The authors have declared that no competing interests exist.
Conceived and designed the experiments: SR. Analyzed the data: SR. Contributed reagents/materials/analysis tools: SR ALN. Wrote the paper: SR ALN.
The cochlear amplifier is a hypothesized positive feedback process responsible for our exquisite hearing sensitivity. Experimental evidence for or against the positive feedback hypothesis is still lacking. Here we apply linear control theory to determine the open-loop gain and the closed-loop sensitivity of the cochlear amplifier from available measurements of basilar membrane vibration in sensitive mammalian cochleae. We show that the frequency of peak closed-loop sensitivity is independent of the stimulus level and close to the characteristic frequency. This implies that the half-octave shift in mammalian hearing is an epiphenomenon of the cochlear amplifier. The open-loop gain is consistent with positive feedback and suggests that the high-frequency cut-off of the outer hair cell transmembrane potential in vivo may be necessary for cochlear amplification.
Our ability to hear low-level sounds is due to an amplification mechanism called the “cochlear amplifier”
In this article, we use a linear frequency-domain model
To derive the closed-loop sensitivity and open-loop gain of the cochlear amplifier from the measurements of BM vibration in sensitive mammalian cochlea the following assumptions are made about the feedback loop: (1) the active response of the cochlea to varying stimulus levels is considered to be quasi-linear following de Boer’s EQ-NL theorem
The closed-loop sensitivity can be derived as a function of the open-loop gain as follows (see
For other details, see text.
The passive displacement at the sensor is given by
The active displacement at the sensor, which is for the feedback loop closed, is given by
The actuator signal is
The active and passive displacements at the sensor are therefore related as:
As is well known, the measured BM vibrations relative to acoustic stimulus demonstrate a downward shift in the frequency of the peak as the stimulus level is increased
The left panel (
The closed-loop sensitivity derived using Eq. (5) is shown in
Similar behavior is also seen in the response predicted by the mechano-electrical-acoustic finite element model of the cochlea
The phase (bottom panel) demonstrates lead below about 16 kHz and lag above 16 kHz. The CF is 18 kHz for this data. The numbers on the plot indicate the stimulus level.
The complex open-loop gain for varying stimulus levels is derived from the complex closed-loop sensitivity using Eq. (4) for BM vibration from
The CF is 18 kHz for this data. The frequency range is 13 kHz to 18.5 kHz; insets zoom into 17.5 kHz to 18.5 kHz.
As the stimulus level increases the magnitude of the open-loop gain decreases as shown in
In this article, linear control theory is applied to derive the closed-loop sensitivity and open-loop gain of the cochlear amplifier using the simplifying assumptions of quasi-linear behavior and local feedback. The implications of the results for cochlear mechanics are discussed below.
We show that the closed-loop sensitivity (
The frequency of peak closed-loop sensitivity at a given tonotopic location does not shift as the stimulus level changes, and this frequency is very close to the CF. This peak-frequency therefore appears to be a characteristic of the organ of Corti. It could be indicative of a second resonance in the organ of Corti
A mechanical network model of the organ of Corti, such as used in
The literature in the field of cochlear mechanics has widely questioned the efficacy of the OHC somatic electromotility process by virtue of the high-frequency cut-off of its transmembrane potential (see