The rst suggestion of active processes in the cochlea was made in a visionary paper by Gold in 1948 [38, 39]. Although Gold relied heavily on the (incorrect) \resonance" model [37], he reasoned (correctly) that the frequency selectivity of the cochlea could not be achieved by a purely passive system, and thus, some positive mechanical feedback must be present to counteract the inherently high damping of the passive system. He predicted that the cochlear microphonic was the result of a uctuating load on an electrochemical power source [38, p. 495]. He predicted that oscillations could occur in the active mechanical system, but was unable to measure those oscillations (Kemp was the rst worker to measure
were suitably positioned to act as mechanical eectors [38, p. 496]. This truly visionary work went unrecognized for three decades!
Many models have contributed to the modern understanding of nonlinear and active cochlear mechanics [52, 80, 77, 16, 81, 75, 34, 76, 35, 55, 130, 133]. The essential ideas in most modern models are listed below.
1. The outer hair cells are responsible for the observed nonlinearity. The basilar mem- brane and remaining cells in the organ of Corti are linear.
2. The outer hair cells are the active (energy-producing) elements in the organ of Corti.
The basilar membrane and remaining cells in the organ of Corti are mechanically passive.
3. Because the tips of the tallest stereocilia of the outer hair cells are attached to the tectorial membrane, the outer hair cells are stimulated in proportion to their stereocilia displacement, which is proportional to the displacement of the basilar membrane.
4. The outer hair cells respond to displacement of their stereocilia by exerting a force on the basilar membrane.
5. The outer hair cells are limited in how much force they can exert on the basilar membrane. For quiet sounds, the outer hair cells can amplify the wave signicantly, whereas for louder sounds, the outer hair cells are too weak to have much eect. The net result is that the forces exerted by the outer hair cells saturate at high ampli- tudes; this component-level saturation leads to the system-level saturation observed by Rhode [91].
6. The outer hair cells are assumed to be capable of providing forces on a cycle-by-cycle basis at audio frequencies. Evidence for this assumption is accumulating [97]. If this statement is true, the outer hair cells would be among the fastest-moving biological mechanical eectors in existence.
The above general ideas are very plausible and are not controversial. However, it is not clear exactly what type of force the outer hair cells are exerting on the basilar membrane.
Most modelers assume that the outer hair cells exert a force in phase with the velocity of the basilar membrane in a critical region just before the best place|that is, they act like a negative damping [16, 81, 77].
How might this negative damping be achieved? The most commonly held view is that upward deection of the basilar membrane causes a shearing motion of the reticular lamina and the tectorial membrane, causing the stereocilia of the outer hair cells to be bent away from the spiral sulcus, as shown in Figure 2.11. Ashmore has shown, in vitro, that bending the outer-hair-cell stereocilia in that direction leads to depolarization of the cell membrane, and that depolarization of the cell leads to a decrease in the length of the cell, which would presumably lead to an upward force on the basilar membrane relative to the tectorial membrane [4].
This complicated chain of events results in an upward force in response to an upward displacement of the basilar membrane, which acts to reduce the inherent restoring force of the basilar-membrane stiness. Since the force and the stimulus have the same direction, this model is called a positive-feedback model [76]. However, Ashmore has also shown that there is a time delay from membrane deection to applied force. For very low frequencies, the time delay is negligible, and the exerted force looks like a negative stiness. At a particular higher frequency, however, the time delay will correspond to a quarter-cycle phase shift, and the force will be acting in anti-phase with the membrane velocity|the force acts like a positive damping. At a higher frequency still, the phase shift will increase to a half-cycle, and the force will appear as a positive stiness. At a three-quarter cycle phase shift, the applied force will be in phase with the membrane velocity, and the negative damping is achieved.
The requirement of a three-quarter cycle phase shift is quite severe; it would be simpler if only a one-quarter cycle were required to achieve negative damping. The active-stiness model of Mountain, Hubbard, and McMullen [77] assumes a negative feedback of forces to the basilar membrane|that is, at very low frequencies, upward displacement of the basilar membrane leads to a downward force on the basilar membrane by the outer hair cells, thus increasing the eective stiness. At higher frequencies, a phase shift of a quarter-cycle leads to a force that is in phase with the membrane velocity, thus decreasing the eective damping.
1. If the upward deection of the basilar membrane does lead, in fact, to a downward force, the negative-feedback model of Mountain, Hubbard, and McMullen would be vindicated, and Ashmore's micromechanical argument would have to be revised.
2. If Ashmore's positive-feedback description is correct, the negative damping still may be achieved through the application of a three-quarter-cycle phase shift. In this case, the negative-feedback model would have to be rejected.
3. It is possible that a completely dierent mechanism is dominant. Kolston, for example, has argued on the basis of energy eciency that the outer hair cells should act so as to aect only the stiness or mass components of the basilar-membrane impedance [55]. Zweig has suggested that an outer-hair-cell force with a slow-acting and a fast- acting component may be more appropriate [133]; this suggestion nds support in the measurements of Ashmore [4].
Still other ingenious arguments may surface before the issue is resolved.
Nearly all of the models use pure delays in the implementation of the outer-hair-cell mechanical input-output relationships. While pure delays are very easy to implement in a computer simulation, they are very dicult to implement in a physical medium, and it is most unlikely that the outer hair cells can be modeled accurately in such a way. A more reasonable assumption would be that the outer hair cells respond with a rst- or second-order ltered version of their input stimulus.