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. Author manuscript; available in PMC: 2023 Apr 4.
Published in final edited form as: Otol Neurotol. 2022 Jul 1;43(6):e679–e687. doi: 10.1097/MAO.0000000000003554

Statistical Shape Model of the Temporal Bone Using Segmentation Propagation

Andy S Ding *,†, Alexander Lu *,†, Zhaoshuo Li ‡, Deepa Galaiya *, Masaru Ishii *, Jeffrey H Siewerdsen †,‡, Russell H Taylor ‡, Francis X Creighton *
PMCID: PMC10072910  NIHMSID: NIHMS1880179  PMID: 35761465

Abstract

Hypothesis:

Automated image registration techniques can successfully determine anatomical variation in human temporal bones with statistical shape modeling.

Background:

There is a lack of knowledge about inter-patient anatomical variation in the temporal bone. Statistical shape models (SSMs) provide a powerful method for quantifying variation of anatomical structures in medical images but are time-intensive to manually develop. This study presents SSMs of temporal bone anatomy using automated image-registration techniques.

Methods:

Fifty-three cone-beam temporal bone CTs were included for SSM generation. The malleus, incus, stapes, bony labyrinth, and facial nerve were automatically segmented using 3D Slicer and a template-based segmentation propagation technique. Segmentations were then used to construct SSMs using MATLAB. The first three principal components of each SSM were analyzed to describe shape variation.

Results:

Principal component analysis of middle and inner ear structures revealed novel modes of anatomical variation. The first three principal components for the malleus represented variability in manubrium length (mean: 4.47 mm; ±2-SDs: 4.03–5.03 mm) and rotation about its long axis (±2-SDs: −1.6° to 1.8° posteriorly). The facial nerve exhibits variability in first and second genu angles. The bony labyrinth varies in the angle between the posterior and superior canals (mean: 88.9°; ±2-SDs: 83.7°−95.7°) and cochlear orientation (±2-SDs: −4.0° to 3.0° anterolaterally).

Conclusions:

SSMs of temporal bone anatomy can inform surgeons on clinically relevant inter-patient variability. Anatomical variation elucidated by these models can provide novel insight into function and pathophysiology. These models also allow further investigation of anatomical variation based on age, BMI, sex, and geographical location.

Keywords: Segmentation propagation, Statistical shape model, Temporal bone, Variation

INTRODUCTION

The temporal bone and lateral skull base contain a complex three-dimensional (3D) geometry of nerves, arteries, veins, as well as the organs for both hearing and balance (1). Due to this complex anatomy, multiple efforts over the years have aimed at defining the anatomical norms and variations of specific temporal bone structures, such as the ossicles, sigmoid sinus, and cochlea (2-4). These efforts have sought to better understand surgical landmarks and to investigate the biological significance of these anatomical variations. Traditionally, these studies have been performed by analyzing individual CT scans and manually measuring angles and distances of specific structures (2-4). While such studies have improved surgeons’ understanding of temporal bone anatomy, more powerful analytical methods are needed for emerging research endeavors, such as understanding the effects of anatomical variation on biologic function, creating improved surgical navigation and simulation (5), and developing autonomous and semi-autonomous surgical robotics in the field (6-12).

Statistical shape models (SSMs) are one such powerful analytical method that can mathematically define the geometrical properties (i.e., average shape and structural variation) of a set of 3D objects (13), for instance a set of facial nerves. SSMs are a valuable tool in helping to define and analyze human anatomy because they can comprehensively capture the total shape of an object, rather than using predefined, fixed measurements of lengths and angles as done in traditional manual investigations of the temporal bone (14-17). Furthermore, SSMs allow researchers to objectively define regions, or modes, of variation in anatomical structures, through a method called principal component analysis (PCA).

Due to the potential power of SSMs in delineating anatomical variation, several groups have developed SSMs for individual structures in the temporal bone, most notably the cochlea (3,18-20). Unfortunately, building robust SSMs requires a substantial number of manually segmented images. Since high-quality manual segmentation of relevant anatomical structures in the temporal bone can take several minutes to hours per scan depending on the number of included labels (21,22), generating a large quantity of comprehensively segmented temporal bone datasets is prohibitively time-consuming. Therefore, the majority of studies focus only on individual structures or specific regions of the lateral skull base, which limits our ability to fully understand the entire geometrical variation and inter-structure relationships of the temporal bone. Our group has recently developed and validated a method to automatically segment relevant temporal bone structures through a segmentation propagation pipeline (22). This pipeline allows for efficient segmentation of temporal bone imaging, opening the possibilities to create high volume SSM datasets of relevant temporal bone anatomy. In this study, we present, to the best of our knowledge, the first SSMs of temporal bone anatomical structures generated via an autonomous pipeline and investigate the modes of variation of these structures.

METHODS

This study was approved by the Johns Hopkins Medicine Institutional Review Board. De-identified and cropped cone-beam CT scans of patient temporal bones were obtained from the Johns Hopkins Department of Otolaryngology-Head and Neck Surgery. Scans that showed radiographic evidence of canal dehiscence or of other temporal bone pathology that would result in abnormal anatomy were excluded from analysis. Therefore, only temporal bones that did not have radiographic evidence of anatomical abnormalities were included in this study. Our automated SSM pipeline was split into two main tasks. First, temporal bone CT images were automatically segmented using a previously described image registration technique (22,23). Second, these segmented datasets were used to generate an SSM atlas of the temporal bone containing statistical information about structural variability among its constituent datasets. The resolution of temporal bone images used in this study were 0.1 mm per voxel length, with image dimensions of 512 × 512 × N voxels, where N refers to the number of axial CT slices for a given image.

Segmentation Propagation for Temporal Bone Anatomical Labelling

An automated segmentation propagation technique was implemented, as previously described (22,23), which involves generating an “average template” temporal bone dataset and then segmenting relevant anatomy within the average template. The segments of this average template are then mapped onto an unlabeled CT image using deformable image registration methods, and then propagated to iteratively form robust predicted anatomical labels for the target image. The Advanced Normalization Tools (ANTs) Python package (24) was used to coregister 16 temporal bone datasets and generate the average template. Then, the open-source software 3D Slicer was used to label the average template through manual segmentation of relevant anatomical structures (e.g., ossicles, bony labyrinth, and facial nerve). The segmentations of this average temporal bone template were then propagated by deformably registering the average template and corresponding labels to unsegmented CT images. To minimize bias, a separate set of 53 temporal bone datasets, which were not included in generating the average temporal bone template, were then designated as target images and appropriately labelled using segmentation propagation.

Mesh-Based Temporal Bone SSM Atlas Generation

The 53 temporal bone datasets labelled with the automated segmentation pipeline were used to generate temporal bone SSMs. First, 3D meshes of a particular anatomical structure or group of structures were built using the marching cubes method (25). These meshes were processed through a previously described SSM-generation pipeline that involves principal component analysis (PCA) of 3D structures (26). First, one of the 53 meshes was designated as a sentinel mesh to which the remaining 52 meshes were rigidly registered. The designated sentinel mesh was then deformed to approximate the 52 nonsentinel meshes. This was done to generate meshes that have the same number of vertices and faces (a requirement for PCA) but still accurately represent the meshes of all 53 constituent datasets. PCA was then performed on these deformed meshes, with the resultant principal components and their respective mode weights forming the SSM.

Analysis of Anatomical Variability

For each anatomical structure, 3D meshes for the mean shape were generated using a standard marching cubes algorithm (25). Anatomical variability was then evaluated in two ways. First, we identified specific regions within each anatomical structure that exhibit greatest variability. For a given anatomical structure, the 53 constituent meshes used to create its SSM were compared against the mean shape. Then, for each vertex in the mean shape, the distance in millimeters (mm) to its corresponding vertex on each of the constituent meshes was calculated and averaged. These distances were then displayed on the mean shape as a heatmap to label areas of high and low shape variability.

Second, we performed PCA, as previously described (27), to determine and describe the modes of variability for each structure. PCA is a well-established statistical method which helps to simplify and define variations of complex datasets. The utility of PCA is that it can describe where the majority of dimensional variability exists within a set of similar geometric shapes and ultimately can predict the ranges of statistically expected shapes in a population. The output of a PCA is a set of principal components, where each component represents a particular mode of shape variation that describes a set of shapes. Importantly, shape variations present in each component are independent from the shape variations in the other components. This means that any shape in a described population can be represented as a weighted sum of principal components and the mean shape. By convention, principal components are ordered by the amount of variability they explain within a population, where the first component explains the most variability and the last component explains the least. For a given anatomical structure, meshes at ±2 standard deviations (SDs) along its first three principal components, were generated and overlaid onto the mean shape. Finally, the variation in the first three principal components were described qualitatively and measured quantitatively with landmark lengths and relevant angles relative to the mean shape using 3D Slicer. We further report relevant measurements for each principal component within 2 SDs of the mean, hereafter defined as the ±2-SD range.

RESULTS

Shape-Sensitive Regions in Temporal Bone Anatomy

Statistical shape models were successfully created for the malleus, incus, stapes, bony labyrinth, and facial nerve via our automated pipeline. Average point-correspondence distances were calculated, with mean shape meshes for each anatomical structure shown in Figure 1. The overall magnitude of shape variation was lower for the malleus, incus, and stapes compared to the bony labyrinth and facial nerve. For the malleus, the position of the umbo varied the most with an average distance of 0.45 to 0.50 mm for vertices representing this region (Fig. 1A). The articular facet, along with the short process of the incus also showed notable variability with average distances of 0.30 to 0.40 mm in these regions (Fig. 1B). Importantly, the lenticular process of the incus exhibited the most variability with average distances of 0.40 to 0.45 mm in this region. For the stapes, the head, as well as the junction of the crura with the stapedial footplate showed the most variation with average distances of 0.15 to 0.25 mm in these areas (Fig. 1C). For the bony labyrinth, the apices of the semicircular canals, particularly the superior and posterior canals, showed the most variation with average distances of 0.60 to 0.80 mm (Fig. 1D). In contrast, the shape of cochlea was relatively well-preserved. Finally, the first and second genus of the facial nerve exhibited the most shape variation with average distances of 0.60 to 0.70 mm for vertices in the first genu and 0.70 to 0.80 mm for those in the second genu (Fig. 1E). The endpoints of the mesh, both at the beginning of the labyrinthine segment and the end of the mastoid segment, also showed high variability, though this can be attributed to variable segmentation at these free ends (i.e., the fundus of the internal auditory canal and the stylomastoid foramen).

FIG. 1.

FIG. 1.

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Heatmaps depicting areas of high and low shape variability overlaid onto the mean shape for the A, malleus, B, incus, C, stapes, D, bony labyrinth, and E, facial nerve.

Modes of Variation: Malleus

Analysis of the first three principal components of the malleus, which account for 67.5% of shape variance, showed that most of its variability was explained by differences in manubrium length, which we define as the distance between the tip of the lateral process and the umbo (Fig. 2A). The first and second principal components both described changes in manubrium length either due to lateral process size or position of the umbo. Overall, mean manubrium length was 4.47 mm with a ±2-SD range of 4.03 to 5.03 mm for the first principal component. In addition to manubrium length, the size of the malleolar head varies widely, as described in the first principal component. The maximal diameter of the malleolar body in the mean shape was 2.59 mm with a ±2-SD range of 2.14 to 3.15 mm in the first principal component. Variation in orientation of the manubrium was also captured in the second principal component with a ±2-SD range of −1.6° to 1.8° posteriorly from the mean shape.

FIG. 2.

FIG. 2.

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Shape variation of the A, malleus, B, incus, and C, stapes described by their first three principal components. ±2 standard deviations for each principal component are overlaid onto their respective mean shapes.

Modes of Variation: Incus

The first three principal components of the incus, which account for 70.2% of shape variance, showed notable skewing of the main body, affecting the angle between the long and short processes (Fig. 2B). The mean angle between the short and long processes of the incus was measured to be 94.2° with a ±2-SD range of 83.0° to 106.6°. The second principal component captured variation in length of the short process of the incus, defined as the distance between the centroid of the incus to the tip of the short process. The mean shape exhibited a short process length of 2.82 mm, with a ±2-SD range of 2.51 to 3.19 mm in the second principal component. Finally, the third principal component captured variation in the orientation of the long process and the length of the lenticular process. Relative to the mean shape, the orientation of the long process with respect to the centroid of the incus had a ±2-SD range of −4.2° to 4.9° posteromedially from the mean shape. The length of the lenticular process in the mean shape was 0.77 mm with a ±2-SD range of 0.69 to 0.88 mm in the third principal component.

Modes of Variation: Stapes

Shape variation of the stapes captured within the first three principal components of its SSM showed notable variation in the size of the stapes as well as its orientation with respect to its articulation point with the incus (Fig. 2C). Overall, the first three principal components accounted for 90.2% of shape variance. The first principal component captured variation in the span of the stapedial footplate, with a mean span of 2.47 mm and a ±2-SD range of 1.95 to 3.06 mm. This component also captured variation in the length of the stapes, with a mean length of 3.22 mm and a ±2-SD range of 2.92 to 3.57 mm. While the mean shape of the incus was relatively symmetric, the second principal component captured variation in asymmetric skew of the footplate with respect to the stapedial crura, with a ±2-SD range of − 10.3° to 12.4° anterolaterally from the mean shape. Finally, the third principal component for the stapes explains variation in the angle of elevation relative to the stapedial head, with a ±2-SD range of −3° to 2.2° superiorly from mean shape.

Modes of Variation: Bony Labyrinth

Analysis of the first three principal components for the bony labyrinth, which account for 52.2% of shape variance, show particular variation in both the size and orientation of the semicircular canals (Fig. 3A). The first principal component captures variation in the angle between the posterior and superior semicircular canals. While the superior canal maintains the same orientation, the anteroposterior orientation of the posterior canal varies widely in the first principal component, resulting in an average angle of 88.9° and a ±2-SD range of 83.7° to 95.7°. The first principal component also captures variability in the width of the superior semicircular canal, defined as the outer diameter between the top of the common crus to the opposite side of the canal above the ampulla. The mean width of the superior semicircular canal was 7.76 mm with a ±2-SD range of 6.99 to 8.67 mm in the first principal component. In addition to canal variation, the first principal component captured variability in the orientation of the cochlear basilar turn relative to the vestibule, with a ±2-SD range of −4.0° to 3.0° anterolaterally from the mean shape. The second principal component captured variation in the height of the superior semicircular canal, measured from the arcuate eminence to the utricle, with a mean height of 6.80 mm and a ±2-SD range of 6.18 to 7.53 mm. The second principal component also captured variation in the angle of elevation of the horizontal semicircular canal, with a ±2-SD range of −4.3° to 4.5° superiorly from the mean shape. Finally, the third principal component described variation in height of the posterior semicircular canal, defined as the distance between its apical extent to the utricle, with a mean height of 6.79 mm and a ±2-SD range of 6.27 to 7.53 mm.

FIG. 3.

FIG. 3.

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Shape variation of the bony labyrinth described by its first three principal components. ±2 standard deviations for each principal component are overlaid onto its respective mean shape.

Modes of Variation: Facial Nerve

The first two principal components of the facial nerve captured angle variation in the second genu (Fig. 4). Although the first two principal components both described variation of the second genu angle, the first principal component explains this variation by changing the orientation of the tympanic segment while the second principal component explains this variation by changing the orientation of the mastoid segment. Overall, the average angle of the second genu was 107.3° with ±2-SD ranges of 101.4° to 114.8° and 102.2° to 112.5° for the first and second principal components, respectively. The third principal component described skew of the facial nerve’s distal mastoid segment with a ±2-SD range of −15° to 13.8° medially from the mean shape. Overall, the first three principal components of the facial nerve accounted for 62.9% of shape variance.

FIG. 4.

FIG. 4.

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Shape variation of the facial nerve described by its first three principal components. ±2 standard deviations for each principal component are overlaid onto its respective mean shape.

Overall Capture of Variance for SSMs

Upon evaluation of the resultant principal component modes from these shape models, we found that all anatomical structures required less than 15 modes to explain more than 90% of the variation among the constituent datasets (Fig. 5). For both the malleus and incus, the first seven principal components of their SSMs were sufficient to explain over 90% of their shape variation. The first three principal components were sufficient to explain the same degree of variation in the stapes, while the facial nerve required eight principal components. The bony labyrinth, however, required the first 12 principal components to explain over 90% of its variation, which is within expectation due to the relatively complex geometry of this structure. Importantly, the first three principal components for all anatomical structures included in this study were sufficient to explain over 50% of shape variability.

FIG. 5.

FIG. 5.

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Cumulative explained shape variance for temporal bone anatomical structures with respect to the number of principal components used to model their variation.

DISCUSSION

Clinical Implications

This is the first study to our knowledge that presents an automated pipeline for generating robust statistical shape models of the temporal bone using deformable image registration techniques. The method used in this study for generating SSMs, originally described in orthopedic imaging (13,26,28,29), has recently been applied to describe natural variations of paranasal sinuses for anterior skull base procedures (23). This article demonstrates its ability to extend this technique to the temporal bone to evaluate inter-patient variations in anatomy in an automated fashion.

The ability to automate this process is a crucial step in bringing improved statistical analysis to our understanding of temporal bone anatomy. Due to the significant time requirements for manual segmentation and SSM development, prior statistical analyses of the temporal bone have been limited to smaller datasets (2,4,16,19). We believe the ability to automate this process demonstrated in this paper will open avenues for large scale population analyses to evaluate anatomical differences in age, gender and ethnicity, which are currently not feasible with manual methods. Likewise, we hope, large scale data sets will help to guide the development of future robotic and manual surgical tools, surgical approaches, and prostheses for temporal bone surgery. This has been seen in prior work where SSM creation of the cochlea was used to develop cochlear implants and to automate electrode programming (30,31). Our work helps to expand SSMs to areas beyond the cochlea and could be of significant use in the development of future ossicular implants, middle ear implants, middle ear microphones (32,33), or vestibular implants (34,35). We also believe SSMs will have clinical significance in developing training models and simulators to allow novice surgeons to practice on “average” temporal bones before expanding their skills to work on abnormal or pathologic anatomy (36).

While the major impact of this paper is the demonstration of an automated methodology to generate SSMs, the results of this article also add to the literature of temporal bone anatomy. These results go beyond simplified point-to-point and angle measurements and help to provide surgeons with a better volumetric, three-dimensional understanding of relevant surgical anatomy. Importantly, these results also help to objectively describe the regions of greatest variation within these landmarks, which is both surgically relevant and helpful in studying how anatomical variations affect auditory and vestibular function. While several other groups have published SSMs of temporal bone anatomy, the majority of have focused on single structures (3,4,15,17,19,20), and none to the best of our knowledge have described the variability of multiple structures at a scale seen in this study. For example, understanding the second genu has the greatest variation along the course of the facial nerve can help to inform surgeons of where it is important to proceed with particular caution in a translabyrinthine approach or total facial nerve decompression. Similarly, while traditional teaching is that the semicircular canals are all orthogonal to each other (37), the results of this study clearly show variation in the orientation of these canals which is relevant surgically, but also opens questions about how this may affect vestibular function.

Study Limitations

There are several limitations inherent to this study. First, since only the first three principal components were described, a significant proportion of shape variation for each anatomical structure was not assessed. While the first three principal components were sufficient to capture the majority of variation for all structures included in this study, we recognize that including more principal components for analysis would more comprehensively describe the natural variance within this cohort of temporal bones. From a logistical standpoint, we felt that including more principal components has the potential to complicate shape variation analysis.

Second, while ground truth SSMs could be evaluated against automated SSMs in a general fashion by investigating their mean shapes, the actual shape variation captured within their constituent principal components is much more difficult to compare (38). This is because small errors between automated and manual segmentations can lead to differing PCA results that may still adequately capture shape variance but with different modes of variance (39). Therefore, the principal components of SSMs generated from this automated pipeline cannot be feasibly compared to the corresponding principal components of SSMs generated from manual segmentations. Despite this limitation, we have previously demonstrated submillimeter accuracy for the segmenting all included anatomical structures using this automated method, which by extension retains the accuracy of the SSMs in this study (22).

Third, the modes of variation described in this study were determined qualitatively by the authors. We recognize that high-level interpretation of SSM principal components is inherently subjective, which can lead to emphasis on different aspects of shape variation for these structures depending on clinical and surgical relevance. For example, though variation of the malleus focused on the lateral process and manubrium, we did observe variation in anterior process position. Given the degree of anterior process position variation was much smaller than other malleolar metrics, we did not include this variation in our analysis. Furthermore, as a word of caution when interpreting anatomical metrics presented in this study, we emphasize that the lengths and angles described in this study are to quantitatively illustrate, to the best of our abilities, qualitative descriptions of how each anatomical structure varies within given principal components. Since principal components capture complex 3D shape variability, standalone lengths and angles selected to illustrate variability often do not correlate linearly with principal component mode weights. Because of this, the lengths and angles described in this study often do not have symmetric ±2-SD ranges (i.e., the mean shape measurement of lengths and angles often does not fall at the midpoint of the ±2-SD range for a given principal component).

Fourth, 10 of the 53 temporal bone scans analyzed had a contralateral temporal bone scan from the same patient that was also included in this study. As there is very little intra-individual variability described for some anatomical structures of the temporal bone (40), the variability described in this study may underestimate the true shape variability of temporal bone anatomy. Variation analyses after excluding contralateral temporal bones from identical patients, however, showed virtually no difference in reported shape variability. Finally, while cone-beam CTs of temporal bones possess a high resolution sufficient for analyzing shape variation, we recognize that microCT imaging would offer higher resolution for more reliable segmentation of fine temporal bone structures, such as the lenticular process of the incus or the stapes superstructure. Regardless of these limitations, we believe that this automated pipeline has successfully generated robust SSMs that can be useful for evaluating natural shape variation within the temporal bone.

CONCLUSION

While SSMs are powerful tools for capturing anatomical variation, existing methods require time-intensive manual segmentation of relevant structures. This study demonstrated an automated method for generating SSMs of the temporal bone using a previously validated segmentation pipeline. We have shown that these SSMs can highlight key modes of variation for structures of the temporal bone, which can be used to further investigate variation in surgical landmarks and to evaluate the clinical significance of these variations. Future work will explore creation of large population datasets to evaluate anatomical differences in age, gender, and ethnicity, as well as to investigate potential effects of anatomical variation on biological function.

Acknowledgments

Funding and equipment support was provided by a contract between Galen Robotics and Johns Hopkins University.

Footnotes

Presentation Disclosure: This study was previously accepted as a poster presentation at the AAO-HNSF 2021 Annual Meeting.

Under a license agreement between Galen Robotics, Inc. and the Johns Hopkins University, Dr Russell H. Taylor and the University are entitled to royalty distributions on technology related to technology described in the study discussed in this publication. Dr Taylor also is a paid consultant to and owns equity in Galen Robotics, Inc. This arrangement has been reviewed and approved by the Johns Hopkins University in accordance with its conflict-of-interest policies.

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