How the Ear Tunes In to Sounds: A Physics Approach

Listening is a complex sound selection process thought to be located in the auditory cortex. A biophysically motivated Hopf model of the mammalian cochlea reveals that pitch, a main characteristic in the perception of sound, is already materialized at the level of the mammalian hearing sensor. Here, we provide evidence that major elements of listening may similarly be implemented at the auditory periphery by means of efferent connections to the cochlea that tune the hearing sensor towards an auditory object of interest. The cochlea model we use in our investigations is advocated by its performance quality, the simplicity by which efferent control can be implemented, and by the closeness of the control results compared to the biological data. We tune the Hopf parameters to target on a sound, using pitch as the guiding feature. How well we achieve our goal is tested on real-world sounds and measured by a specifically developed tuning-error measure. The results provide a first estimate of how much the peripheral hearing system can assist a listener in focusing on an auditory signal and, thus, what is contributed by the auditory cortex.

Figure 1

“Perceived pitch” $f_p$ in the cat ventral cochlear nucleus. Three-frequency stimulation $(f_c-f_{\mathrm{mod}})$, $f_c$, $(f_c+f_{\mathrm{mod}})$, ($f_{\mathrm{mod}}=200\mathrm{Hz}$). Black crosses: Inverse of most frequent interspike intervals, onset-L-cell response [32] ($\mathrm{CF}=1100\mathrm{Hz}$, 50 dB sound pressure level). Red dots: $f_p$ from section 11 of a full cochlea [ [35] $\mathrm{CF}=1136\mathrm{Hz}$, $-60\mathrm{dB}$, cochlea settings as in Figs. 6 and 7, “flat tuning” (see text)].

Figure 2

Cochlea with efferent feedback. (a) Mammalian example. (b) Our model, where efferent inhibitory input to the cochlea’s outer hair cells is realized by tuning the sectional Hopf parameters away from criticality (“$\mu$ tuning”).

Figure 3

Gain isointensity curves at section 5 of a full Hopf cochlea ($\mathrm{CF}=10.42\mathrm{kHz}$, 18 sections covering a range from 20 to 1.25 kHz) without (solid lines) and with (dashed lines) MOC efferent input. Full curves are fully consistent with animal data [36]; data corresponding to the dashed curves are not available. Flat tuning ($\mu =-0.1$) for the non-MOC case. MOC stimulation is implemented by shifting ${\mu }_5$ to ${\mu }_5=-1.0$ (curves for $-80$ and $-100\mathrm{dB}$ collapse).

Figure 4

BM level shifts (arrows) at section 2, $\mathrm{CF}=16.99\mathrm{kHz}$ (18 sections, 20–1.25 kHz), when stimulated by a 16 and 19 kHz (left and right) pure tone. Open circles: Flat tuning ($\mu =-0.05$). Filled circles: MOC stimulation; ${\mu }_2$ is shifted to $-0.5$. Insets: Corresponding animal data [37].

Figure 5

Phase shift at section 5 ($\mathrm{CF}=10.42\mathrm{kHz}$), ${\mu }_5$ is tuned away from flat tuning $\mu =-0.1$ (18 sections, range 20 to 1.25 kHz, stimulation at $-25\mathrm{dB}$). Phase delays result for frequencies below CF, phase leads above CF. Inset: Phase level dependence relative to $-25\mathrm{dB}$ (single oscillator, $\mathrm{CF}=10\mathrm{kHz}$, $\mu =-0.1$). Decreased low-frequency input levels lead to small phase leads; increased input levels lead to phase lags.

Figure 6

TE improvement by $\mu$ tuning. (a) Frequency spectrum at section 8 ($\mathrm{CF}=1964\mathrm{Hz}$). Blue: Flat tuning ($-80\mathrm{dB}$, target cornett $f_0=392\mathrm{Hz}$, disturber flute $f=2216\mathrm{Hz}$). Cross-combination tones (CT, two explicitly labeled) between the flute fundamental $f$ and higher harmonics of the cornett. Red: Optimized tuning. $f$ (flute) and cross-combination frequencies are suppressed, leaving a harmonic series of the target (small arrows). (b) Averaged TE over 13 different fundamental target frequencies (steps of 1 semitone) demonstrates input amplitude independence. Blue lines: Flat tuning. Red lines: Optimized $\mu$ tuning. Left panel: (full lines) target sound cornett (277 to 554 Hz), disturbing sound flute (at 277 Hz); (dashed lines) same target but flute at 2216 Hz. Right panel: Same experiment but target and disturber are interchanged. TE improvements: Arrows in (b).

Figure 7

(a) Tuning patterns, dynamical case. Colors indicate the Hopf parameter values of the sections. Left: Cornett vs flute (disturber). Right: Flute vs cornett (disturber). (b) TE for the two target signals of (a). Black: Flat tuning. Red: $\mu$ tuning. Full: Cornett target. Dashed: Flute target. (c) NSACF, NACF for the two target signals of (a),(b) at a chosen target ground frequency. Black: Flat tuning. Red: $\mu$ tuning. Blue: Target signal. Targets at 392 Hz, disturbers at 2216 Hz.