**3. Role of the electric currents flowing in the structure of the cochlea**

It is generally accepted that most important processes of acoustic signal processing (power amplification and frequency selectivity) occur in the inner ear. In the outer ear and the middle ear, the power of the received sound is not amplified, since the outer and middle ears are pas‐ sive devices. In the middle ear there is only a mechanical impedance matching, whereas the power of travelling sound is not amplified.

#### **3.1. What is the impedance?**

In general, the impedance is a measure of opposition displayed by mechanical (damper, spring, mass) or electrical (resistor, capacitor, inductor) elements to external driving forces (mechanical stresses or electrical voltage, respectively). In case of an electrical excitation the electrical impedance is defined as the ratio of voltage applied to the electrical element to the current flowing through the element. On the other hand, the mechanical impedance is defined as the ratio of force applied to the mechanical element to the velocity at which the element moves. For harmonic (sinusoidal) excitations, the electrical and mechanical impedances can be conveniently described by complex number quantities. The above definitions for mechani‐ cal and electrical impedances are valid only for so‐called lumped elements, i.e., the elements without spatial dimensions. Lumped elements are subject of the circuit theory. Somewhat different definitions of the impedance are introduced for acoustic and electromagnetic waves propagating in the three‐dimensional media. However, in case of the cochlear amplifier the wavelength of the acoustic waves reaching the OHC (1.5 m at a frequency of 1000 Hz) is much higher than physical dimensions of the OHC (90 µm). Therefore, the circuit theory description holds [12].

The incoming acoustic wave passes through the outer ear to the middle ear, where it causes vibrations of the bones (hammer an anvil and stapes). Vibrations of the stapes through the oval window excite acoustic waves in liquids contained in the cochlea of the inner ear. This acoustic wave motion generates a transverse acoustic wave propagating along the basilar membrane. This mechanical wave travelling in the BM excites to vibration OHCs that are located between the BM and TM, see **Figure 1**.

Mechanical displacement of stereocilia, located on top of the OHCs, opens ion channels which provokes the flow of ionic current (K+ cations) in a closed circuit starting from the stria vascularis (DC voltage source) to the body of the OHC and then back to the stria vascu‐ laris. Sinusoidal deflection of stereocilia produces a sinusoidal in time flow of electric current (ions K+ ) in this circuit. Produced in this way (AC) current source pumps energy into the Power Amplification and Frequency Selectivity in the Inner Ear: A New Physical Model http://dx.doi.org/10.5772/66542 67

**Figure 1.** The flow of ionic currents (K+ ) in a closed circuit including a DC voltage source (stria vascularis), scala media (+80 mV), OHC (‐70 mV), and scala tympani (0 mV). Demonstratively, only one OHC is shown in the figure. Stria vascularis powers the activity of the cochlear amplifier.

nonlinear capacitance, which constitutes a part of the cochlear parametric amplifier. The existence of this nonlinear capacitance was confirmed experimentally [13]. This parametric amplifier provides the necessary selectivity of the frequency characteristics of the cochlear amplifier that is based on a single OHC. The above mentioned problems will be explained in more detail in Sections 9–11.

#### **3.2. Electric currents in the cochlea**

(*P* <sup>2</sup> /*P* <sup>1</sup>), measured in decibels (dB). Here, the symbol "log" stands for the logarithm to base

equals 10 log(1/10 <sup>−</sup><sup>6</sup> ) = 60 dB. The dynamics of the cochlear amplifier can reach 120 dB. Colloquially speaking, the dynamics tells us about the difference between the loudest and the

It is generally accepted that most important processes of acoustic signal processing (power amplification and frequency selectivity) occur in the inner ear. In the outer ear and the middle ear, the power of the received sound is not amplified, since the outer and middle ears are pas‐ sive devices. In the middle ear there is only a mechanical impedance matching, whereas the

In general, the impedance is a measure of opposition displayed by mechanical (damper, spring, mass) or electrical (resistor, capacitor, inductor) elements to external driving forces (mechanical stresses or electrical voltage, respectively). In case of an electrical excitation the electrical impedance is defined as the ratio of voltage applied to the electrical element to the current flowing through the element. On the other hand, the mechanical impedance is defined as the ratio of force applied to the mechanical element to the velocity at which the element moves. For harmonic (sinusoidal) excitations, the electrical and mechanical impedances can be conveniently described by complex number quantities. The above definitions for mechani‐ cal and electrical impedances are valid only for so‐called lumped elements, i.e., the elements without spatial dimensions. Lumped elements are subject of the circuit theory. Somewhat different definitions of the impedance are introduced for acoustic and electromagnetic waves propagating in the three‐dimensional media. However, in case of the cochlear amplifier the wavelength of the acoustic waves reaching the OHC (1.5 m at a frequency of 1000 Hz) is much higher than physical dimensions of the OHC (90 µm). Therefore, the circuit theory description

The incoming acoustic wave passes through the outer ear to the middle ear, where it causes vibrations of the bones (hammer an anvil and stapes). Vibrations of the stapes through the oval window excite acoustic waves in liquids contained in the cochlea of the inner ear. This acoustic wave motion generates a transverse acoustic wave propagating along the basilar membrane. This mechanical wave travelling in the BM excites to vibration OHCs that are

Mechanical displacement of stereocilia, located on top of the OHCs, opens ion channels which provokes the flow of ionic current (K+ cations) in a closed circuit starting from the stria vascularis (DC voltage source) to the body of the OHC and then back to the stria vascu‐ laris. Sinusoidal deflection of stereocilia produces a sinusoidal in time flow of electric current

) in this circuit. Produced in this way (AC) current source pumps energy into the

**3. Role of the electric currents flowing in the structure of the cochlea**

and *P* <sup>1</sup> = 10 <sup>−</sup><sup>6</sup> W/m <sup>2</sup>

, then the dynamics

10. For example, if power density *P* <sup>2</sup> = 1 W/m <sup>2</sup>

weakest sound that we can still hear.

66 Advances in Clinical Audiology

power of travelling sound is not amplified.

located between the BM and TM, see **Figure 1**.

**3.1. What is the impedance?**

holds [12].

(ions K+

Presence of natural (physiological) sources of a DC voltage (stria vascularis) and conductive liquids (electrolytes) in the cochlea creates favorable conditions for flow of electrical currents. It should be emphasized that ionic currents in the cochlea must flow in a closed circuit, according to the classical circuit theory. **Figure 1** shows an example of an ionic current flowing through one of the 20,000 OHCs in the cochlea. This ionic current (K+ cations) flows from the positive pole of the stria vascularis voltage source (battery), through the scala media (SM; +80 mV) and ion chan‐ nels at the top (apical) part of the OHC, into the bulk of the OHC (‐70 mV). Then, through chan‐ nels in the lower (basolateral) part of the OHC to perilymph, which has a zero (0 mV) electric potential (right grounding in **Figure 1**). The current loop closes in the negative pole of the stria vascularis battery (grounding in the left side of **Figure 1**).

#### **3.3. Zero of electric potential**

It should be remembered that the value of an electric potential at any point is measured with respect to the potential at a reference point, assumed to be zero. As a result, we can only mea‐ sure the potential difference (voltage). In the cochlear structure in **Figure 1** we assume as 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 and frequency selectivity, which occur in the cochlea.
