- Research Article
- Open Access
Computer Aided Modeling of Human Mastoid Cavity Biomechanics Using Finite Element Analysis
© Chia-Fone Lee et al. 2010
- Received: 27 April 2009
- Accepted: 16 June 2009
- Published: 4 August 2009
The aim of the present study was to analyze the human mastoid cavity on sound transmission using finite element method. Pressure distributions in the external ear canal and middle ear cavity at different frequencies were demonstrated. Our results showed that, first, blocking the aditus improves middle ear sound transmission in the 1500- to 2500-Hz range and decreases displacement in frequencies below 1000 Hz when compared with the normal ear. Second, at frequencies lower than 1000 Hz, the acoustic pressures were almost uniformly distributed in the external ear canal and middle ear cavity. At high frequencies, higher than 1000 Hz, the pressure distribution varied along the external ear canal and middle ear cavity. Third, opening the aditus, the pressures difference in dB between the middle ear cavity and external ear canal were larger than those of the closed mastoid cavity in low frequency (<1000 Hz). Finally, there was no significant difference in the acoustic pressure between the oval window and round window is noted and increased by 5 dB by blocking the aditus. These results suggest that our complete FE model including the mastoid cavity is potentially useful and can provide more information in the study of middle ear biomechanics.
- Finite Element Model
- Tympanic Membrane
- Acoustic Pressure
- Sound Transmission
- Finite Element Result
The human middle ear, including the tympanic membrane (TM) and the three auditory ossicles (malleus, incus, and stapes), is the mechanical system for sound transmission from the outer to the inner ear. A number of parameters such as the shape and stiffness of the TM, shape and volume of the external ear canal, and volume and pressure of the middle ear cavity directly affect acoustic-mechanical transmission through the middle ear. Changes in these parameters are often related to pathophysiologic conditions of the ear. The function of human hearing was investigated through the use of models. Among these models, the following models for the middle ear represent the state of the art in the area. In general, there are two groups of models. The first group consists of electroacoustic circuit models based on the close link between acoustics and electrical engineering [1–8]. The second group is composed of structural mechanical models, mainly finite element (FE) models of the tympanic membrane and ossicles in humans [9–19] and in animals [20–22].
FE analysis is a computer simulation technique used in engineering and biomechanical analysis. The first FE model of the cat ear drum was reported by Funnell and Laszlo . Since then, FE modeling of middle ear biomechanics has become a rapidly growing area of research. The advent of high-resolution computed tomography (HRCT) made it possible to perform virtual instead of physical sectioning, and computer assistance facilitated the construction of reliable three-dimensional (3D) mathematical anatomic models. Using the combined technologies of FE analysis and 3D reconstruction of the middle ear from HRCT, we developed an FE model of the human middle ear with TM, ossicular bone, middle ear ligament, and middle ear boundaries . This model was validated by comparing data from it to published experimental measurements, and it was tested in several otologic applications [24, 25].
To date, the FE model represents the precise geometric configurations of the ossicles, TM, and ligaments/muscles and has the capability for analysis of transmission of sound through the middle ear. The FE model should, however, also include the external ear canal, middle ear cavity, and cochlea to simulate the complete acoustic-mechanical transmission in the ear. Gan et al.  created a two-chamber FE model (ear canal and middle ear cavity) to further simulate middle ear mechanics. They reconstructed the 3D model from a set of histological images. But the mastoid cavity was not included in their FE model, possibly due to the limited size of the histologic images. Therefore, the effects of the mastoid cavity on the sound transmission were unclear. In this paper, we report a three-chamber (ear canal, middle ear, and mastoid cavity) FE model of the right ear, incorporating middle ear ossicles, external ear canal, middle ear cavity, and mastoid cavity. The geometry and surface generation were created from HRCT images obtained in a 47-year-old man. The model was then validated by comparing the results with published experimental measurements. Acoustic-structural coupled analysis was performed to determine the function of external ear canal, middle ear cavity, and mastoid cavity for acoustic-mechanical transmission through the human middle ear.
2.1. High-Resolution Computed Tomography of Temporal Bone
2.2. A 3D FE Model of the Middle Ear
Mechanical properties used for the middle ear finite element model.
Data for the finite element model
Young's modulus (pars flaccida)
Structure boundary conditions used for the middle ear finite element model.
Middle ear components
Young's modulus or spring constant
Superior mallear ligament
Lateral mallear ligament
Posterior incudal ligament
Anterior mallear ligament
Posterior stapedial muscle
Tensor tympani muscle
0.06 N s/m
Stapedial annular ligament
0 N s/m
The air in the external ear canal, tympanic cavity, and mastoid cavity, which enclosed the air volume 1442 mm3, 693 mm3, and 6438 mm3, respectively, was meshed with acoustic elements. The external ear canal was expressed as a bent tube with rigid walls based on the dimensions obtained through HRCT scanning. The length of canal from the umbo to the entry section along the canal axis was about 3.04 cm and close to result of Egolf et al. . The canal length superiorly was 2.86 cm and the length inferiorly was 3.21 cm. The cross-sectional area varied from 65.45 mm2 (near the TM) to 96.19 mm2 at the canal entrance. The published anatomical data for the external air volume would be ranged from 830 to 1972 mm3 . A large difference in volume of the middle ear cavity exists between individual subjects; this volume varies from 2000 to 22000 mm3 . The volume of tympanic cavity, however, is within the range of approximately 500–1000 mm3 . The volume of middle ear cavity is also within the range.
2.3. FE Analysis
The acoustic analysis in ANSYS (ANSYS Inc., Canonsburg, PA) programs only involves modeling the fluid medium and the surrounding structure . A coupled acoustic analysis takes the fluid-structure interaction into account. The acoustic pressure in the fluid medium is determined by the wave equation. The interaction of the fluid and the structure at a mesh interface caused the acoustic pressure to exert a force applied to the structure and the structure motion produces an effective fluid load. The governing finite element matrix equations produce the following:
where is acoustic pressure, is the speed of sound, and is the fluid medium, the mean fluid density, the bulk modulus of fluid, and is the time. The speed of sound and density of the air were assumed as 343 m/s and 1.2 kg/m3, respectively. The acoustic absorption coefficient of FSI ( ) is defined as the fraction of absorbed acoustic energy to total incident energy [32, 33]. The absorption coefficient values are: 0.007 (TM), 0.02 (canal wall), 0.04 (cavity wall), 0.04 (ossicles), and 0.02 (ligament/muscles), respectively, .
2.4. Validation of the FE Model
The FE model was first tested and validated by comparing the responses of the middle ear system to harmonic pressure on the lateral surface of the TM between the FE analysis and published experimental measurements. Applied 120 dB SPL (20 Pa) to the canal was the same as McElveen's experiments, the harmonic analysis was conducted on the model over a frequency range of 200–8000 by using ANSYS. McElveen et al.  conducted a total 6 temporal bone experiments to study the effect of mastoid cavity modification on middle ear sound transmission. Measurements of umbo displacement were made at 200 Hz intervals from 500 to 7000 Hz at the TM. After the initial baseline umbo displacement measurements, the aditus and antrum were blocked with a saline-filled balloon (Fogarty catheter) inserted through a hole in the tegmen made prior to taking the measurements and closed with clay. The balloon was inflated, the hole on the tegmen was closed with clay and the measurement was repeated. Peak-to peak umbo displacement, aditus open versus closed in McElveen's human temporal bone 3 was used for model validation.
This model is the first one characterized by accurate structural dimensional and geometric shapes of middle ear structures, external ear canal, and mastoid cavity in the human. To confirm the validity of this model, the vibration amplitude of the umbo obtained with this model was compared with that derived from experimental measurement data. The predicted vibration amplitude of stapes was also shown. It was difficult to measure stapes vibration amplitude without opening the middle ear cavity. If a complete FE model of the middle ear were constructed, spatial variations in displacement on the TM, three ossicular vibrations, and spatial pressure distributions in the middle ear cavity and external ear canal could clarified without direct measurement, which are difficult to perform. It appeared that the results from the temporal bone experiments and the FE-predicted results match, namely that blocking the aditus improves middle ear sound transmission in the 1500 to 2500 Hz range and decreases displacement in the low frequencies below 1000 Hz when compared with the normal ear. Blocking the aditus eliminates the compliance of the mastoid cavity thus stiffening the TM and decreasing low frequency transmission, while opening the aditus increases middle ear cavity compliance, decrease TM stiffness and improves the low-frequency response. It has been reported that the effect of the mastoid cavity on the vibration of the TM is remarkable at low frequency and that it behaves like a spring [17, 30, 36]. The mastoid cavity would enhance sound transmission at low frequency ( 1000 Hz) because the spring constant of the air in the mastoid cavity is inversely proportional to its volume. In McElveen's experimental results , blocking the aditus decreased transmission in two bones and increased transmission in one bone. The effects were small between results. Because of the small numbers of bone studies and the individual variations between bones, any conclusion about the clinical significance of the temporal bone results might be cautiously. The real results could be affected by confounding variables including middle ear injury, stiffness of TM, and the mobility status of the ossicular chains. Therefore, more large numbers of temporal bone studies should be needed. Some small peaks in umbo displacement were noted in McElveen's results. According to umbo and stapes displacement measurements in temporal bones and living humans, in some 30% of ears, the tympanic membrane (TM) does not produce a smooth frequency response over the important hearing frequencies . Goode  reported that measurements of umbo displacement for a constant sound pressure level (SPL) at the TM in 22 frequencies between 200 and 6000 Hz showed peaks and valleys of more than 10 dB. This is possibly the result of previous injuries, both major and minor, to the TM, and perhaps to the ossicles . Our FE model curve is lower than the experimental curve; however, the trend was similar to the experimental curve. The difference between the FE model and the experimental data may also result from the variations of individual temporal bone.
The acoustic pressure distributions in the external ear canal and middle ear cavity are spatially visualized and quantified by our FE model. Our result is the complete FE model, including the external ear canal, TM, ossicles, ligaments/muscles, tympanic cavity, and mastoid cavity. The results demonstrated that acoustic pressure distributions in ear canal and middle ear cavity are functions of frequency and different pressure measurement locations (Figure 3). The difference of acoustic pressure between the ear canal and middle ear cavity was caused by high acoustic impedance of the TM that was induced by attached middle ear and inner ear structure. In the FE coupled analysis, the mastoid cavity effect was taken into the consideration for acoustic impedance. The air vibration in the middle ear cavity was lower than the air vibration in the canal. At low frequencies ( Hz), the acoustic pressure was uniformly distributed in the ear canal (Figure 4(a). At high frequencies ( Hz), the pressure distribution varied along the canal (Figure 4(b). The results reflect superposition of the incident and reflected sound wave from the TM and canal wall in the canal. The sound pressure difference in dB in the middle ear cavity is expected to vary with the air volume of the cavity (Figure 5). The acoustic pressure in the closed mastoid cavity is 10–25 dB lower than that of the canal entrance over the frequency range of 100–8000 Hz. With open aditus, the acoustic pressure in the middle ear cavity is 10–45 dB lower than that of the canal entrance over the frequency range of 100–8000 Hz. This big drop of acoustic pressure in the cavity is caused by the high acoustic impedance of the TM induced by the attached middle ear and inner ear structure.
There was no significant difference of the acoustic pressure measured at different locations in the middle ear cavity at low frequency. As frequency increases, the pressure difference in dB between the oval window and round window is noted and increased by less than 5 dB. These results demonstrate that window pressure difference of the acoustic pathway for sound transmission to the inner ear is insignificant. The same conclusion is also obtained from experimental measurements on the temporal bone by Voss et al. , Peake et al. , and FE results by Gan et al. .
In conclusion, we created an FE model that not only includes the external ear canal and tympanic cavity but also the mastoid cavity, which can help us to understand the mastoid cavity effect on sound transmission. Tympanomastoid surgery modifies the middle ear cavity in various ways. These modifications might have important effects on sound transmission of the middle ear . The acoustic effects of cavity modification by different types of tympanoplasty and mastoidectomy are difficult to determine clinically because TM and ossicular reconstruction are often undertaken as well. These results suggest that the FE model is potentially useful in the study of middle ear biomechanics and in the design and testing of the implantable middle ear hearing devices . It would be possible to predict how middle ear function is affected by various kinds of middle ear pathologies and to understand how individual differences in middle ear structures affect that function prior to surgery. The model could be further improved in several aspects as finding more accurate boundary conditions and adding the structure of cochlea and the cochlear fluid into the model . The overall thickness of TM (0.1 mm) was adopted in our model. Fay et al.  incorporates the measurement of the geometry of the ear canal, the 3D asymmetrical geometry of the eardrum and the details of the eardrum fiber structure. To develop a more comprehensive 3D FE model of human ear for multi-field FE analysis using detail TM structures and coupling the current FE model is our next goals. In addition, ligaments/tendons have a clear different behavior in tension and compression, in fact, stiffness in tension is much higher than in compression. The ligaments/tendons in the middle ear were traction free and essentially one-direction member. The behavior was dominant in axial direction. Therefore, if we chose the proper values, the hypothesis of isotropic behavior can be appropriated. A variety of mechanical tests have been reported to measure properties of soft tissue, such as uniaxial tensile, strip biaxial tension, and shear tests. In addition to experimental measurement, numerous material models have been developed to simulate the behavior of tissue in analytical ways . Weiss et al.  used a hyperelastic material model with an exponential strain energy function to fit experimental curves of human medial collateral ligament through FEA. There are several nonlinear hyperelastic material models available for analyzing mechanical properties of biological soft tissue, such as the Ogden, Mooney-Rivlin and Yeoh models. In the future, these methods can be used to improve our FE model of human ear. The further study will focus on how the alteration in structure, pathology, collagen fiber layer in tympanic membrane and different air volume sizes of mastoid cavity would affect the acoustic-mechanical transmission through the ear canal and middle ear to the inner ear.
This work was supported by a grant from the National Taiwan University Hospital to T.C.L. (Grant no. NTUH 96A01) and a grant from the Buddhist Tzu Chi General Hospital to C.F.L. (Grant no. TCRD 9703, 9704, 9801, and 9802).
- Onchi Y: Mechanism of middle ear. Journal of the Acoustical Society of America 1961, 33: 794. 10.1121/1.1908801View ArticleGoogle Scholar
- Zwislocki J: Analysis of middle ear function. I. Input impedance. Journal of the Acoustical Society of America 1962, 34: 1514-1523. 10.1121/1.1918382View ArticleGoogle Scholar
- Shera CA, Zweig G: Phenomenological characterization of eardrum transduction. Journal of the Acoustical Society of America 1991, 90(1):253-262. 10.1121/1.401295View ArticleGoogle Scholar
- Peake WT, Rosowski JJ, Lynch TJ III: Middle-ear transmission: acoustic versus ossicular coupling in cat and human. Hearing Research 1992, 57(2):245-268. 10.1016/0378-5955(92)90155-GView ArticleGoogle Scholar
- Goode RL, Killion M, Nakamura K, Nishihara S: New knowledge about the function of the human middle ear: development of an improved analog model. American Journal of Otology 1994, 15(2):145-154. 10.1016/0196-0709(94)90064-7View ArticleGoogle Scholar
- Rosowski JJ, Merchant SN: Mechanical and acoustic analysis of middle ear reconstruction. American Journal of Otology 1995, 16(4):486-497.Google Scholar
- Hudde H, Weistenhöfer C: A three-dimensional circuit mof the middle ear. Acustica 1997, 83(3):535-549.MATHGoogle Scholar
- Puria S, Allen JB: Measurements and model of the cat middle ear: evidence of tympanic membrane acoustic delay. Journal of the Acoustical Society of America 1998, 104(6):3463-3481. 10.1121/1.423930View ArticleGoogle Scholar
- Williams KR, Lesser THJ: A finite element analysis of the natural frequencies of vibration of the human tympanic membrane I. British Journal of Audiology 1990, 24(5):319-327. 10.3109/03005369009076572View ArticleGoogle Scholar
- Wada H, Metoki T, Kobayashi T: Analysis of dynamic behavior of human middle ear using a finite-element method. Journal of the Acoustical Society of America 1992, 92(6):3157-3168. 10.1121/1.404211View ArticleGoogle Scholar
- Eiber A, Kauf A: Berechnete Verschiebung der Mittelohrknochen unter statischer Belastung. HNO 1994, 42(12):754-759.Google Scholar
- Williams KR, Blayney AW, Rice HJ: Middle ear mechanics as examined by the finite element method. In Middle Ear Mechanics in Research and Otosurgery: Proceedings of the International Workshop on Middle Ear Mechanics, 1997 Edited by: Hüttenbrink KB. 40-47.Google Scholar
- Beer H-J, Bornitz M, Hardtke H-J, et al.: Modelling of components of the human middle ear and simulation of their dynamic behaviour. Audiology and Neuro-Otology 1999, 4(3-4):156-162. 10.1159/000013835View ArticleGoogle Scholar
- Bornitz M, Zahnert T, Hardtke H-J, Hüttenbrink K-B: Identification of parameters for the middle ear model. Audiology and Neuro-Otology 1999, 4(3-4):163-169. 10.1159/000013836View ArticleMATHGoogle Scholar
- Prendergast PJ, Ferris P, Rice HJ, Blayney AW: Vibro-acoustic modelling of the outer and middle ear using the finite-element method. Audiology and Neuro-Otology 1999, 4(3-4):185-191. 10.1159/000013839View ArticleGoogle Scholar
- Ferris P, Prendergast PJ: Middle-ear dynamics before and after ossicular replacement. Journal of Biomechanics 2000, 33(5):581-590. 10.1016/S0021-9290(99)00213-4View ArticleGoogle Scholar
- Koike T, Wada H, Kobayashi T: Modeling of the human middle ear using the finite-element method. Journal of the Acoustical Society of America 2002, 111(3):1306-1317. 10.1121/1.1451073View ArticleGoogle Scholar
- Gan RZ, Feng B, Sun Q: Three-dimensional finite element modeling of human ear for sound transmission. Annals of Biomedical Engineering 2004, 32(6):847-859.View ArticleGoogle Scholar
- Fay J, Puria S, Decraemer WF, Steele C: Three approaches for estimating the elastic modulus of the tympanic membrane. Journal of Biomechanics 2005, 38(9):1807-1815. 10.1016/j.jbiomech.2004.08.022View ArticleGoogle Scholar
- Funnell WRJ, Laszlo C: Modeling of the cat eardrum as a thin shell using the finite-element method. Journal of the Acoustical Society of America 1978, 63(5):1461-1467. 10.1121/1.381892View ArticleGoogle Scholar
- Funnell WR, Decraemer WF, Khanna SM: On the damped frequency response of a finite-element model of the cat eardrum. Journal of the Acoustical Society of America 1987, 81(6):1851-1859. 10.1121/1.394749View ArticleGoogle Scholar
- Ladak HM, Funnell WRJ: Finite-element modeling of the normal and surgically repaired cat middle ear. Journal of the Acoustical Society of America 1996, 100(2):933-944. 10.1121/1.416205View ArticleGoogle Scholar
- Lee C-F, Chen P-R, Lee W-J, Chen J-H, Liu T-C: Three-dimensional reconstruction and modeling of middle ear biomechanics by high-resolution computed tomography and finite element analysis. Laryngoscope 2006, 116(5):711-716. 10.1097/01.mlg.0000204758.15877.34View ArticleGoogle Scholar
- Lee C-F, Hsu L-P, Chen P-R, Chou Y-F, Chen J-H, Liu T-C: Biomechanical modeling and design optimization of cartilage myringoplasty using finite element analysis. Audiology and Neurotology 2006, 11(6):380-388. 10.1159/000095900View ArticleGoogle Scholar
- Lee C-F, Chen J-H, Chou Y-F, Hsu L-P, Chen P-R, Liu T-C: Optimal graft thickness for different sizes of tympanic membrane perforation in cartilage myringoplasty: a finite element analysis. Laryngoscope 2007, 117(4):725-730. 10.1097/mlg.0b013e318031f0e7View ArticleGoogle Scholar
- Gan RZ, Sun Q, Feng B, Wood MW: Acoustic-structural coupled finite element analysis for sound transmission in human ear-pressure distributions. Medical Engineering and Physics 2006, 28(5):395-404. 10.1016/j.medengphy.2005.07.018View ArticleGoogle Scholar
- Egolf DP, Nelson DK, Howell HC III, Larson VD: Quantifying ear-canal geometry with multiple computer-assisted tomographic scans. Journal of the Acoustical Society of America 1993, 93(5):2809-2819. 10.1121/1.405802View ArticleGoogle Scholar
- Donaldson JA, Miller JM: Anatomy of the ear. In Otolaryngology: Basic Sciences and Related Disciplines. Volume 1. Saunders, Philadelphia, Pa, USA; 1973:75-110.Google Scholar
- Molvær OI, Vallersnes FM, Kringlebotn M: The size of the middle ear and the mastoid air cell. System measured by an acoustic method. Acta Oto-Laryngologica 1978, 85(1-2):24-32.View ArticleGoogle Scholar
- Voss SE, Rosowski JJ, Merchant SN, Peake WT: Acoustic responses of the human middle ear. Hearing Research 2000, 150(1-2):43-69. 10.1016/S0378-5955(00)00177-5View ArticleGoogle Scholar
- Debruyne H, Lesaint O: About the significance of PD measurements in liquids. IEEE Transactions on Dielectrics and Electrical Insulation 2003, 10(3):385-392. 10.1109/TDEI.2003.1207462View ArticleGoogle Scholar
- Pierce AD: Acoustic-An Introduction to Its Physical Principles and Applications. McGraw-Hill, New York, NY, USA; 1981.Google Scholar
- Kinsler LE, Frey AR, Coppens AB, Sanders JV: Fundamentals of Acoustics. 4th edition. John Wiley & Sons, New York, NY, USA; 2002.Google Scholar
- McElveen JT, Miller C, Goode RL, Falk SA: Effect of mastoid cavity modification on middle ear sound transmission. Annals of Otology, Rhinology and Laryngology 1982, 91(5):526-532.View ArticleGoogle Scholar
- Shaw ENG: The external ear. In Handbook of Sensory Physiology. Volume 1. Edited by: Keidel WD, Nef WD. Springer, Berlin, Germany; 1974.Google Scholar
- Kirikae I: The Structure and Function of Middle Ear. Tokyo University Press, Tokyo, Japan; 1960.Google Scholar
- Goode RL, Nakamura K, Gyo K: Comments on: acoustic transfer characteristics in human middle ears studied by a SQUID magnetometer method. Journal of the Acoustical Society of America 1987, 82: 1646-1654. 10.1121/1.395156View ArticleGoogle Scholar
- Goode RL: Current status and future of implantable electromagnetic hearing aids. Otolaryngologic Clinics of North America 1995, 28(1):141-146.Google Scholar
- Lee C-F, Chen J-H, Chou Y-F, Liu T-C: The optimal magnetic force for a novel actuator coupled to the tympanic membrane: a finite element analysis. Biomedical Engineering 2007, 19(3):171-177.Google Scholar
- Gan RZ, Reeves BP, Wang X: Modeling of sound transmission from ear canal to cochlea. Annals of Biomedical Engineering 2007, 35(12):2180-2195. 10.1007/s10439-007-9366-yView ArticleGoogle Scholar
- Cheng T, Gan RZ: Experimental measurement and modeling analysis on mechanical properties of tensor tympani tendon. Medical Engineering and Physics 2008, 30(3):358-366. 10.1016/j.medengphy.2007.04.005MathSciNetView ArticleGoogle Scholar
- Weiss JA, Gardiner JC, Bonifasi-Lista C: Ligament material behavior is nonlinear, viscoelastic and rate-independent under shear loading. Journal of Biomechanics 2002, 35(7):943-950. 10.1016/S0021-9290(02)00041-6View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.