A canonical oscillator model of cochlear dynamics

Abstract

Nonlinear responses to acoustic signals arise through active processes in the cochlea, which has an exquisite sensitivity and wide dynamic range that can be explained by critical nonlinear oscillations of outer hair cells. Here we ask how the interaction of critical nonlinearities with the basilar membrane and other organ of Corti components could determine tuning properties of the mammalian cochlea. We propose a canonical oscillator model that captures the dynamics of the interaction between the basilar membrane and organ of Corti, using a pair of coupled oscillators for each place along the cochlea. We analyze two models in which a linear oscillator, representing basilar membrane dynamics, is coupled to a nonlinear oscillator poised at a Hopf instability. The coupling in the first model is unidirectional, and that of the second is bidirectional. Parameters are determined by fitting 496 auditory-nerve (AN) tuning curves of macaque monkeys. We find that the unidirectionally and bidirectionally coupled models account equally well for threshold tuning. In addition, however, the bidirectionally coupled model exhibits low-amplitude, spontaneous oscillation in the absence of stimulation, predicting that phase locking will occur before a significant increase in firing frequency, in accordance with well known empirical observations. This leads us to a canonical oscillator cochlear model based on the fundamental principles of critical nonlinear oscillation and coupling dynamics. The model is more biologically realistic than widely used linear or nonlinear filter-based models, yet parsimoniously displays key features of nonlinear mechanistic models. It is efficient enough for computational studies of auditory perception and auditory physiology.

Keywords: Auditory; Cochlea; Dynamics; Modeling; Oscillation.

Figure 1

Top: Fits of the unidirectionally coupled model to low (A), mid (B), and high (C) frequency AN fibers from the Joris et al. (2011) data set. Bottom: Resonance regions of the bidirectionally coupled model for low (D), mid (E), and high (F) frequency AN fibers, using the same parameters. Coupling from the OC to BM was chosen so that spontaneous amplitude was slightly below threshold amplitude, $r_{oc}^{\ast }=0.1$. The red contours show threshold amplitude. The BM-OC model phase-locks to external forcing in the parameter regions where the fixed point is either a stable node (orange) or a stable spiral (yellow). Non-phase-locked regions (saddle points) are shown in blue.

Figure 2

Unidirectional parameter fit for ten representative tuning curves.

Figure 3

Compression curves for low, mid, and high frequencies of the BM layer by itself (A-C) and of the OC layer of the unidirectionally coupled model (D-F). The BM approximates a Gammatone filterbank response alone, while the compression response of the complete model approximates compression data obtained from the cochlea itself, such as that of Ruggero (1992). Stimulus intensities are shown from 0 to 120 dB SPL in 20 dB steps.

Figure 4

Calculation of Q_ERB (A), half-octave tip-to-tail level difference (B), and tip level (C) from the complete Joris et al. (2011) data set. Data points are blue dots, and smoothed curves used for fitting oscillator parameters as a function of center frequency are green lines.