**5. The cochlea as a set of nonlinear oscillators**

The cochlea is characterized by tonotopic organization, i.e., its resonant properties are a func‐ tion of the longitudinal position (a given stimulus frequency corresponds to a given location) and vary along the cochlea from base to apex. Structurally, the cochlea can be modeled as a series of radial sections [cochlear partitions (CPs)] starting at the base and ending at the apex. Each section of the CP is considered to be a highly resonant structure, which can vibrate pref‐ erably at only one frequency named as characteristic frequency (CF). The resonant frequency of each section of the CP is governed by the average mass, stiffness, and damping of the cor‐ responding elements, e.g., basilar membrane, OHCs, and tectorial membrane constituting this section.

The elements responsible for the active processes occurring in the cochlea are OHCs. Manifestations of this active process are high sensitivity and frequency selectivity with respect to week stimuli, nonlinear compression of input stimuli with small and large amplitudes, and spontaneous otoacoustic emissions [14].

From a mathematical point of view, all this features are consistent with the operation of a set of nonlinear oscillators within the inner ear that are tuned to different frequencies [15].

In other words, the cochlear amplifier can be treated as a set of nonlinear electromechani‐ cal oscillators, represented by CPs with the corresponding OHCs, with the fundamental Power Amplification and Frequency Selectivity in the Inner Ear: A New Physical Model http://dx.doi.org/10.5772/66542 69

zero potential (grounding), the potential of perilymph in scala vestibuli and scala tympani (0 mV). With respect to this reference point, the potential in scala media (SM) is +80 mV and the potential inside the OHC is equal to ‐70 mV. As it will be shown later in this chapter, the flow of electric currents in the cochlea plays a primary role in the phenomena of power amplification

A fundamental role in the cochlear amplifier, besides the OHCs, is played by the stria vas‐ cularis, which produces a source of DC voltage between endolymph and perilymph. This potential difference, resulting from difference in ion concentrations in endolymph and peri‐ lymph, is sustained by metabolic processes occurring in the cochlea. This source of a DC voltage stores energy in the form of an electrical (potential) energy. In fact, the cochlear ampli‐ fier draws energy from the stria vascularis battery to amplify power of an incoming acoustic wave. The stria vascularis battery will play a key role in the generation of electrical signals and currents (both direct and alternating) flowing in the cochlear amplifier. In the circuit model of physical phenomena in the cochlea, the stria vascularis is represented by a (DC) voltage

The cochlea is characterized by tonotopic organization, i.e., its resonant properties are a func‐ tion of the longitudinal position (a given stimulus frequency corresponds to a given location) and vary along the cochlea from base to apex. Structurally, the cochlea can be modeled as a series of radial sections [cochlear partitions (CPs)] starting at the base and ending at the apex. Each section of the CP is considered to be a highly resonant structure, which can vibrate pref‐ erably at only one frequency named as characteristic frequency (CF). The resonant frequency of each section of the CP is governed by the average mass, stiffness, and damping of the cor‐ responding elements, e.g., basilar membrane, OHCs, and tectorial membrane constituting

The elements responsible for the active processes occurring in the cochlea are OHCs. Manifestations of this active process are high sensitivity and frequency selectivity with respect to week stimuli, nonlinear compression of input stimuli with small and large amplitudes, and

From a mathematical point of view, all this features are consistent with the operation of a set of nonlinear oscillators within the inner ear that are tuned to different frequencies [15].

In other words, the cochlear amplifier can be treated as a set of nonlinear electromechani‐ cal oscillators, represented by CPs with the corresponding OHCs, with the fundamental

and frequency selectivity, which occur in the cochlea.

**4.1. Direct current (DC) voltage source in the cochlea**

source, see the upper left part of **Figure 1**.

spontaneous otoacoustic emissions [14].

**5. The cochlea as a set of nonlinear oscillators**

**4. Stria vascularis**

68 Advances in Clinical Audiology

this section.

**Figure 2.** (a) Cochlea as a set of nonlinear oscillators (represented by OHCs), (b) a set of IHCs in the cochlea acts as a sensor. It should be noted that the OHCs and IHCs operate in a liquid environment, not air.

frequencies of vibrations extending approximately from 20 Hz to 20 kHz. The nonlinear electromechanical oscillators are stimulated to vibrations by transverse acoustic waves travel‐ ing along the basilar membrane, see **Figure 2a** and **b**.

Mechanical input signal that stimulates the wave traveling in the BM (see **Figure 2a**) rep‐ resents the input acoustic signal, which reaches the inner ear through the oval window. Vibrations of the oval window excite acoustic waves in liquids (perilymph, endolymph) fill‐ ing the cochlea. This wave motion in turn generates a pressure distribution that induces mechanical transverse waves propagating along the BM. This transverse acoustic (mechani‐ cal) wave traveling in the BM, when moving from base to apex, stimulates to vibrations OHCs, which rest on the BM. The OHCs which are located in the vicinity of the partition with CF (characteristic frequency) that corresponds to the frequency of the input acoustic signal are excited to oscillate.

In **Figure 2a** we can see the OHC, which is located at the area where the BM displacement is maximal. It is this OHC (with a natural frequency of, e.g., 1000 Hz) which will be excited to vibration. The vibrations of this OHC amplify deflection of BM and TM. Mechanical energy forwarded by this OHC to TM is transferred through TM to the stereocilia of the IHC (see **Figure 2b**) with a proper frequency (i.e., 1000 Hz). In this IHC, transformation of mechanical energy into electrical energy occurs, which stimulates afferent nerve endings that produce a series of electrical impulses transmitted to the central nervous system.

If the frequency of the input acoustic signal is, for example, 1000 Hz, then this wave stimulates vibrations of the oscillator with a natural frequency equaled also to 1000 Hz. These vibrations are further amplified actively in this resonant circuit, see **Figure 2a**. The resonant curve of the nonlinear oscillator can be quite narrow (high selectivity) and can be therefore characterized by a high quality factor. For weak acoustic signals, the electrical and mechanical power at the output of the oscillator may exceed many times (e.g., 500 times) the power of the input acous‐ tic wave. In this manner, in the nonlinear (active) electromechanical oscillator (represented by the OHC), phenomena of power amplification and frequency discrimination occur.
