The mechanics of hearing: A comparative case study in bio-mathematical modelling

ANZIAM Journal

Volumn 52, Issue 3, 2011, Pages 225-249

  Champneys, A R ^a   Avitabile, D ^b   Homer, M ^a   Szalai, R ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

dynamical systems; hearing; mathematical biology

Indexed keywords

EID: 82955174877     PISSN: 14461811     EISSN: 14468735     Source Type: Journal    
DOI: 10.1017/S1446181111000733     Document Type: Article

References (41)

1. J. Ashmore et al., "The remarkable cochlear amplifier", Hear. Res. 266 (2010) 1-17; doi:10.1016/j.heares.2010.05.001.
2. J. A. Assad and D. P. Corey, "An active motor model for adaptation by vertebrate hair cells", J. Neurosci. 12 (1992) 3291-3309.
3. D. Avitabile, M. Homer, A. R. Champneys, J. C. Jackson and D. Robert, "Mathematical modelling of the active hearing process in mosquitoes", J. Roy. Soc. Interface 7 (2010) 105-122; doi:10.1098/rsif.2009.0091.
4. G. Békésy, Experiments in hearing (McGraw-Hill, New York, 1960).
5. C. de Boor and B. Swartz, "Collocation at Gaussian points", SIAM J. Numer. Anal. 10 (1973) 582-606; doi:10.1137/0710052.
6. W. E. Brownell, C. R. Bader, D. Bertrand and Y. de Ribaupierre, "Evoked mechanical responses of isolated cochlear outer hair cells", Science 227 (1985) 194-196; doi:10.1126/science.3966153. (Pubitemid 15154227)
7. N. P. Cooper and W. S. Rhode, "Nonlinear mechanics at the apex of the guinea-pig cochlea", Hearing Res. 82 (1995) 225-243; doi:10.1016/0378-5955(94)00180-X.
8. P. Dallos, "Cochlear amplification, outer hair cells and prestin", Current Opinion Neurobiol. 18 (2008) 370-376; doi:10.1016/j.conb.2008.08.016.
9. P. Dallos, "Prestin-based outer hair cell motility is necessary for mammalian cochlear amplification", Neuron 58 (2008) 333-339; doi:10.1016/j.neuron.2008.02.028. (Pubitemid 351615184)
10. E. J. Doedel, H. B. Keller and J. P. Kernévez, "Numerical analysis and control of bifurcation problems, part II: Bifurcation in infinite dimensions", Int. J. Bifur. Chaos Appl. Sci. Engrg. 1 (1991) 745-772; doi:10.1142/S0218127491000555.
11. V. M. Eguíluz, M. Ospeck, Y. Choe, A. J. Hudspeth and M. O. Magnasco, "Essential nonlinearities in hearing", Phys. Rev. Lett. 84 (2000) 5232-5235; doi:10.1103/PhysRevLett.84.5232.
12. S. J. Elliott, E. M. Ku and B. Lineton, "Time domain model of a nonlinear inhomogeneous cochlea"', in: Concepts and challenges in the biophysics of hearing (eds N. P. Cooper and D. T. Kemp), (World Scientific, Singapore, 2009) 74-81.
13. G. Frank, W. Hemmert and A. W. Gummer, "Limiting dynamics of high-frequency electromechanical transduction of outer hair cells", Proc. Natl. Acad. Sci. USA 96 (1999) 4420-4425; doi:10.1073/pnas.96.8.4420. (Pubitemid 29190351)
14. C. D. Geisler, "A realizable cochlear model using feedback from motile outer hair cells", Hearing Res. 68 (1993) 253-262; doi:10.1016/0378-5955(93)90129-O. (Pubitemid 23266748)
15. R. Ghaffari, A. J. Aranyosi and D. M. Freeman, "Longitudinally propagating traveling waves of the mammalian tectorial membrane", Proc. Natl. Acad. Sci. USA 104 (2007) 16510-16515; doi:10.1073/pnas.0703665104. (Pubitemid 350211049)
16. M. C. Göpfert and D. Robert, "Motion generation by Drosophila mechanosensory neurons", Proc. Natl. Acad. Sci. USA 100 (2003) 5514-5519; doi:10.1073/pnas.0737564100. (Pubitemid 36542736)
17. J. Guckenheimer and P Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Volume 42 of Applied mathematical sciences (Springer, New York, 1986).
18. H. Helmholtz, On the sensation of tone (Dover, New York, 1863).
19. A. Hubbard, "A traveling-wave amplifier model of the cochlea", Science 259 (1993) 68-71; doi:10.1126/science.8418496. (Pubitemid 23036087)
20. A. J. Hudspeth, "Making an effort to listen: mechanical amplification in the ear", Neuron 59 (2008) 530-545; doi:10.1016/j.neuron. 2008.07.012.
21. A. J. Hudspeth, F. Jülicher and P. Martin, "A critique of the critical cochlea: Hopf - a bifurcation - is better than none", J. Neurophysiology 104 (2010) 1219-1229; doi:10.1152/jn.00437.2010.
22. J. C. Jackson and D. Robert, "Nonlinear auditory mechanism enhances female sounds for male mosquitoes", Proc. Natl. Acad. Sci. USA 103 (2006) 16734-16739; doi:10.1073/pnas.0606319103. (Pubitemid 44737322)
23. J. C. Jackson, J. F. C. Windmill, V. G. Pook and D. Robert, "Synchrony through twice-frequency forcing for sensitive and selective auditory processing", Proc. Natl. Acad. Sci. USA 106 (2009) 10177-10182; doi:10.1073/pnas.0901727106.
24. F. Jülicher, D. Andor and T. Duke, "Physical basis of two-tone interference in hearing", Proc. Nat. Acad. Sci. USA 98 (2001) 9080-9085; doi:10.1073/pnas.151257898. (Pubitemid 32743872)
25. K. D. Karavitaki and D. C. Mountain, "Evidence for outer hair cell driven oscillatory fluid flow in the tunnel of corti", Biophysical J. 92 (2007) 3284-3293; doi:10.1529/biophysj.106.084087. (Pubitemid 46684587)
26. H. J. Kennedy, A. C. Crawford and R. Fettiplace, "Force generation by mammalian hair bundles supports a role in cochlear amplification", Nature 443 (2005) 880-883; doi:10.1038/nature03367. (Pubitemid 40314898)
27. H. J. Kennedy, M. G. Evans, A. C. Crawford and R. Fettiplace, "Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells", Nature Neuroscience 6 (2003) 832-836; doi:10.1038/nn1089. (Pubitemid 36929704)
28. M. M. M. Lagarde, M. Drexl, V. A. Lukashkina, A. N. Lukashkin and I. J. Russell, "Determining the identity of the cochlear amplifier: Electrical stimulation of the tecta mouse cochlea", in: Concepts and challenges in the biophysics of hearing (eds N. P. Cooper and D. T. Kemp), (World Scientific, Singapore, 2009) 106-112.
29. M. B. Lesser and D. A. Berkley, "Fluid mechanics of the cochlea. Part 1", J. Fluid Mech. 51 (1972) 497-512; doi:10.1017/S0022112072002320.
30. J. Lighthill, "Energy flow in the cochlea", J. Fluid Mech. 106 (1981) 149-213; doi:10.1017/S0022112081001560.
31. J. Meaud and K. Grosh, "The effect of tectorial membrane and basilar membrane longitudinal coupling in cochlear mechanics", J. Acoust. Soc. Am. 127 (2010) 1411-1421; doi:10.1121/1.3290995.
32. D. Ó Maoiléidigh and F. Jülicher, "The interplay between active hair bundle motility and electromotility in the cochlea", J. Acoust. Soc. Am. 128 (2010) 1175-1190; doi:10.1121/1.3463804.
33. W. S. Rhode, "Basilar membrane mechanics in the 6-9 kHz region of sensitive chinchilla cochleae", J. Acoust. Soc. Am. 121 (2007) 2792-2804; doi:10.1121/1.2718397. (Pubitemid 46701275)
34. M. A. Ruggero, N. C. Rich, A. Recio, S. S. Narayan and L. Robles, "Basilar-membrane responses to tones at the base of the chinchilla cochlea", J. Acoust. Soc. Am. 101 (1997) 2151-2163; doi:10.1121/1.418265. (Pubitemid 27163980)
35. C. R. Steele and K.-M. Lim, "Cochlear model with three-dimensional fluid, inner sulcus and feedforward mechanism", Audiol. Neurotol. 4 (1999) 197-203; doi:10.1159/000013841. (Pubitemid 29151504)
36. R. Szalai, A. R. Champneys, M. Homer, D. Ó Maoiléidigh, H. J. Kennedy and N. P. Cooper, "On the origins of the compressive cochlear nonlinearity", J. Acoust. Soc. Am., to appear.
37. R. Szalai, B. Epp, A. R. Champneys and M. Homer, "On time-delayed and feed-forward transmission line models of the cochlea", J. Mech. Mat. Struct. 6 (2011) 557-568; doi:10.2140/jomms.2011.6.557.
38. J. Tinevez, F. Jülicher and P. Martin, "Unifying the various incarnations of active hair-bundle motility by the vertebrate hair cell", Biophysical J. 93 (2007) 4053-4067; doi:10.1529/biophysj.107.108498. (Pubitemid 350223820)
39. J. Zheng, W. Shen, D. Z. Z. He, K. B. Long, L. D. Madison and P. Dallos, "Prestin is the motor protein of cochlear outer hair cells", Nature 405 (2000) 149-155; doi:10.1038/35012009. (Pubitemid 30313525)
40. G. Zweig, "Finding the impedance of the organ of corti", J. Acoust. Soc. Am. 89 (1991) 1229-1254.
41. J. Zwislocki, "Theorie der schneckenmechanik: qualitative und quantitative analyse", Acta Oto- Laryngologica 72 (1948) 1-76.