Assigning viscoelastic and hyperelastic properties to the middle-ear soft tissues for sound transmission

  • Jing Zhang
  • Chunxiao Jiao
  • Donglin Zou
  • Na Ta
  • Zhushi RaoEmail author
Original Paper


A finite element model of the human ear considering viscoelasticity and hyperelasticity of the middle-ear (ME) soft tissues is developed in this paper. The present model is validated by comparing the static and dynamic responses to experimental data. The model-derived results are in good agreement with existing measurements. On this basis, the dynamic response of the ME under static pressure is re-evaluated. The results show that the static pressure mainly affects the low-frequency responses of the ME below 1000 Hz. In the case of static pressure preloading, the low-frequency displacement of the tympanic membrane and the stapes footplate (SF) and the ME gain are decreased, while the reverse ME impedance is increased. This is because the effective stiffness of the ME is increased due to large deformation and material nonlinearity, resulting in a decrease in the forward response of the ME at frequencies below 1000 Hz. Furthermore, the contribution of viscoelasticity to the ME sound transmission is also discussed. With the consideration of viscoelasticity, the magnitude of the SF displacement increases at frequencies above 3000 Hz, and the phase is mainly increased in the frequency band of 2000–5000 Hz. Moreover, viscoelasticity is more important for the SF displacement under static pressure. Given that only one type of material property (hyperelasticity or viscoelasticity) is considered in most published models, the consideration of both viscoelasticity and hyperelasticity helps to establish an accurate human ear model.


Middle ear Viscoelastic property Hyperelastic property Static pressure Finite element 



The authors acknowledge the financial support of this study by the National Natural Science Foundation of China (Grant no. 11172168).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

Although the object of this study is the human ear, the FE method is adopted in this study to study the mechanical properties of the human ear. All analysis procedures performed in this study do not involve any human participants and animals.


  1. Aibara R, Welsh JT, Puria S, Goode RL (2001) Human middle-ear sound transfer function and cochlear input impedance. Hear Res 152:100–109CrossRefGoogle Scholar
  2. Charlebois M, Motallebzadeh H, Funnell WRJ (2012) Visco-hyperelastic law for finite deformations: a frequency analysis. Biomech Model Mechanobiol 12:705–715CrossRefGoogle Scholar
  3. Cheng T (2007) Mechanical properties of human middle ear tissues. Ph.D dissertation, University OF OklahomaGoogle Scholar
  4. Claes R, Muyshondt PGG, Assche FV, Hoorebeke LV, Aerts P, Dirckx JJJ (2018) Eardrum and columella displacement in single ossicle ears under quasi-static pressure variations. Hear Res 365:141CrossRefGoogle Scholar
  5. De GD, Pires F, Dirckx JJ (2017) Effects of model definitions and parameter values in finite element modeling of human middle ear mechanics. Hear Res 344:195–206CrossRefGoogle Scholar
  6. Elyasi N, Taheri KK, Narooei K, Taheri AK (2017) A study of hyperelastic models for predicting the mechanical behavior of extensor apparatus. Biomech Model Mechanobiol 16:1077–1093CrossRefGoogle Scholar
  7. Gan RZ, Dai C, Wood MW (2006) Laser interferometry measurements of middle ear fluid and pressure effects on sound transmission. J Acoust Soc Am 120:3799CrossRefGoogle Scholar
  8. Gan RZ, Reeves BP, Wang XL (2007) Modeling of sound transmission from ear canal to cochlea. Ann Biomed Eng 35:2180–2195CrossRefGoogle Scholar
  9. Gan RZ, Yang F, Zhang X, Nakmali D (2011) Mechanical properties of stapedial annular ligament. Med Eng Phys 33:330–339CrossRefGoogle Scholar
  10. Gentil F, Parente M, Martins P, Garbe C, Jorge RN, Ferreira A, Tavares JMR (2011) The influence of the mechanical behaviour of the middle ear ligaments: a finite element analysis. Proc Inst Mech Eng Part H J Eng Med 225:68–76CrossRefGoogle Scholar
  11. Gentil F et al (2013) The influence of muscles activation on the dynamical behaviour of the tympano-ossicular system of the middle ear. Comput Methods Biomech Biomed Eng 16:392–402CrossRefGoogle Scholar
  12. Gerig R et al (2015) Contribution of the incudo-malleolar joint to middle-ear sound transmission. Hear Res 327:218–226CrossRefGoogle Scholar
  13. Hibbitt D, Karlsson B, Sorensen P (2016) Abaqus theory guide, Version 2016. Simulia Corp, ProvidenceGoogle Scholar
  14. Homma K, Shimizu Y, Kim N, Du Y, Puria S (2010) Effects of ear-canal pressurization on middle-ear bone-and air-conduction responses. Hear Res 263:204–215CrossRefGoogle Scholar
  15. Hüttenbrink K-B (1988) The mechanics of the middle-ear at static air pressures: the role of the ossicular joints, the function of the middle-ear muscles and the behaviour of stapedial prostheses. Acta Otolaryngol 451:1–35CrossRefGoogle Scholar
  16. Ihrle S, Lauxmann M, Eiber A, Eberhard P (2012) Nonlinear modelling of the middle ear as an elastic multibody system—applying model order reduction to acousto-structural coupled systems. J Comput Appl Math 246:18–26MathSciNetCrossRefGoogle Scholar
  17. Ihrle S, Gerig R, Dobrev I, Röösli C, Sim JH, Huber AM, Eiber A (2015) Biomechanics of the incudo-malleolar-joint—experimental investigations for quasi-static loads. Hear Res 340:69–78CrossRefGoogle Scholar
  18. Ladak HM, Funnell WRJ, Decraemer WF, Dirckx JJ (2006) A geometrically nonlinear finite-element model of the cat eardrum. J Acoust Soc Am 119:2859–2868CrossRefGoogle Scholar
  19. Liu H, Zhang H, Yang J, Huang X, Liu W, Xue L (2019) Influence of ossicular chain malformation on the performance of round-window stimulation: a finite element approach. Proc Inst Mech Eng Part H J Eng Med 233:584–594CrossRefGoogle Scholar
  20. Machiraju C, Phan A-V, Pearsall A, Madanagopal S (2006) Viscoelastic studies of human subscapularis tendon: relaxation test and a Wiechert model. Comput Methods Programs Biomed 83:29–33CrossRefGoogle Scholar
  21. Motallebzadeh H, Charlebois M, Funnell WRJ (2013) A non-linear viscoelastic model for the tympanic membrane. J Acoust Soc Am 134:4427CrossRefGoogle Scholar
  22. Murakami S, Gyo K, Goode RL (1997) Effect of middle ear pressure change on middle ear mechanics. Acta Otolaryngol 117:390–395CrossRefGoogle Scholar
  23. Muyshondt PGG, Claes R, Aerts P, Dirckx JJJ (2018) Quasi-static and dynamic motions of the columellar footplate in ostrich (Struthio camelus) measured ex vivo. Hear Res 357:10–24. CrossRefGoogle Scholar
  24. Nakajima HH, Dong W, Olson ES, Merchant SN, Ravicz ME, Rosowski JJ (2009) Differential intracochlear sound pressure measurements in normal human temporal bones. J Assoc Res Otolaryngol 10:23–36CrossRefGoogle Scholar
  25. Nakajima HH, Merchant SN, Rosowski JJ (2010) Performance considerations of prosthetic actuators for round-window stimulation. Hear Res 263:114–119CrossRefGoogle Scholar
  26. O’Connor KN, Cai H, Puria S (2017) The effects of varying tympanic-membrane material properties on human middle-ear sound transmission in a three-dimensional finite-element model. J Acoust Soc Am 142:2836CrossRefGoogle Scholar
  27. Ogden RW (2003) Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue. Biomech Soft Tissue Cardiovasc Syst 441:65–108CrossRefGoogle Scholar
  28. Ogden RW, Giuseppe S, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34:484–502CrossRefGoogle Scholar
  29. Puria S (2003) Measurements of human middle ear forward and reverse acoustics: implications for otoacoustic emissions. J Acoust Soc Am 113:2773–2789CrossRefGoogle Scholar
  30. Qi L, Funnell WRJ, Daniel SJ (2008) A nonlinear finite-element model of the newborn middle ear. J Acoust Soc Am 124:337CrossRefGoogle Scholar
  31. Rosowski JJ, Nakajima HH, Hamade MA, Mafoud L, Merchant GR, Halpin CF, Merchant SN (2012) Ear-canal reflectance, umbo velocity, and tympanometry in normal-hearing adults. Ear Hear 33:19CrossRefGoogle Scholar
  32. Stieger C, Rosowski JJ, Nakajima HH (2013) Comparison of forward (ear-canal) and reverse (round-window) sound stimulation of the cochlea. Hear Res 301:105–114CrossRefGoogle Scholar
  33. Tian J, Huang X, Rao Z, Ta N, Xu L (2015) Finite element analysis of the effect of actuator coupling conditions on round window stimulation. J Mech Med Biol 15:1550048CrossRefGoogle Scholar
  34. Volandri G, Di Puccio F, Forte P, Manetti S (2012) Model-oriented review and multi-body simulation of the ossicular chain of the human middle ear. Med Eng Phys 34:1339–1355CrossRefGoogle Scholar
  35. Voss SE, Rosowski JJ, Merchant SN, Peake WT (2000) Acoustic responses of the human middle ear. Hear Res 150:43–69CrossRefGoogle Scholar
  36. Wang X, Cheng T, Gan RZ (2007) Finite-element analysis of middle-ear pressure effects on static and dynamic behavior of human ear. J Acoust Soc Am 122:906CrossRefGoogle Scholar
  37. Wang X, Keefe DH, Gan RZ (2016) Predictions of middle-ear and passive cochlear mechanics using a finite element model of the pediatric ear. J Acoust Soc Am 139:1735CrossRefGoogle Scholar
  38. Xu D, Liu H, Zhou L, Cheng G, Yang J, Huang X, Liu X (2016) The effect of actuator and its coupling conditions on eardrum-stimulated middle ear implants: a numerical analysis. Proc Inst Mech Eng Part H J Eng Med 230:1074–1085CrossRefGoogle Scholar
  39. Zhang X, Gan RZ (2011) Experimental measurement and modeling analysis on mechanical properties of incudostapedial joint. Biomech Model Mechanobiol 10:713–726CrossRefGoogle Scholar
  40. Zhang X, Gan RZ (2013) Finite element modeling of energy absorbance in normal and disordered human ears. Hear Res 301:146–155CrossRefGoogle Scholar
  41. Zhang J, Tian J, Na T, Rao Z (2018) Transient response of the human ear to impulsive stimuli: a finite element analysis. J Acoust Soc Am 143:2768–2779CrossRefGoogle Scholar
  42. Zhao F, Koike T, Wang J, Sienz H, Meredith R (2009) Finite element analysis of the middle ear transfer functions and related pathologies. Med Eng Phys 31:907–916CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Vibration, Shock and Noise, State Key Laboratory of Mechanical System and VibrationShanghai Jiao Tong UniversityShanghaiChina

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