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The Discordant Eardrum

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The Discordant Eardrum The discordant eardrum Jonathan P. Fay*, Sunil Puria*†‡, and Charles R. Steele* Departments of *Mechanical Engineering and †Otolaryngology-HNS, Stanford University, Stanford, CA 94305 Edited by Eric I. Knudsen, Stanford University School of Medicine, Stanford, CA, and approved November 3, 2006 (received for review May 13, 2006) At frequencies above 3 kHz, the tympanic membrane vibrates superior wall of the ear canal rather than being a nearly chaotically. By having many resonances, the eardrum can transmit perpendicular termination of the canal as is often depicted. the broadest possible bandwidth of sound with optimal sensitivity. The eardrum consists of a large pars tensa area and a smaller In essence, the eardrum works best through discord. The eardrum’s pars flaccida area. The pars flaccida is more compliant than the success as an instrument of hearing can be directly explained pars tensa, and thus its mechanical significance is less important through a combination of its shape, angular placement, and except in some desert animals like the gerbil (7). The pars tensa composition. The eardrum has a conical asymmetrical shape, lies at is composed of four main layers (Fig. 1d shows a schematic a steep angle with respect to the ear canal, and has organized representation): an outer epidermal layer, two fibrous collagen- radial and circumferential collagen fiber layers that provide the fiber layers in the lamina propria segment, and an inner mucosal scaffolding. Understanding the role of each feature in hearing layer. Scanning electron micrographs show a well organized arrangement of circular and radial fibers (8, 9). The two separate transduction will help direct future surgical reconstructions, lead to fibrous collagen layers of the eardrum are unique to mammals improved microphone and loudspeaker designs, and provide a (reviewed in ref. 10). The radial fibers are the dominant fiber basis for understanding the different tympanic membrane struc- layer within the inner conical region of the eardrum. As one tures across species. To analyze the significance of each anatomical progresses outward into the toroidal region, the fiber density and feature, a computer simulation of the ear canal, eardrum, and thickness of the circumferential fiber layer gradually increases. ossicles was developed. It is shown that a cone-shaped eardrum Eventually, the circumferential fibers become very dense and can transfer more force to the ossicles than a flat eardrum, form the annular ligament, where the eardrum attaches to the especially at high frequencies. The tilted eardrum within the ear ear canal wall. The collagen fiber layers determine the mechan- canal allows it to have a larger area for the same canal size, which ical stiffness of the eardrum. The outer epidermal and the inner increases sound transmission to the cochlea. The asymmetric ear- mucosal layers are relatively flexible, and they mostly contribute drum with collagen fibers achieves optimal transmission at high to the overall mass of the eardrum. Because the subepidermal frequencies by creating a multitude of deliberately mistuned layer and the submucosal layer consist of connective tissue and resonances. The resonances are summed at the malleus attachment are also relatively flexible, they are part of the epidermal and to produce a smooth transfer of pressure across all frequencies. In mucosal layers, respectively (Fig. 1d). An extensive review of the each case, the peculiar properties of the eardrum are directly layers that make up the eardrum can be found in the literature responsible for the optimal sensitivity of this discordant drum. (10–12). A detailed description of the fiber layers has not been previously incorporated into a model of the eardrum (13–18). collagen fibers ͉ hearing sensitivity ͉ middle ear ͉ transducers In this work, these anatomical features have been embodied into a mathematical model of the eardrum and ear canal [see supporting information (SI) Fig. 6]. The model encompasses experimentally he function of the middle ear in terrestrial mammals is to measured geometries and orientations of the ear canal, eardrum, Ttransfer acoustic energy between the air of the ear canal to the and middle ear bones. The best available estimates for material fluid of the inner ear. The first and crucial step of the transduction properties of the eardrum were used. In addition, the acoustics of process takes place at the tympanic membrane, which converts the ear canal were fully coupled to the vibration of the eardrum. sound pressure in the ear canal into vibrations of the middle ear The open middle ear cavity was represented as a radiation imped- bones. Understanding how the tympanic membrane manages this ance. The model used a combination of rigid bodies, finite element, task so successfully over such a broad range of frequencies has been and asymptotic methods to ensure accuracy over the entire fre- a subject of research since Helmholtz’s publication in 1868 (1, 2). quency range of 200 Hz through 20 kHz. By using a combination of Even though the function of the eardrum is clear and the methods, the strengths of each were exploited while avoiding their anatomy of the eardrum is well characterized, the connection shortcomings. The specifics of the model are discussed in more between the anatomical features and the ability of the eardrum detail in Methods. The animal of choice was the domestic cat (Felis to transduce sound has been missing. The missing structure– catus) because there is a significant amount of anatomical data, function relationships can be summarized by the following three physiological data, and material properties known for the middle questions. Why does the mammalian eardrum have its distinctive ear of that species. It is also an animal that spans a relatively wide frequency range (19, 20). conical and toroidal shape? What is the advantage of its angular placement in the ear canal? What is the significance of its highly Results organized radial and circumferential fibers? To validate the mathematical model, five different outputs were The shape of the human and feline eardrum is known from compared against experimental measurements: ear canal im- detailed Moire´interferometry contour maps (refs. 3 and 4 and Fig. 1a). From the contour maps, three-dimensional reconstructions reveal the striking similarity of the two eardrums. In both cases, the Author contributions: J.P.F., S.P., and C.R.S. designed research; J.P.F. performed research; eardrum has an elliptical outer boundary, whereas the central C.R.S. contributed new analytic tools; J.P.F. and S.P. analyzed data; and S.P. and J.P.F. wrote portion has a distinctive conical shape (Fig. 1b). As one moves away the paper. from the center, the cone starts to bend forming an outer toroidal The authors declare no conflict of interest. region (Fig. 1 b and c). This article is a PNAS direct submission. The angular placement of the eardrum within the ear canal is Freely available online through the PNAS open access option. well documented. Measurements of the cat ear canal indicate ‡To whom correspondence should be addressed. E-mail: [email protected]. that the angle between the eardrum and the inferior canal wall This article contains supporting information online at www.pnas.org/cgi/content/full/ BIOPHYSICS ranged between 30° and 45° (5). In humans, the angle is between 0603898104/DC1. 45° and 60° (6). In the human and cat, the eardrum forms the © 2006 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0603898104 PNAS ͉ December 26, 2006 ͉ vol. 103 ͉ no. 52 ͉ 19743–19748 Downloaded by guest on September 28, 2021 a Superior b Y Slice Lines 1.2 Data Contour lines 1.0 ∆Ζ = 0.1 mm 0.8 Fit Toroid Section 0.6 Posterior 0.4 Cone Section 0.2 z-coordinate, (mm) Anterior X 0.0 -0.2 Tick marks 0.40.8 1.2 1.6 2.0 2.4 every 0.5 mm r-coordinate, (mm) Inferior d µ c 5.5 m Epidermal & Subepidermal 1.0 µm 17.0 µm 8.0 µm Radial Fibers 1.5 1.0 µm 1 1.0 µm 0.5 z (mm) Cir 0 cumferentia umbo Muc l Fibers 8.0 µm 6 ous & Submuc 4 r 4 3 osal µ 2 5.5 m 2 1 y (mm) Outer edge 0 x (mm) 0 −1 −2 −2 −3 Fig. 1. Eardrum anatomy and microstructure. (a) Contour plot of cat tympanic membrane using Moire´interferometry (4) with slice lines used to divide the eardrum. (b) Each slice in a is fit in the inner section as a cone and in the outer section as a toroid. This slice is from the anterior–superior quadrant, but the fit to the contour data (red squares) is typical. (c) Approximation of the eardrum obtained after slicing and fitting with cone and toroid sections. The blue line represents the annulus of the eardrum. (d) Schematic representation of the thickness profile for each slice from the umbo to the outer edge (annulus). The thickness is taken to taper linearly toward the umbo. The vertical dimension is greatly exaggerated to illustrate the four-layer composite of the eardrum. The inner radial and circumferential collagen fiber layers provide the scaffolding for the tympanic membrane (8, 11). pedance and reflectance, umbo (center of the eardrum near the properties by having so many resonances that no single reso- malleus tip) velocity to ear-canal-pressure ratio, middle-ear- nance can dominate the response. The eardrum appears to have cavity pressure to ear-canal-pressure ratio, middle-ear pressure many mistuned resonances that average out to an overall high gain, and eardrum displacement patterns. Some of these results output at the malleus handle. This partially explains how, in a were for the open middle-ear cavity case, whereas others were variety of species, sound transmission through the middle ear can for the closed cavity case.
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