**2. Role of the outer hair cells in the cochlear amplification**

It is generally accepted that most important processes governing the selectivity and sensitiv‐ ity of the human ear occur in the organ of Corti located in the cochlea. The cochlea contains about 20,000 outer hair cells (OHCs) spanned between the basilar membrane (BM) and the tectorial membrane (TM). The outer hair cells (OHCs) are nonlinear electro‐mechanosen‐ sory cells and are critically important for the high sensitivity and frequency selectivity of the human ear. The electromechanical properties of the outer hair cells (OHCs) are believed to be the critical component of the cochlear Amplifier (CA) concept, but its internal "circuitry" still remains unknown. Mode of operation of this amplifier still arouses controversy and it is still unclear.

The OHC is a layered piezoelectric cylinder, with a diameter of about 9 µm and length that varies from 15 to 90 µm, depending on their location in the cochlea. The OHC wall thickness is equal to 100 nm. The membrane capacitance of the OHC comprises a linear component and nonlinear component. The most striking feature of the OHC is its giant piezoelectric effect, which is four order of magnitude higher than that in the best known piezoelectric materials. Therefore, piezoelectric phenomena have been included in the modeling of the OHC opera‐ tion. Other observations provide also an evidence that movements of electrical charges within the OHC walls are directly coupled with mechanical elongation and shortening of the OHC structure. At the top of sensory cells (OHCs and IHCs) a tuft (called hair bundle–HB) of a few tens to a few hundreds of stereocilia is located.

Existing so far theories of the amplification in a single OHC and in the entire cochlea do not describe all the phenomena experimentally observed, or they are entirely phenomenological theories, not related to actual physical (physiological) processes occurring in a single OHC and in the entire inner ear. Similarly, the previously published electromechanical models of a single OHC and the whole cochlea only reflect their external characteristics and not the physical processes in them.

A characteristic feature of the OHC is the presence of the piezoelectric effect. Electric volt‐ age applied across the walls of the cell membrane of the OHC results in a change (increase or decrease) of its length (inverse piezoelectric effect). Similarly, change in the length of the OHC generates electrical voltage across the walls of the cell membrane of the OHC (direct piezoelectric effect). Thanks to the piezoelectric effect, amplified in the OHC (on the electric side) acoustic signal is transferred to the tectorial membrane (TM) and subsequently to the inner hair cells (IHCs).

In summary, OHCs as elements of the cochlear amplifier provide:


nerve endings, where they are transformed into a series of electrical impulses that are trans‐ mitted into the central nervous system. It is assumed that there is no phenomenon of the power amplification in the IHC, which works as a passive sensor. Effectively, the IHC is a mechano‐electrical transducer that converts the mechanical signal received from the OHC, into a useful electrical signal, which is an "electrical image" of the received acoustic waves

In this chapter, the author emphasizes the crucial role of the electrical phenomena in the processes of power amplification of input acoustic signals and sharpening of the frequency characteristics of the cochlea. In the second part of this chapter (Sections 9–13), the results of the original author's research, i.e., new model and concept of the cochlear amplifier are

It is generally accepted that most important processes governing the selectivity and sensitiv‐ ity of the human ear occur in the organ of Corti located in the cochlea. The cochlea contains about 20,000 outer hair cells (OHCs) spanned between the basilar membrane (BM) and the tectorial membrane (TM). The outer hair cells (OHCs) are nonlinear electro‐mechanosen‐ sory cells and are critically important for the high sensitivity and frequency selectivity of the human ear. The electromechanical properties of the outer hair cells (OHCs) are believed to be the critical component of the cochlear Amplifier (CA) concept, but its internal "circuitry" still remains unknown. Mode of operation of this amplifier still arouses controversy and it is

The OHC is a layered piezoelectric cylinder, with a diameter of about 9 µm and length that varies from 15 to 90 µm, depending on their location in the cochlea. The OHC wall thickness is equal to 100 nm. The membrane capacitance of the OHC comprises a linear component and nonlinear component. The most striking feature of the OHC is its giant piezoelectric effect, which is four order of magnitude higher than that in the best known piezoelectric materials. Therefore, piezoelectric phenomena have been included in the modeling of the OHC opera‐ tion. Other observations provide also an evidence that movements of electrical charges within the OHC walls are directly coupled with mechanical elongation and shortening of the OHC structure. At the top of sensory cells (OHCs and IHCs) a tuft (called hair bundle–HB) of a few

Existing so far theories of the amplification in a single OHC and in the entire cochlea do not describe all the phenomena experimentally observed, or they are entirely phenomenological theories, not related to actual physical (physiological) processes occurring in a single OHC and in the entire inner ear. Similarly, the previously published electromechanical models of a single OHC and the whole cochlea only reflect their external characteristics and not the

A characteristic feature of the OHC is the presence of the piezoelectric effect. Electric volt‐ age applied across the walls of the cell membrane of the OHC results in a change (increase

**2. Role of the outer hair cells in the cochlear amplification**

that we can hear.

64 Advances in Clinical Audiology

presented.

still unclear.

tens to a few hundreds of stereocilia is located.

physical processes in them.

**4.** generation of otoacoustic emissions.

#### **2.1. What is the power amplification?**

In order to verify whether a given system or device, such as the cochlea, is passive or active it is necessary to determine the balance of power flowing in and out of the device. To this end, the device should be surrounded by a closed surface with its normal vector *n* → pointing outwards. Then, one has to identify all power components (electrical and mechanical) flowing through the surface and calculate the corresponding fluxes of the power density. A negative value of the total flux (power) is the signature of the fact that the system is a passive one, in which the power is dissipated (more power is flowing into the system than outflows from it). An example of such a system can be an electrical network consisting of resistors, induc‐ tors, and capacitors. A positive value of the total flux (power) indicates that the device is an active element, i.e., more power is flowing out of the device than flowing into the device. An example of such a system (device) can be either a bipolar transistor or a field effect transistor (MOS) operating in the amplifier circuit.

Simply speaking, if the output useful power exceeds the input signal power, then the device amplifies the power.

### **2.2. What is the frequency selectivity?**

The frequency selectivity of the system is its ability to unambiguously discriminate between two signals with very close frequencies. This property occurs, for example, in narrow band resonant circuits with quartz resonators. High frequency selectivity of the cochlear amplifier is an evidence that the frequency characteristics of the cochlea can be tuned to a narrow fre‐ quency band, e.g., from 1000 to 1002 Hz. This frequency selectivity is essential for comprehen‐ sion of speech and music perception.

#### **2.3. What is the dynamics?**

The dynamic range (dynamics) of the device is the ratio *P* <sup>2</sup> /*P* <sup>1</sup> of the maximum *P* <sup>2</sup> and mini‐ mum power *P* <sup>1</sup> of the input signal, which can be handled properly by the device (cochlea). For convenience, the dynamics is represented in a logarithmic scale, i.e., *Dynamics* = 10 log

(*P* <sup>2</sup> /*P* <sup>1</sup>), measured in decibels (dB). Here, the symbol "log" stands for the logarithm to base 10. For example, if power density *P* <sup>2</sup> = 1 W/m <sup>2</sup> and *P* <sup>1</sup> = 10 <sup>−</sup><sup>6</sup> W/m <sup>2</sup> , then the dynamics 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 weakest sound that we can still hear.
