Eardrum displacement and strain in the Tokay gecko (Gekko gecko) under quasi-static pressure loads

Journal Pre-proof Eardrum displacement and strain in the Tokay gecko (Gekko gecko) under quasistatic pressure loads Pieter Livens, Kilian Gladiné, Joris J.J. Dirckx PII:

S0378-5955(19)30388-0

DOI:

https://doi.org/10.1016/j.heares.2019.107877

Reference:

HEARES 107877

To appear in:

Hearing Research

Received Date: 3 September 2019 Revised Date:

27 November 2019

Accepted Date: 25 December 2019

Please cite this article as: Livens, P., Gladiné, K., Dirckx, J.J.J., Eardrum displacement and strain in the Tokay gecko (Gekko gecko) under quasi-static pressure loads, Hearing Research (2020), doi: https:// doi.org/10.1016/j.heares.2019.107877. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Pieter Livens: Conceptualization, Methodology, Software, Writing - Original Draft Joris J.J. Dirckx: Conceptualization, Writing - Review & Editing, Supervision Kilian Gladiné: Methodology, Software, Writing - Review & Editing

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Eardrum displacement and strain in the Tokay gecko (Gekko gecko) under quasistatic pressure loads

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Pieter Livens1,a; Kilian Gladiné1,b; Joris J.J. Dirckx1,c

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1) University of Antwerp, Laboratory of Biophysics and Biomedical Physics, Groenenborgerlaan 171, 2020 Antwerp, Belgium

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a) Corresponding author: [email protected]

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b) [email protected]

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c) [email protected]

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Abstract

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The eardrum is the primary component of the middle ear and has been extensively investigated in humans. Measuring

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the displacement and deformation of the eardrum under different quasi-static loading conditions gives insight in its mechanical

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behavior and is fundamental in determining the material properties of the eardrum. Currently, little is known about the

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behavior and material properties of eardrums in non-mammals. To explore the mechanical properties of the eardrum in non-

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mammalian ears, we investigated the quasi-static response of the eardrum of a common lizard: the Tokay gecko (Gekko gecko).

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The middle ear cavity was pressurized using repetitive linear pressure cycles ranging from -1.5 to 1.5 kPa with pressure change

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rates of 0.05, 0.1 and 0.2 kPa/s. The resulting shape, displacement and in-plane strain of the eardrum surface were measured

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using 3D digital image correlation. When middle-ear pressure is negative, the medial displacement of the eardrum is much

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larger than the displacement observed in mammals; when middle-ear pressure is positive, the lateral displacement is much

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larger than in mammals, which is not observed in bird single-ossicle ears. Peak-to-peak displacements are about 2.8 mm, which

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is larger than in any other species measured up to date. The peak-to-peak displacements are at least five times larger than

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observed in mammals. The pressure-displacement curves show hysteresis, and the energy loss within one pressure cycle

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increases with increasing pressure rate, contrary to what is observed in rabbit eardrums. The energy lost during a pressure cycle

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is not constant over the eardrum. Most energy is lost at the region where the eardrum connects to the hearing ossicle. Around

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this eardrum-ossicle region, a 5% increase in energy loss was observed when pressure change rate was increased from 0.05

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kPa/s to 0.2 kPa/s. Other parts of the eardrum showed little increase in the energy loss. The orientation of the in-plane strain on

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the eardrum was mainly circumferential with strain amplitudes of about +1.5%. The periphery of the measured eardrum surface

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showed compression instead of stretching and had a different strain orientation. The TM of Gekko gecko shows the highest

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displacements of all species measured up till now. Our data show the first shape, displacement and deformation measurements

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on the surface of the eardrum of the gecko and indicate that there could exist a different hysteresis behavior in different

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species.

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Abbreviations:

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DIC, digital image correlation; FE, Finite-element; ME, middle ear; TM, tympanic membrane; PME, Middle ear pressure

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Keywords:

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Lizard middle ear; Quasi-static pressures; tympanic membrane; full-field strain measurement; Digital image correlation

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1. Introduction

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The mammalian middle ear (ME) contains three hearing ossicles. In the other tetrapod lineages, a single ossicle ME

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evolved independently (Christensen-Dalsgaard and Manley, 2013; Manley, 2017). This ossicle is called the columella and

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connects to the eardrum (or tympanic membrane, TM) at the extracolumella. The acousto-mechanical functioning and material

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properties of the mammalian ME, and especially of the eardrum, have been investigated extensively using various approaches.

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The non-mammalian ME has been investigated to a lesser extent. Within mammalian MEs, a lever system is present with the

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joints located between the different ossicles, but in non-mammals this joint is incorporated within the extracolumella, which

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bends to create the needed piston motion of the columella (Manley, 1990a). However, there is little experimental data that

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quantifies how much deflection and deformation the non-mammalian ME undergoes under quasi-static loading compared with

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the mammalian ME, and how this different behavior is related to the quasi-static response of the TM. For birds, some data is

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available (Claes et al., 2018); chickens have similar TM surface areas as rabbits, but in chickens, TM displacements are tenfold

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the values observed in rabbits (Gladiné and Dirckx, 2019) under similar pressure loads. Muyshondt et al. (2019) built a finite

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element (FE) model based on the data of Claes et al. (2018), where a relatively low Young’s modulus of the extracolumella was

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used to adequately match experimental data, indicating higher flexibility of the TM and/or the connecting ME components in

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birds than in mammals. The higher flexibility in avian MEs is thought to be important for certain birds to regulate large quasi-

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static pressure changes, for example when diving underwater to catch prey. In lizards, the ME cavities are not separated from

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the mouth cavity, so a more flexible ME apparatus may protect against mechanical disturbances caused by eating and chewing.

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Note that flexibility within the ME may be the result of either a relative movement between two ME components or bending of

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one specific ME component (Mason and Farr, 2013). Flexibility, in this paper, will not discern between these two possible

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sources, since only the TM is measured.

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This paper investigates the mechanical behavior of the TM in lizards, specifically in Gekko gecko (commonly called the

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Tokay gecko). While auditory responses have been measured in lizards such as the Tokay (Christensen-Dalsgaard and Manley,

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2005; Manley, 1972a, 1972b; Saunders and Johnstone, 1972), little is known about the mechanical properties and behavior of

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the TM in lizards under quasi-static pressure loads. In the anole lizard (Anolis sagrei), a FE model (Livens et al., 2019) also

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displayed relative low Young’s moduli of ME components like the extracolumella, indicating higher flexibility in the ME of lizards

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compared to mammals.

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Geckos are nocturnal and unique in their rich, and loud, vocalization (Manley et al., 2014). Calls serve either for

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intraspecific communication or as warning sounds, reaching sound levels of 68 dB (Brumm and Zollinger, 2017, sound level

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measured at approx. 1.9 m). The outer ear is shallow, only a couple of millimeters deep, and can be closed by contraction of an

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L-shaped closure muscle to protect from damage by foreign objects (Saunders et al., 2000; Wever, 1973). The TM of geckos is

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slightly elliptical in shape and measures around 8 by 6 mm along the two major axes (Manley, 1972b) (Fig. 1A). The eardrums of

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birds, reptiles and amphibians are not flat but rather ‘tent-shaped’ and protrude laterally (outward), contrary to the medially

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(inward) pointing mammalian eardrums. The TM itself is partially supported by a C-shaped bone on the anterior margin. The

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remaining part of the TM is not as securely anchored and mainly connects to skin and fascia, which in turn connects to bony and

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cartilaginous elements of the head and jaw (Werner and Wever, 1972). The ossicle in the avian, reptilian, and amphibian ear is

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called the columella. It traverses the ME cavity rostrally to insert into the oval window, and distally terminates at right angles

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with the extracolumella (Carr et al., 2016) (Fig. 1B). The cartilaginous extracolumella can be seen from the lateral side of the TM

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(Fig. 1A). In mammals, the ME cavity is separated from the pharynx by the Eustachian tube, which only opens when swallowing

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to equalize the pressure at both sides of the TM. The ME cavity of the Tokay, and lizards in general, is not separated from the

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pharynx and the ME cavities are continuous with the mouth and throat. If the floor of the mouth is removed, both MEs can be

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visually observed from the inside (Werner and Wever, 1972; own observations).

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The objective of this paper is to measure the shape, displacement, and in-plane strain of the TM in Gekko gecko under

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quasi-static pressure loads, using digital image correlation (DIC, see section 2.2). Different pressures levels are applied inside the

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ME cavity at different rates, making the TM bulge in- or outwards depending on the direction of the pressure gradient over the

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TM. These observations result in full-field information on the deformation behavior of the TM of Gekko gecko and allow for a

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quantitative comparison with other species. Future work on the mechanical behavior of the gecko ME may benefit from these

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findings, since the material properties of the TM may be estimated from these data, for example in a finite element updating

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approach. Since large static pressure changes may still damage human ME prosthesis, including such flexible components in

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human ME prosthesis may improve current designs (Arechvo et al., 2013).

Fig. 1. Image of the head of Gekko gecko (A). The semi-transparent tympanic membrane (TM) bulges outwards, and the extracolumella can be seen from the lateral side of the TM. Some skin around the posterior edge of the TM was removed to allow for a better optical view of the lateral surface of the TM. The middle ear of the gecko contains only one hearing ossicle: the columella (B). The bony columella does not terminate on the TM, but connects to the cartilaginous extracolumella. On its proximal end, the columella terminates at the footplate. Fig. 1B was adapted from Mason and Farr (2013), their Figure 1b.

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2. Materials and methods

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2.1.

Animals and specimen preparation

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The geckos used in the present study were bought from a local breeder. After the geckos were acquired, they were

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euthanized and freshly frozen immediately afterwards. Before a gecko was used for the experiment, it was slowly defrosted in a

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refrigerator. All specimens reported in this paper will be referred to by a serial number (G1, etc.). To create a pressure gradient

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over the TM, an airtight enclosure needs to be formed inside the mouth cavity, in which the pressure level can be regulated.

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Two metal suction tips with a diameter of 1 mm were inserted in the mouth to respectively apply and measure the pressure at

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the medial side of the TM; see section 2.3. The mouth and nostrils were subsequently closed with two-component silicone paste

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(Otoform Akx, Dreve Otoplastik, Unna, Germany). To allow for a better optical view of the TM, some of the skin of the external

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auditory meatus was removed under a microscope with surgical scissors (Fig. 1A). Nine Tokay geckos were used in this study;

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hence eighteen ears were measured. Samples G1, G2, and G9 were eventually omitted from the final analysis; see the discussion

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for more details. We treated each ear as an individual measurement in samples G3-G8. Therefore, TM displacement averages

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and their variances in the results section (Fig. 3A-3C) are calculated with a sample size of twelve. Samples G3-G8 had an average

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head width of 28.36 ± 3.86 mm and a head length of 37.07 ± 2.16 mm. The experiments were approved by the Ethical

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Committee for Animal Testing of the University of Antwerp (reference number 2018-65).

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2.2.

Displacement and strain measurement

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To measure displacements and strains of the TM under quasi-static pressure loading, digital image correlation (DIC) was

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used. DIC is an image-based optical method and uses the captured images of the object surface to determine the shape,

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displacement, and in-plane strain of an object. One of the advantages of DIC is therefore that it is a so-called full-field technique,

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since it returns the position and displacement fields of the surface measured and not only a result on a single location on the

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TM. Commercially available software (ISTRA 4D 4.4.7, Dantec Dynamics, Skovlunde, Denmark) was used to perform the image

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capturing and DIC analysis. Two cameras were used in the experiments, with a resolution of 2056x2464 pixels each. The two

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cameras allow the DIC software to capture the 3D shape of the lateral TM surface. The DIC method works by subdividing the

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captured images into rectangular pixel groups, so-called facets. The software defines one image as a reference and searches for

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the corresponding facets in the images captured by the other camera, here called the target. The correlation of the facets

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between reference and target is usually done by an intensity-based matching of the pixel values, which tries to find the best

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matching facet in the target image by comparing the intensities of one reference facet to all possible target facets. Before each

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experiment, the cameras are calibrated using a checkerboard pattern, so their relative and absolute locations are known. If a

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facet is successfully found in both cameras, the software can determine the location of the facets in space. Since the facets are

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defined on the object surface by the measured gray values, the resultant data is linked to the object surface and not the

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reference frame of the measurement system. This is one of the major advantages of DIC: since all data is captured on the object

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itself, DIC allows for accurate recording of shape, displacement, and in-plane strain. For a review and more information on DIC,

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see Pan (2018).

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An optimal correlation between the facets in the reference and target images requires the intensity texture of each facet

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to be as distinct as possible. Ideally, the measured surface should have a locally varying intensity pattern to facilitate a good

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distinction between facets. However, the TM is relatively homogeneous in color and semitransparent. Therefore, a stochastic

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pattern is sprayed on the TM. Fluorescent powder is suspended in denaturalized alcohol and sprayed on the lateral TM surface

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with an airbrush. Using an airbrush enables pattern generation suitable for microscale objects (Berfield et al., 2007). After

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evaporation of the alcohol, a sparse coating of fluorescent speckles remains. Irradiating the TM with a green laser (532 nm,

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100mW) allows the generated fluorescent light to be captured by the cameras. The advantages of using a laser are twofold: 1)

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the illumination intensity is high, allowing for short shutter times and thus reducing motion blur and 2) the well-defined

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wavelength of the fluorescent dye makes it possible to use color filters to attenuate specular reflections.

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The relevant DIC settings found to give the best trade-off between computation time and resulting data accuracy for the

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experiments were a facet size of 45 pixels and a grid step of 30 pixels. The corresponding distance between the DIC evaluation

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points with these settings is 110 µm and is visualized in Fig. 2. Note that the conversion of pixel to spatial coordinates depends

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on the object to camera distance, the object surface geometry, and the DIC settings.

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2.3.

Pressure generation and monitoring

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A custom-built pressure generator was used to apply positive and negative pressures in the ME cavity. Pressures were

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swept using triangular-shaped cycles, with an amplitude of 1.5 kPa (3 kPa peak to peak). Five cycles in total were recorded, of

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which the first served for preconditioning. Note that positive pressure refers to positive pressures inside the ME cavity, thus

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making the TM move outward, while negative pressures make the TM move inward. Displacement values are indicated as

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positive when motion is in the lateral direction. To allow for comparison with literature data using similar pressure amplitudes,

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pressure change rates of 0.05 kPa/s, 0.1 kPa/s, and 0.2 kPa/s were used. A 3 kPa peak to peak pressure amplitude corresponds

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to frequencies of 8.3, 16.7 and 33.3 mHz or periods of 120, 60, 30 seconds, respectively. Cycles were digitally generated in

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Matlab (Mathworks, Natick, MA, USA), converted to an analog signal using a 16 bit I/O device (NI USB-6251 BNC, National

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Instruments, TX, USA) and sent to the analog input of the generator. The pressure output nozzle of the generator was connected

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to one of the two suction tips inside the gecko head using rubber tubing. For every change of 0.1 kPa of the input signal, an

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image was taken in ISTRA 4D, resulting in 307 frames per measurement. Small leaks may be present so the actual pressure in the

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ME may differ slightly from the value set by the pressure generator. Therefore, the obtained pressure was recorded using a

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pressure transducer (Druck Limited, Leicester, UK), which was connected to the second suction needle using the same diameter

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rubber tubing. The signal of the pressure transducer was recorded in ISTRA 4D simultaneously with the DIC images. Therefore,

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values reported in the results section are the actual pressures measured inside the ME cavity and not the applied pressure from

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the generator. In this paper, pressure values are indicated as positive when ME pressure is above ambient pressure.

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Displacement values are indicated as positive when motion is in the lateral direction.

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2.4.

Data post-processing and visualization

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To calculate the strain values on the TM, the displacement fields are numerically differentiated. However, numerical

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differentiation is sensitive to noise. To diminish the effect of noise on the strain fields, the displacement fields were smoothed

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using the built-in smoothing spline tools of ISTRA 4D. Smoothing allows more accurate and representative strain fields to be

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calculated since small local variations in the displacement field (i.e. noise) are removed (Pan et al., 2009). The effect of

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smoothing DIC data in ISTRA 4D has been discussed in previous work (Gladiné and Dirckx, 2019, their Fig. 4) and we will only

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emphasize here that it removes local extrema in the strain fields and helps with the interpretation of the direction of the strain

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over the surface. The final (smoothed) data was then exported from ISTRA 4D using the HDF5 file format and imported into

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Matlab.

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Comparing between the displacements of the different TMs measured requires some problems to be addressed.

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Firstly, it is difficult to position each TM in exactly the same way between measurements, so the displacements may look

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different because of the different orientations of the TMs. Secondly, one has to keep in mind that the reference system of the

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DIC measurements is determined at calibration. Since we had to calibrate between measurements of different TMs, the

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reference systems of the different TMs are not exactly the same and the displacement data is not readily comparable.

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Additionally, the displacement data in literature is most often reported by taking the z-component of the displacement. We

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found that by calculating a best-fitting plane through all the data points on the TM surface, the most dominant displacement of

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the TM surface was normal to this plane. We therefore calculated a best-fitting plane for each of the TMs measured and

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performed a linear transformation to align the normal of each of the TM-planes to our chosen reference frame. The result of

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this transformation is that all the normals of the best-fit planes lay perpendicular with each other and their z-displacements can

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be readily compared. The z-component of the displacement is commonly called the ‘piston’-component and is the largest

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component of displacement. From here on, we will use the ‘z-component of the displacement’ and the ‘displacement’

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synonymously, except if explicitly stated otherwise.

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A final post-processing step we performed was to exclude visualizations on the extracolumella in the surface plots.

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Because the extracolumella is a relatively steep ridge running over the TM, a facet in the reference image may not be seen in the

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target image. Consequently, the DIC algorithm fails to evaluate the data points on the extracolumella and data is relatively

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sparse in this region. Therefore, we removed the region of the extracolumella from the visualization in the paper to allow for a

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clearer overview of the results only on the TM. In Fig. 2 this can be seen by the somewhat rectangular cut-out on the TM surface

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in the dorsal region.

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Since the DIC experiments resulted in a large amount of data, we will only show one surface figure for a representative

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TM in this paper. To compare data of other samples, the reader is referred to the supplementary material files. Note that in the

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supplementary material, the data points on the extracolumella were not removed.

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3. Results

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3.1.

The shape of the TM of Gekko gecko

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A surface map of the lateral side of the TM of Gekko gecko is shown in Fig. 2. Colors represent the height of the right TM

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of sample G7, relative to the lowest part of the TM which could be measured, i.e., the minimal z-value of the DIC measurement.

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The (black) dots on top of the colored surface indicate the locations at which the DIC determined the height value. The results

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show that the TM of the Tokay is elliptical in shape, with the major axis parallel to the infrastapedial process of the

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extracolumella and the second axis perpendicular to this process, which is also seen in Fig. 1. The TM is nearly flat over a large

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part of its surface. As seen in Fig. 2, the color distribution is fairly homogenous over the TM and has an average value of 0.35

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mm. The height increases rapidly around the most ventral tip of the extracolumella. The cone shape of the TM is thus clearly

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visible in Fig. 2. For all specimens measured we found similar characteristics of the TM surface, indicating a cone-height of the

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TM around 0.9 mm.

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‘S1_TM_surface_and_apex_displacement.pdf’.

For the TM surfaces of other geckos, the reader is referred to the supplementary file

Fig. 2. Height distribution of the TM of Gekko gecko (G7, right ear). The color indicates the height relative to the lowest point in the field of view. The (black) dots on top of the colormap show the locations at which the DIC algorithm was evaluated. The distance between these evaluation points is 110 µm. The arrows show the direction of the lateral TM surface relative to the body axes. For interpretation of the color in this figure, the reader is referred to the Web version of this article.

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3.2.

TM displacement and deformation in Gekko gecko

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3.2.1.

Displacement of the TM

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Displacement of the TM apex: As described in section 2.3, pressures were swept between -1.5 and 1.5 kPa at three

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selected pressure rates. For each rate, five cycles were recorded. The first cycle was used for preconditioning. For all specimens,

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we observed that the TM quickly reached a steady-state condition and that from the second cycle onwards no noticeable

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change in TM motion was present between subsequent cycles. All reported data are taken from the second cycle.

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To construct the pressure-displacement curve, we selected a point in the vicinity of the tip of the extracolumella, i.e., the

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apex of the TM. Despite the small anatomical asymmetry between the left and right ears observed in some lizards (Werner et

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al., 1991) the left and right ears in the present study showed very similar displacement curves, and only the pressure rate

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seemed to be the distinguishing factor of the TM motion, so we grouped those in our analysis. Therefore, average TM

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displacement values are calculated with a sample size of twelve, using both the measurements of the left and right TMs of

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geckos G3-G8.

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In Figures 3A-3C, the average pressure-displacement curve at the TM apex is shown for each of the measured pressure

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change rates. The mean displacement curve is drawn as a solid (black) line, and the standard deviation of the dataset is shown

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as a shaded (red) area over the mean curve. Figures 3A-3C show clear asymmetry of the S-shaped displacement curves between

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negative and positive ME pressures. The TM displacements in the medial direction under negative ME pressures (-1.5±0.2 mm

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at -1.5 kPa, Fig. 3A) are larger than the lateral displacements under positive pressures (1.2±0.3 mm at 1.5 kPa, Fig. 3A). The

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gecko ME is thus more compliant for displacements in the medial direction, independent of the pressure rate used. All three

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cycles also show hysteresis: the loading curves do not coincide with the unloading curves, indicating path history and the loss of

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energy during a cycle. The amount of energy lost during a cycle is related to the area enclosed within the loop, see Fig. 3D. Since

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we measure pressure, and not force, the enclosed surface area (W) has units of m.Pa or J/m , thus giving the energy lost per

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unit area at the chosen location on the TM. The definition of the work done on the TM (W) is then

2

=

(1)

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with P the applied pressure and z the amplitude of the displacement along the pressure-displacement curve c. Note that W is

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positive if P and z have the same sign and the work is negative if they differ in sign. The average values of W are shown in the

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legends of Fig. 3A-3C. Even though the standard deviations of W overlap between the different pressure rates, an increase in W

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seems to be present for increasing pressure rates, as seen in Figures 3A-3C. The reader is referred to the supplementary file

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‘S1_TM_surface_and_apex_displacement.pdf’ for pressure-displacement curves of individual measurements. The hysteresis

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values for each of the individual measurements are summarized in Table 1. The last column of Table 1 shows the relative change

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in W between the pressure rate of 0.05 kPa/s and 0.2 kPa/s, calculated as (

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twelve ears measured showed an increase in W between 0.05 kPa/s and 0.2 kPa/s.

.

−

.

)/

.

. For our dataset, nine out of

W (m.Pa) at 0.05 kPa/s

W (m.Pa) at 0.1 kPa/s

W (m.Pa) at 0.2 kPa/s

Relative change (%)

L

0.55

0.56

0.59

7,27

R

0.46

0.47

0.48

4,35

L

0.45

0.50

0.50

11,11

R

0.53

0.54

0.53

0,00

G3

G4

L

0.47

0.49

0.55

17,02

R

0.58

0.63

0.68

17,24

L

0.62

0.62

0.61

-1,61

R

0.61

0.61

0.65

6,56

L

0.45

0.45

0.47

4,44

R

0.46

0.47

0.51

10,87

L

0.44

0.46

0.46

4,55

R

0.43

0.44

0.43

0,00

G5

G6

G7

G8 224 225

Table 1. Hysteresis losses W (in m.Pa) for each of the TMs measured. The relative change of W between a rate of 0.05

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kPa/s and 0.2 kPa/s is given in the last column. In the 12 ears measured, 9 showed an increase in energy loss with

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increasing pressure rates.

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Asymmetry of the pressure-displacement curve under quasi-static loads has been observed in several species. In Figure

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4, we compare the displacements found in the Tokay (the top mean curve of Fig. 3A) with data of chicken (Claes et al., 2018),

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human (Dirckx and Decraemer, 1991), New-Zealand white rabbit (Gladiné and Dirckx, 2019) and gerbil (Dirckx and Decraemer,

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2001). The left vertical axis shows the displacement scale for non-mammals (blue), and the right vertical axis shows the relevant

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scale for mammals (red). The difference between the maximal and minimal displacement is the so-called peak-to-peak

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displacement and can be used as a measure to compare the scale of pressure-displacement curves. The peak-to-peak

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displacements of Fig. 4 are 2.8, 1.6, 0.51, 0.32, and 0.15 mm for the gecko, chicken, human, gerbil, and rabbit, respectively. The

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TM of the gecko thus displaces a factor 1.7, 5.4, 8.8, and 19 more than the chicken, human, gerbil, and rabbit, respectively.

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Chicken and gecko peak-to-peak displacements are thus comparable, but mammalian MEs tend to move far less under similar

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loads.

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Displacement of the TM surface: Figure 5 shows the full-field displacement of the left TM of G7 under two ME pressures

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(PME). When the ME cavity pressure is -1.5 kPa, the TM moves in the medial direction (Fig. 5A). When PME is +1.5 kPa, the

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movement is towards the lateral side (Fig. 5B). For both positive and negative PME, the movement of the TM is not

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homogeneous over the TM surface. Regions where the TM moves the most are indicated with dashed ellipses in Fig. 5. For

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medial displacements, the central part of the TM moves the most. For lateral displacement the maximal displacement is found

244

at the posterior region of the TM. Similar observations were made for all the TMs measured, which can be seen in the

245

supplementary file ‘S2_TM_surface_min_and_max_displacement.pdf’. Fig. 5 shows that different parts of the TM move

246

differently depending on the direction and amplitude of the pressure. Therefore, the values of W over the TM may differ with

247

differences in displacement amplitude. To enable a relative comparison of the energy loss between different points on the TM,

248

the energy loss

249

contribution (PME>0, Fig. 3D, Ap in blue) and the negative pressure contribution (PME<0, Fig. 3D, An in red) using formula (1). The

250

sum of the areas Ap and An gives the total energy input (in m.Pa) of the TM under the pressure range investigated. If the

251

displacement at a specific TM location becomes larger or smaller, the total energy input will scale accordingly. The ratio of W to

252

the energy input then gives a dimensionless indication of the hysteresis loss at each TM location, which we denote the

253

normalized energy loss (

254

of

was normalized to the total energy input at each point during one cycle. We integrated the positive pressure

). Fig. 6 shows the normalized energy loss on the left TM of G7 for all pressure rates measured. Values

are visualized using a color map ranging from 20% to 50% to better show the data range. Irrespective of pressure rate, the

255

region of the TM-extracolumella connection (marked as the region within the dashed lines) shows the most considerable loss,

256

while the ventral parts lose less energy within one cycle (Fig. 6A-6C). For a rate of 0.05 kPa/s, the loss around the extracolumella

257

is 35% (Fig. 6A, see the dashed region), but a rate of 0.2 kPa/s yields a loss of 40% in the same region (Fig. 6C, see the dashed

258

region). The current observations therefore indicate that 5% more energy is lost around the extracolumella-TM connection for

259

an increase of 0.15 kPa/s in pressure rate, as can be seen from comparing Fig. 6A and Fig. 6C. The

260

measured TMs can be found in the supplementary file ‘S4_TM_surface_energy_losses.pdf’.

surfaces of the other

Fig. 3. Mean displacement curves of the Gecko TM as a function of input pressure (A-C). The solid (black) lines show the mean displacement for the corresponding ME pressure. The shaded area (red) delineates the standard deviation on the data. The arrows indicate the direction in which the cycles are traversed. The energy loss during a cycle appears to increase with increasing pressure rates. The enclosed area within a loop, denoted W, gives the energy loss per 2

cycle in units of m.Pa or J/m (D, shaded region). To compare W over the TM, a normalization is performed by taking the ratio of W with the total area (Ap + An). The resulting normalized energy loss is denoted shown in the upper left corner of Fig. 3D.

, as

261

262

Fig. 4. A comparison of gecko ME displacement (the top mean curve of Fig. 3A) is made with chicken (Claes et al., 2018),

263

human (Dirckx and Decraemer, 1991), New-Zealand white rabbit (Gladiné and Dirckx, 2019), and gerbil (Dirckx and Decraemer,

264

2001). The left vertical axis shows the scale for non-mammals (blue), and the right vertical axis shows the mammalian scale

265

(red). When ME-cavity pressure is negative, the TM moves in the medial direction, and non-mammalian MEs displace the most.

266

Under positive ME-cavity pressures, the human TM shows larger lateral displacements than in chickens, but smaller

267

displacements than in the gecko. The lateral TM displacement in chickens is larger than in gerbil and rabbit.

268

269

Fig. 5. Full-field displacement of the left TM of G7 under maximal negative and positive ME cavity pressure PME. When

270

PME is negative, the TM moves medially (A). When PME is positive, the movement is lateral (B). For both positive and negative PME,

271

the movement is not homogeneous. Regions where the TM moves the most are indicated with dashed ellipses. For medial

272

displacements, the central part of the TM moves the most. For lateral displacements, the maximal values are found more on the

273

posterior region of the TM. For interpretation of the color in this figure, the reader is referred to the Web version of this article..

274 275

Fig. 6. Normalized hysteresis values on the left TM of G7 for three different pressure rates. For all pressure rates, the

276

energy loss is highest around the TM-extracolumella connection (marked as the region within the dashed line) and decreases

277

when going to the ventral part of the TM. The energy loss increases when the pressure change rate is raised from 0.05 kPa/s (A)

278

to 0.1 kPa/s (B) and grows even further at 0.2 kPa/s (C). The difference between the energy loss within the dashed region for (A)

279

and (C) is 5%, while other parts of the TM show a lower increase and at some places even a decrease in energy loss with

280

increasing pressure change rate, indicating that different parts of the TM have distinct hysteresis behavior. For interpretation of

281

the color in this figure, the reader is referred to the Web version of this article.

282

3.2.2.

In-plane strain distribution of the TM

283

As the DIC method delivers 3D position values of the facets on the object surface, the method allows direct calculations

284

of local in-plane stretching or compression of the TM surface under pressure loads. Strain is calculated by differentiation of the

285

displacement field of adjacent points on the surface (Herbst and Splitthof, n.d.) with respect to the spatial coordinates

286

corresponding to these points. By doing the differentiation with respect to either the initial configuration or the current

287

configuration of spatial coordinates, the engineering strain or true strain are obtained, respectively. Both of these measures are

288

tied to the coordinate system used. A more informative visualization is found by computing the so-called principal strains, which

289

are system independent. By performing a diagonalization of the engineering strain tensor with components {

290

}, the engineering principal strain tensor with components {

,

} is obtained. By definition,

,

,

=

is the most positive

291

eigenvalue and

the least positive eigenvalue. The corresponding eigenvectors give the direction of the principal strain field in

292

Cartesian coordinates. It was observed that

293

very negative. To present our data as concisely as possible, we followed the procedure of Gladiné and Dirckx (2019) and

294

calculated the maximum of the two principal strains in an absolute sense for all points on the TM surface. Visualizing only the

295

most dominant eigenvalue, with the proper sign, allows for inspecting the deformation of the TM in one figure, instead of

296

having to compare two strain fields with most of the strain values in one of the two fields close to zero.

was negligible when

was large, and that

was negligible when

was

297

In Fig. 7, the strain on the TM surface is shown for the right ear of sample G6 (Fig. 7A-7B) and the left ear of sample G8

298

(Fig. 7C-7D). The color range shows the amount of extension (positive values) or compression (negative values) on the TM and

299

was truncated between -5% and 5% to better show the data range. Figures 7A and 7C show the deformation of the TM at

300

negative PME, while Figures 7B and 7D show the deformation under positive PME. We found for both positive and negative PME

301

that the TM mainly extended, as seen in Fig. 7. The amount of extension on the TM was around 1.5%, regardless of the sign of

302

the ME pressure. Fig. 7A shows a large amount of extension (up to +7%) at the TM apex for negative ME pressures, contrary to

303

Fig. 7B which shows a large amount of compression (up to -10%) at the TM apex. Comparing the TM edges in Fig. 7A and 7B, we

304

find that in both cases the TM mainly stretches, with a maximum value around +15% in both figures. In Fig. 7C we observe

305

compression at the TM apex, with values up to -10%. Fig. 7D shows extension of the TM at the TM apex up to +3%. Comparing

306

the TM edges in Fig. 7C and 7D, we find that they both indicate a large amount of compression of the TM with values up to -

307

10%. Due to the lack of DIC data available on the extracolumella, it is difficult to notice a general pattern, but the TM seems to

308

mainly get compressed for both negative and positive PME. Another feature which we observed in almost all our measurements

309

was the circular orientation of the principle strain around the extracolumella, as opposed to a radial direction of the strain. This

310

circular orientation is best visible in Fig. 7D, where it can be seen that the solid black lines seem to follow a path around the

311

extracolumella. We also observed that the circular orientation of the strain field is only present relatively close to the

312

extracolumella and disappears when the deformation closer to the TM periphery is observed. For the strain fields of other

313

measurements, the reader is referred to the supplementary file ‘S3_TM_surface_min_and_max_strain.pdf’.

314

Fig. 7. Maximal engineering principle strains measured on the right TM of G6 (A-B) and the left TM of G8 (C-D). The value

315

of the in-plane strain is indicated by the color scale, while the corresponding strain direction is shown with solid lines.

316

Underpressure (A-C) and overpressure (B-D) in the ME cavity (PME) both tend to stretch the TM by about 1.5%. As expected, the

317

TM significantly deforms under the applied ME pressures, but the strain values around the extracolumella and TM edge are not

318

consistent between measurements. At the TM apex of G6, extension up to +7% (A) or compression up to -10% (B) is observed

319

when PME is respectively negative or positive. At the TM apex of G8 the opposite is seen, with dominant compression up to -10%

320

when PME is negative (C) and extension up to +3% when PME is positive (D). In G8 we see mainly compression of the TM edge (C-

321

D), but G6 shows mainly extension (A-B). A common feature observed in almost all measurements is the circular strain direction

322

over the TM around the extracolumella. The black lines seem to follow a path around the extracolumella. The strain orientation

323

at the TM periphery again differs between measurements.

324

4. Discussion

325

4.1.

Discussion of the methodology

326

To improve the view of the lateral TM surface, part of the skin of the external auditory meatus was removed (Fig. 1). The

327

posterior edge of the external meatus is relatively flaccid, and we noticed no significant change in TM shape before and after

328

cutting away the skin. The TM was sprayed with ethanol, in which fluorescent particles were suspended. The effect of possible

329

mass loading by the fluorescent dye was explored in previous work (Gladiné and Dirckx, 2019). After evaporation of the ethanol,

330

it was found that the dye particles are deposited with a density of 0.015 µg/mm by the airbrush. Using an eardrum area of 38

331

mm (see section 4.2), one finds an added mass of only 0.57 µg. Gladiné and Dirckx (2019) also observed a decline in the

332

displacement amplitudes during pressure cycles due to dehydration of the sample. However, their experiments pressurized the

333

ear canal and subsequently measured the medial TM surface, which is normally enclosed by the ME-cavity. In the current paper,

334

the mouth cavity was sealed and the lateral TM surface was measured. We did not observe any change in the pressure

335

displacement curves over time, indicating that no dehydration occurred.

2

2

336

For samples G1 and G2, we were not able to reach the desired pressures of ±1.5 kPa in the ME cavity, indicating a small

337

pressure leak. We could not determine the source of the leak, which could either be from a perforation of the TM or a small

338

hole in the two-component hardening paste around the mouth and nostrils. Therefore, these samples were omitted from the

339

analysis. Sample G9 was excluded because the DIC results differed too much from the other measurements. For the left TM, we

340

observed a very dense fiber running from the TM apex to the ventral part of the TM, which could explain the different shape

341

and strains measured. The right TM was wrinkled, indicating that it had been damaged. Therefore, we only included samples G3

342

to G8 in the data analysis.

343

We observed no systematic differences between left and right ears and therefore included both the left and right ears in

344

the mean curves of Fig. 3. Other authors have observed a slight anatomical asymmetry between the left and right ear of some

345

lizard species, but question if this could be of any functional use: “Asymmetry of the external and middle ear may rapidly attain

346

a level at which it is deleterious because optimal function of this organ intricately depends on dimensions” (Werner et al., 1991).

347

The DIC settings used were chosen based on the trade-off between computation time and spatial resolution. A smaller

348

grid step results in a denser spatial evaluation but makes the analysis highly computationally intensive. The optimal spatial

349

evaluation density used in this paper is shown in Fig. 2. ISTRA 4D recommends a facet size of 4/3 times the grid step. This makes

350

the facets slightly overlap for each evaluation point, but keeps them independent enough to determine the local behavior within

351

the facet. Larger facets tend to smooth out the data, and smaller facets reduce the amount of information used in the

352

correlation. The size of the fluorescent speckles is also an important parameter for determining the accuracy of the results, but

353

is difficult to control. When a speckle fills a large part of the facet, there is almost no variation of gray values within the facet,

354

and the algorithm will fail to determine the displacement. For speckle sizes which are too small, the image will contain many

355

sharp transitions in gray value between the background and the speckles, leading to a broad spectral content. This may lower

356

the accuracy of the measured displacements (Lecompte et al., 2007). For speckles which are too small, the resolution of the

357

camera will no longer be adequate to resolve the location of a speckle so that aliasing may occur. We used an airbrush to

358

deposit the fluorescent speckles onto the TM, so the resulting speckle sizes are suitable for microscale objects (Berfield et al.,

359

2007). Therefore, the reported facet size of 45 pixels was used as an optimum for the chosen grid step of 30 pixels and the size

360

of the speckles on the TM. For the effect of smoothing DIC data (in ISTRA 4D), we refer to previous work for more details

361

(Gladiné and Dirckx, 2019, their Fig. 4).

362

4.2.

Discussion of the experimental results

363

We calculated the mean head widths and lengths of samples G3-G8, which were 28.36±3.86 mm and 37.07±2.16 mm,

364

respectively. These values correspond reasonably well with literature data, where widths of 37.56 mm and lengths of 41.34 mm

365

were reported (Werner and Igic, 2002).

366

TM shape. Comparing the TM shape found with our DIC measurements with literature data is more complicated. The

367

TM of lizards is not supported by a well-defined rim but is continuous with the surrounding fascia and skin. Therefore,

368

measuring the dimensions of the TM may produce different results depending on the observer. Manley (1972b) reported that

369

the eardrums of the Tokay were 8 by 6 mm, which corresponds to a surface area of 38 mm (assuming an elliptical shape). In

370

Werner and Igic (2002), TM areas of 38.11 mm were reported for the Tokay. The data of Fig. 2 shows a TM of 6 by 3 mm with

371

an area of 14.14 mm or 37% of the mentioned reference area. The difference can be partially explained due to the fact that DIC

372

is only able to calculate data for points on the TM surface imaged with both cameras, which inevitably leads to loss of

373

information at the edges as these parts are often missed by one of both cameras. Nevertheless, DIC enables accurate

374

measurement of the lateral surface of the TM, as seen in Fig. 2.

2

2

2

375

TM displacement. The mean pressure-displacement curves of Fig. 3 showed that the gecko ME moved more in the

376

medial direction under negative ME pressures than in the lateral direction under positive ME pressure. The pressure-

377

displacement curves observed in both mammals and non-mammals highlight the non-linear response of the ME components

378

under quasi-static pressures. Before comparing the Gecko displacement curves with other species, we will discuss the different

379

methodologies used in the literature to generate the pressure-displacement curves of Fig. 4.

380

Measurements on the TM of the New-Zealand white rabbit were performed by Gladiné and Dirckx (2019) using the

381

same DIC setup as in this paper, by pressurizing the ear canal and thus the lateral TM surface. Dehydration of the samples after

382

a certain period of measuring was observed, presumably by exposure of the medial TM surface to the outside air. Gladiné and

383

Dirckx (2019) reported the z-displacement under the applied pressures, so these data are readily comparable to our results.

384

Similar to our experiments, Claes et al. (2018) pressurized the inside of the intracranial cavity in the chicken. Micro-CT scanning

385

was employed to image the ME at each pressure stage, which allows the displacement of the ME to be determined by

386

comparing the different volume datasets. The TM displacement was analyzed by tracking the movement of the tip of the

387

extrastapedius. Advantages of this approach are: almost the entire ME chain is measured for each pressure step, the very high

388

resolution, and keeping the ME cavity intact minimizes the risk of dehydration. Some drawbacks are: the time consuming

389

segmentation and the fact that, without clear markers, the user has to define which points correspond to each other at each

390

pressure stage. Additionally, if one wanted to visualize thin structures like the TM using Micro-CT, staining would be required for

391

better contrast, which may alter the behavior of the pressure-displacement curve. Using DIC requires visible access and a

392

suitable speckle pattern, but tracking of the displacement and the corresponding strain are then automatic fulfilled. Also note

393

that Claes et al. (2018) reported the absolute displacement, while we only report the z-component, but since our peak-to-peak

394

values are already larger than the data of Claes et al. (2018), using the absolute displacement on the gecko data would only

395

cause even larger peak-to-peak values. For the data of the human TM (Dirckx and Decraemer, 1991) and the TM of gerbil (Dirckx

396

and Decraemer, 2001), phase shifted moiré profilometry was used. Profilometry allows for a depth resolution of tens of

397

microns, but as with DIC requires the TM to be coated and optical access. Since the acquisition time is in the order of seconds

398

for each ME pressure, deformation measurements at different pressurization rates are not possible (Dirckx et al., 2006). Dirckx

399

and Decraemer (1991) pressurized the ME cavity and thus the medial TM surface and measured from the lateral side, while

400

Dirckx and Decraemer (2001) reversed the pressurized and measurement surface and measured from the medial side. Both

401

papers report the z-displacement, which is readily comparable to our data in Fig. 4.

402

The gecko and chicken displacement amplitudes in the medial direction, i.e., for negative pressure inside the ME cavity,

403

nearly coincide. The data of the gecko show that non-mammalian MEs are also capable of moving significantly in the lateral

404

direction. The chicken ME moved relatively little in the lateral direction, while the gecko ME showed significant lateral

405

movement. Compared to chicken, the rabbit and gerbil TMs moved less in the lateral direction, while the gecko moved further

406

than all animals currently measured in the literature. While the peak-to-peak displacement of the gecko was 1.7 times that of

407

the chicken, the mammalian MEs had peak-to-peak displacements at least 5.4 times smaller than the gecko ME. Claes et al.

408

(2018) argued that the significantly larger peak-to-peak displacement in the chicken was the result of the high amount of

409

flexibility within the single ossicle avian ME. Our data indicate that the single ossicle ear of lizards is also more compliant than

410

the three ossicle mammalian ME, and appears to be even more flexible than the bird ME in the lateral direction. The

411

observation of the relatively flexible avian and lizard MEs have successfully been used in FE models of the single ossicle ME,

412

where lower Young’s moduli were used for the ME components coupled to the TM than in mammals to match experimental

413

data (Muyshondt et al., 2019; Livens et al., 2019). The asymmetry in the pressure-displacement curves between medial and

414

lateral displacement may be attributed to the conical shape of the TM (Claes et al., 2018). For the outward pointing non-

415

mammalian ME, lateral displacements tend to stretch the TM. Medial displacements will tend to ‘fold’ the TM inwards and

416

slacken it, which is easier than stretching an already protruding membrane. It is therefore not surprising that the non-

417

mammalian ME allows for easier medial displacements than lateral displacements. Since mammalian TMs are also conically

418

shaped but point inwards, the contrary holds, as was seen in Fig. 4. The smaller lateral displacements of chicken compared to

419

gecko may be attributed to the angle of the hearing ossicle with the TM and the shape of the extracolumellar complex. In birds,

420

the hearing ossicle forms an acute angle with the TM. Additionally, the three arms of the extracolumella in birds resemble a

421

curved brace connecting to the TM, contrary to the more straightforward rod-like extracolumellar-TM connection in lizards

422

(compare Muyshondt et al. (2018) Fig. 1A and our Fig. 1B). Lateral displacements can, therefore, be larger in lizards, since a

423

rotation is possible before significant bending of the extracolumella occurs. In birds, the anatomical setup allows for less

424

rotation and requires the processes to bend and/or stretch when moved laterally, which may explain the smaller lateral

425

displacements. The relative stiffness between bird and lizard MEs may compound to this effect since it is argued that lizard MEs

426

are even more flexible than avian ME (Manley, 1990b).

427

Energy losses during pressure cycles due to hysteresis have been reported in rabbits (Dirckx et al., 2006; Gladiné and

428

Dirckx, 2019) and humans (Gaihede, 1999). For rabbits, hysteresis losses (W) of 0.089 m.Pa at 0.25 kPa/s were reported (Gladiné

429

and Dirckx, 2019). Rabbits thus experience less energy loss during pressure cycles than in geckos (

430

the pressure rates are comparable. Figures 3A-3C indicate that hysteresis increases with increasing pressure rate. While this

431

result may seem obvious, the contrary has been observed in rabbit ears (Dirckx et al., 2006). Data measured by Gaihede (1999)

432

delivered W = 0.250 m.Pa at 1.1 kPa/s in humans. A comparison with human hysteresis is therefore more difficult, since it is

433

unknown how much the hysteresis changes from 1.1 kPa/s to the values used in this paper or in Dirckx et al. (2006). More

434

experimental data at different pressure change rates and on other (non-)mammalian species would be of great value in

435

determining if this increase in hysteresis with increasing pressure rate is a common property or if it is a peculiarity of the gecko

436

ME. The data of Fig. 6 showed that the normalized hysteresis ( ) increased with pressure change rate around the

437

extracolumella and that the rest of the TM experienced less of an increase in energy loss. An increase in hysteresis of 5% was

438

observed at the TM apex for an increase of 0.15 kPa/s in the pressure rate.

≈ 0.5 m.Pa, Fig. 3), since

439

TM in-plane strain distribution. The majority of the TM of the Tokay stretched by +1.5% in our experiments,

440

independent of the sign of the ME pressure (Fig 7). A general conclusion about the sign of the strain around the TM apex is

441

difficult. While Fig. 7A showed extension up to +7% at the TM apex, Fig. 7C showed compression up to -10% in the same region.

442

Fig. 7B showed compression up to -10% at the TM apex, while Fig. 7D showed extension up to +3%. It was also observed that

443

the edges of the right TM of G6 showed mainly extension (Fig. 7A-7B), but mainly compression was seen in the left TM of G8

444

(Fig. 7C-7D). In general, we find that an extension of the TM will appear under positive and negative ME cavity pressures with an

445

amplitude of 1.5 kPa, but regions were the TM connects with other structures show a high amount of variability between

446

measurements. Circumferential strains are observed in all measurements, i.e. the strain direction seems to follow a path around

447

the extracolumella. The TM has a typical tent-like shape, so pressurization may produce a dominant stretch in the

448

circumferential direction, since deformation in the radial direction can be obstructed by the TM shape. Our data corresponds

449

well with the strains observed for the rabbit ear (Gladiné and Dirckx, 2019) under positive ME pressure. Note that in the rabbit

450

ears, they applied pressures in the ear canal and recorded the TM from the medial side. Their experiments with negative

451

pressure inside the ear canal therefore correspond to our experiments with positive pressure inside the ME cavity. Similar to our

452

data, the TM of the rabbit mainly stretched by +1% to +3.5%, and around the manubrium the medial surface of the TM was

453

compressed, but with higher values of up to -13%. They were able to image the edge of the TM and observed a compression of

454

the TM’s medial surface, with values around -2.5% to -1%. For negative ME pressure, Gladiné and Dirckx (2019) observed that

455

the TM mostly compresses, opposite of what we observed in Fig. 7A and 7C. Looking at the strain fields of the lowest negative

456

ME pressures (see supplementary material ’S5_TM_strain_evolution.pdf’), we did observe a compression of the TM. However,

457

the large displacement and flexibility in geckos makes the TM invert its conical shape at the lowest pressures inside the ME

458

cavity. At a ME pressure of -1.5 kPa (Fig. 7A and 7C) the gecko TM has reached a state far beyond the point of inverting its cone

459

shape, showing a stretching of the membrane instead of the compression seen by Gladiné and Dirckx (2019) in rabbit. A circular

460

direction of the strain on the rabbit TM similar as in the gecko was observed and discussed in Gladiné and Dirckx (2019). If we

461

were to pull on the TM at a certain location perpendicularly to its surface, a radial orientation of the stretch would be expected.

462

At the edges of the TM and at the extracolumella such a local pulling effect seems to be present. Fig. 7 shows that some of the

463

strain components are indeed oriented radially at the edges, but the lack of data at the extracolumella and the TM edges makes

464

a decisive statement about the strain direction at these regions impossible. For the rabbit data mentioned earlier, this radial

465

orientation of the stretch at the edges was clearly seen.

466

Conclusion

467

Using 3D-DIC, the shape, displacement, and in-plane strain of the TM of the Tokay gecko (Gekko gecko) were investigated for

468

different quasi-static pressures inside the ME cavity. It was found that the TM of the Tokay is elliptical in shape, protrudes

469

laterally with a height of 0.9 mm, and has an average height of 0.35 mm. The medial displacement of the TM of the Tokay under

470

negative ME pressures is larger than the lateral displacement for positive ME pressures, irrespective of the pressure rate used.

471

The larger medial displacements are attributed to the lateral orientation of the TM cone, similar to what is found in chickens.

472

Comparing the displacements of the TM under both positive and negative ME pressures in gecko with other species, we find

473

that the TM of the gecko displaced the most. This indicates a higher flexibility in both the medial and lateral direction of the

474

gecko ME compared to other species. The peak-to-peak displacements of the TM of the gecko are 1.7, 5.4, 8.8, and 19 times

475

larger than in chicken, human, gerbil, and rabbit, respectively. The energy loss within a pressure-displacement cycle increases

476

with increasing pressure rate, contrary to what is observed in rabbits. The energy loss is larger than in other species investigated

477

in the literature, but this may be caused by the larger displacements of the gecko TM. The hysteresis loss is not constant over

478

the TM of the Tokay. Most of the energy is lost around the extracolumella, and the amount energy lost around the

479

extracolumella increases faster compared to the rest of the TM for increasing pressure rates. For an increase of the pressure

480

rate of 0.05 kPa/s to 0.2 kPa/s the loss around the extracolumella increases by 5%, while the rest of the TM shows little increase

481

in hysteresis loss. The direction of the principal strain of the TM for ±1.5 kPa ME pressure is mostly circumferential, but the

482

strain orientation at the TM edges is less ordered and differs between samples. The average TM principle strain is +1.5%, with

483

much higher stretching or compression occurring at the ventral region or around the extracolumella. The TM of Gekko gecko

484

shows the largest displacements of all species measured to date.

485

Declaration of conflict of interest

486

None.

487

Contributors

488

P. Livens performed the measurements, analyzed the data, and wrote the manuscript. K. Gladiné built the DIC setup and

489

wrote part of the code to analyze the data. J.J.J. Dirckx participated in the design of the study. All authors gave their final

490

approval for publication.

491

Acknowledgements

492

The authors thank C. Broeckhoven for donating some of the geckos used in this work and housing the specimens before

493

euthanasia. We also thank J. Scholliers for euthanizing the geckos. P. Livens was financed by the Research Foundation-Flanders

494

(FWO), grant no. 11D4319N.

495

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Supplementary material See the supplementary files provided.

Highlights:     

The eardrum in gecko moves significantly under quasi-static loads Displacements are at least 5.4 times larger as in mammals Eardrum energy loss increases with increasing pressure rate Eardrum energy loss is not constant over the membrane but shows local variation Eardrum strains are mainly orientated circumferentially around the extracolumella