Paradoxical waves and active mechanism in the Cochlea

Mohammad T. Manzari, Charles Peskin

Research output: Contribution to journalArticle

Abstract

This paper is dedicated to Peter Lax. We recall happily Lax's interest in the cochlea (and in all things biomedical), culminating in his magical solution of one version of the cochlea problem, as detailed herein. The cochlea is a remarkable organ (more remarkable the more we learn about it) that separates sounds into their frequency components. Two features of the cochlea are the focus of this work. One is the extreme insensitivity of the wave motion that occurs in the cochlea to the manner in which the cochlea is stimulated, so much so that even the direction of wave propagation is independent of the location of the source of the incident sound. The other is that the cochlea is an active system, a distributed amplifier that pumps energy into the cochlear wave as it propagates. Remarkably, this amplification not only boosts the signal but also improves the frequency resolution of the cochlea. The active mechanism is modeled here by a negative damping term in the equations of motion, and the whole system is stable as a result of fluid viscosity despite the negative damping.

Original languageEnglish (US)
Pages (from-to)4531-4552
Number of pages22
JournalDiscrete and Continuous Dynamical Systems
Volume36
Issue number8
DOIs
StatePublished - Aug 1 2016

Fingerprint

Damping
Acoustic waves
Insensitivity
Damping Term
Amplification
Thing
Wave propagation
Wave Propagation
Pump
Equations of motion
Equations of Motion
Viscosity
Extremes
Pumps
Fluid
Fluids
Motion
Energy
Sound

Keywords

  • Active mechanism
  • Basilar membrane
  • Cochlea
  • Immersed boundary method
  • Paradoxical waves

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Paradoxical waves and active mechanism in the Cochlea. / Manzari, Mohammad T.; Peskin, Charles.

In: Discrete and Continuous Dynamical Systems, Vol. 36, No. 8, 01.08.2016, p. 4531-4552.

Research output: Contribution to journalArticle

Manzari, Mohammad T. ; Peskin, Charles. / Paradoxical waves and active mechanism in the Cochlea. In: Discrete and Continuous Dynamical Systems. 2016 ; Vol. 36, No. 8. pp. 4531-4552.
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