Abstract
For better understanding of bone-conducted (BC) hearing, a mechanical BC model is formulated using the Wentzel–Kramers–Brillouin (WKB) method. The BC hearing can be generally described by three main mechanisms: (1) cochlear fluid inertia, (2) in-phase motion of the outer bony shell, and (3) out-of-phase motion of the outer bony shell. Specifically, the second and third mechanisms can be identically explained by symmetric pressure compression–expansion and anti-symmetric compression–expansion, respectively. In this study, simulation results show that both the symmetric and anti-symmetric compression–expansion modes become significant at frequencies above 7 kHz while the fluid inertial mode is dominant at lower frequencies. The density difference between the scala fluid and soft cells of basilar membrane and the amplitude of the anti-symmetric compression–expansion input are identified as the difference between the air conduction and bone conduction. The natural frequency of the cochlear duct wall determines the magnitudes between the three mechanism and is approximated to be in the order of 10 MHz and above.
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References
Aibara R, Welsh JT, Puria S, Goode RL (2001) Human middle-ear sound transfer function and cochlear input impedance. Hear Res 152(1–2):100–109. https://doi.org/10.1016/S0378-5955(00)00240-9 ISSN 0378-5955
Bohnke F, Arnold W (2006) Bone conduction in a three-dimensional model of the cochlea. ORL J Oto-rhino-laryngol Relat Spec 68(6):393–396. https://doi.org/10.1159/000095283 ISSN 0301-1569
Chan WX, Lee SH, Kim N, Shin CS, Yoon Y-J (2017) Mechanical model of an arched basilar membrane in the gerbil cochlea. Hear Res 345:1–9. https://doi.org/10.1016/j.heares.2016.12.003 ISSN 0378-5955
Greenwood DD (1990) A cochlear frequency-position function for several species-29 years later. J Acoust Soc Am 87:2592–2605
Herzog H (1926) Das knochenleitungsproblem. Theoretische erwagungen. Zeitschreift fur Hals Nasen Ohrenheilk 15:300–306
Kim N, Homma K, Puria S (2011) Inertial bone conduction: symmetric and anti-symmetric components. J Assoc Res Otolaryngol 12(3):261–279. https://doi.org/10.1007/s10162-011-0258-3 ISSN 1525-3961, 1438-7573
Kim N, Steele CR, Puria S (2014) The importance of the hook region of the cochlea for bone-conduction hearing. Biophys J 107(1):233–241. https://doi.org/10.1016/j.bpj.2014.04.052 ISSN 0006-3495
Krainz W (1926) Das knochenleitungsproblem. Experimentelle Ergebnisse. Zeitschreift fur Hals Nasen Ohrenheilk 15:306–313
Krouskop TA, Dougherty DR, Vinson FS (1987) A pulsed Doppler ultrasonic system for making noninvasive measurements of the mechanical properties of soft tissue. J Rehabil Res Dev 24(2):1–8 ISSN 0748-7711
Lim K-M, Steele CR (2002) A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method. Hear Res 170(1–2):190–205. https://doi.org/10.1016/S0378-5955(02)00491-4 ISSN 0378-5955
Purcell D, Kunov H, Madsen P, Cleghorn W (1998) Distortion product otoacoustic emissions stimulated through bone conduction. Ear Hear 19(5):362–370
Rossi G, Solero P, Rolando M, Olina M (1988) Delayed oto-acoustic emissions evoked by bone-conduction stimulation: experimental data on their origin, characteristics and transfer to the external ear in man. Scand Audiol 29:24
Schick F (1991) An electrical model for the simulation of bone and air conducted hearing. Acta Acust United Acust 74(2):134–142
Schratzenstaller B, Janssen T, Alexiou C, Arnold W (2000) Confirmation of G. von Békésy’s theory of paradoxical wave propagation along the cochlear partition by means of bone-conducted auditory brainstem responses. ORL J Oto-rhino-laryngol Relat Spec 62(1):1–8 ISSN 0301-1569
Steele CR, Taber LA (1979) Comparison of WKB calculations and experimental results for three-dimensional cochlear models. J Acoust Soc Am 65(4):1007–1018. https://doi.org/10.1121/1.382570
Stenfelt S (2011) Acoustic and physiologic aspects of bone conduction hearing. Adv Otorhinolaryngol 71:10–21. https://doi.org/10.1159/000323574 ISSN 0065-3071
Stenfelt S (2015) Inner ear contribution to bone conduction hearing in the human. Hear Res 329:41–51. https://doi.org/10.1016/j.heares.2014.12.003 ISSN 0378-5955
Stenfelt S, Goode R L (2005) Bone-conducted sound: physiological and clinical aspects. Otol Neurotol 26(6):1245–1261 ISSN 1531-7129
Stenfelt S, Håkansson B (2002) Air versus bone conduction: an equal loudness investigation. Hear Res 167(1–2):1–12. https://doi.org/10.1016/S0378-5955(01)00407-5 ISSN 0378-5955
Stenfelt S, Puria S, Hato N, Goode RL (2003) Basilar membrane and osseous spiral lamina motion in human cadavers with air and bone conduction stimuli. Hear Res 181(1–2):131–143. https://doi.org/10.1016/S0378-5955(03)00183-7 ISSN 0378-5955
Tchumatchenko T, Reichenbach T (2014) A cochlear-bone wave can yield a hearing sensation as well as otoacoustic emission. Nat Commun 5:4160. https://doi.org/10.1038/ncomms5160 ISSN 2041-1723
Thorne M, Salt AN, DeMott JE, Henson MM, Henson OWJ, Gewalt SL (1999) Cochlear fluid space dimensions for six species derived from reconstructions of three-dimensional magnetic resonance images. Laryngoscope 109:1661–1668
Tonndorf J (1966) Bone conduction. Studies in experimental animals. Acta Oto-Laryngol, pages Suppl 213:1. ISSN 0001–6489
von Békésy G (1932) Zur Theorie des Hörens bei der Schallaufnahme durch Knochenleitung. Ann Phys 405(1):111–136. https://doi.org/10.1002/andp.19324050109 ISSN 1521-3889
von Békésy G, Wever EG (1960) Experiments in hearing. McGraw-Hill, New York OCLC: 14607524
Ward SR, Lieber RL (2005) Density and hydration of fresh and fixed human skeletal muscle. J Biomech 38(11):2317–2320. https://doi.org/10.1016/j.jbiomech.2004.10.001 ISSN 0021-9290
Wever GV (1949) Theory of hearing. Wiley, New York
Yoon Y-J, Steele CR, Puria S (2011) Feed-forward and feed-backward amplification model from cochlear cytoarchitecture: an interspecies comparison. Biophys J 100(1):1–10. https://doi.org/10.1016/j.bpj.2010.11.039 ISSN 0006-3495
Acknowledgements
This work was funded by the Basic Science Research Program through the National Research Foundation of Korea (NRF), the Ministry of Science, ICT & Future Planning (NRF-2015R1C1A1A02037735), and the Incheon National University Research Grant in 2015.
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Chan, W.X., Yoon, YJ. & Kim, N. Mechanism of bone-conducted hearing: mathematical approach. Biomech Model Mechanobiol 17, 1731–1740 (2018). https://doi.org/10.1007/s10237-018-1052-5
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DOI: https://doi.org/10.1007/s10237-018-1052-5