Micron 135 (2020) 102874 Contents lists available at ScienceDirect Micron journal homepage: www.elsevier.com/locate/micron Evaluating fidelity of CT based 3D models for Zebrafish conductive hearing T system Jordi Marcé-Noguéa,b, Juan Liua,* a Department of Pathology and Anatomical Sciences, Jacobs School of Medicine and Biomedical Sciences, University at Buffalo, State University of New York, NY, USA b Institut Català de Paleontologia Miquel Crusafont, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Barcelona, Spain ARTICLE INFO ABSTRACT Keywords: The zebrafish Weberian apparatus is an emerging model for human conductive hearing system. Their Weberian Zebrafish apparatus comprises minute bones and ligamentary links, and conducts sound pressure transmission from the gas Weberian apparatus bladder to inner ear through four pairs of Weberian ossicles along the vertebral column. We herein present a CT imaging methodological study using MicroCT to image the Weberian apparatus for biomechanical and morphological Finite element analysis analysis. The aim of this work is to evaluate computational models generated from multiple MicroCT scans with different parameters, to identify the most feasible scan combination for practical (minimized scan time) yet accurate (relative to highest resolution) biomechanical simulations. We segmented and created 3D models from CT scan image stacks at 4.64 μm, 5.05 μm, 9.30 μm and 13.08 μm voxel resolutions, respectively. Then, we used geometric morphometrics analysis to quantify inter-model shape differences, as well as a series of finite element modal and harmonic analyses to simulate auditory signal vibrations. Relative to the highest resolution and most accurate model, the Model 9.30 is closest in overall geometry and biomechanical behavior of all lower resolution models. The differences in resolution and quality of the CT substantially affect the segmentation and re- construction process of the three-dimensional model of the ossicles, and the subsequent analyses. We conclude that scan voxel resolution is a key factor influencing outcomes of biomechanical simulations of delicate and minute structures, especially when studying the harmonic response of minute ossicles connected by ligaments using finite element modeling. Furthermore, contrast variations in CT images as determined by x-ray power and scan speed, also affect fidelity in 3D models and simulation outcomes. 1. Introduction system is an emerging and promising direction in hearing research. The Weberian apparatus in zebrafish conducts sound pressure Zebrafish (Danio rerio) is a versatile model organism in biomedical transmission from gas bladder to inner ear through Weberian ossicles, and organismal biology research. Studies using osteological elements of and is analogous to the human middle ear, which conducts sound vi- zebrafish with the aid of various imaging tools have seen a dramatic bration and transmit sound pressure from the temporal membrane to increase in recent years, towards improved understanding of the normal the inner ear through three middle ear ossicles (Evans, 1925; Weber, function and pathological consequences in diverse areas such as mus- 1820). Previous research using behavioral features and evoked poten- culoskeletal systems (Fleming et al., 2005; Harris et al., 2014; Weigele tial audiograms have shown that fishes with Weberian apparatus and Franz-Odendaal, 2016), developmental characteristics (Bird and (otophysians) have increased hearing range compared to those without Mabee, 2003; Cubbage and Mabee, 1996; Siomava et al., 2018), ver- (Ladich and Fay, 2013; Ladich and Wysocki, 2003; Lechner and Ladich, tebrate evolution (Hernandez et al., 2007), hormone disorders (Brown, 2008; Popper, 1972). Developmental biology evidence of zebrafish 1997; Keer et al., 2019), environmental toxicity (Baker et al., 2013), hearing suggests that the Weberian ossicles gradually increase the range and others. Whereas zebrafish has been widely used as model organisms of frequencies available to the inner ear during zebrafish growth, just as in investigations of the genetic basis and sensorineural aspects of middle ear development increases frequency range in mammal onto- hearing (Blanco-Sánchez et al., 2017; Nicolson, 2017; Whitfield, 2002), geny (Higgs et al., 2003). Furthermore, Weberian ossicles conduct computational modeling of bony structures in its conductive auditory sound pressure from gas filled bladder to the fluid filled sinus impar of ⁎ Corresponding author at: Department of Pathology and Anatomical Sciences, Jacobs School of Medicine and Biomedical Sciences, University at Buffalo, State University of New York, NY, USA. E-mail address: liujuan@berkeley.edu (J. Liu). https://doi.org/10.1016/j.micron.2020.102874 Received 16 December 2019; Received in revised form 4 April 2020; Accepted 5 April 2020 Available online 22 April 2020 0968-4328/ © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/). J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 Fig. 1. A) reconstructed image slice (cross-sectional view) of zebrafish from MicroCT scan; B) Contour detected (in red) intercalarium bone using Amira build-in algorithm; C) STL model obtained after the segmentation; D) CAD file after smoothing and repairing the STL model. the inner ear (Popper and Fay, 2011; Retzius, 1881). This particular Weberian apparatus consist of minute bony structures (ossicles) and conduction pathway is functionally analogous to the air-bone-fluid non-mineralized tissues (ligament). Fortunately, limits CT scanning for conduction system of the middle ear ossicles of human. Therefore, the non-mineralized tissue is compensated with histological staining prior Weberian ossicles chain in zebrafish is an ideal structural system for to scan (Babaei et al., 2016; Metscher, 2009), which make CT more modeling auditory sound conduction in humans. appropriate to our imaging needs. Moreover, with dramatic technolo- Weberian ossicles are developmentally derived from elements of the gical advances in the past decade, lab-based or commercial MicroCT first four vertebrae in zebrafish. These minute bones form an ossicles (versus Synchrotron radiation CT, SrCT) is now efficient, cost-effective, chain along with associated ligaments. The paired ossicle chains are and high accurate in generating calibrated 3D image data, and should located bilaterally to the vertebral column. From anterior to posterior, potentially meet our imaging requirements. the ossicles are claustrum, scaphium, intercalarium, and tripus (Fig. 1). Previous studies utilizing CT imaging techniques on zebrafish in- The tripus is connected to the anterior portion of the gas bladder via clude SrCT analysis to model biomineralization in teeth and skeleton ligaments, while the scaphium and claustrum are coupled to the inner (Neues et al., 2006), contrast-enhanced MicroCT for monitoring the ear fluid space (the atrium of the sinus impar). The Weberian ossicles regeneration of cardiac tissue, MicroCT-based methods for phenotyping mechanically couple vibrations of the gas bladder induced by sound to (Hur et al., 2017), and SrCT scan at sub-micro resolution and 3D whole the inner ear fluid, allowing sound to be transduced into electrical organism image for histotomography (Ding et al., 2019). Here we signals by the sensory cells of the inner ear. present a study using MicroCT to image the Weberian apparatus for Morphological characteristics of Weberian ossicles have been stu- biomechanical analysis. The aims of this project are two-fold: 1) eval- died from the perspectives of skeletogenesis (Fisher and Mabee, 2004), uate models generated from multiple MicroCT scans with different development (Bird and Mabee, 2003), ontogeny (Grande and Young, parameters to find the most feasible scan combination for practical yet 2004), growth (Bird and Hernandez, 2009), and response to hormone accurate images for biomechanical simulations; 2) hypothesize prac- levels (Keer et al., 2019). Two previous biomechanical studies on the tical scan parameter combinations for similar-sized structures in zeb- Weberian apparatus also elucidated functional morphological traits of rafish, or the same structure in other small animal models. Weberian ossicles (Alexander, 1962; Finneran and Hastings, 2000). Microscopic dissection, clearing and staining methods, histological 2. CT scan to 3D model workflow slice, and two-dimensional (2D) radiograph were extensively used in previous research to investigate and capture the morphology of We- Functional morphology studies use reverse engineering concepts to berian ossicles. These classical yet prevalent methods are essential and understand biological structures and explore the relationships of func- accurate to examine and image morphology of Weberian ossicles. tion and form. Whereas forms can be quantified by computational However, in order to quantify the shape and build three-dimensional morphological analytical methods such as geometric morphometrics (3D) models to understand the mechanism of this sound conductive (GMM) (Polly et al., 2016), functions are evaluated by biomechanical system, we aim to leverage an imaging modality allowing for the modelling techniques, for instance finite element analysis (FEA) characterization of ossicles and related structures in calibrated 3D, (Rayfield, 2007), computational fluid dynamics (CFD) (Rahman, 2017) natural shape, orientation, and spatial intra-relationships and inter-re- and multi-body dynamic analysis (Curtis, 2011). All of these meth- lationships with surrounding structures (ligament, gas bladder, and odologies require sufficiently accurate and complete morphological and fluid sac). anatomical data. Image stacks generated from X-ray based CT scan of Techniques including magnetic resonance imaging (MRI) and biological structures are ideal to visualize, and then segmented into 3D computed tomography (CT) allow the non-invasive 3D visualization of models. Although there are a number of workflows and software external and internal structures at different resolutions from cells, to available to utilize CT data for different purposes (Sutton et al., 2016), organ system, and whole organism levels (Cheng et al., 2011; Walter the general steps of converting CT images into 3D models follow the et al., 2010). CT scans uses x-ray technology with a small dose of io- workflow as below. nizing radiation whereas MRI uses radio waves and powerful magnets to produce images. In general, CT scans are more powerful for obtaining 2.1. Image segmentation high-contrast images of bony structures, whereas MRI capture better images on soft tissues, joints, tendons and ligaments. However, the Image segmentation is used to locate region of interest (ROI) and 2 J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 build 3D digital models, after CT image stack are reconstructed from surfaces using interpolation methods. CAD files also contain data for the raw projection data generated by specimen scanning. Image seg- Non-uniform rational basis spline curves (NURBS) and surfaces (Piegl mentation is a technique in digital image processing and analysis to and Tiller, 1997). These are mathematical representations of the curves partition an image into multiple parts or regions to identify regions of or surfaces which are smoother and maybe more accurate than that of interest (ROI). Image segmentation could involve separating fore- STL file which depends on the number of triangles or cloud points. ground from background, or clustering regions of pixels based on si- Therefore, we prefer CAD files for the biomechanical simulations in this milarities in grayscale or shape. There are two types of segmentation: study. manual and algorithm-based automatic segmentations. Different algo- rithms and techniques for image segmentation have been developed 2.4. Model Accessibility using domain-specific knowledge to effectively segment ROI. These applications include medical imaging, automated driving, video sur- As a common good practice in scientific research to advance veillance, and machine vision. However, segmentations of biological knowledge based on open flow of information, access to image stack data for high fidelity models usually require additional manual ad- from X-ray based CT scan as well as 3D models should be facilitated. justment because of structural complexity. In our current project, we Data underlying a published study should deposited in a suitable re- used a built-in segmentation algorithm in the software Amira 6.0 to pository, and many researchers are already doing so. Although there is analyzes each image based on grayscale thresholding (Fig. 1a), then currently no agreement on how much and what type of data should be went through each image slice to ensure the ROI was accurately seg- made available for studies using digital morphology, Davies et al. mented (Fig. 1b). ROI from every slice are subsequently combined into (2017) propose a set of recommendations for minimum standards and 3D geometry and saved as stereolithography (STL) file, which is a raw best practice for three-dimensional digital data publication. These re- 3D geometry composed of a mesh of triangles with coordinates for commendations include the availability of all the data upon publication nodes and vertices (Fig. 1c). There are a number of self-developed, open in accessible standard formats and with a standard copyright license. source (e.g., 3D Slicer), and commercial software (e.g., Mimics, Avizio, This license should cover terms to specify ethical use and degree of Dragonfly etc.) available for CT image segmentation. commercial activities or modification allowed based on the shared data. The goal should be to allow research replication while crediting the 2.2. Geometry refinement source properly. There are often defects in the geometry of STL file, which are 3. Material and Methods usually caused by the orientation of the scanning and the precision of the scanner. For refinement, smoothing and element reduction proce- 3.1. Materials dure is usually performed. As it is observed in Fig. 1d, the segmented geometry has non-biological irregularities on the surface. That geo- A fixed and 70% ethanol preserved wild adult zebrafish, Danio rerio, metry was cleaned and smoothed at very low level to fulfill require- KU 22656, was loaned from Division of Ichthyology, Biodiversity ments of quality and consistency, without modifying its original mor- Institute, University of Kansas (KU). It was stained in 0.3% phospho- phology. The “quality” here refers to shapes of the triangular elements tungstic acid in 70% ethanol prior to CT scan following the procedure in the STL mesh that is measured by skewness or aspect ratio described by Metscher (2009). Euthanization, dissection and observa- (Weatherill et al., 1998), whereas the “consistency” is to avoid possible tion of laboratory fishes in this study proceeded under protocol topological errors with smooth operations. PTH04058N, reviewed and approved by the Institutional Animal Care and Use Committee, University at Buffalo. 2.3. STL versus CAD models 3.2. CT scanning Most of biomechanical and morphological analysis can be per- formed with STL files. STL file, displayed as a mesh of triangles, de- A single specimen of an adult zebrafish (Danio rerio) was scanned scribes the surface geometry of a three-dimensional object without using four different parameters and using two different MicroCT scan- color, texture or other model attributes. Models built in STL format are ners (Table 1) in the Institute of Biotechnology, Cornell University usually relatively smooth. STL formats are an excellent file option for (Ithaca, NY, USA). 3D anatomical visualization and morphological analysis using mor- The Xradia Zeiss VersaXRM-520 CT scanner uses proprietary inter- phometrics, because STL models can provide sufficient fidelity for changeable focusing optics that allows users to locate and scan small shape analyses (Engelkes et al., 2019; Marcy et al., 2018). sub-regions within a specimen as large as 30 cm in height and 30 cm in However, for biomechanical analyses such as FEA and CFD, some diameter. This is followed by seamless digital stitching of multiple researchers generate a CAD (Computer-Aided Design) solid model from scanned sub-regions. On the other hand, Bruker Skyscan 1276 scanner the STL mesh (Barbero and Ureta, 2011). A CAD model is a vector- is more cost-effective and time-efficient, using lower radiation doses graphic standard for three-dimensional design used in mechanical de- and producing lower resolution scans. sign and engineering, unlike STL format file which involves triangula- The original measured length of the Weberian apparatus of the tion of the geometry. CAD models can avoid possible mathematical specimen is 2.59 mm (Fig. 2D). For further comparison, we compute a errors caused by presence of non-biological angles in the geometry. factor called “resolution factor” (length of Weberian ossicles chain/ CAD models (file type IGS or STP) have the boundary formed by curved Voxel size), which describes the number of slices needed to cover the Table 1 Parameters of the four different scans regarding voxel size, power, speed of scan, and computed Resolution Factor. MODEL VOXEL SIZE [μm] CT radiation energy Scan speed Resolution Factor Model 4.64 4.64 Xradia Zeiss VersaXRM-520 100kV, 9 W 1601 images/4S/exposure 558.2 Model 5.05 5.05 Bruker Skyscan 1276 55kV, 200 micro amps 900 images/675 ms/exposure 512.9 Model 9.30 9.30 Xradia Zeiss VersaXRM-520 100kV, 9 W 1601 images/4S/exposure 278.5 Model 13.08 13.08 Xradia Zeiss VersaXRM-520 100kV, 9 W 1601 images/4S/exposure 198.0 3 J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 Fig. 2. Geometry and model boundary condition of Weberian apparatus. A) Lateral view and B) Medial view with the 41 landmarks used in the geometric mor- phometrics analysis. C) Dorsal view, D) Lateral view and E) Medial view with the loading area, fixed conditions areas, and spring-based ligaments of the FEA model. Orange dots labeled with numbers 1- 41, landmark 1 through 41; L1 through L4, Ligament 1 through 4; Loc, length of Weberian ossicles chain. body of the Weberian apparatus (Table 1). This is a comparable index FEA. Note that the FEA mesh is different from that of a STL mesh be- applicable in evaluating scans of other structures and differently sized cause the FEA mesh covers the inner thickness of the model in addition fishes. to representing the surfaces. Material properties defined in these analyses were adopted from 3.3. Segmentation and reconstruction previous FEA publications: Young modulus 16 GPa (Soons et al., 2010); coefficient of Poisson 0.3 (Areias et al., 2016; De Greef et al., 2017; CT images were imported to the software Amira 6.0 (Thermo Funnell et al., 1992); density of the bone 2100 g/cm3 (De Greef et al., Scientific, Houston, TX, USA) to perform a region of interest (ROI) 2014; Alexander, 1959). Boundary conditions were defined in the segmentation. The scan was segmented using threshold selection and model to constrain the movements that the ossicles of the Weberian manual adjustment. To eliminate the variability of different users, apparatus experience during simulated function (Fig. 2). Four ligaments segmentations for all models were performed by the first author who were included in the model (Alexander, 1962) with rigidity of the li- has decades of experience in segmenting biological structures from CT gament set at 1.5 N/mm (De Greef et al., 2017, 2014). Furthermore, the images. 3D surface model was built from segmentations for the four direct contact of the ossicles with the vertebra has been defined using ossicles of the Weberian apparatus: claustrum, scaphium, intercalarium three different types of connection: spherical joints, leaf spring, and a and tripus respectively. total fixation. Moreover, the cushioning capsule of Weberian ossicles is Irregularities in the surface resulting from segmentation to model defined as Rayleigh damping β = 0.0001 s and α = 0 Hz (Areias et al., conversion were repaired using refinement and smoothing tools of 2016; Caminos et al., 2018; De Greef et al., 2014; Volandri et al., 2011), Geomagic Wrap (3D Systems, v. 12, Rock Hill, SC, USA). All models and elastic stiffness Kcush = 0.0025 N/mm3 (Marcé-Nogué and Liu, in were oriented using the best-fit alignment tool (with default settings) prep). Lastly, a force of 0.001 N was applied to obtain the nominal within Geomagic Wrap to ensure that the four models are equally unitary harmonic response in the tip of the tripus where the gas bladder aligned. Models then were converted to a CAD files for further analysis contacts the ossicle. A sweeping analysis of frequency values was con- (Marcé-Nogué et al., 2011). ducted between 10 Hz and 10000 Hz. We sampled the amplitude of the displacement and the velocity and its phase from 200 points regularly 3.4. Geometric Morphometrics analysis distributed throughout the different ossicles. We collected 41 landmarks in cartesian coordinates on the surface 4. Results of the Weberian apparatus of the 4 different models. These coordinates were analyzed using the ‘geomorph’ R package (Adams and Otárola- 4.1. Qualitative comparison of segmented 3D models Castillo, 2013) and are available in the document S1 of the Supple- mentary information. A Procrustes superimposition was performed to The 3D geometry models obtained after the segmentation, and the remove the differences due to scale, translation, and rotation, leaving CAD files after the conversion process, are shown in Fig. 3A, 3B, 3C and only variables directly related to shape. Next, these shape variables 3D. Generally speaking, the larger the structure, the less the difference were visualized for morphological differences among models using between models. Model 4.64 shows a complete Weberian apparatus principal component analysis (PCA). with all the ossicles details, whereas the other three models show more or less incompleteness in the claustrum and the foramen at the superior 3.5. Finite Element Analysis (FEA) process of the tripus. On the other hand, the overall shape of the tripus exhibits no visual differences across models. FEA (specifically, modal and harmonic response analyses) were performed to study the biomechanical performance of the ossicles of the 4.2. Quantitative comparison of the models using geometric morphometrics Weberian apparatus using the finite element package ANSYS 17.1 (Ansys, Canonsburg, USA) and a Dell Precision Workstation 7820 with In quantitative comparison, there are slight differences between the 64 GB RAM, and 16 cores Intel(R) Xeon(R) Silver 4110 processor. models in the volume and surface area of each ossicle (Table 2). There Modal and harmonic response analyses were performed in all four is a general trend towards smaller values in models built from higher models respectively (Table 1) to evaluate the influence of the image resolution data. The most apparent differences can be found in the quality/resolution towards FEA outputs. The 3D geometry models were scaphium; regions of the scaphium are incomplete in Models 5.05 and solid meshed using the ANSYS mesh module with an adaptive mesh of 13.08. tetrahedral elements (Marcé-Nogué et al., 2015). The mesh of the The Model 4.64 is the most accurate model (supported by ob- model consists of approximately 300,000 elements that will be used in servation from dissection and the visualization of CT images), so that 4 J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 Fig. 3. Geometry obtained after segmentation in .stl format (left) and CAD format (right) for A) Model 4.64 B) Model 5.05 C) Model 9.30 and D) Model 13.8; E) Morphospace of the first three morphometric PCs occupied by the four models. Table 2 Table 3 Differences in the computed volume (mm3) and area (mm3) of the Weberian Frequencies of the first six modes of vibration obtained for each model ossicles for the four different models MODEL MODE 1 MODE 2 MODE 3 MODE 4 MODE 5 MODE 6 Tripus Intercalarium Scaphium Claustrum [Hz] [Hz] [Hz] [Hz] [Hz] [Hz] VOLUME [mm3] Model 4.64 866 1009 1270 21796 33084 37558 Model 4.64 0.047629 0.03271 0.09803 0.01949 Model 5.05 874 1040 2213 19698 44134 68841 Model 5.05 0.066382 0.03439 0.01324 0.01912 Model 9.30 796 1057 1214 17228 28361 37966 Model 9.30 0.047104 0.02819 0.09725 0.01886 Model 13.08 823 1036 1142 17956 36968 40548 Model 13.08 0.044479 0.02601 0.01025 0.01415 SURFACE [mm2] Model 4.64 2.1791 0.20011 0.51465 0.15424 models, but substantial differences between models in Mode 3, 4, 5, and Model 5.05 2.1185 0.20534 0.50924 0.10057 6. Model 9.30 1.9906 0.18131 0.49825 0.12438 Model 13.08 1.9152 0.15776 0.44941 0.08216 Harmonic analysis results characterize the response of the Weberian ossicles to the sound pressure exerted by the gas bladder (Fig. 4). Re- sults for tripus, intercalarium and scaphium were recorded in the si- this model is served as a reference point for comparison with the re- mulations. Claustrum is not included in the analysis because no in- maining models. PCA of the morphometric data resulted in three PCs dependent response is expected, as claustrum is described as being that summarize 100% of the variance (Fig. 3E). The Procrustes distance fused to the first vertebra to support the wall of the sinus impar atrium, to the reference model is 0.084 for the Model 5.05, 0.062 for the Model and thus immobile in zebrafish (Bang et al., 2001). 9.30, and 0.061 for the Model 13.08. This result suggests that in spite of A resonance peak at around 900 Hz is present in all models. The relatively high-resolution factor, the Model 5.05 is the least accurate for differences among the amplitude of the intercalarium and the scaphium replicating the highest resolution model. are more apparent than that among tripus. The amplitude of the vi- With the loadings of each landmark (components x, y, and z sepa- bration of the scaphium in Model 5.05 is unexpectedly and abnormally rately), we calculate the contribution of each landmark vectorially low, compared to that of other models. Both Model 9.30 and 13.08 summing the x, y, and z loadings. Then, we sum the total contribution generate tripus resonance and peak amplitude frequencies close to that of each landmark vectorially summing the contribution in PC1, PC2 and of the Model 4.64. In contrast, intercalarium and scaphium values for PC3 to obtain the most influential landmarks in the shape differences. the same models diverge from each other. The tripus vibrations are The landmarks that vary the most among the four models are the nearly in phase in all of the models (Fig. 4). Intercalarium vibrations of landmark 23, 8, 33, 40, 22 and 24, which help pinpoint the principal Model 13.08 are out of phase, whereas scaphium vibrations of Model morphological differences between models built from scans of different 5.05 are out of phase comparing to the rest. Using the highest fidelity resolutions. These landmarks are mostly located in the tip of the in- Model 4.64 as a reference, ossicles of Model 9.30 are all relatively in tercalarium where the ligaments are attached and in the contact areas phase except moderate shift in intercalarium values at high frequencies. between the scaphium and the claustrum. Given the variations at such The overall behavior of Model 9.30 in both modal analysis (Table 3) important loci, the fidelity of the models may affect the subsequent and harmonic analysis (Table 4, Fig. 4) is closest to Model 4.64 out of biomechanical analysis. the three remaining models. 4.3. Biomechanical comparisons using FEA 5. Discussion Given the modal analysis is mathematically mandatory before the Morphological and biomechanical differences are evident from harmonic analysis, it was performed first. Table 3 reports the first six comparative analyses of four zebrafish Weberian apparatus models with modes of vibration for each model obtained in the modal analysis. varying scanning resolutions. The first important difference between There are only minor differences in the first two modes among all the models are the completeness of the Weberian ossicle models derived 5 J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 Fig. 4. Harmonic response between 10 and 10000 Hz in the tripus, intercalarium and the scaphium under the application of a 1 Pa pressure in the contact area of the gasbladder with the tripus. X axis is responding frequency displayed in logarithmic scale, Y axis is amplitute and vibration phase of three ossicles respectively. Note the scaphium of Model 5.05 does not resonant (upper right figure), which explained the unexpected low value in Table 4. Also note, intercarlarium of Model 13.08 and scaphium of Model 5.05 are out of phase (lower middle and right). from segmentation. Model 4.64 shows the most complete Weberian tripus is transmitted via the ligaments to the intercalarium and to the ossicles chain, whereas the other three models exhibit incomplete scaphium. It can be an important factor which may contribute to dif- portions on the claustrum and the scaphium. These differences are ferences in the simulated harmonic responses of the intercalarium potentially responsible for differences in FEA outputs in terms of (Fig. 4). boundary condition variability. For example, the missing area on the Biomechanical simulation outputs also differ among models and dorsal surface of the claustrum, where movement constraint was ap- among bony elements of the hearing system. The harmonic response in plied, could result in different displacement patterns compared to the tripus is the least affected from the effect of scan resolution, likely constraints placed on a model with complete morphology. Also, missing because tripus is the biggest ossicle and least affected in geometry. part of the scaphium, where a joint is supposed to be located, could Therefore, comparisons of biomechanical performance in tripus alone, have resulted in varying model behavior because of different joint an- without considering the transmission of the vibration to the other os- gles created in models with incomplete morphology. These important sicles, appear to be immune to the effects of CT scan resolution. differences may explain the low fidelity of Model 5.05 outputs in both The quality of the CT-scans for morphological models has been GMM analysis and harmonic response. discussed in previous studies, and the conclusion was that low-resolu- Quantitative geometric comparisons reveal anatomically and func- tion scans can provide a sufficiently accurate geometry for 3D shape tionally important differences in the models built from varying scan analyses (Marcy et al., 2018). Also, models built from more time-effi- resolutions. Apparent differences were detected at the landmarks 22, 23 cient, lower-resolution scans may provide valid results in a comparative and 24 from GMM analysis. These landmarks are located in the areas context when perform static FEA (McCurry et al., 2015). This could be where the ligaments 3 and 4 are connected to the intercalarium. These true for analysis on larger structures such as jaw bones (comparing to variations are in an important location, where the vibration of the the minute ossicles). However, our results show that the dynamic Table 4 Frequency of resonance and peak amplitude of the harmonic response in each model. Tripus Intercalarium Scaphium MODEL Frequency [Hz] Amplitude [μm] Frequency [Hz] Amplitude [μm] Frequency [Hz] Amplitude [μm] Model 4.64 912 0.4089 821 0.2732 912 0.0180 Model 5.05 793 0.4778 821 0.1840 1084 0.0001* Model 9.30 944 0.3657 766 0.1325 944 0.0374 Model 13.08 912 0.4281 977 0.0851* 944 0.0860 * indicate unexpected low or high value comparing to Model 4.64. 6 J. Marcé-Nogué and J. Liu Micron 135 (2020) 102874 analysis (modal analysis and harmonic analysis) of FEA require high CT Areias, B., Santos, C., Natal Jorge, R.M., Gentil, F., Parente, M.P.L., 2016. Finite element scan resolutions for more resolved models. The morphological fidelity modelling of sound transmission from outer to inner ear. Proc. Inst. Mech. Eng. Part H J. Eng. Med 230, 999–1007. https://doi.org/10.1177/0954411916666109. of a model generated from CT images is affected by two main factors. Babaei, F., Hong, T.L.C., Yeung, K., Cheng, S.H., Lam, Y.W., 2016. 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P.M., Bates, K.T., Bengtson, S., Benson, R.B.J., Boyer, D.M., Braga, J., Bright, J.A., Claessens, L.P.A.M., Cox, P.G., Dong, X.-P., Evans, A.R., Falkingham, P.L., Friedman, CRediT authorship contribution statement M., Garwood, R.J., Goswami, A., Hutchinson, J.R., Jeffery, N.S., Johanson, Z., Lebrun, R., Martínez-Pérez, C., Marugán-Lobón, J., O’Higgins, P.M., Metscher, B., Orliac, M., Rowe, T.B., Rücklin, M., Sánchez-Villagra, M.R., Shubin, N.H., Smith, S.Y., Jordi Marcé-Nogué: performed analyses and wrote Starck, J.M., Stringer, C., Summers, A.P., Sutton, M.D., Walsh, S.A., Weisbecker, V., manuscript.Juan Liu: captured the idea collected data performed Witmer, L.M., Wroe, S., Yin, Z., Rayfield, E.J., Donoghue, P.C.J., 2017. Open data and analyses and wrote manuscript. digital morphology. Proc. R. Soc. B Biol. Sci. 284, 20170194. https://doi.org/10. 1098/rspb.2017.0194. De Greef, D., Aernouts, J., Aerts, J., Cheng, J.T., Horwitz, R., Rosowski, J.J., Dirckx, J.J.J., 6. 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Elife 8, 1–28. https://doi. org/10.7554/eLife.44898. The authors thank Andy Bentley, Leo Smith, and Gloria Arratia Engelkes, K., Helfsgott, J., Hammel, J.U., Büsse, S., Kleinteich, T., Beerlink, A., Gorb, S.N., (University of Kansa) for specimen loan; Jack Tseng for stylistic im- Haas, A., 2019. Measurement error in μCT-based three-dimensional geometric mor- provement; Teresa Porri (University of Cornell) for CT scan and grants phometrics introduced by surface generation and landmark data acquisition. J. Anat. that funded the CT (NIH S10OD012287 for the ZEISS/Xradia Versa 520 https://doi.org/10.1111/joa.12999. Evans, H.M., 1925. A Contribution to the Anatomy and Physiology of the Air-Bladder and X-ray Microscope, and NIH S10OD025049 for the SkyScan 1276); Weberian Ossicles in Cyprinidae. Proc. R. Soc. B Biol. Sci. 97, 545–576. https://doi. Kemper Lewis and Department of Mechanical and Aerospace org/10.1098/rspb.1925.0018. 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