Numerical investigation of the basilar membrane vibration induced by the unsteady fluid flow in the human inner ear

Journal title

Archive of Mechanical Engineering




vol. 67


No 4


Wahl, Philipp : Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany ; Ziegler, Pascal : Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany ; Eberhard, Peter : Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany



human cochlea ; basilar membrane ; unsteady viscous fluid flow ; fluid-structure interaction ; pressure-displacement-based fluid element ; viscous boundary layer ; layer tonotopy ; auditory threshold

Divisions of PAS

Nauki Techniczne




Polish Academy of Sciences, Committee on Machine Building


[1] L. Robles and M.A. Ruggero. Mechanics of the mammalian cochlea. Physiological Reviews, 81(3):1305–1352, 2001. doi: 10.1152/physrev.2001.81.3.1305.
[2] M. Fleischer. Mehrfeldmodellierung und Simulation der äußeren Haarsinneszelle der Cochlea (Multifield modelling and simulation of the outer hair cells of the cochlea). Doctoral Thesis. Technische Universität Dresden, Germany, 2012. (in German).
[3] J. Baumgart. The hair bundle: Fluid-structure interaction in the inner ear. Doctoral Thesis. Technische Universität Dresden, Germany, 2010 .
[4] J. Tian, X. Huang, Z. Rao, N. Ta, and L. Xu. Finite element analysis of the effect of actuator coupling conditions on round window stimulation. Journal of Mechanics in Medicine and Biology, 15(4):1–19, 2015. doi: 10.1142/S0219519415500487.
[5] R.Z. Gan, B.P. Reeves, and X. Wang. Modeling of sound transmission from ear canal to cochlea. Annals of Biomedical Engineering, 35:2180–2195, 2007. doi: 10.1007/s10439-007-9366-y.
[6] L. Xu, X. Huang, N. Ta, Z. Rao, and J. Tian. Finite element modeling of the human cochlea using fluid-structure interaction method. Journal of Mechanics in Medicine and Biology, 15(3):1–13, 2015. doi: 10.1142/S0219519415500396.
[7] H.W. Ades and H. Engström. Anatomy of the inner ear. In: Keidel W.D., Neff W.D. (eds) Auditory System. Handbook of Sensory Physiology, vol. 5/1. Springer, Berlin, 1974. doi: 10.1007/978-3-642-65829-7_5.
[8] C.R. Steele, G.J. Baker, J.A. Tolomeo, and D.E. Zetes-Tolometo. Cochlear mechanics. In: J.D. Bronzino (ed.) The Biomedical Engineering Handbook, CRC Press, 2006.
[9] S. Iurato. Functional implications of the nature and submicroscopic structure of the tectorial and basilar membranes. The Journal of the Acoustical Society of America, 34(9):1386–1395, 1962. doi: 10.1121/1.1918355.
[10] H. Herwig. Strömungsmechanik: Einführung in die Physik von technischen Strömungen (Introduction to the Physics of Technical Flows). Springer Vieweg, Wiesbaden; 2008. (in German).
[11] H. Schlichting and K. Gersten. Boundary-Layer Theory, vol. 7. Springer-Verlag, Berlin, 2017.
[12] G.H. Keulegan and L.H. Carpenter. Forces on cylinders and plates in an oscillating fluid. Journal of Research of the National Bureau of Standards, 60:423–440, 1958.
[13] E. Zwicker. Über die Viskosität der Lymphe im Innenohr des Hausschweines (About the viscosity of the lymph in the inner ear of the domestic pig). Acta Otolaryngologica, 78(1-6): 65–72, 1974. (in German). doi: 10.3109/00016487409126327.
[14] M. Lesser and D. Berkley. Fluid mechanics of the cochlea. Part 1. Journal of Fluid Mechanics, 51(3):497–512, 1972. doi: 10.1017/S0022112072002320.
[15] A. De Paolis, H. Watanabe, J. Nelson, M. Bikson, M. Marom, M. Packer, and L. Cardoso. Human cochlear hydrodynamics: A high-resolution μCT-based finite element study. Journal of Biomechanics, 50:209–216, 2017. doi: 10.1016/j.jbiomech.2016.11.020.
[16] L. Papula. Mathematische Formelsammlung (Mathematical Formula Collection). Springer Verlag, Wiesbaden, 2014. (in German).
[17] O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu. The Finite Element Method: Its Basis and Fundamentals, 6 ed. Elsevier Butterworth-Heinemann, Oxford, 2006.
[18] J.E. Sader. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. Journal of Applied Physics, 84(1):64–76, 1998. doi: 10.1063/1.368002.
[19] E. de Boer. Auditory physics. Physical principles in hearing theory. Part 1. Physics Reports, 62(2):87–174, 1980. doi: 10.1016/0370-1573(80)90100-3.
[20] M.J. Wittbrodt, C.R. Steele, and S. Puria. Developing a physical model of the human cochlea using microfabrication methods. Audiology and Neurotology, 11(2):104–112, 2006. doi: 10.1159/000090683.
[21] C.R. Steele and J.G. Zais. Effect of coiling in a cochlear model. The Journal of the Acoustical Society of America, 77(5):1849–1852, 1985. doi: 10.1121/1.391935.
[22] J. Wysocki. Dimensions of the human vestibular and tympanic scalae. Hearing Research, 135(1-2):39–46, 1999. doi: 10.1016/S0378-5955(99)00088-X.
[23] M. Thorne, A.N. Salt, J.E. DeMott, M.M. Henson, O.W. Henson, and S.L. Gewalt. Cochlear fluid space dimensions for six species derived from reconstructions of resonance images. Annals of Otology, Rhinology & Laryngology, 109(10):1661–1668, 1999. doi: 10.1097/00005537-199910000-00021.
[24] G. Herrmann and H. Liebowitz. Mechanics of Bone Fractures. Academic Press, New York, 1972.
[25] J. Kirikae. The Middle Ear. Tokyo: University of Tokyo Press, 1960.
[ 26] F. Atturo, M. Barbara, and H. Rask-Andersen. Is the human round window really round? An anatomic study with surgical implications. Otology and Neurotology, 35(8):1354–1360, 2014. doi: 10.1097/MAO.0000000000000332.
[27] M.V. Goycoolea and L. Lundman. Round window membrane. Structure, function and permeability. A review. Microscopy Research and Technique, 36(3):201–211, 1997. doi: 10.1002/(SICI)1097-0029(19970201)36:3201::AID-JEMT8>3.0.CO;2-R.
[28] M. Kwacz, M. Mrówka, and J. Wysocki. Round window membrane motion before and after stapedotomy surgery. An experimental study. Acta of Bioengineering and Biomechanics, 13(3):27–33, 2011.
[29] X. Zhang and R.Z. Gan. Dynamic properties of human round window membrane in auditory frequencies running head: Dynamic properties of round window membrane. Medical Engineering & Physics, 35(3):310–318, 2013. doi: 10.1016/j.medengphy.2012.05.003.
[30] A.A. Poznyakovskiy, T. Zahnert, Y. Kalaidzidis, N. Lazurashvili, R. Schmidt, H.J. Hardtke, B. Fischer, and Y.M. Yarin. A segmentation method to obtain a complete geometry model of the hearing organ. Hearing Research, 282(1-2):25–34, 2011. doi: 10.1016/j.heares.2011.06.009.
[31] P. Leichsenring. Aufbereitung von Geometriedaten der menschlichen Cochlea (Preparation of geometry data for the human cochlea). Master Thesis. Technische Universität Dresden, Germany, 2012. (in German).
[32] E.G. Wever. The width of the basilar membrane in man. Annals of Otology, Rhinology & Laryngology, 47:37–47, 1938.
[33] F. Böhnke. Finite Elemente Analysen zur Berechnung der Signalverarbeitung in der Cochlea (Analyses for computation of signal processing in the cochlea). Doctoral Thesis. Technische Universität Ilmenau, Germany, 1999. (in German).
[34] L.M. Cabezudo. The ultrastructure of the basilar membrane in the cat. Acta Oto-Laryngologica, 86(1-6):160–175, 1978. doi: 10.3109/00016487809124733.
[35] S. Newburg, A. Zosuls, P. Barbone, and D. Mountain. Mechanical response of the basilar membrane to lateral micromanipulation. In: Concepts and Challenges in the Biophysics of Hearing. Proceedings of the 10th International Workshop on the Mechanics of Hearing, pages 240–246, 2009. doi: 10.1142/9789812833785_0038.
[36] V. Tsuprun and P. Santi. Ultrastructure and immunohistochemical identification of the extracellular matrix of the chinchilla cochlea. Hearing Research, 129(1-2):35–49, 1999. doi: 10.1016/S0378-5955(98)00219-6.
[37] I.U. Teudt and C.P. Richter. The hemicochlea preparation of the guinea pig and other mammalian cochleae. Journal of Neuroscience Methods, 162(1-2):187–197, 2007. doi: 10.1016/j.jneumeth.2007.01.012.
[38] M. Fleischer, R. Schmidt, and A.W. Gummer. Compliance profiles derived from a three-dimensional finite-element model of the basilar membrane. The Journal of the Acoustical Society of America, 127(5):2973–2991, 2010. doi: 10.1121/1.3372752.
[39] J. Baumgart, M. Fleischer, and C. Steele. The traveling wave in the human inner ear studied by means of a finite-element model including middle and outer ear. In: Proceedings of the 23rd International Congress on Sound and Vibration, Greece, 2016.
[40] H. Altenbach, J.W. Altenbach, and W. Kissing. Mechanics of Composite Structural Elements. Springer-Verlag, Berlin, 2013.
[41] R.C. Naidu and D.C. Mountain. Basilar membrane tension calculations for the gerbil cochlea. The Journal of the Acoustical Society of America, 121(2):994–1002, 2007. doi: 10.1121/1.2404916.
[42] S. Liu and R.D. White. Orthotropic material properties of the gerbil basilar membrane. The Journal of the Acoustical Society of America, 123(4):2160–2171, 2008. doi: 10.1121/1.2871682.
[43] C.E. Miller. Structural implications of basilar membrane compliance measurements. The Journal of the Acoustical Society of America, 77(4):146–1474, 1985. doi: 10.1121/1.392041.
[44] L. Schweitzer, C. Lutz, M. Hobbs, and S.P. Weaver. Anatomical correlates of the passive properties underlying the developmental shift in the frequency map of the mammalian cochlea. Hearing Research, 97(1-2):84–94, 1996. doi: 10.1016/S0378-5955(96)80010-4.
[45] R.C. Naidu and D.C. Mountain. Measurements of the stiffness map challenge. A basic tenet of cochlear theories. Hearing Research, 124(1-2):124–131, 1998. doi: 10.1016/S0378-5955(98)00133-6.
[46] H. Wada and T. Kobayashi. Dynamical behavior of middle ear: Theoretical study corresponding to measurement results obtained by a newly developed measuring apparatus. The Journal of the Acoustical Society of America, 87(1):237–245, 1990. doi: 10.1121/1.399290.
[47] M. Kwacz, P. Marek, P. Borkowski, and M. Mrówka. A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery. Biomechanics and Modeling in Mechanobiology, 12:1243–1261, 2013. doi: 10.1007/s10237-013-0479-y.
[48] P. Wahl. Simulation der Fluidströmung und Basilarmembranschwingung im menschlichen Innenohr (Simulation of fluid flow and basilar membrane vibrations in the human inner ear). Doctoral Thesis. Universität Stuttgart, Germany, 2018. (in German).
[49] J.H. Sim, M. Chatzimichalis, M. Lauxmann, C. Röösli, A. Eiber, and A. Huber. Complex stapes motion in human ears. Journal of the Association for Research in Otolaryngology, 11(3):329–341, 2010. doi: 10.1007/s10162-010-0207-6.
[50] S. Huang and E.S. Olson. Auditory nerve excitation via a non-traveling wave mode of basilar membrane motion. Journal of the Association for Research in Otolaryngology, 12:559–575, 2011. doi: 10.1007/s10162-011-0272-5.
[51] G. von Békésy. Experiments in Hearing. McGraw-Hill, New York, 1960.
[52] T.Ren. Longitudinal pattern of basilar membrane vibration in the sensitive cochlea. Proceedings of the National Academy of Sciences, 99(26):17101–17106, 2002. doi: 10.1073/pnas.262663699.
[53] S. Stenfelt, S. Puria, N. Hato, and R.L. Goode. Basilar membrane and osseous spiral lamina motion in human cadavers with air and bone conduction stimuli. Hearing Research, 181(1-2):131–143, 2003. doi: 10.1016/S0378-5955(03)00183-7.
[54] S. Ramamoorthy, N.V. Deo, and K. Grosh. A mechano-electro-acoustical model for the cochlea: response to acoustic stimuli. The Journal of the Acoustical Society of America, 121(5):2758–2773, 2007. doi: 10.1121/1.2713725.
[55] W.E. Langlois and M.O. Deville. Slow Viscous Flow. 2nd ed. Springer, Cham, 2014. doi: 10.1007/978-3-319-03835-3.
[56] E. Olson. Direct measurement of intra-cochlear pressure waves. Nature, 402:526–529, 1999. doi: 10.1038/990092.
[57] D.D. Greenwood. A cochlear frequency-position function for several species – 29 years later. The Journal of the Acoustical Society of America, 87(6):2592–2605, 1990. doi: 10.1121/1.399052.
[58] H.G. Boenninghaus and T. Lenarz. HNO: Hals-Nasen-Ohrenheilkunde (Otorhinolaryngology). Springer, Berlin, 2007. (in German).




Artykuły / Articles


DOI: 10.24425/ame.2020.131701 ; ISSN 0004-0738, e-ISSN 2300-1895


Archive of Mechanical Engineering; 2020; vol. 67; No 4; 381-414