Micro‐CT of the human ossicular chain: Statistical shape modeling and implications for otologic surgery

Abstract

The ossicular chain is a middle ear structure consisting of the small incus, malleus and stapes bones, which transmit tympanic membrane vibrations caused by sound to the inner ear. Despite being shown to be highly variable in shape, there are very few morphological studies of the ossicles. The objective of this study was to use a large sample of cadaveric ossicles to create a set of three‐dimensional models and study their statistical variance. Thirty‐three cadaveric temporal bone samples were scanned using micro‐computed tomography (μCT) and segmented. Statistical shape models (SSMs) were then made for each ossicle to demonstrate the divergence of morphological features. Results revealed that ossicles were most likely to vary in overall size, but that more specific feature variability was found at the manubrium of the malleus, the long process and lenticular process of the incus, and the crura and footplate of the stapes. By analyzing samples as whole ossicular chains, it was revealed that when fixed at the malleus, changes along the chain resulted in a wide variety of final stapes positions. This is the first known study to create high‐quality, three‐dimensional SSMs of the human ossicles. This information can be used to guide otological surgical training and planning, inform ossicular prosthesis development, and assist with other ossicular studies and applications by improving automated segmentation algorithms. All models have been made publicly available.

A large sample of cadaveric ossicles was used to create a set of statistical shape models (SSMs) to study the divergence of morphological features. Results revealed that ossicles were most likely to vary in overall size, but that more specific feature variability was found at the manubrium of the malleus, the long process and lenticular process of the incus, and the neck and footplate of the stapes. Changes along the chain resulted in a wide variety of final stapes positions.

1. INTRODUCTION

The ossicular chain consists of three communicating bones in the middle ear and is responsible for transmitting sound from the outer ear to the cochlea within the inner ear. The malleus, incus, and stapes bones which form the ossicular chain are the smallest bones in the human body, embedded deep within the temporal bone, and are therefore difficult to visualize and study. Knowledge of the ossicular chain's complex anatomy is important for hearing research and surgical procedures concerning the middle ear. The ossicular chain is known to vary naturally in humans (Kamrava & Roehm, 2017) and can present with congenital malformations (Noussios, Chouridis, Kostretzis, & Natsis, 2016); however, more information on its variation across the population is needed for better understanding of normal and pathological function.

A recent meta‐analysis revealed that relatively few morphological or morphometrical studies have been done on the ossicular chain over the past 50 years, and in these studies the method of analysis and morphometrical results varied greatly (Noussios et al., 2016). While older studies relied on publishing morphometrical measurements to study ossicle shape and orientation (Kamrava & Roehm, 2017; Noussios et al., 2016), newer imaging technologies allow for three‐dimensional (3D) model derivation from two‐dimensional (2D) image slices, providing much greater detail on ossicle structure and function. Initial studies producing 3D models of the ossicular chain used low‐resolution, clinical computed‐tomography (CT) images to create models. More recent studies have produced high‐fidelity models of the ossicles using micro‐computed tomography (μCT); however, these studies had small sample sizes resulting in few reconstructions (Bradel et al., 2017; Chou, Yu, & Chen, 2011; Decraemer, Dirckx, & Funnell, 2003; Kwacz, Wysocki, & Krakowian, 2012; Lee et al., 2010; Salih et al., 2012; Valoriani, Profico, Buzi, Manzi, & Moggi‐Cecchi, 2017). Furthermore, many previous studies focused only on a single ossicle (Dass, Grewal, & Thapar, 1966; Rousset et al., 2014) or a single unit (e.g. the incudo‐malleolar complex) (Chien et al., 2009; Sim & Puria, 2008; Soons et al., 2016). There is a need for more comprehensive models of the entire ossicular chain created using a larger sample size.

Ossicular anatomy and analysis is crucial for a number of applications, both scientific and clinical. In the field of biomechanics, for example, many studies use a technique called finite element modeling (FEM) to analyze the mechanical properties of the ossicular chain. Traditionally these studies have relied upon histological, clinical CT (Yao et al., 2012), or single μCT samples (Mikhael, Funnell, & Bance, 2005) and could benefit from a more comprehensive model of the ossicles. Other applications of ossicular analysis include surgical planning, image‐guided or robotic surgery, and development of middle ear prostheses. Virtual reality surgical simulators are increasingly being used for middle ear surgery training and can incorporate patient‐specific anatomy (Locketz et al., 2017). Three‐dimensional (3D) printed ossicles are being used for educational and surgical training purposes (Cohen & Reyes, 2015; Nguyen et al., 2017; Rose et al., 2015), and are also being proposed for use as prostheses for surgical ossicular chain reconstruction (Hirsch, Vincent, & Eisenman, 2017).

Statistical shape modeling is a technique for morphological study which uses a database of 3D model samples to calculate an average geometry and analyze how this geometry varies across samples (Cootes, Taylor, Cooper, & Graham, 1995). Statistical shape modeling has been used in the study of many anatomical entities, for example, the nasal cavity (Keustermans et al., 2018), the sigmoid sinus (Van Osch et al., 2019), and the facial nerve (Hudson, Gare, Allen, Ladak, & Agrawal, 2020). Not only are statistical shape models (SSMs) useful for direct study of structure but they also serve as a basis for creating automated segmentation algorithms, the development of which would replace exhaustive manual image segmentation (subdividing the region of interest from surrounding anatomy). Although one study presented a SSM of the incudo‐malleolar complex (Soons et al., 2016), to our knowledge, SSMs of the entire ossicular chain have not yet been produced.

In the present study, SSMs were used to accurately model, measure, and study the variation within the ossicular chain. The primary objective was to create the first comprehensive set of SSMs of the ossicular chain components using high‐resolution cadaveric μCT images. Results revealed the characteristic shape of each ossicle, along with statistically important variants. High‐quality ossicular models and SSMs generated in this study will be made available for collaborative research purposes and for developing automated segmentation algorithms.

2. MATERIALS AND METHODS

2.1. Imaging

Thirty‐three cadaveric temporal bones were obtained in accordance with the Anatomy Act of Ontario and Western's Committee for Cadaveric Use in Research with permission from the body bequeathal program at Western University, London, Ontario (Ethics approval #09052019). The specimens were collected from pathology‐free donors of varying ages. Eleven of the specimens were male, five were female, and the remaining seventeen came from donors of unknown sex. Twenty specimens were scanned using the GE Healthcare explore Locus micro(μ)‐CT scanner (GE Healthcare, Chicago, IL) at an isometric voxel size of 20 μm; the scanner was operated with a voltage of 80 kV and a current of 0.45 mA. Nine‐hundred projections with five frame averaging were captured at an incremental angle of 0.4 degrees. The other 13 samples were scanned using a GE eXplore speCZT scanner (GE Healthcare, Chicago, IL) at an isometric voxel size of 50 μm, operated with a voltage of 90 kV and a current of 40 mA. Again, 900 projections were captured at an incremental angle of 0.4 degrees. The scanner used was based upon availability and maintenance schedules at the Robarts Research Institute, Western University (London, Ontario, Canada).

2.2. 3D model generation

The CT scans were visualized using the open source software Slicer v4.8.1 (http://www.slicer.org) (Fedorov et al., 2012). For each sample, each of the ossicles were individually segmented using thresholding and region‐growing techniques. Consensus interpretation of each segmentation was achieved by three experts. The module Fast‐Grow‐Cut (Zhu, Kolesov, Gao, Kikinis, & Tannenbaum, 2014) was used to extrapolate on initial seeds to identify the ossicles on each slice of the 3D CT scan, followed by manual editing and smoothing, to reach a final 3D model.

One sample from a left ear was chosen at random for use as the standard and all right‐sided temporal bones were then mirrored to match the left‐sided standard. All 3D models were pre‐aligned using rigid body fiducial registration (as implemented in the Slicer platform) using the head of the malleus, the short process of the malleus, the short process of the incus, the incudo‐stapedial joint, and the anterior crus of the stapes as landmarks for fiducials.

Eleven fiducials (F1 through F11) were placed on the 3D models of the ossicles. These fiducials, using x, y, and z coordinates, were used to calculate the following distances and angles (see Figure 1):

1. Malleus manubrium length from the tip to manubrium to the tip of the short process

2. Malleus lateral process to malleus head length

3. Malleus total length from the manubrium tip to head

4. Incus short process length from the tip of the short process to head

5. Incus lenticular process length from the tip of the lenticular process to head

6. Incus length between the lenticular process tip and short process tip

7. Stapes length from head to baseplate

8. Stapes width of footplate

9. Malleus angle among the manubrium, lateral process, and head

10. Incus angle between the lenticular process and short process

11. Stapes angle between the posterior crus and anterior crus

FIGURE 1.

Three views of an ossicular chain with superimposed fiducials used to calculate distances. F1 – Tip of manubrium of malleus. F2 – Tip of lateral process of malleus. F3 – Head of malleus. F4 – Tip of lenticular process of incus. F5 – Body of incus. F6 – Tip of short process of incus. F7 – Head of stapes. F8 – Anterior tip of footplate of stapes. F9 – Posterior tip of footplate of stapes. F10 – Middle of footplate of stapes

2.3. Statistical shape modeling

The mean ossicular shapes, and variation around the mean, were determined using statistical shape modeling. Each ossicle was modeled separately, resulting in three separate SSMs; one per ossicle. The pre‐aligned models were exported as computational surface meshes and used as inputs for the SSM. Deformetrica Software (www.deformetrica.org) (Bône, Louis, Martin, & Durrleman, 2018) was used to analyze the SSM. An SSM framework was used to process and visualize the shapes, avoiding the need for point‐to‐point correspondence. The average ossicular shape of the malleus, or the malleus ‘template’, was calculated. The software was used to compute the deformation vectors from the template toward each sample's specific shape, which quantified the amount of variation in the sample population from the template. Principal component analysis (PCA) was used to translate the deformation vectors into a series of shape modes, where each shape mode visually displayed a specific aspect of variability in ossicle shape. These modes are able to provide greater insight into anatomical variability than standard measurements alone as they describe changes in the population relative to the mean. Each mode was visualized by deforming the template, or average shape, from low to high values; −3 standard deviations (SD) to +3 SD of the deformation vectors.

3. RESULTS

Segmentation of the CT scans resulted in high‐quality 3D models of the ossicles. An example of a 20 μm voxel sample and the resulting 3D models for the malleus, incus, and stapes are shown in Figures 2, 4, and 6, respectively. The two‐dimensional X, Y, and Z planes are shown in their post‐segmentation completed stage, along with the generated 3D model.

FIGURE 2.

Twenty micrometers sample displayed on the Slicer program. Segmentation results are shown in upper left, lower left, and lower right quadrants. The result of the 3D model generation is shown on the upper right quadrant. Malleus cross sections and the final model are highlighted in green

FIGURE 4.

Twenty micrometers sample displayed on the Slicer program. Segmentation results are shown in upper left, lower left and lower right quadrants. The result of the 3D model generation is shown on the upper right quadrant. Incus cross sections and the final model are highlighted in green

FIGURE 6.

Twenty micrometers sample displayed on the Slicer program. Segmentation results are shown in upper left, lower left, and lower right quadrants. The result of the 3D model generation is shown on the upper right quadrant. Stapes cross sections and the final model are highlighted in green

The distances and the angles calculated are summarized in Table 1a and 1b, along with their SD, minimum values, and maximum values. These data further support the hypothesis that ossicle size and shape are indeed variable.

TABLE 1.

a) Anatomical distances calculated using fiducials. Average values are displayed alongside standard deviations, minimums, and maximums. b) Anatomical angles calculated using fiducials. Average values are displayed alongside standard deviations, minimums, and maximums

a) Anatomical Distances	Average (mm)	Standard Deviation (mm)	Min (mm)	Max (mm)
Malleus manubrium length from the tip to manubrium to the tip of the short process $(\overline{F1F2})$	4.94	0.37	4.26	5.71
Malleus lateral process to malleus head length $(\overline{F2F3})$	4.84	0.45	2.60	5.38
Malleus total length from the manubrium tip to head $(\overline{F1F3})$	4.82	0.63	4.28	8.10
Incus short process length from the tip of the short process to the body $(\overline{F4F5})$	6.79	0.30	6.19	7.22
Incus lenticular process length from the tip of the lenticular process to the body $(\overline{F5F6})$	4.79	0.40	3.65	5.41
Incus length between the lenticular process tip and short process tip $(\overline{F4F6})$	5.91	0.35	5.25	6.56
Stapes length from head to baseplate $(\overline{F7F10})$	3.39	0.20	2.95	3.79
Stapes width of footplate $(\overline{F8F9})$	2.83	0.22	2.35	3.16

b) Anatomical Angles	Average (°)	Standard Deviation (°)	Min (°)	Max (°)
Malleus angle between the manubrium, lateral process, and head $(\angle \mathrm{F}1\mathrm{F}2\mathrm{F}3)$	66.01	5.15	56.88	75.67
Incus angle between the lenticular process and short process $(\angle \mathrm{F}4\mathrm{F}5\mathrm{F}6)$	58.32	2.88	51.65	66.89
Stapes angle between the posterior crus and anterior crus $(\angle \mathrm{F}8\mathrm{F}7\mathrm{F}9)$	46.40	2.35	66.89	50.93

Statistical shape models (SSMs) generated for the mallei, incuses, and stapes demonstrated significant variation in shape even among non‐pathological specimens. Specific regions on the template shape that contained the most amount of variation among samples are shown as color‐mapped surfaces of the malleus, incus, and stapes (Figures 3a, 5a, 7a, respectively).

FIGURE 3.

(a) Malleus template with a heat map representing high and low variability regions. (b) Malleus modes 1 and 2 showing deformations of the computed template from low to high values. Grey shapes indicate the template, blue shapes indicate +SD, and red shapes indicate ‐SD

FIGURE 5.

(a) Incus template with a heat map representing high and low variability regions. (b) Incus modes 1 and 2 showing deformations of the computed template from low to high values. Grey shapes indicate the template, blue shapes indicate +SD, and red shapes indicate ‐SD. (c) 3D: Incus Mode 2 in the side view highlighting changes in long processes and lenticular processes

FIGURE 7.

(a) Stapes template with a heat map representing high and low variability regions. (b) Stapes modes 1 and 2 showing deformations of the computed template from low to high values. Grey shapes indicate the template, blue shapes indicate +SD, and red shapes indicate ‐SD. (Superior view. Posterior crus on the left). (c) Mode 2 Stapes footplate in the posterior view. Grey shape indicates the template, blue shape indicates +SD, and red shape indicates ‐SD; all overlaid. The difference in footplate angle can be appreciated

The first two shape modes for each ossicle are presented in Figures 3b, 5b, and 7b, for the malleus, incus, and stapes, respectively. By superimposing the high and low values of each mode onto the mean shape and comparing these values side by side, the traits manifested by each mode can be seen. Figure 5c illuminates the feature changes in the long and lenticular processes of the incus and Figure 7c provides another perspective of the features of the stapes footplate.

Analysis of connected‐chain samples revealed ossicular chains with significantly different stapes placements when normalized for malleus placement. Figure 8 displays ossicular chains at all extremes of position and orientation.

FIGURE 8.

Overlaid chain samples representing extremes in stapes position within the dataset. Samples are anchored at the malleus. (a) Anterior view, (b) Superior view, and (c) Medial view

4. DISCUSSION

The current study applied statistical shape modeling to better understand the complex anatomy of the human ossicular chain. Previous studies of the ossicular chain anatomy were limited by a low sample size (Bradel et al., 2017; Chou et al., 2011; Decraemer et al., 2003; Kwacz et al., 2012; Lee et al., 2010; Salih et al., 2012; Valoriani et al., 2017), low‐resolution imaging (Todd & Daraei, 2014; Tóth, Moser, Rösch, Grabmair, & Rasp, 2013), or by only focusing on one or two of the three ossicles (Chien et al., 2009; Dass, Grewal, & Thapar, 1966; Rousset et al., 2014; Sim & Puria, 2008; Soons et al., 2016). The current study presents complete and detailed models of all three ossicles, as well as calculations of a number of important anatomical parameters. Furthermore, by using statistical shape modeling, it was possible to represent the anatomical variation that exists across samples as two separate shape modes.

Qualitative analysis of the SSMs showed that the overall morphology of the ossicles was consistent across samples; however, each ossicle revealed variability in certain features. The greatest divergences in the malleus were in head size and in manubrium curvature. Malleus modes indicated that samples contained manubriums on a spectrum from convexity to concavity relative to the tympanic membrane. The incus modes revealed that the majority of variation was accounted for by the shrinking or enlarging of the body and short process of the incus. At the long process of the incus, there was substantial diversity in length and curvature. In addition, the lenticular process changed in angle relative to the long process. Analysis of the stapes revealed that the neck and footplate shape showed the most variability. The first stapes mode demonstrated once again that overall size was the feature most likely to change from sample to sample. The second stapes mode showed the crura of the stapes to be either more linear or more curved, and that the posterior crus specifically could be longer in overall length, bending to create an asymmetrical stapes. The footplate could, therefore, be found in a range of angles. Overall, first modes often demonstrated overall change in size rather than shape. Second modes revealed more specific changes in morphometry. Analysis of the chain as a whole showed that the ultimate position of the stapes, relative to a standardized malleus position, could move along all three axes. Furthermore, quantitative analysis of pertinent ossicular dimensions and angles confirmed the observations of previous studies and meta‐analyses that ossicle size does indeed vary among subjects (Noussios et al., 2016).

Knowledge of ossicular anatomy may inform future understanding of function – or dysfunction, in pathological cases – within the hearing process. SSMs have a range of applications, including to create ossicular protheses, to improve surgical training simulators, or to inform surgeons during pre‐operative planning. For instance, the high variability of the stapes with respect to the malleus found here has implications on the ease or difficulty in performing a stapedectomy surgery. Often, scutum removal is needed to properly visualize the stapes and oval window (Hunter et al., 2016; Nassiri et al., 2018; Surmelioglu et al., 2017) and ultimate stapes positioning will affect the amount of scutum removal needed.

Traditional methods for analyzing the anatomy of the ossicular chain require time‐intensive manual image segmentation, which often limits the sample size and, in turn, the generalizability of findings. Recent work has aimed at developing semi‐automated or fully automated segmentation algorithms to be used in these studies. Atlas‐based and deep learning techniques present emerging solutions to automated segmentation (Ferreira, Tavares, & Gentil, 2012) but require a large sample size of high‐fidelity models to adequately train the algorithms. To date, no such models have been publicly available. Statistical shape modeling is another technique for building automated and semi‐automated segmentation algorithms, and the models generated in this study could serve this purpose. The impact of having automated segmentation readily available would be manifold; for example, these automated algorithms could be combined with FEM, which has been cited as a way to simulate different middle ear conditions and potentially achieve ideal prothesis design (Daniel, Funnell, Zeitouni, Schloss, & Rappaport, 2001). This would allow an otolaryngologist to use a patient‐specific model and provide optimized surgical management.

Literature on ossicle shape is limited. Previously reported values for ossicle size have shown great variance across studies (Kamrava & Roehm, 2017; Noussios et al., 2016), which is consistent with the qualitative and quantitative findings in the present study. Previous morphological studies report large variation in morphology, which is also corroborated here. To our knowledge, only one other SSM has been made of the ossicular chain, specifically the incudo‐malleolar complex (Soons et al., 2016). The authors reported that the most variation is found in overall size and angle, which is again consistent with the present findings.

The reproducibility of this study is limited by the need for manual segmentation of the ossicles, with segmentation of each ossicle taking up to 1 hour to complete. The stapes, in particular, being the smallest and most intricate of the ossicles, could require many iterations of manual editing and smoothing to produce an accurate shape. Manual segmentation and fiducial placement may also introduce inter‐observer error; however, this was mitigated in the present study by having multiple experts achieve a consensus interpretation of the segmentations and fiducials. Iterative cycles of generating initial models then correcting segmentations manually were used to increase accuracy, and smoothing tools within the Slicer framework were used to remove outliers at the voxel level. However, the high‐resolution scans used for this study allowed for fairly clear identification of features. The memory usage and computing power required to build the models were feasible. All analyses were performed on a desktop computer with a core‐i7 CPU, 24 GB of memory, and a Nvidia Geforce GTX 970 graphic card. All models presented here will be made publicly available for other groups to use for SSMs, atlas‐based algorithms, finite element models, or deep learning.

The present sample size of 33 was large with respect to previous studies; however, future studies may benefit from a larger sample size or the inclusion of pathological samples to achieve a greater understanding of the morphological and morphometrical divergence within the population. Future works could also emphasize variation in intra‐ossicle and even intra‐temporal relationships and perform additional analyses, for example, on chain vibration or sound transmission.

5. CONCLUSION

This study is the first to present statistical shape models (SSMs) of the entire ossicular chain, based on a large sample of 3D models derived from cadaveric micro‐CT specimens. These models provide greater insight into the stereotypical shape of the ossicles and how they vary within the population. Individual ossicular analysis revealed that, in general, ossicles maintained a characteristic shape, but could scale either larger or smaller; all anatomical distances and angles measured showed significant variability. Morphological deviations were seen at the manubrium of the malleus, the long processes and lenticular process of the incus, and the crura and footplate of the stapes. Overall, cumulative changes along the chain resulted in a greatly varied stapes position and orientation. The high‐fidelity images and models created for this study are made publicly available on the Auditory Biophysics Laboratory website (abl.uwo.ca).

CONFLICTS OF INTEREST

The authors declare no conflict of interests.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are openly available in the Auditory Biophysics Laboratory Data Repository at https://abl.uwo.ca/data_repository/Ossicles.html