Amplification in the auditory periphery: The effect of coupling tuning mechanisms

Abstract

A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms have been postulated to contribute to the amplification and tuning properties of the hair cells. Models of each of these mechanisms have been shown to be poised near a Hopf bifurcation. Through a weakly nonlinear analysis that assumes weak periodic forcing, weak damping, and weak coupling, the physiologically based models of the two mechanisms are reduced to a system of two coupled amplitude equations describing the resonant response. The predictions that follow from an analysis of the reduced equations, as well as performance benefits due to the coupling of the two mechanisms, are discussed and compared with published experimental auditory nerve data.

Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

“…A deterministic model of weakly coupled nonlinear mechanical and electrical compartments was studied in Ref. [46] showing that the electrical oscillator may enhance amplification and nonlinear compression in the vicinity of Andronov-Hopf bifurcation. A model of a linear electrical resonator coupled bidirectionally to stochastic hair bundle oscillator was used in Ref.…”

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

“…For the Hopf-type amplifier, the dependencies of the response regarding the nonlinearity parameter : as well as the amplitude 0 a and the frequency T of the excitation are well studied [3][4][5][6]. The influence of the imaginary part I σ on the steady-state response of the Hopf-type amplifier is much less taken into account for modeling or general investigations [7,9,10]. In this paper we focus on the parameter dependencies of the complex coefficient σ of the nonlinear term in the driven normal form equation of the Andronov-Hopf bifurcation (1).…”

“…The input-output behavior shows a strong amplification of faint input signals with a sharper resonance for a smaller distance to the bifurcation point. This is one of the main effects a cochlea model has to exhibit [1][2][3][4][5][6][7]. In resonance ) ( …”

“…Besides this amplification characteristic, the cochlea exhibits also a sharper tuning for weaker input stimuli [1,2]. To describe these biological features, the (truncated) normal form equation of the Andronov-Hopf bifurcation endowed with an excitation was proposed [3] and is widely used as basis element for several models of the auditory system [4][5][6][7]. To achieve the nonlinear amplification characteristic, the Hopf system is tuned close to the onset of the self-sustained limit cycle oscillation [3,4].…”

“…Despite the nonlinearity of the so called Hopf-type amplifier, the study of the response characteristic has exposed, that a sinusoidal input signal leads to a pure sinusoidal output signal with the same frequency and without any harmonic distortions [3][4][5][6][7][8][9]. That means, apart from the specific nonlinear amplification characteristic, this Hopf-type amplifier acts on single-tone excitations like a linear system concerning the spectral behavior [8,9].…”