**8. Contemporary models of the cochlear amplifier**

Below, we present an overview of recently developed models of operation of the OHC and the entire Cochlea.

#### (1) Model presented in Ref. [21]

**6. State of the art**

70 Advances in Clinical Audiology

Hermann von Helmholtz was the first who created mechanical model of the cochlea in 1863 [16]. In his model the BM is represented as a system of harmonic oscillators tuned to different frequen‐ cies. In this model, the cochlea is treated as a kind of a spectrum analyzer. Next significant cochlear model was proposed by Georg von Békésy in 1928 [17]. In his model the mechanism of hearing is described in terms of the traveling wave propagating in the passive BM (*in vitro*). Position of the maximum of the wave depends on the frequency. In other words, the basilar membrane was found to be tonotopically organized: a given stimulus frequency corresponds to a given location. However, the theory of Bekesy was not able to explain the phenomenon of power amplification and frequency selectivity as well as other actual properties of the cochlea in living humans.

In 1948, Gold [5] concluded that the inner ear cannot act only passively. Only the active ele‐ ment can provide amplification and experimentally observed selectivity. As a model of such an element Gold introduced a valve regenerative amplifier. But these were suggestions, purely hypothetical, and not supported by any physical and physiological data. Therefore, they were not accepted at that time. Thirty years later Kemp experiments [18] concerning oto‐ acoustic emissions and works of Davis [6] confirmed the existence of active processes in the organ of Corti. For many years, discussions continued on what is the physical mechanism of this phenomenon. It is now widely accepted that the active component is the cochlear ampli‐

fier. Still, the controversy raises a mechanism of action of this amplifier [19, 20].

and the whole cochlea, but do not reflect their physical structure.

**8. Contemporary models of the cochlear amplifier**

the entire Cochlea.

the mechanism of the signal processing phenomena occurring in the cochlea.

**7. Deficiencies of the existing models of the OHC and whole cochlea**

So far the existing models (theories) of the amplification in a single outer hair cell (OHC) and the entire cochlea do not take into account all the physical phenomena experimentally observed. They are phenomenological theories, not related to actual physical (physiological) processes occurring in a single OHC and in the entire inner ear. In recent years a theory has gained popu‐ larity, which attributed the phenomenon of the cochlear amplification to Hopf bifurcations [21]. This theory, however, raised many doubts among others concerning the problem of stability [22]. Many authors of papers published very recently stated that in the theory of the cochlear amplification many unresolved problems still exist and work on it must be continued [14, 23–27]. A similar discussion applies considering electronic models of a single OHC and the entire cochlea. These models to a greater or lesser extent, describe the characteristics of a single OHC

In conclusion, one can state that none of the existing theories of hearing explains satisfactorily

Below, we present an overview of recently developed models of operation of the OHC and

In this model the operation of an individual OHC is described in terms of a Hopf bifurcation. The cochlear amplifier (based on an individual OHC) has the dynamical characteristics of a Hopf bifurcation. This model can explain the nonlinear effects, selectivity, and resonance phenomena.

Critique: there is no description of power amplification, it is a purely phenomenological model, not a physical one. Electrical phenomena are not taken into account. There is no expla‐ nation of the role of ionic currents in the processes of power amplification and sharpening of the frequency characteristics.

#### (2) Model introduced in Ref. [28]

This model describes the resonant effects in a single OHC and the entire cochlea. The phe‐ nomenological parameters are introduced to match the theoretical and experimental curves.

Critique: there is no description of power amplification, it is a phenomenological model.

(3) Model presented in [29]

This model describes the behavior of a single OHC and the entire cochlea. The mechanical aspects of the model are characterized by using the concepts from hydrodynamics. Resonant characteristics of the cochlea are obtained by superposition of acoustic waves propagating in fluids inside the organ of Corti.

Critique: there is no description of power amplification, it is a phenomenological and a purely mechanical model. Electrical phenomena are not considered. The explanation of resonant phenomena is very complicated. To this end, an exotic concept of so‐called squirting waves is employed. There is no explanation of the role of ionic currents in the processes of power amplification and sharpening of the frequency characteristics.

(4) Model introduced in Ref. [30]

This model interprets the nonlinear resonant phenomena in a single OHC in terms of a Hopf bifurcation. To obtain proper resonant curves two phenomenological parameters are introduced.

Critique: There is no description of the power amplification, this is a purely phenomenologi‐ cal model. There is no analysis of electrical phenomena.

(5) Model presented in Ref. [31]

This model describes acoustic, mechanical, and electrical phenomena in a single OHC and the entire cochlea. The phenomenological parameter is introduced to match the experimental and theoretical curves. Some nonlinear effects are discussed.

Critique: there is no description of power amplification. The presence of nonlinear capaci‐ tance is ignored.

(6) Model introduced in Ref. [32]

This model gives an electrical equivalent circuit of an individual OHC. Elements of an equiva‐ lent circuit have their counterparts in the actual structure of the cochlea. The model is a physi‐ cal model. Nonlinear phenomena are modeled by the nonlinear stiffness and capacitance.

Critique: there is no description of power amplification. The theory is incomplete.

(7) Model presented in Ref. [33]

The model analyses the electromechanical phenomena in a single OHC using black boxes and flow chart diagrams. Amplitude responses to sine wave and random noise excitations are given.

Critique: there is no description of power amplification, this is a purely phenomenologi‐ cal model. No correspondence between physical elements in an actual OHC and model elements.

(8) Model introduced in Ref. [34]

This is an experimental, piezoelectric, and hydrodynamic model of the cochlea operation. Theoretical analysis is performed for motion of BM along with surrounding liquids. Resonant characteristics of the cochlea are obtained.

Critique: there is no description of power amplification, it is a phenomenological model. There is no description of ion currents flow. Nonlinear analysis is not carried out.

(9) Model presented in Ref. [35]

In this model the role of HB motility and electromotility is presented. Resonant characteristic of the cochlea are given.

Critique: there is no description of power amplification, incomplete theory.

(10) Model introduced in Ref. [36]

The model comprises finite element method analysis of the mechanical part of the cochlear partition. Electrical representation of the OHC is given. Responses of an isolated OHC to electrical stimuli are analyzed.

Critique: there is no description of power amplification, it is an incomplete theory. The pres‐ ence of nonlinear capacitance is ignored.

(11) Model presented in Ref. [37]

Time domain and resonant characteristics of the cochlea are obtained by solving a set of non‐ linear partial differential equations.

Critique: there is no description of power amplification, it is a phenomenological model, a purely mechanical model. Electrical phenomena are not considered.

(12) Model published in Ref. [38]

The macromechanical and micromechanical model of the cochlea is presented. Electrical model of a single OHC and the organ of Corti is given. Time domain and frequency domain analysis of electric signals in the cochlea structure is performed.

Critique: in the model there is no description of power amplification. The theory is incomplete.

(13) Model published in [39]

Critique: there is no description of power amplification. The theory is incomplete.

The model analyses the electromechanical phenomena in a single OHC using black boxes and flow chart diagrams. Amplitude responses to sine wave and random noise excitations

Critique: there is no description of power amplification, this is a purely phenomenologi‐ cal model. No correspondence between physical elements in an actual OHC and model

This is an experimental, piezoelectric, and hydrodynamic model of the cochlea operation. Theoretical analysis is performed for motion of BM along with surrounding liquids. Resonant

Critique: there is no description of power amplification, it is a phenomenological model.

In this model the role of HB motility and electromotility is presented. Resonant characteristic

The model comprises finite element method analysis of the mechanical part of the cochlear partition. Electrical representation of the OHC is given. Responses of an isolated OHC to

Critique: there is no description of power amplification, it is an incomplete theory. The pres‐

Time domain and resonant characteristics of the cochlea are obtained by solving a set of non‐

Critique: there is no description of power amplification, it is a phenomenological model, a

The macromechanical and micromechanical model of the cochlea is presented. Electrical model of a single OHC and the organ of Corti is given. Time domain and frequency domain

Critique: in the model there is no description of power amplification. The theory is incomplete.

There is no description of ion currents flow. Nonlinear analysis is not carried out.

Critique: there is no description of power amplification, incomplete theory.

purely mechanical model. Electrical phenomena are not considered.

analysis of electric signals in the cochlea structure is performed.

(7) Model presented in Ref. [33]

72 Advances in Clinical Audiology

(8) Model introduced in Ref. [34]

(9) Model presented in Ref. [35]

(10) Model introduced in Ref. [36]

electrical stimuli are analyzed.

(11) Model presented in Ref. [37]

linear partial differential equations.

(12) Model published in Ref. [38]

ence of nonlinear capacitance is ignored.

of the cochlea are given.

characteristics of the cochlea are obtained.

are given.

elements.

The author formulated an original theory of cochlea functioning using a concept of a laser. The theory is interesting; however, it seems to be rather nonphysical.

Critique: there is no description of power amplification, incomplete theory, theory is rather qualitative.

(14) Model published in Ref. [3]

The macromechanical and micromechanical model of the cochlea is presented.

Critique: the theory is only mechanical. There is no description of power amplification. The theory is incomplete.

In summary, it is evident that the existing models of hearing processes exhibit numerous defi‐ ciencies. The physical (mechanical and electrical) processes occurring in the cochlear ampli‐ fier are not well understood.

In the following of this chapter, the author presents his new and original concepts and physi‐ cal models for the phenomena of power amplification and sharp frequency tuning occurring in the cochlea.
