Question

I've read that it's generally understood that deeper parts of the cochlea are sensitized to lower frequencies, and regions closer to the oval window are sensitive to high frequencies. In a sense, a frequency distribution is converted to a spatial distribution along the length of the cochlea.

Is there a precise model that can predict exactly where excitation will occur along the basilar membrane? I.e., can we compute, with relative precision, exactly how to convert between a frequency distribution to a spatial distribution of hair cell excitation?

I'm well aware that a Fourier transform breaks down a sound into constituent frequencies, and if the cochlea were perfectly idealized, that would suffice to take a Fourier transform and then map the result to the basilar membrane. But we're talking about a biological system, which is certainly not ideal. It's not a given that what actually happens is anything like a Fourier transform.

A few things that I'm not sure how to answer are:

The basilar membrane is coupled to itself. If one part of the membrane is vibrating, presumably the adjacent areas are too. How is the vibration isolated into frequencies down to the level of precision that we know humans can distinguish?
The wavelength of sound in water at audible frequencies is much much longer than the length of the entire (unrolled) cochlea. To what extent (and how) are phase differences actually relied on by the mechanism?
The vestibular and basilar canals are coupled at the tip of the cochlea, and there will be a phase difference between them, and this will be involved in the vibration of the basilar membrane. How does is this phase difference involved in the spatial distribution of basilar membrane vibration? (Is there any impedance mismatch at the opening between them? Will there be wave reflections that matter?)
A pure Fourier transform mapping of frequency to length along the cochlea does not explain why harmonically related sounds are also perceived as related by the listener. This phenomenon would be well explained if frequency ω also excited 2ω, 3ω, 4ω, ... modes within the cochlea, so that harmonically-related tones would have very similar patterns of excitation (and thus similar perception). How might this be modeled? Has this been looked at?
I have read that it may be true that hair cells are capable of motion (!?) and may be individually tuned to mechanically resonate at particular frequencies. Is this true? If so, how is this involved in the distribution of hair cell excitation? How much is known about the mechanism/dynamics?
What are the best models/research about this question?

Answer 1

The hair cells are arranged on the basilar membrane in an orderly way, and the basilar membrane vibrates in different regions based on the frequency of sound waves. Place theory explains how different frequencies selectively vibrate specific regions of the basilar membrane, and hair cells in these regions respond to the corresponding frequencies. The difference in response frequency between adjacent inner hair cells is about 0.2 percent.

Step-by-step explanation:

The hair cells are arranged on the basilar membrane in an orderly way. The basilar membrane vibrates in different regions, according to the frequency of the sound waves impinging on it. Likewise, the hair cells that lay above it are most sensitive to a specific frequency of sound waves. Hair cells can respond to a small range of similar frequencies, but they require stimulation of greater intensity to fire at frequencies outside of their optimal range. The difference in response frequency between adjacent inner hair cells is about 0.2 percent

Place theory, which is the model for how biologists think pitch detection works in the human ear, states that high frequency sounds selectively vibrate the basilar membrane of the inner ear near the entrance port (the oval window). Lower frequencies travel farther along the membrane before causing appreciable excitation of the membrane. The basic pitch-determining mechanism is based on the location along the membrane where the hair cells are stimulated. The place theory is the first step toward an understanding of pitch perception. Considering the extreme pitch sensitivity of the human ear, it is thought that there must be some auditory 'sharpening' mechanism to enhance the pitch resolution.