**13. Role of the electrical phenomena**

Remarkable properties of the hearing human organ (cochlea) are due to the presence in the cochlea of the sensory hair cells, i.e., OHCs and IHCs.

Electrical and mechanical phenomena occurring in the cochlea are mutually coupled. It is amazing that the flow of ionic currents (e.g., K+ ions) in the cochlea is governed by the same laws as the flow of electric currents in conventional electronic circuits (i.e., Ohm's and the Kirchhoff's laws). Therefore, it was possible to establish an equivalent electrical circuit for the cochlear amplifier. Moreover, to model the operation of the cochlea (cochlear amplifier) we can employ elements well‐known in the classical circuit theory, such as resistors, capacitors, inductors, voltage sources, and current sources both direct current (DC) and also alternating current (AC). In fact, the capacitors, inductors, and resistors in the equivalent electrical circuit of the cochlear amplifier are built of biological materials. In addition, these elements in the electrical equivalent circuit of the cochlear amplifier are lumped elements.

As it was shown in previous sections the role of electrical phenomena in the hearing process is enormous, since signal processing, power amplification, and frequency selectivity takes place on the electric side of the cochlear amplifier. The energy necessary to amplify the power of an input acoustic signal is drawn from the stria vascularis (DC voltage battery). Power ampli‐ fication occurs in a circuit that consists of the following elements: input electromechanical transistor (formed by hair bundle stereocilia and ion channels), body of the OHC, and stria vascularis.

The fundamental element of the proposed cochlear amplifier is a parametric amplifier using the nonlinear capacitance of the OHC and its piezoelectric effect. The cochlear parametric amplifier is pumped by an electrical current source formed by ionic currents triggered by deflection of stereocilia (input electromechanical transistor). In the cochlear amplifier, a DC electric power is converted to an AC electric power. Moreover, the transformation of electrical to mechanical energy and vice versa occurs due to direct and inverse piezoelectric effect. In this parametric amplifier the sharpening of frequency selectivity occurs.

Operation of the cochlear amplifier can be compared to the operation of an "old fashioned" analog "straight" radio receiver (i.e., a receiver with a direct amplification, without frequency mixing). In a classical analog transistor, "straight" radio receiver, one can enumerate the fol‐ lowing elements:


Similar elements and associated processes can be found in the human cochlea. Namely, the role of the antenna in the cochlea is played by the outer ear and middle ear, the role of the selective and power amplifier is played by the cochlear amplifier, and the main components of the cochlear amplifier are OHCs. The role of loudspeaker is played by afferent nerves endings.

#### **13.1. Novelty of the proposed parametric‐piezoelectric model**

Novelty of the model proposed by the author relies on the use of well‐known electronics idea of parametric amplification. Exploration of this concept was motivated by the existence in the actual structure of the cochlea and the nonlinear electrical capacitance of the OHC. It is worth noticing that in existing models of the cochlear amplifier, the presence of nonlinear capacitance is ignored.

The model proposed by the author is able to explain in a logical, natural, and complete way the following so far unresolved physical processes occurring in the cochlear amplifier: (1) power amplification, (2) selectivity of acoustic signals reception, and (3) nonlinear phenomena.

#### **13.2. Physical (physiological) model**

can employ elements well‐known in the classical circuit theory, such as resistors, capacitors, inductors, voltage sources, and current sources both direct current (DC) and also alternating current (AC). In fact, the capacitors, inductors, and resistors in the equivalent electrical circuit of the cochlear amplifier are built of biological materials. In addition, these elements in the

As it was shown in previous sections the role of electrical phenomena in the hearing process is enormous, since signal processing, power amplification, and frequency selectivity takes place on the electric side of the cochlear amplifier. The energy necessary to amplify the power of an input acoustic signal is drawn from the stria vascularis (DC voltage battery). Power ampli‐ fication occurs in a circuit that consists of the following elements: input electromechanical transistor (formed by hair bundle stereocilia and ion channels), body of the OHC, and stria

The fundamental element of the proposed cochlear amplifier is a parametric amplifier using the nonlinear capacitance of the OHC and its piezoelectric effect. The cochlear parametric amplifier is pumped by an electrical current source formed by ionic currents triggered by deflection of stereocilia (input electromechanical transistor). In the cochlear amplifier, a DC electric power is converted to an AC electric power. Moreover, the transformation of electrical to mechanical energy and vice versa occurs due to direct and inverse piezoelectric effect. In

Operation of the cochlear amplifier can be compared to the operation of an "old fashioned" analog "straight" radio receiver (i.e., a receiver with a direct amplification, without frequency mixing). In a classical analog transistor, "straight" radio receiver, one can enumerate the fol‐

Similar elements and associated processes can be found in the human cochlea. Namely, the role of the antenna in the cochlea is played by the outer ear and middle ear, the role of the selective and power amplifier is played by the cochlear amplifier, and the main components of the cochlear amplifier are OHCs. The role of loudspeaker is played by afferent nerves endings.

Novelty of the model proposed by the author relies on the use of well‐known electronics idea of parametric amplification. Exploration of this concept was motivated by the existence in the actual structure of the cochlea and the nonlinear electrical capacitance of the OHC. It is worth noticing that in existing models of the cochlear amplifier, the presence of nonlinear capacitance is ignored.

electrical equivalent circuit of the cochlear amplifier are lumped elements.

this parametric amplifier the sharpening of frequency selectivity occurs.

**13.1. Novelty of the proposed parametric‐piezoelectric model**

vascularis.

86 Advances in Clinical Audiology

lowing elements:

**2.** selective amplifier,

**4.** power amplifier, and

**1.** antenna,

**3.** detector,

**5.** loudspeaker.

The model proposed by the author is a physical and a not phenomenological model. The main element of the model is the parametric amplifier providing adequate gain, sensitivity, frequency selectivity, and dynamics. Elements of the model are uniquely linked to the actual physical (physiological) components that are present in a single OHC and in the entire cochlea. Moreover, these elements are directly related to the physical phenomena occurring in a single OHC and in the inner ear (electromotility, the flow of ionic currents, piezoelectricity, nonlinear capacitance, stereocilia movements, movements of the basilar membrane, nonlinear effects, generation of electrical potentials by metabolic processes in the stria vascularis, etc.). The model is internally coherent, consistent with experimental data published in the literature and it describes compre‐ hensibly (qualitatively and quantitatively) the phenomena of the cochlear amplification.

#### **13.3. Results of numerical simulations with the new model**

The results of numerical calculations (simulations) with the new model have been presented previously by the author in his two former papers [40, 43]. Here, we will repeat briefly some results showing increased frequency selectivity due to the parametric effect occurring in the OHC parametric amplifier.

Applying the Kirchhoff's laws to the linearized equivalent circuits (series and parallel), describing the operation of the parametric amplifier built around a single OHC, gives rise to linear ordinary differential equations of the Mathieu and Ince types [43]. The resulting dif‐ ferential equations of the second order with variable in time coefficients were solved numer‐ ically (for various values of frequency) using a Scilab software package. In the numerical simulations the resonant frequency of the resonant circuit (OHC oscillator) was assumed as *f* <sup>0</sup> = 1000 Hz.

The following values of the parameters of the equivalent (parallel Norton) circuit were applied:


The above numerical values of the elements of the equivalent circuit are compatible with the physiological data [8, 24, 35, 44–46].

The results of numerical calculations with the Scilab package show that using the above parameters, the parametric effect increases the quality factor of the OHC resonator from *Q* = 12 to *Q* = 120 (10 times). It is noteworthy that the passive OHC resonator with the qual‐

ity factor 12 has an effective frequency bandwidth of 80 Hz (8%), for example, from 960 to 1040 Hz. On the other hand, the active OHC resonator with the quality factor 120 has an effec‐ tive frequency bandwidth of 8 Hz (0.8%), for example, from 996 to 1004 Hz. The latter case represents a remarkable frequency selectivity (0.8%) enabling for frequency discrimination much narrower than one semitone in modern musical scales (6%).

#### **13.4. Consequences resulting from the author's model**

