Sensitivity max ). The average sensitivity for a high number of rotational axes can also be calculated (Sensitivity ave ). The Sensitivity max and Sensitivity ave values calculated for specimens used in this study are listed in Table 4. Both sensitivity values were calculated using Bubbles.mat [35] software, which is described in detail by Yang and Hullar [25], Rodgers [32], and Malinzak et al. [32]. Bubbles.mat uses both the orientation and radius of curvature of the six semicircular canals to calculate estimated sensitivity of the vestibular system to angular accelerations in three dimensions. According to the Bubbles.mat results, the calculated Sensitivity max is a function of both canal orientations and canal radii but Sensitivity ave is entirely determined by canal radii. These effects are illustrated in Figure 2, which shows the relationship between 90 var and the ratio of our observed sensitivities to sensitivity calculated with canals constrained to strict orthogonality (OSensitivity max and OSensitivitymin ) through setting all ipsilateral canal angles as 90u bilaterally, and setting ASC and PSC 45u away from the sagittal plane for Bubbles.mat calculations. In Figure 2, the ratio of Sensitivity ave to OSensitivity ave is always 1.0 across a range of 90 var values which indicates that Sensitivity ave is solely a function of R. By comparison, the ratio of Sensitivity max to OSensitivity max is always greater than 1.0 and tends to increase with increases in 90 var ( Figure 2). This ratio of Sensitivity max : OSensitivity max reflects the fact that artificially constraining strict orthogonality leads to a decrease in the maximum estimated sensitivity of the vestibular system according to the Bubbles.mat calculations. The implications of these effects for our analyses of canal orientation an estimated sensitivity are discussed below.

Statistical Analysis
All statistical tests were performed in R using the ape and nlme packages [44][45][46]. A normal distribution for all continuous data was confirmed using Shapiro-Wilk tests for normality. Raw data for 90 var and Angle Symmetry dev deviated significantly from normality, so these data were log10 transformed to satisfy the assumptions of parametric statistical tests. A normal distribution for both 90 var and Angle Symmetry dev following log10 transformation was confirmed with a Shapiro-Wilk test. Data for Coplanarity dev , Sensitivity max , and Sensitivity ave did not deviate significantly from normality and were therefore included in analyses without transformation.
Two types of statistical tests were used assess the relationship between the morphology and estimated sensitivity of the semicircular canals. First, Pearson product-moment correlations were calculated for our three measures of canal morphology (90 var , Angle Symmetry dev , and Coplanarity dev ) and our two estimates of sensitivity to angular accelerations in three dimensions (Sensitivity max and Sensitivity ave ). (Table 5). Because we expect deviations from orthogonality (i.e., greater 90 var values), deviations from equality in corresponding contralateral angle pairs (i.e., greater Angle Symmetry dev values), and deviations from coplanarity in synergistic canal pairs (i.e., greater Coplanarity dev values) to be negatively correlated with vestibular sensitivity, all correlations were one-tailed. Second, phylogenetic generalized least-squares regression (PGLS) [47] was used to examine the relationships between canal morphology and estimated sensitivity while controlling for phylogenetic relationships. Tree topology and branch lengths for the included taxa follow Bininda-Emonds et al. [48,49]. The strength of the phylogenetic signal (i.e., the degree to which data approximate a Brownian-motion model of evolution) in each PGLS analysis was quantified using Pagel's lambda (l) [50].

Deviations from orthogonality, angle symmetry, and coplanarity
We find that the angle between two ipsilateral canals ranges between 58.8u and 121.2u for the species in our sample (Table 2; Figure 3). The smallest canal pair angle in our sample (LASC]LLSC in Chrysochloris) is 31.2u less than 90u, while the largest canal pair angle in our sample (LASC]LPSC in Notoryctes) is 31.2u greater than 90u. The mean angle for all ipsilateral canal pairs across all taxa is 88.9u (st. dev. = 7.8u) and the average deviation from orthogonality for all ipsilateral canal pairs is 6.0u (st. dev. = 5.1u). Similarly, 90 var ranges from a low value of 2.3u in Potorous to a high value of 15.5u in Notoryctes (mean = 6.0u, st. dev. = 2.6u). Of the ipsilateral canal pairs, ASC]LSC is smallest, with a mean angle of 84.5u (st. dev. = 7.3u) and a 95% mean confidence interval of 83u-86u (i.e., excluding orthogonality). By comparison, mean ASC]PSC is 91.9u (st. dev. = 8.1u) and mean LSC]PSC is 90.3u (st. dev. = 5.9u) ( Table 3).
In addition to these deviations from orthogonality, our data demonstrate that ipsilateral canal pair angles differ by an average of 4.3u (st. dev. = 2.6u) between the right and left sides of individual specimens. Mean Angle Symmetry dev values range from a low of 0.8u in Lepus to a high of 11.6u in Notoryctes. Angles between synergistic canal pairs range from 0.5u (Enhydra LPSC ]RASC) to 27.7u (Caluromys LLSC ]RLSC). The mean deviation from coplanarity is 9.5u (st. dev. = 5.2u) for the two ASC]PSC pairs and 11.2u (st. dev. = 7.5u) for the LSC]LSC pair ( Table 3). The mean deviation of all three synergistic canal pair angles from coplanarity is 10.1u (st. dev. = 6.1u).

Canal orientation and vestibular sensitivity
As expected, there is a negative correlation between the two estimates of vestibular sensitivity and the three measures of semicircular canal orientation (Table 5). This relationship is significant at P,0.05 for all comparisons except that of Angle Symmetry dev and Sensitivity max , which are negatively correlated at P = 0.054. These data demonstrate that species with lower   estimated sensitivity to angular accelerations tend to have semicircular canals that deviate more from orthogonality, angle symmetry, and coplanarity. However, the strength of these negative correlations is relatively modest, with correlation coefficients ranging between 20.262 and 20.335 (Table 5). Furthermore, when these relationships are analyzed using PGLS regression to control for phylogenetic non-independence, the results for Angle Symmetry dev and Coplanarity dev are nonsignificant. By contrast, the PGLS regression of 90 var and Sensitivity ave remains significant at P = 0.029 ( Figure 4) and the PGLS regression of 90 var and Sensitivity max is near significance at P = 0.060. Lambda values for all six comparisons demonstrate that the relationships between these variables do not follow a strict Brownian motion model of evolution, nor are they completely free of the influence of phylogeny (Table 5). According to these results, phylogenetic proximity has the smallest influence on the relationship between Angle Symmetry dev and vestibular sensitivity (l,0.64-0.68) and the greatest influence on the relationship between Coplanarity dev and vestibular sensitivity (l,0.76-0.79).

Discussion
Our results reveal that the canonical model of semicircular canal orientation is not strictly correct for a wide range of mammalian species. In our comparative sample, angles between pairs of ipsilateral semicircular canals deviate from orthogonality by an average of 6.0u, corresponding left-right canal pair angles differ by an average of 4.3u, and synergistic canals deviate from coplanarity by an average of 10.1u. Although the angle between any two ipsilateral semicircular canals does approach 90u when data are averaged for all canal pairs across all taxa, it is nevertheless clear that all mammals deviate from canal orthogonality to some degree. For example, Potorous, Pedetes, and Wallabia all have ipsilateral canal pair angles that diverge from 90u by an average of between only 2u and 3u. By contrast, Notoryctes, Chrysochloris, and Allactaga all have ipsilateral canal pair angles that diverge from 90u by an average of nearly 10u or more. These data further underscore the fact that none of the taxa considered in this analysis has truly orthogonal semicircular canals, and that substantial deviations from orthogonality, symmetry, and coplanarity appear to be a common feature of vestibular anatomy in mammals. However, it is also important to acknowledge that our comparative sample does not address questions related to intraspecific variation in canal orientation, so it is currently unclear how representative the values reported here are for each species in our dataset (Tables 1, 2). Our results also demonstrate that the mean angle between the anterior and lateral canals is considerably less than 90u and is 6.4u-7.4u lower than the mean angle between the other two ipsilateral canal pairs. In a functional context, is not presently clear why the angle between ipsilateral anterior and lateral canals is systematically lower than that for other ipsilateral canal pairs, but this finding further reinforces the inaccuracy of general characterizations of semicircular canals as orthogonal [3][4][5][6][7][8][9][10][11][12][13][14][15][16].
Previously published studies of semicircular canal morphology in 43 living and fossil species support our general finding that substantial deviations from the canonical model are the norm for mammals (Table 6). When unilateral measurements are considered, these analyses document a range of ipsilateral canal pair angles between 52.2u and 117.0u and an average 90 var for all ipsilateral canal pairs of 7.9u (st. dev. = 4.4u). As in the species we examined, the published data also show that across taxa the angle between the anterior and lateral canals (ASC]LSC mean = 82.6u, st. dev. = 11.3u) is considerably smaller than the angle between the other two ipsilateral canal pairs (ASC]PSC mean = 93.6u, st. dev. 9.7u; LSC]PSC mean = 91.4u, st. dev. = 7.4u). The published taxa also show a mean deviation from coplanarity of 16.9u (st. dev. = 6.7u) for both ASC]PSC pairs and 13.3u (st. dev. = 6.9u) for the LSC]LSC pair. The mean deviation of all three synergistic canal pair angles from coplanarity is 15.8u (st. dev. = 6.9u).
From a practical standpoint, these data have important implications for the use of lateral canal orientation as an indicator of the horizontal plane in reconstructions of head posture in fossil mammals [31,39,[51][52][53]. In our comparative sample, 7 of the 39 species have right and left lateral canals that deviate from coplanarity by more than 20u (Table 2). This large amount of bilateral variation in lateral canal orientation within individual specimens suggests that the lateral canal is an imprecise indicator of habitual head orientation (resting or active) in fossil species, particularly if reconstructions are based on unilateral measurements of semicircular canals [54].
Our data also generally confirm the expectation that there are important functional consequences of the degree to which a species' vestibular anatomy deviates from the canonical model. In particular, deviations from canal orthogonality (as measured by 90 var ) are negatively correlated with both of our estimates of vestibular sensitivity (Table 5). This result is most pronounced for the relationship between 90 var and mean sensitivity (Sensitivity ave , Figure 4). As noted previously, the values for Sensitivity ave reported here are determined entirely by canal radii of curvature ( Figure 2), so the significant negative relationship between 90 var and Sensitivity ave is unrelated to our methods for estimating canal sensitivity. By the same token, deviations from orthogonality tend to increase the maximum vestibular sensitivity (i.e., result in higher Senstivity max : OSensitivity max ratio; Figure 2) according to the methods employed here. In other words, based on our estimates of canal sensitivity, constraining canals to be perfectly orthogonal always decreases Senstivity max (Figure 2, Table 4). Accordingly, our results for 90 var and Sensitivity max (Table 5) should be interpreted with caution because estimated maximum vestibular sensitivity is determined both by the radii and orientations of canals. Nevertheless, our analysis demonstrates that as the average deviation from canal orthogonality in our interspecific comparative sample increases (i.e., higher 90 var ), the mean estimated sensitivity to angular head accelerations tends to decrease. As a result, species with more orthogonal semicircular canals tend to have higher mean vestibular sensitivity than species with less orthogonal semicircular canals (Figure 4). Although canal radius of curvature remains a major determinant of semicircular canal sensitivity, these findings imply that selection for greater sensitivity    to Tim Hullar, who helped immensely in providing and implementing Bubbles.mat, and for conversations describing calculation of sensitivity. We thank editor Andrew Farke and reviewers Justin Georgi and Rich Kay for their assistance in revising the first submission of this manuscript. Thanks also to Charlie Nunn, Denné Reed, and Sally Amen for statistical advice. Scanning help was graciously provided by Jessie Maisano, Matt Colbert, Rich Ketcham and the staff of the UTCT lab. Mark Coleman, Tim Hullar, Ted Macrini, and Blaire Van Valkenburgh gave permission to use high resolution X-ray computed tomographic scans of their specimens for this study.