A cochlear model with delayed active terms in the stiffness function has been analyzed, as for-mulated by Talmadge et al. (1998, JASA 104, 1517-1543). According to this model, the rectified cochlea is modeled as a rectangular box divided by the basilar membrane (BM) in two cavities, that is, the Scala Vestibuli and the Scala Tympani. A fluid-dynamics partial differential equation describes the propagation of the cochlear fluid between the two cavities. On the other hand, each microelement along the BM is described as a forced damped single harmonic oscillator. Forcing terms are the local differential pressure of the cochlear fluid, and the pressure driven by the outer hair cells (OHCs) through a nonlinear active feedback mechanism. The active action of this latter mechanism is described by two additional forces, each one proportional to the BM displacement delayed by a slow and a fast feedback constant time delay, respectively. Moreover the cochlear nonlinearity is introduced as a quadratic function of the BM displacement in the passive linear damping function. The numerical integration of the delayed stiffness cochlear model has been yielded by finite differencing with respect to the space variable in the state space (the semidiscrete model), and then by advancing in time by means of a numerical scheme for constant delay differ-ential equations (the fully discrete model) in Matlab. The algebraic properties of the semidiscrete model will be discussed in order to support the choice of the more convenient time solver. Then, numerical experiments will be shown by supplying a sinusoidal tone.

Botti, T., Sisto, R., Moleti, A., & Bertaccini, D. (2015). Delayed stiffness cochlear model. In Proceedings of the 22nd International Congress on Sound and Vibration. ;P O Box 13.

### Delayed stiffness cochlear model

#### Abstract

A cochlear model with delayed active terms in the stiffness function has been analyzed, as for-mulated by Talmadge et al. (1998, JASA 104, 1517-1543). According to this model, the rectified cochlea is modeled as a rectangular box divided by the basilar membrane (BM) in two cavities, that is, the Scala Vestibuli and the Scala Tympani. A fluid-dynamics partial differential equation describes the propagation of the cochlear fluid between the two cavities. On the other hand, each microelement along the BM is described as a forced damped single harmonic oscillator. Forcing terms are the local differential pressure of the cochlear fluid, and the pressure driven by the outer hair cells (OHCs) through a nonlinear active feedback mechanism. The active action of this latter mechanism is described by two additional forces, each one proportional to the BM displacement delayed by a slow and a fast feedback constant time delay, respectively. Moreover the cochlear nonlinearity is introduced as a quadratic function of the BM displacement in the passive linear damping function. The numerical integration of the delayed stiffness cochlear model has been yielded by finite differencing with respect to the space variable in the state space (the semidiscrete model), and then by advancing in time by means of a numerical scheme for constant delay differ-ential equations (the fully discrete model) in Matlab. The algebraic properties of the semidiscrete model will be discussed in order to support the choice of the more convenient time solver. Then, numerical experiments will be shown by supplying a sinusoidal tone.
##### Scheda breve Scheda completa Scheda completa (DC)
22nd International Congress on Sound and Vibration, ICSV 2015
Florence, Italy
2015
Rilevanza internazionale
Settore FIS/07 - Fisica Applicata(Beni Culturali, Ambientali, Biol.e Medicin)
English
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84971273024&partnerID=40&md5=1c5d57f526a0d9039c8300a2c3e45e29
Intervento a convegno
Botti, T., Sisto, R., Moleti, A., & Bertaccini, D. (2015). Delayed stiffness cochlear model. In Proceedings of the 22nd International Congress on Sound and Vibration. ;P O Box 13.
Botti, T; Sisto, R; Moleti, A; Bertaccini, D
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/2108/165534`
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