Skip to main content

Modeling the Nonlinear Cochlea

  • Chapter
  • First Online:
Cochlear Mechanics
  • 1003 Accesses

Abstract

This chapter presents an introduction to nonlinear cochlear modeling. It starts with some general definitions, goes to the basic DEs, and discusses tools to solve these. The art of minimizing errors by not using signal analysis tools that are only valid in linear systems is advocated. Starting with a circuit example, we move on to the cochlea.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • ANSI S (2004) Acoustical Terminology. American National Standards Institute, Inc.

    Google Scholar 

  • de Boer E (1980) Auditory physics. Physical principles in hearing theory. I. Physics Reports 62:87–174

    Google Scholar 

  • Broer HW, Takens F (2009) Dynamical Systems and Chaos. Appl. Math. Series 172, Springer, New York

    Google Scholar 

  • Butcher JC, Wanner G (1996) Runge-kutta methods: some historical notes. Appl Numer Math 22:113–151

    Article  Google Scholar 

  • Cai H, Manoussaki D, Chadwick R (2005) Effects of coiling in the micromechanics of the mammalian cochlea. J R Soc Interface 2:341–348

    Article  PubMed  Google Scholar 

  • Cooper NP, Kemp DT (eds) (2008) The Biophysics of Hearing, Mechanics of Hearing, World Scientific, Singgapore

    Google Scholar 

  • Dallos P (1973) The Auditory Periphery. Academic, New York

    Google Scholar 

  • Davis H (1983) An active process in cochlear mechanics. Hear Res 9:79–90

    Article  PubMed  CAS  Google Scholar 

  • Diependaal R (1988) Nonlinear and active cochlear models: Analysis and solution methods. PhD thesis, TU-Delft, Netherlands

    Google Scholar 

  • Diependaal RJ, Duifhuis H, Hoogstraten HW, Viergever MA (1987) Numerical methods for solving one-dimensional cochlear models in the time domain. J Acoust Soc Am 82:1655–1666

    Article  PubMed  CAS  Google Scholar 

  • Duifhuis H, Hoogstraten HW, van Netten SM, Diependaal RJ, Bialek W (1985) Modelling the cochlear partition with coupled Van der Pol oscillators. In: Allen JB, Hall JL, Hubbard AE, Neely ST, Tubis A (eds) Peripheral Auditory Mechanisms, Springer, New York, pp 290–297

    Google Scholar 

  • Duke TAJ, Jülicher F (2008) Critical oscillators as active elements in hearing. In: Manley GA, Fay RR, Popper AN (eds) Active Processes and Otoacoustic Emissions, SHAR, vol 30, Springer, New York, chap 3, pp 63–93

    Google Scholar 

  • Eguíliuz VM, Ospeck M, Choe Y, Hudspeth AJ, Magnasco MO (2000) Essential nonlinearities in hearing. Phys Rev L 84:5232–5235

    Article  Google Scholar 

  • Furst M, Goldstein JL (1982) A cochlear nonlinear transmission-line model compatible with combination tone psychophysics. J Acoust Soc Am 72:717–726

    Article  PubMed  CAS  Google Scholar 

  • Furst M, Lapid M (1988) A cochlear model for acoustic emissions. J Acoust Soc Am 84:222–229

    Article  PubMed  CAS  Google Scholar 

  • Gold T (1948) Hearing. II. The physical basis of the action of the cochlea. Proc Royal Soc London, Series B, Biol Sc 135(881):492–498

    Google Scholar 

  • Greenwood DD (1961) Critical bandwidth and the frequency coordinates of the basilar membrane. J Acoust Soc Am 33:1344–1356

    Article  Google Scholar 

  • Greenwood DD (1990) A cochlear frequency-position function for several species—29 years later. J Acoust Soc Am 87:2592–2605

    Article  PubMed  CAS  Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer-Verlag, New York

    Google Scholar 

  • Harris FJ (1978) On the use of windows for harmonic analysis with the discrete fourier transform. Proc IEEE 66:51–83

    Article  Google Scholar 

  • van Hengel PWJ (1993) Comment on: Shera & Zweig ‘Periodicity in otoacoustic emissions’. In: Duifhuis H, Horst JW, van Dijk P, van Netten SM (eds) Biophysica of Hair Cell Sensory Systems, World Scientific, Singapore, p 62

    Google Scholar 

  • Inselberg A (1978) Cochlear dynamics: The evolution of a mathematical model. SIAM Review 20:301–351

    Article  Google Scholar 

  • Kern A, Stoop R (2003) Essential role of couplings between hearing nonlinearities. Phys Rev Lett 91(12):128,101–1–128,101–4

    Google Scholar 

  • Kim DO, Molnar CE, Matthews JW (1980) Cochlear mechanics: Nonlinear behavior in two-tone responses as reflected in cochlear-nerve-fiber responses and ear-canal sound pressure. J Acoust Soc Am 67:1701–1721

    Article  Google Scholar 

  • Kinsler LA, Frey AR, Coppens AB, Sanders JV (1982) Fundamentals of Acoustics, 3rd edn. Wiley, New York

    Google Scholar 

  • de Kleine E (2001) Boundary conditions of otoacoustic emissions. PhD thesis, University of Groningen, Groningen, Netherlands

    Google Scholar 

  • Kohllöffel LUE (1990) Cochlear mechanics: Coiling effects (I,II) and the absorption equation (III). Hear Res 49:19–28

    Article  PubMed  Google Scholar 

  • Lamb H (1895) Hydrodynamics, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Lesser MB, Berkley DA (1972) Fluid mechanics of the cochlea. Part 1. J Fluid Mech 51:497–512

    Article  Google Scholar 

  • Magnasco MO (2003) A wave traveling over a Hopf instability shapes the cochlear tuning curve. Phys Rev Lett 90(5):058,101–1–058,101–4

    Google Scholar 

  • Mauermann M, Uppenkamp S, van Hengel PWJ, Kollmeier B (1999a) Evidence for the distortionproduc frequency place as a source of distortionproduct otoacoustic emission (dpoae) fine structure in humans. i. fine structure and higher-order dpoae as a function of the ratio f2/f1. J Acoust Soc Am 106:3473–3483

    Article  PubMed  CAS  Google Scholar 

  • Mauermann M, Uppenkamp S, van Hengel PWJ, Kollmeier B (1999b) Evidence for the distortionproduc frequency place as a source of distortionproduct otoacoustic emission (dpoae) fine structure in humans. ii. fine structure for different shapes of cochlear hearing loss. J Acoust Soc Am 106:3484–3491

    Article  PubMed  CAS  Google Scholar 

  • Middleton D (1960) An Introduction to Statistical Communication Theory. McGraw-Hill, New York

    Google Scholar 

  • Neely ST (1983) The cochlear amplifier. In: de Boer E, Viergever MA (eds) Mechanics of Hearing, Nijhoff/Delft Univ. Press, Netherlands, pp 111–118

    Google Scholar 

  • Neely ST, Kim DO (1986) A model for active elements in cochlear biomechanics. J Acoust Soc Am 79:1472–1480

    Article  PubMed  CAS  Google Scholar 

  • van Netten SM, Duifhuis H (1983) Modelling an active, nonlinear cochlea. In: de Boer E, Viergever MA (eds) Mechanics of Hearing, Delft Univ. Press/Nijhoff, pp 143–151

    Google Scholar 

  • O’Connor KN, Puria S (2008) Middle-ear circuit model parameters based on a population of human ears. J Acoust Soc Am 123:197–211

    Article  PubMed  Google Scholar 

  • Olson ES (1998) Observing middle and inner ear mechanics with novel intracochlear pressure sensors. J Acoust Soc Am 103:3445–3463

    Article  PubMed  CAS  Google Scholar 

  • Olson ES (1999) Direct measurement of intra-cochlear pressure waves. Nature 402:526–529

    Article  PubMed  CAS  Google Scholar 

  • Olson ES (2001) Intracochlear pressure measurements related to cochlear tuning. J Acoust Soc Am 110:349–367

    Article  PubMed  CAS  Google Scholar 

  • Olson ES (2004) Harmonic distortion in intracochlear pressure and its analysis to explore the cochlear amplifier. J Acoust Soc Am 115:1230–1241

    Article  PubMed  Google Scholar 

  • Peterson LC, Bogert BP (1950) A dynamical theory of the cochlea. J Acoust Soc Am 22:369–381

    Article  Google Scholar 

  • Puria S, Allen JB (1991) A parametric study of cochlear imput impedance. J Acoust Soc Am 89:287–309

    Article  PubMed  CAS  Google Scholar 

  • Puria S, Allen JB (1998) Measurements and model of the cat middle ers: Evidence for tympanic membrane acoustic delay. J Acoust Soc Am 104:3463–3481

    Article  PubMed  CAS  Google Scholar 

  • Rayleigh JWS (1894) The Theory of Sound, vol I, 2nd edn. MACMILLAN, London, [Dover edition: 1945]

    Google Scholar 

  • Rayleigh JWS (1896) The Theory of Sound, vol II, 2nd edn. MACMILLAN, London, [Dover edition: 1945]

    Google Scholar 

  • Schneider S (2004) Amplitude and phase characteristics of distortion product otoacoustic emissions. PhD thesis, University of Leiden, Leiden, Netherlands

    Google Scholar 

  • Schneider S, Prijs VF, Schoonhoven R (1999) Group delays of distortion product otoacoustic emissions in the guinea pig. J Acoust Soc Am 105:2722–2730

    Article  PubMed  CAS  Google Scholar 

  • Steele CR, Taber LA (1979) Comparison of WKB and finite difference calculations for a two-dimensional cochlear model. J Acoust Soc Am 65:1001–1006

    Article  PubMed  CAS  Google Scholar 

  • Steele CR, Zais J (1985) Effect of coiling in a cochlear model. J Acoust Soc Am 77:1849–1852

    Article  PubMed  CAS  Google Scholar 

  • Tinevez JY, Jülicher F, Martin P (2007) Unifying the various incarnations of active hair-bundle motility by the vertebrate hair cell. Biophys J 93:4053–4067

    Article  PubMed  CAS  Google Scholar 

  • Tinevez JY, Martin P, Jülicher F (2009) Active hair-bundle motility by the vertabrate hair cell. In: Cooper NP, Kemp DT (eds) The Biophysics of Hearing, Mechanics of Hearing 10, 2008, World Scientific, Singapore, pp 415–424

    Chapter  Google Scholar 

  • Viergever MA (1978) Basilar membrane motion in a spiral-shaped cochlea. J Acoust Soc Am 64:1048–1053

    Article  PubMed  CAS  Google Scholar 

  • Zweig G (1991) Finding the impedance of the organ of Corti. J Acoust Soc Am 89:1229–1254

    Article  PubMed  CAS  Google Scholar 

  • Zweig G, Lipes R, Pierce JR (1976) The cochlear compromise. J Acoust Soc Am 59:975–982

    Article  PubMed  CAS  Google Scholar 

  • Zwislocki J (1965) Analysis of some auditory characteristics. In: Luce R, Bush R, Galanter E (eds) Handbook of Mathematical Psychology, Vol. III, Wiley, New York, pp 1–97

    Google Scholar 

  • Zwislocki JJ (1974) Cochlear waves: interaction between theory and experiments. J Acoust Soc Am 55:578–583

    Article  PubMed  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hendrikus Duifhuis .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Duifhuis, H. (2012). Modeling the Nonlinear Cochlea. In: Cochlear Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6117-4_5

Download citation

Publish with us

Policies and ethics