Back

Download the PDF version

All rights reserved. No part of this publication may be reused or republishing in any form without written permission of the authors, except by a reviewer who may quote brief passages in a review.




COCHLEAR SAMPLING THEORY
AND AUDITORY PATHOPHYSIOLOGY





ROLAND CARRAT, MD.


Laureate of the Medicine Academy of Paris

Head of Children's Audiophonology Center in Tours

E N T Surgeon in Saint Grégoire's Clinic. Tours. France.



XAVIER CARRAT, MD.


Past Senior Registrar in Bordeaux Hospital

Graduated in Audiology

E N T Surgeon in Saint Augustin Clinic. Bordeaux. France.





KEY WORDS: Audiology

Auditory physiology

Deafness

Hearing





Institut d'Audiophonologie. 16 rue de la Pierre. 37 000 TOURS. France



E mail : r.carrat@wanadoo.fr

xavier.carrat@free.fr















TABLE OF CONTENTS


PREFACE


PART I. THEORY OF COCHLEAR SAMPLING



1. INTRODUCTION


1. Classical theories. A general view

2. State of the art in cochlear physiology

3. Everlasting paradoxes


2. BASIC DATA FOR A NEW AUDITORY THEORY


1. New data in cochlear mechanics

2. The sensori-neural systematization

3. The mathematical theory of communication


3. THEORY OF COCHLEAR SAMPLING


1. Principles

2. External cochlear sampling

3. Internal cochlear sampling


4. COCHLEAR MECHANICS AND BONE CONDUCTION

Experimental and physiological aspects.


5. THE THIRD COCHLEAR WINDOW


6. THE COCHLEAR FUNCTIONAL UNIT


7. THE INNER EAR: A TRANSCRIBER BAR CODE




PART II. COCHLEAR SAMPLING AND PSYCHOACOUSTICS


1. COCHLEAR SAMPLING AND AUDITORY FREQUENTIAL RANGE


2. THE LOWER FREQUENCY OF THE AUDITORY SCALE


3. THE UPPER FREQUENCY OF THE AUDITORY SCALE


4. THE AUDITORY THRESHOLD WITH A WHITE NOISE


5. 1000 Hz: THE "FLIP-FLOP" FREQUENCY


6. PHASE AND PITCH OF A COMPLEX SOUND


7. THE MISSING FUNDAMENTAL FORMANT CASE


8. PSYCHOACOUSTICS OF THE TRANSIENTS


9. THE PITCH GENERATED BY RECURRENT CLICKS




PART III. COCHLEAR SAMPLING AND AUDITORY PHYSIO-PATHOLOGY


1. THEORY OF COCHLEAR SAMPLING AND IMPAIRMENT OF SOUNDS


2. DEAFNESS AND COCHLEAR SAMPLING


3. AUDIOMETRIC PATTERN AND AUDITORY PHYSIO-PATHOLOGY


4. ACOUSTIC TRAUMA


5. HEARING LOSS, AUDITORY THRESHOLD WITH WHITE NOISE


AND COCHLEAR SAMPLING


6. IMPAIRED SPEECH PERCEPTION WITH NORMAL TONAL AUDIOGRAM


7. COCHLEAR SAMPLING AND ALIASING


8. COCHLEAR SAMPLING THEORY AND HEARING AID


9. PARADOXICAL AUDIOMETRIC CURVES IN PROFOUND DEAFNESS


10. COCHLEAR SAMPLING AND COCHLEAR IMPLANT



CONCLUSION



ACKNOWLEDGMENTS



SELECTED REFERENCES






FOREWORD




The main purpose of this booklet is a new theory about hearing and especially about the Cochlear Sampling Theory. It brings up-to-date information rewieved in various papers since 1973 and in the 1986 book published in Paris (*).


New experiences, new applications and comments and new suggestions on auditory pathology will help us to rethink what was well established so far. Actually, the reader will discover several quite original conceptions - never defined or proposed up to now - such as the Third Cochlear Window, the Cochlear Functional Unit, a classification of sensorineural hearing losses, a model of cochlear action of a random noise, an explanation of the case of the missing fundamental formant, a new elucidation of the acoustic trauma, etc.


In each chapter all the illustrations, tables and figures will be an extremely useful guide for the researchers who are familiar with that field, for those who want to extend their knowledge beyond their areas of specialization, and for those who are ready for new prospects.


This specific presentation will provide an overview which different and scattered papers were unable to exhibit to date and will be a help to formulate an original pattern about Hearing. Some scientists might disagree with these new theories but isn't the main purpose of a publication to launch new ideas to step forward the research ?.

According to existing literature, idioms have been unquestioningly admitted that:

  1. the frequential analysis of complex acoustical signals is provided by the ear,

  2. each component has its proper localisation on the basilar membrane,

  3. each nervous auditory fiber is the transmitter of a given frequency (FC).


But numerous experiments in psychoacoustics come to disagree with the established pattern and will therefore provide incentives for a new theory which will be inevitably emodeled by other new data before long.



__________________________________________________________

(*) Théorie de l'Echantillonnage Cochléaire. Editions Arnette, Paris, 1986.












PART I





THEORY OF COCHLEAR

SAMPLING







1. INTRODUCTION.




1.1. CLASSICAL THEORIES. AN OVERVIEW.


Numerous modifications have been brought to the theory of the tone localisation suggested by Von Békesy (1928) (1, 2, 3). These modifications include:

- volley principle (Wever)(1930) (70, 71),

- lateral inhibition (Von Békesy)(1951)(3),

- second filter (Evans and Wilson )(1973)(24),

- membranary mechanical retroaction (Gold)(1948)(28),

- intervention of central auditive centers (Goldstein,1978)(29),

(Wightman 1973)(72), (Evans, 1978)(23),

- periodicity detection (Schouten, 1940)(53),

- impulsional analysis (Huggins, 1952)(32), (Lafon 1962)(40),

- membranary contractibility of the external hair cells (Kemp,

(1978)(35), (1986)(36).


1.2. STATE OF THE ART OF COCHLEAR PHYSIOLOGY.


To date, the stimulation of the cochlea by a mild or a moderate intensity tone is thought to induce successive events:


1. a propagation of pressure waves into labyrinthic liquids and production of a displacement of the basilar membrane. The area of the maximum displacement depends on the frequency of the stimulating tone. However this tonotopy is not accurate enough and the selectivity is rather poor (fig 1).


2. a relative shift of the membrana tectoria on Outer Hair Cells (OHC) is seen;


3. a shearing of hairs resulting in a depolarization (48);


4. a contraction of OHC (by an active mechanism) (27, 5) inducing a maximal displacement of the basilar membrane in a very straight area and making the frequential selectivity much more accurate (36);


5. a very located stimulation of Inner Hair Cells (IHC) produced by this amplified mechanical displacement. The opening of ionic channels of the hairs involves a depolarization of the sensorial cell;


6. a transmission of a message at the synapses of the base of IHC and information sent by nervous fibers to Central Nervous System (CNS) (52). At this step, mediation of numerous chemical transmitters are probably regulating the action of efferent nervous system (51).


In short,


1. the contractility of OHC might be the main point of the cochlear frequency selectivity. This mechanism is supposed to replace the action of a second filter;


2. the OHC might allow the acoustical information reaching IHC;


3. the IHC might only be passive transmitters able to translate acoustical energy in bioelectrical phenomenons;


4. every fiber of auditory nerve might carry along two pieces of information: frequency and intensity;


5. the coding of frequency might be determined by each cochlear fiber (frequency characteristic: FC);


6. the coding of intensity might induce two mechanisms:

- the rate of spikes of the fibers (it increases with intensity),

- the number of stimulated fibers (it increases with intensity).

In spite of all these new data, von Békésy's concept about tonotopy remains still largely admitted.





Fig. 1. Pattern of the basilar membrane vibration induced by a sinusoidal signal. According to the classical theories of hearing, low frequencies are detected at the top of the cochlea (a), and high frequencies are detected at the base of the cochlea (b). An analysis of complex sound signals is made through the cochlea (c) (from Loeb G., 1985).



1.3. SOME PERSISTENT PARADOXES.


However, here are the facts which remain unexplained by these above additional explanations (12):


- in psychoacoustics, beat perception, the perception of differential sound (42), sound combinations, the absent first formant, the phenomenon SHOUTEN's residual sound, the tonal nature of white noise in the closeness of the auditive threshold (20)(fig 2), the

tonal nature of clicks, etc. In short, as the ear perceives a subjective sound, the spectral analysis is not able to detect any objective sound vibration;


- in anatomy, the antagonism between the irregularity of the dia meter of the cochlea and the existence of a regular series of re sonators, the opposite directional orientations of IHCs and OHCs, which suggest an opposite action, the differences between the num ber of internal and external afferent neurons (58, 59, 47), the incompatibility of fine spatial frequential discrimination with dendritic spreading of external afferent neurons, the constant neuronal density along the basilar membrane incompatible with a restricted frequency map at the cochlear basis;


- in anatomo-pathology, the frequent discordance between the site of neuro-sensorial lesions and their theoritical localisation (presbycusis, ototoxic deafness, sound trauma (49, 10) (fig 3);


- in cochlear mechanics, the impossibility to link tonotopy with the membranary rigidity gradient (33). Actually, the decrease of the vibration amplitude of high frequency sound associated with the increase of the membranary rigidity at the basis of the cochlea tends to suppress the mechanical excitation of the cells;


- in electrophysiology, the predominant role of the envelope of the signal in opposition to its frequential content, both in the isolated nerve fiber response (fig 4) and in the whole nerve, the impossibility of obtaining a direct and objective tonal audiogram by BERA from clicks or filtered clicks.






Fig. 2. Tonality of a white noise at the auditory threshold. When the acoustical level of a white noise is decreasing, the psycho-acoustical perception remains unchanged, down to the auditory threshold. However at the auditory lowest limit, the perception should be identical to that of a sound band centered around 1000 - 2000 Hz.



Therefore, these difficulties which are met by classical auditory theories lead to the necessity of finding another model of the auditory function. Besides, this achievement is justified because it is not possible to know accurately the coding of the internal ear :


- either by a calculating operation (convolution),

- or by neuro-physiological experiments (on account of the discontinuity of the spikes and the impossibility to record simultaneously and separately all the responses of each auditory nerve fiber.






Fig. 3. Audiogram and cyto-cochleogram of a man with deafness induced by recurrent otitis (from Walby A.P., 1983). Note the absence of correlation between the pure tone loss and the supposed location of impaired areas (the altered parts in black are expressed in percentage).







Fig. 4. Frequency threshold curves and the shape of the signal. For each fiber, typical V shaped threshold tuning curves can be obtained from recurrent tone-bursts ( whith the same central frequency).

In (a), Frequency Threshold Curves (FTC)) of individual cochlear fibers (continuous lines). Each top of these curves corresponds to the Characteristic Frequency (FC). Altogether, these tops draw a line which looks like the response obtained by Cochlear Action Potential recording (CAP “audiogram") for a good hearing guinea pig (dotted lines joining black circles).

In (b), when using stimuli with various linear envelope (various rise and fall times), the response can vanish (Harrisson R.V., Evans E.F., 1977). The shape of the signal is more important than its frequential contents. So, concerning the FTC, note that the front of the different tone-pips varies with their frequencies. Concerning the "CAP audiogram”, note that when using the same frequency, the response of the fiber is only determined by the onset and the offset of the signal.




1.2. BASIC DATA FOR A NEW AUDITORY THEORY.



The Theory of Information combined with our data of cochlear mechanics allows us to propose a model of simple cochlear functioning which is suitable to modern data on signal treatment and recent histologic data.


In order to realize a new model, three groups of data should be kept in mind:

- personal new and recent data of cochlear mechanics,

- the sensori-neural systematization of the inner ear,

- the mathematical theory of communication and the sampling theory


1. NEW DATA IN COCHLEAR MECHANICS (15,17, 8, 9)(chart I).


The basilar membrane response observed on several mechanical cochlear models depends on numerous parameters. Some anatomical and functional conditions of the internal ear must be protected, such as:

  1. the absence of any links for the basilar membrane at the distal extremity (which is commonly found with a healthy helicotrema) (fig. 5, 6, 7),

  2. the use of liquids with the same degree of viscosity as with the inner ear (fig 8),

  3. the dynamic similitude between the ear and the models with essentially equal Reynolds numbers,

  4. the pure excitation signals ( the signal obtained from a tuning fork is not a sinusoidal one, but is made of a large number of transients)(fig. 9).


Under these conditions, a traveling wave can be found (fig 10), but this wave has different shapes according to the signal type as follows :

-1) for a given frequency: the membrane always vibrates along its entire length. The membrane shows sinusoidal waves whose envelope have no maximum deviation. The amplitude of the vibrations increases proportionally with intensity. When the frequency increases, the envelope approaches the axis of the membrane and simultaneously the number of vibrations increases up to a superior limit of frequency (fig. 11).


-2) for a transient signal, there is a propagated vibration which is damped when going from the basis towards the apex. The amplitude and the extent of this traveling wave depends on signal energy and rigidity of the membrane (fig. 12).

-3) for a random signal, random vibrations are scattered along the entire extent of the membrane. The amplitude of these vibrations varies in direct proportion with the signal intensity and the elasticity of the membrane (fig. 13).


When these entire experimental conditions are not respected altogether, the classical pattern of traveling wave can be observed again (fig.8).


To sum up, according to our own new experiments, a location of vibrations on basilar membrane can only be noted with transient signals. Thus, in opposition to classical theories, no tonotopic location with pure tones and random vibrations can be observed.






Chart I






Fig.5. Cochlear mechanical von Békésy model (1928). In this model:

- here the distal part of the membrane is fixed on the frame, unlike the anatomic data concerning helicotrema,

- the liquids have an abnormally high viscosity,

- the electrically sustained tuning fork does not provide a pure sinusoidal signal, but contains transients.

The membranary response pattern is bound to be modified on account of these abnormal parameters.









Fig. 6. Cochlear mechanical Tonndorf model. Same observations as for von Békésy’s model, except for the signal. (adapted from Tonndorf, 1957, [44]).





Fig. 7. Photography of the apical end in the guinea pig's cochlea (helicotrema).

A very thin wire has been introduced through the scala vestibuli, under the arched and loose extremity of the basilar membrane. (from Carrat R. 1986 [20]).







Fig. 8. Reproduction of von Békésy traveling wave. The membranary response for a sinusoidal signal according to von Békésy's description can easily be reproduced with high viscosity liquids, whatever the signal is a pure one or a transient one, and even if the end of the membrane remains loose. Actually this experimental condition does not take Reynolds number into account. (Carrat R., 1979 [32]).





Fig. 9. Frequential analysis of the signal obtained from the electrically sustained tuning fork:

- with a loose mechanical coupling, the signal is almost sinusoidal ( a & b);

- with a tight mechanical coupling, note that a spectrum of a high energy shock is obtained (c & d). (Carrat R. & all. 1978 [45]), Mercier J. 1962 [46]).






Fig. 10 a. Mechanical models used by Carrat R. (1979).








Fig. 10 b. Mechanical models used by Carrat R. (1979).







Fig. 11. Pattern of membranary vibrations produced by a sinusoidal signal.

It should be noted that:

- the membrane exhibits oscillations all along its length whatever the frequency of the signal is,

- the vibration amplitude is the same wherever it is,

- the vibration amplitude decreases when the signal frequency increases. (Carrat R., 1975 [47]).








Fig. 12. Pattern of the membranary response to a transient signal.

A traveling wave occurs and is damping more or less quickly. The vibration amplitude and the spreading of the wave vary according to the signal parameters.

a: strongly damped response,

b: weakly damped response. (Carrat R., 1975 [47]).





Fig. 13. Pattern of the membranary response to a random signal.

With the light of a stroboscope, a sinusoidal-like response can be observed. This response is changing with frequency of the electric flashes. The maximal displacement lies in the distal part which is the most elastic area. The membrane appears to be blurred. When the frequency of lightning is modified, a changing area with a maximum vibration of the membrane is never found. If the model carried out a frequential analysis, a maximum displacement would be observed. These data are not suitable with the concept of tonotopy. (Carrat R., 1979 [31, 32]).







2. THE SENSORI-NEURAL SYSTEMATIZATION IN THE COCHLEA.



For a long time, the major auditory innervation was thought to be connected with OHC, as being the most numerous among all HCs. In that way, the role and the importance of the IHC was neglected. Actually, numerous issues have shown a duality of the internal and

external afferent neuro-sensorial system (58, 59, 60, 61, 62, 63, 64, 65, 46, 47).


Roughly speaking:

- the IHC, the less numerous cells, are connected with the greater part of afferent fibers. Each fiber is connected to only one IHC, but each IHC is in contact in man with about twenty fiber endings;

- the OHC , the most numerous HCs, are connected with a small number of afferent fibers. Each fiber is connected by ramifications with about ten OHC, while each OHC is connected with several fiber collaterals (fig. 14).

- concerning the efferent cochlear-olivo system, the ending type is also different according to the OHC or the IHC system. As for the OHC, the fibers are directly in contact with the basis of the hair cell. On the contrary, for the IHC the fiber ending meets

with the side of an afferent fiber (34, 37, 66, 57).


This systematization may suggest a regulator feed back mechanism (fig. 15, 16, 17).






Fig. 14. Layout of afferent auditive nervous system.







Fig. 15. Because of the neural connections between the outer hair cells, a frequency selectivity located at an isolated outer hair cell is mechanically impossible. In the same way, and conversely, a frequency selectivity located at an isolated afferent outer nervous fiber cannot be observed without the intervention of a supposed second filter.




Fig. 16. Pattern of the auditory sensori-neural junction.

Note the great number of vesicles of the efferent fibers. These fibers are linked to:

- the bottom of OHC,

- the side of afferent fibers coming from IHC.

Note that afferent fibers contain few vesicles.







Fig. 17. The auditory nervous systematization reminds a feed-back loop mechanism:

- brake mechanism,

- amplifier mechanism.


Green: Afferent fibers from IHC

Red: Afferent fibers from OHC

Blue: Efferent system: feed back system.




3. THE MATHEMATICAL THEORY OF COMMUNICATION AND THE SAMPLING THEORY



The auditory system is one of the five communication canals by which the organism enters in relation with environment. In this canal, the ear is one of the links of the communication line in charge of transmitting acoustics signals. By this way, this system depends on the mathematical theory of information and communication.


Hartley R.W., Nyquist H., Einstein A.,[45] had already an approach of this theory but it was only asserted by Shannon C.E. in 1948 [56] and Weaver W. and Shannon C.E., in 1949 [69, 56].


This theory implies:

- a communication line with its well-known links such as transmitter, canal and receiver (fig.18);

- the transformation by this line of the message shape, without any modification of its contents.


The main point issue is to reduce any message to a combination of signals, 0 or 1 (on or off). The value of this message depends on the unpredictable successive combinations of 0 or 1 (Moles A.[45, 22].


Moreover, a continuous signal can be reduced to discontinuous signals which are likely to be distinguished and analysed. In other words, any continuous signal can be significantly performed by sampling of discrete elements at regular periods. Yet, the frequency of sampling must be at least the double of the maximum frequency of the signal.


This Shannon's theorem can be applied to a certain extent to a spatial sampling with a shape (fig.19, 20)(chart II).




Fig. 18. General pattern of the communication applied to audition. Functional model of auditory system. (from Leipp, E., 1977, [42]).

a) The auditory system consists of a line of communication for acoustic messages made of different links:

- mechanics (external ear and middle ear),

- electronics (cochlear analog-to-digital converter, central memories),

- compunterizing (compunter and central memory in order to identify, to compare and to associate the given images).

b) The traditional theories about hearing locate the decoding process in the brain. They are different from coding mechanism (acoustical cochlea resonators, cochlea compared to a microphone), and from nervous coding (microphonic current, temporal and spatial patterns of nervous discharges…).





Fig. 19. Quantization of a signal.

The exact amplitude for an isolated sample is able to have an infinity of values. But when taking into account the amplitude steps, this value is replaced by a finite number of elementary amplitudes (quantization).





Fig. 20. Spatial analysis of a pattern.

a). Quantization of the pattern amplitude.

b). Decreasing resolution effect. Sampling of a bi-dimensional pattern with decreasing resolutions. The different patterns are obtained with a superposition of rougher and rougher networks on the model. When a part of the model pattern fits with the center of a square of the network, the whole square is coloured in black; if not, the square remains in white. So, a digitalized pattern is obtained from discrete parts, like with time series.



It can be performed on a continuous function by "using analog technics". with converting the function into a series of discrete numerical values or "time series". This process is known as sampling. So that this series should be an adequate representation of the original function, the sampling rate must be at least twice the highest frequency of any component in the signal. According to the sampling theorem developed by Nyquist (1928) two samples per cycle will completely characterize a band limited signal.

The frequency of the signal that corresponds to that minimum sampling rate or Nyquist Frequency, is then one-half the minimum of sampling frequency. The corresponding maximum duration between samples which is the reciprocal of the minimum sampling frequency is called the Nyquist Interval.

Most communication processes use of sampling: either a sampling in time (as explained before), or a sampling in space. In this latter, different points of a pattern are detected, which allows to rebuild the whole primary pattern. Time series are replaced by spatial series, in a scale or a frame with more or less large steps .

The conversion of the continuous value into one of a limited set of values is called quantization. These values are usually a discrete series of whole numbers. With coding, the sampled information is expressed through numbers.

At last, Shannon (1949) in the General Theory of Information, showed that any message can be reduced to a combination (arrangement) of binary signals 1 or 0, or on-off states (all or no response for the nervous fiber).


Chart II . Sampling principle.







1.3. THEORY OF COCHLEAR SAMPLING: A NEW MODEL OF HEARING



1. PRINCIPLES.



Schematically, the function of the cochlea is to code the acoustic signal, (a continuous signal), into a series of nerve fiber impulsions, (a discontinuous one), in order to transmit

information to the cortical centers. This is an analog-to-digital converter, whose Corti cells are the interface relay.


To be more precise, as a response to sound vibrations transmitted by the tympano-ossiculary chain to the inner ear liquids, the basilary membrane is the site of cochlear patterns which vary according to the parameters of the signal. Corti cells behave like movement captors and are able to transform mechanics energy into electric energy (fig. 21, 22). These captors look like a mosaic; they are set in a network with three lines for the external system, and only one line for the internal system (fig. 23).


As each captor only occupies a minor surface area, the analysis of the cochlear membranary form is obtained by a spatial splitting up of the image, a bidimensional one for the OHCs, a linear one for the IHCs (comparable to a Dirac comb). In other words, we are dealing with a spatial sampling of HC and with corresponding afferent fibers.


Moreover, as these patterns are constantly changing - if not, they would not be able to carry any information - and as the nervous cells only respond in time intervals (temporal window), the analysis of successive positions of the basilary membrane is both spatial and temporal. There is therefore a temporal sampling as well.


The ear is thus an analog-to-digital converter which analyses the membranary image of acoustic forms through temporo-spatial sampling.





Fig. 21. The hair cells are movement captors that are responding to acceleration V2. The cell depolarization results from the shearing and stretching of the apical fibers of the stereocilia. Note that during a vibration cycle, the flexion of stereocilia occurs in two opposite directions and only one provides cell depolarization. The hair cells analyze the deformation by the spatial sampling of the basilar membrane.









Fig. 22. The pressure wave which is propagated through the liquids in the scala induces a displacement towards the three spatial planes:

- longitudinal plane: basilar membrane vibrations,

- vertical plane: upward motion of hair cells,

- radial plane: flexion of stereocilia.






Fig. 23. The cochlear pattern consists of discrete components or pixels, with a layout in line for the internal hair system, and which are arranged in a bidimensional distribution for the outer hair system.

So, the sensorineural transduction mechanism respectively consists of a linear analysis by means of a comb-like sampling, and of a two dimensional analysis, which is spatial, by means of a screen or a frame.

This cochlear pattern may be compared to the well-known pattern observed in typography (belinograph, street information on electric boards, etc). The recognition of a pattern is all the more accurate as the sampling step (interval) is narrower.





Moreover the accuracy of the spatial sampling analysis depends on the surface or on linear density of the captors (step or interval sampling) but does not depend on their total number. In case of temporal sampling it depends on the sampling cadence. Many anatomic and histological data, such as the converging orientation surrounding the CORTI tunnel [42], or the opposite systematization of the afferent nervous system [62], or the elective disappearance of the IHCs in the mutant mouse [21], may suggest functioning duality of the internal and external ciliate systems (chart III).






Chart III. Cochlear Sampling Theory





2. EXTERNAL COCHLEAR SAMPLING




Because of the neural interconnexion of the OHCs which necessarily widens the sampling step (sampling spatial interval) and because of the number of external afferent nerve fibers (about 1500) which would be theorically necessary to transmit high levels of information (about 30-40000), the external sampling can consequently only be but inadequate.


It does not allow the accurate discrimination of high and medium frequencies.


Conversely, the interconnexion of the OHCs with each external afferent fiber is compatible with a mechanism of spatial summation.


This system is therefore very well adapted to the transmission of sound intensity information by acoustic membranary sampling. On the other hand, the nervous efferent systematization may be compatible with a feed-back mechanism (fig. 24, 25).





Fig. 24. Pattern of the outer afferent fiber.

1. The arrangement in a spiral pattern of the outer afferent fiber does not allow an accurate mechanism of sampling concerning the OHC;

2. The dendrite connections of any fiber at the three lines of OHC remind of a recruitment mechanism during the excitation of the fibers.




Fig. 25. Sampling of loudness. Sampling of the sound level by the outer hair system. The OHC are in a network layout and they transmit the information of loudness level.




3. INTERNAL COCHLEAR SAMPLING



The functional separation of each IHC and the existence of a sufficiently large number of afferent fibers (about 28 000), enable us to apply SHANNON's theorem. In this very sampling, frequential discrimination is made possible by simultaneously spatial and temporal sampling.



1. SPATIAL SAMPLING.


For a sinusoidal membranary vibration, interval sampling is determined by the space separating two groups of IHCs which are simultaneously stimulated. The smaller the space, the higher the sampled frequen cy is. At the maximal limit, only one out of two cells is stimulated. Conversely, at the lower frequential limit, only two groups of hair cells are stimulated (fig. 26, 27).



2. TEMPORAL ANALYSIS.


Because of its refractory period, each nerve fiber is theorically able to transmit no more than 1 000 sequences/second. Above 1 000 Hz, the transmission of information is only possible through the intervention of the complementary mechanism of multiplexing. It is

this very mechanism of alternating activation of afferent fibers in relation to each captor which was first suggested by WEVER in 1930 (fig. 28).





Fig. 26. Sampling of pitch. Sampling of the frequency through the Inner Hair system. The IHCs transmit the pitch information. There is also a complementary temporal sampling on the afferent fibers.







Fig. 27. Spatial Sampling through Inner Hair System.






Fig. 28. Temporal sampling through multiplexing on an Inner Hair Cell.

At the highest frequency limit, each IHC oscillates from 16 to 20 times during 1 msec compared with its position at rest. On account of the refractory period of each nervous fiber, the information of frequency is necessarily transmitted through an alternative stimulation of a group of 16 to 20 fibers corresponding to each IHC. But this is the information concerning each half cycle vibration. To code the entire information transmitted by an entire vibration, 32 to 40 impulses should necessarily occur. This condition is in agreement with the extent of Shannon's theorem according to which the sampling frequency is the double of the sampled frequency.







Frequency Coding and Inner Hair Cells.

  1. The IH system consists of 3 000 to 4 000 transducers arranged in a line.
  2. About 16 to 20 afferent fibers are linked to every tranducer.
  3. The sampling step concerning transducers determines a spatial analysis of frequency.
  4. The nervous fiber refractory period determines a minimum temporal sampling of 1 ms.
  5. The coupling of hair cells and auditory neurons provides a spatio-temporal sampling of frequency.



Chart IV




INNER HAIR CELLS, AUDITORY FIBERS AND TEMPORAL SAMPLING

  1. The sampling span carried out at the site of Inner Hair Cell row (and corresponding to the interval between the axis of two juxtaposed cells) allows the sampling of a sinusoidal vibration up to 16,000 Hz on average.
  2. There is no frequency filtering by the I H C, on account of the high speed of repolarization of the cell membrane.
  3. The afferent neurons, which are arranged in bundles at the back of each I H C, may be compared to temporal transducers on account of their refractory period.
  4. The temporal span of each transducer (auditory neuron) reaches approximatively 1 ms.
  5. During a phase of pause of the cochlea, each auditory neuron is shown at different random stages of spontaneous activation. The spontaneous spikes on the global bundle of neurons have also a random temporal distribution.
  6. A rhythmic stimulation of a bundle of nervous fibers involves a stimulation in rotation because of the different stages of the polarization: here is a multiplexing mechanism.
  7. At the upper frequency of the auditory scale, the number of fibers involved into a cycle of vibration ( 2 IHC and about 30 fibers) is sufficient enough to provide this multiplexing mechanism.


Chart V








1.4. COCHLEAR MECHANICS AND BONE CONDUCTION


SOME EXPERIMENTAL AND PHYSIOLOGICAL ASPECTS.



Both air conduction and bone conduction are generally admitted as the same transmitters of the traveling waves in the cochlea. The basilar membrane is moving by a brief differential pressure between the scala vestibuli and scala tympani. Three factors contribute to this bone conduction: inertia of the ossicles, compression of the bony labyrinth, and osseotympanic component.


The sound vibration reaches simultaneously all the parts of the cochlea through the bone conduction. To explain the selectivity which is perceived through this bone conduction, the classical theories suggest the two following mechanisms:


- according to the first explanation, the selectivity is said to result from the stiffness properties of the basilar membrane. The decrease of the rigidity gradient of the basilar membrane provides a location of the maximum displacement which is changing in relation to frequency. Thus, high frequency stimulation is said to carry responses which are confined to the basal region, and low frequency stimulation is thought to carry responses near the apex of the cochlea.


- according to the second explanation, each fiber is said to have a characteristic frequency (CF) which responds by tuning with the frequency of the signal (tuning curves of single fibers and their Characteristic Frequency).


These assumptions are not easy to confirm because:


- the tonality of a white noise never changes while the intensity is decreasing; this tonality should therefore be changed into a sound band of medium centered around 1000-2000 Hz (see the curve of WEGEL) (fig. 2),


- the tonality of a pure tone does not change with increasing of intensity; this tonality should be heard like a band noise because of the close neuron stimulations,


- moreover, the "frequential specificity" of the auditory neurons is not compatible with the general nervous physiology. A neuron cannot transmit more than 1000 spikes per second, on account of its absolute refractory period. This concept of selectivity is unable to explain the way the sounds with a frequency above 1000 Hz could be transmitted by a single auditory fiber.


(A neuron can only respond in an on-off system. The only way this neuron can transmit frequency information itself is by a similar discharge per second since there are cycles in the stimulus (e,g., 720 discharges per second are needed to transmit 720 Hz tone). An upper limit on the number of discharges per second is imposed by the absolute refractory period of the neuron. It lasts about 1 msec. The 1 msec absolute refractory period corresponds to a maximum firing rate of 1000 times per second. However, auditory nerve fibers are wrongly supposed to be fired quickly enough to represent low and high frequencies (the tuning curves and the CF).


Experiments on mechanic cochlear model showed us an identical response when acoustical vibrations are transmitted either through the oval window, or through the frame of the model, supposing that the two windows are free of movement. There is no located frequency place. In the same way, a traveling wave can be observed in response to a transient impulse sent to the frame. If a window is locked, the membranary waves disappear. If then another window is created, in any part of the model, the oscillations reappear (in accordance with von Békésy report). These data may prove that in normal cochlea any hole except those oval and round windows can play exactly the same part (the third window (see page ..).(vascular holes for instance). Besides they may explain the bone response in otosclerosis.




1.5. THE THIRD COCHLEAR WINDOW


Experiments on cochlear mechanic models have shown that the motions of the basilar membrane are present only if the two windows (oval-like window and round-like window) are functional. The place of these windows doesn't modify the traveling wave. On the other hand, if the vibrations are transmitted through the frame of the mechanic model, as a bone-like conduction, there is only a membranary response when two windows are functioning. Inversely, the clamping of one of the two windows produces a disappearance of the wave motions. These data suggest that the bone conduction is only possible when there are at least two functional windows whatever their places are.


In some conductive hearing loss (otosclerosis, congenital middle ear malformations with soldered ossicles,...) the pure tone auditory threshold by air conduction is increased when threshold by bone conduction remains normal. Therefore there must be a third cochlear window which could be located at any hole of the cochlea: either at the cochlear aqueduct, the endolymphatic duct, or at the internal auditory meatus (fig. 29).

Therefore, in our own opinion, here is the evidence of a third cochlear window, which has never been demonstrated so far.







Fig. 29. Diagrammatic sketch of the third cochlear window.

Any hole in the cochlear bone (except the round window), may be considered as a functional window when the stapes is bone-linked (see the endo lymphatic duct with the endolymphatic bag [1], the foramen at the end of internal auditory meatus where the nervous fibers and vessels enter [2], the cochlear aqueduct [3).





1.6. THE COCHLEAR FUNCTIONAL UNIT



There is a striking similarity between the physiology of the eyesight and the cochlear physiology. The minimal angle to separate two close points and the minimal step for cochlear sampling can be thought as similar.


According to HELMHOLTZ concerning the sight and in order to separate two images, a stimulation of two retinal components divided by a nonstimulated one was needed. In other words, the functional sight unit should not have less than three sensorial retinal cells. This hypothesis was confirmed by histological, psychophysical and practical data (pixels in computerized prints).


Concerning hearing, at the upper frequential limit, the minimal step of spatial cochlear sampling sets into action three close auditory internal hair cells for each half period. As the stimulation of cells is only possible for one phase, the central cell cannot be stimulated and the spatial sampling is no longer able to select a higher frequency.


As for HELMOLTZ's hypothesis concerning sight, we may assert that an auditory functional unit with at least three close IHC should be considered.


However, it is necessary to remind that this extreme sampling is efficient only if the associate neural system to each sensorial cell is able to transmit information (at least one fiber for each cell per cycle). Because of the refractory period of the nervous fiber, this information about frequency is bound to also imply a sufficient number of fibers for a multiplexing functioning (fig. 30).





Fig. 30. The cochlear anatomo-functional unit. At the maximal frequency of the auditory scale, the coding from two adjacent inner cells cannot enable a spatial sampling, whereas the coding from three adjacent cells can do it. The Cochlear Anatomo-functional Unit corresponds to this smallest spatial sampling step.







1.7. THE INNER EAR : A BAR CODE LIKE TRANSCRIBER


The information provided by the pattern of stimulated Inner Hair Cells can be compared to the one provided by the system of bar code used in trade computerizing. A bar code is made of a series of modules with equally thick modules whose colours might be light or dark (fig. 31. A).


When these modules are combined in light or dark bars, these combinations represent a message written in a binary language with 0 and 1 (c. d). On both extremes, the light area is called the silence area. The decoding of the pattern is carried out with a system of optical reading that translates the variations of intensity from a reflective light beam into electric signals (e.g. scanning by a laser beam or by a series of adjacent laser beams)(B).


Concerning the inner ear, the Inner Hair Cells row can be compared to a bar code system (a). Each Inner Hair Cell corresponds to a module of this bar code system. Every cell can flip either into a rest condition or into a depolarization condition (b). The reading of the acoustical membranary pattern is carried out through the displacement of hair cells when compared with the membrane. This very displacement corresponds to the optical beam one (c).


According to the direction of hair cell flexion, the cell happens to be depolarized or not. This results in a binary coding of membranary acoustical form which is then transmitted in a binary form by auditory nervous fibers as well (d).








Fig. 31. The Inner Ear: a bar codelike transcriber.






PART II

COCHLEAR SAMPLING AND PSYCHOACOUSTICS




This model of Cochlear Sampling allows linking most objective cochlear anatomo-functional data to available subjective psycho-acoustic data. Here are some of the data to be noticed:

- the close relation between loudness and spatial excitation of OHCs,

- the upper frequential limit of audibility,

- the lower frequential limit of audibility,

- the relationship between the number of afferent fibers, the refractory period and the upper frequential limit of audibility,

- the relationship between the auditory field and the interval sampling,

- the sampling of a complex wave,

- the sampling of a pseudo-sinusoidal wave and the tonal sensation of transient,

- sound beats,

- the problem of bone conduction.



2.1. COCHLEAR SAMPLING AND AUDITORY FREQUENTIAL RANGE



The scala vestibuli and the scala tympani are comparable with an open-organ pipe doubled in two parts around the helicotrema. It contains the perilymph carrying pression waves which result in basilary membrane movements (fig. 32 a).


This basilary membrane is comparable with a whipcord whose distal end is loose regarding the helicotrema. As it was previously specified within the cochlear sampling theory, the traveling wave for transients is more or less damped according to signal parameters (fig. 32 c). For pure tones (sinusoidal signals) all the traveling waves reach the apex (fig. 32 b).





















Fig. 32. Simplified drawing of the basilar membrane

a: without excitation

b: for sustained signal

c: for transient signal















However, the sampling of these vibrations is only possible in a frequential range.

- On the one hand, the lowest frequential limit is determined by the length of the basilar membrane with L = l + l/2.

- On the other hand, the highest frequential limit is in relation ship:

= first, with the rigidity of the membrane. The increase of this rigidity absorbs the smallest energy vibrations;

= secondly, with the diameter of the captors (IHC) which does not allow the analysis of the narrowest movements.




2.2. THE INFERIOR FREQUENCY OF THE AUDITORY SCALE



According to the cochlear sampling theory, with decreasing of sinusoidal signal frequency, each wavelength of the membranary wave is increasing, and simultaneously the group of stimulated IHC is becoming larger and larger (fig. 33). When the frequency is at its lowest limit, the space (interval, step) of the spatial sampling is maximal, and there are three halves of a wavelength. It was found to be the same pattern of vibration as an open-organ pipe (a tube opened at one end with a node at the closed end and an antinode at the open end). In this model, a node can only be found at one end. Concerning the basilar membrane, its vibration looks like a string or a whip.


Consequently:

- the neuro-sensorial pattern is the same whatever the signal phase is;

- but from one cycle to another, a shift of the stimulation pattern can be seen;

- there is only one area of stimulation within each cycle. But to provide the sampling, an excitation in two different areas is absolutely needed. Therefore, in this case, two cycles or one cycle and a half can only be seen at the extreme excitation limit;

- when the first half-cycle is that of a stimulating refaction, the firing of the nerve occurs earlier than in the compression half cycle. This mechanism of refaction has been used in auditory electrophysiology for years.

a) the most inferior frequency limit obtained by calculation is in agreement with psyschoacoustic data. Supposing that the speed of the traveling wave is about 0,5 m/s and that the lowest frequency limit is about 20 Hz, the wavelength is:

b)

 V 0,5 m/s 
λ =------=------------# 23,3 mm
 N 20 c/s 

which corresponds approximatively to the 2/3 of the length of the basilar membrane (35 mm), and to a sampling of one wavelength and a half.






Fig. 33. The inferior frequency limit of the auditory scale.

When the frequency of the acoustical signal is decreasing, the vibrations are fewer and larger on the basilar membrane. The cellular pattern draws thicker strips. At the inferior limit of the auditory scale, there are only 3 half-cycles and the corresponding wave-length is then determined by the whole length of the cochlear oscillating membranary system.



2.3. THE UPPER FREQUENCY OF THE AUDITORY SCALE


According to Theory of Cochlear Sampling, the upper frequential limit of the auditory scale depends on two parameters:


- first, a spatial sampling on the basilar membrane determined by the smallest interval or step of sampling. This interval corresponds to the space between three IHCs, or two IHCs operating in phase,


- second, a temporal sampling induced by the refractory period of the nervous fibers (1 ms). The firing cannot theorically exceed 1,000 Hz for each of them. The excitation by successive rotation of 16 to 18 fibers is sufficient to transmit an information of 16 to 18 KHz coming from each captor thanks to a multiplexing mechanism.


Consequently (fig. 34),


- during the two phases of a cycle of vibration, two adjacent cells are stimulated but in fact they are alternatively stimulated,


- when two cells are simultaneously stimulated, there is no stimulation of the intermediate one. This minimal cellular group may be called a cochlear frequential anatomo-physiological unit, or Cochlear Functional Unit.


- the space determined by three consecutive cells corresponds to a minimal length wave. The upper frequency of a normal ear can be calculated with this length wave. In fact, each cell is spreading up to 9 u and three cells up to 27 u. Supposing that the speed of

the traveling wave is about 0,5 m/s (Pimonow L. [50]):


 V 0,5 
N sup =------=------------# 18 000 Hz
 λ 27.10-6 

Note this above result is significantly suitable with the psychoacoustic data.





Fig. 34. The highest frequential limit of the auditory scale is defined by the anatomo-functional narrowest step (interval) of sampling in the inner ear, that is to say by the space filled with three sensorial transducers side by side (a). Note that at each half wavelength corresponds a single hair cell, whereas two hair cells successively respond at each entire wavelength (b). Moreover, this highest frequency limit also depends on a temporal sampling induced by the refractory period of nervous fibers.



- It has to be noted that the stimulation pattern of the IHC is not modified by the change of phase, that the information of pitch remains exactly the same, and that there is only a shift corresponding to a half wavelength. These quite new findings may explain that the phase change of a pure tone signal does not result in the change of pitch.

- The maximal frequency also depends on the number of auditory neuron fibers. The temporal sampling depends on the number of auditory fibers associated with each IHC. This original concept explains why with approximatively the same spatial arrangement of

IHC in man and cat, a doubling of the number of afferent fibers in cat (about 60,000) provides a doubling of the maximal frequency (about 35,000 Hz).







2.4. THE AUDITORY THRESHOLD WITH A WHITE NOISE :


A NEW APPROACH ON TWO INTERESTING CHARACTERISTICS


Random noise, and particularly white noise, may be defined as a sound whose instantaneous amplitudes occur as a function of time, according to a normal (Gaussian) distribution curve (fig 35 a). A such random acoustic signal produces random vibrations on the basilar membrane in the cochlea.


Two interesting characteristics when hearing white noise may be elucidated with the application of the Cochlear Sampling Theory:

a) first, the constant pitch of the noise whatever its level may be,

b) second, the extreme accuracy when measuring the auditory threshold with white noise.


1. When a white noise (or a pink noise) is submitted to the ear, the tonality of this complex sound does not change when its level is decreasing. Moreover, the pitch of the noise remains the same at the extreme threshold of hearing [20].

However, as the threshold levels of pure tones require more sound pressure levels at the extremes of the frequency range than in the mild frequencies around 1000 - 2000 Hz, and as a white noise is a sound whose spectrum is continuous and regular as a function of frequency, the ear should perceive in case of Fourier analysis, a variation of the pitch when the level of a random mixture of tones (white noise) is decreasing. In short, the tonality at the threshold should be the same as a frequency band centered around 2000 Hz (fig. 35 b).

Actually, these paradoxical data can be explained when taking into account the random signal whatever its level may be, inducing a random spatial and temporal stimulation of the intern sensori-neu ral system. Thus, the random width of the sampling span gives a random pattern of the acoustic signal and consequently prevents the ear from any pitch perception.


2. Concerning the auditory threshold when hearing a white noise, we must keep in mind that the Outer Hair Cells are stimulated both in a random spatial and temporal way. As each fiber is linked to all the lines and to several cells in each line, the rate of fiber spikes corresponds to a summation which oscillates around an average value. The density of stimulated cells increases with the level of the random vibrations induced by the acoustic signal. This relatively constant value explains the data by which the auditory threshold with white noise is surprisingly accurate, within 1 dB [18, 19].






Fig. 35. The auditory threshold with a white noise.

a. The amplitude distribution from a white noise.

b. The auditory threshold with a white noise requires a minimal energy level:

A) for a normal hearing patient, B) for a deaf patient.


2.5. 1000 Hz : THE FLIP-FLOP FREQUENCY



1000 Hz is an original frequency. If each IHC were in relationship with a single auditory neuron, the coding of the information could not go over about 1000 Hz, regarding:

- on one hand the refractory period,

- on the other hand, the necessary intervention of at least two IHCs at each cycle (according to Shannon theorem).


Below this frequency, the coding is possible separately thanks to each fiber along the basilary membrane. This coding is like a sensitivo-motor one and moreover, it is a spatial one.


Above this frequency, each fiber cannot respond to all the vibrations. Here a multiplexing mechanism occurs in groups of fibers. We found a temporo-spatial coding which is a double coding: a sensitive and sensorial one. Note that above 1000 Hz, we only found a sensorial coding.


This totally new concept can explain why the speech intelligibility in profound deafness is very poor because the impaired ear cannot define precisely if the sound perception comes from a sound with all its attributes, or from a tactile vibration without a perception of a sound.


This concept - unpublished to date - can also explain why the results of cochlear implant are better for the late deaf people than for the deaf born children with the same residual hearing. The former ones experience a stimulation like a sound because they have previously memorized it, whereas the latter ones experience this sound like a tactile sensation.


2.6. PHASE AND PITCH OF A COMPLEX SOUND


The resultant waveform of a complex sound is proved to be determined by the number and frequencies of the pure tone components within the signal and its respective magnitudes and phase relationships. The resulting wave pattern is bound to be altered by a change in any of these component parameters. Furthermore, the resultant sound quality is affected differently according to these parameters.



Thus, the complex waveform affected by the phase relationship between the components in the signal should modify the pitch when the relative phase changes. In fact, the experiment tends to refute this explanation of pitch perception.


For example, both complex waveforms formed by amplitude modulating a 1000 Hz sinusoid with a 200 Hz sinusoid, are different if the two stimuli are 180° out of phase with each other (the second waveform is an inverted version of the former one). These two complex sounds will produce different pitches because of the differences in their waveshapes. Actually, there is no change in the complex pitch when listening to any of them.



Only the cochlear sampling theory can explain this auditory perception by proving that the sensori-neural patterns for the two signals are identical (fig. 36).





Fig. 36. Phase and pattern. The sensorial pattern obtained at the Inner Hair Cells by sampling is not modified by the shift of the acoustical signal phase. The acoustical system does not respond to the pure tone phase.


2.7. THE CASE OF THE MISSING FUNDAMENTAL



Nearly everybody hears the complex tone consisting of components 700, 800, 900 and 1000 Hz with approximately the same pitch like a 100 Hz pure tone (the fundamental frequency). The pitch is the same, whether there is energy at the fundamental frequency or not. This mysterious phenomenon is known as the "Case of the Missing Fundamental".


When the place theory is considered alone, this subjective attribute of complex sound cannot be explained. A non linear process between the vibration of the ear drum and the excitation of the neurons of the auditory nerve should be taken into account. Other studies have suggested that the brain may perform a Fourier-like analysis.


An explanation about the Cochlear Sampling Theory may be provided when assessing that the neural pattern is the same when the fundamental frequency is removed or not. This pattern is determined by the upper harmonic frequency.


But as the acoustic recognition depends on the memorizing of these patterns, the cortical brain is not able to find any difference since the neural information which is provided by sampling is exactly the same (fig. 37).






Fig. 37. The missing fundamental frequency.

Note the sensorineural pattern does not change when removing the fundamental frequency from a complex periodic sound.



2.8. PSYCHOACOUSTICS OF THE TRANSIENTS


The auditory sensation caused by a transient significantly varies with signal parameters. Theoretically, as transients have a shorter duration than ear time-constant (between 10 to 60 ms), they should not provide a tonality. However, some tone-bursts are perceived with a definite tonality, and they sound more or less shaded when the signal duration is ranging from 5 to 20 ms. In the same way, the transients obtained with a single sinusoidal

oscillation can still generate a pitch.


Among all the possible parameters, the frequential content is not the only one in the psychoacoustical perception. The waveshape, and particularly the rise-time and the fall-time of the wave is very important. A very short transient seems to be perceived with a click-like quality. Conversely, when the rise-time and fall-time are accurately chosen, the transient can be perceived like a pure tone (for example the MESP described by Korn T.S. and Bosquet J.)[38, 39, 4]. These data may show why the attack and sudden fall of a note are very meaningful for musicians [73].


In short, the more the signal envelope increases, the closer the signal approaches to a DIRAC step function, and the more enlarged the spectrum is.


The envelope of the signal is as important as its contents.


Experiments on mechanic cochlear model have shown that transients generate a typical traveling wave which is damping on the basilar membrane and whose oscillations are more or less numerous and narrowed according to the wave front. It is clear that the sampling of this motion is the same as the sampling of a sinus wave. The shorter the transient is, the higher the pitch is. It must be noted that the sampling is located at the basal part of the membrane (fig. 38).




Fig. 38. The neural pattern of transients.

The "tonality" triggered by an acoustical transient signal may be explained by the sampling of the pseudo-sinusoidal wave occuring on the basilar membrane. The span of this sampling is nearly the same as the sampling of a sinusoidal wave.




2.9. THE PITCH GENERATED BY RECURRENT CLICKS




The auditory sensation generated by recurrent transients varies with the rate of these transients. When they are separated by long intervals of time, they are perceived like isolated clicks which are more or less chinking according to their duration or to their envelope (rise and fall time).


When the density of the transients is increasing, the sensation generated by these closer and closer clicks becomes impossible to define (or to separate) and in the end it is replaced at first by the pitch of a low sound, and then by a higher and higher sound.


It is thought that these variations of sensation depend on the variation of signal periodicity. However, this interpretation cannot explain why a low sound is heard when the spectrum of the transients is spreading on a large scale.


This strange psychoacoustic phenomenon can be explained if the mechanical response of the basilar membrane is taken into account as described in the cochlear sampling theory.

- When an isolated transient occurs, a traveling wave is running all along the membrane from the base to the apex. The same phenomenon can be seen when successive transients occur with a long interval of time. The traveling wave disappears when the next

wave is occuring. Then the sensation is the one of a click with a pitch depending on the numbers of oscillations contained in a membranary pulse and on the span of cochlear sampling.

- When the rate of transients is increasing, a second traveling wave can appear whereas the first traveling wave has not finished its way yet. If this rate becomes faster, the waves are closer and closer until a maximum rhythm and then they are no longer separated. When multiple traveling waves occur, a spatial cochlear sampling may happen with a tonal sensation which is low when the span is large, and higher and higher when the span is shrinking (fig. 39).


Like for the pure tones, the highest periodicity (about 50 to 60 ms) corresponds to the larger span of sampling upon the basilar membrane and allows to define the lowest auditory frequency (20 Hz). Conversely, the smallest periodicity corresponding to the separating ability of the ear (1,14 ms)[41] is not able to define the maximal auditory frequency. Below this value which corresponds to the refractory period of the nervous fiber, the sound seems continuous. This very fact is quite similar to the electrical stimulation of the cochlea by electrical impulses resulting in a simultaneous depolarization of all the fibers.






Fig. 39. Hearing triggered by clicks.

1. When considering an isolated transient, the psychoacoustic sensation is that of a click with a like tone aspect ("tonal color") which depends on the number of the oscillations contained in the membranary displacement and on the sensori-neural cochlear sampling span as well;


2. When considering a series of repeated transients, a cochlear spatial sampling may occur. The pitch is depending on periodicity. Then, we can note:

- either a pitch of low tone when the sampling span is wide (periodicity varying of 50 to 60 ms corresponding to 20 Hz),

- or a higher and higher pitch when the sampling span is decreasing. However, at the shortest periodocity (about 1,14 ms), a tonal merging can be observed because of the refractory period of the nervous fiber (note that it is the same problem as for the electrical stimulation of the fiber with cochlear implant).





PART III

THEORY OF COCHLEAR SAMPLING

AND AUDITORY PHYSIO-PATHOLOGY










3.1. THEORY OF COCHLEAR SAMPLING AND IMPAIRMENT OF SOUNDS



Except hearing loss due to a disorder of nervous conduction, particularly for central deafness, the deficit is linked to peripheric lesions made of :

- either of a pure sensorial impairment,

- or of a pure auditory impairment of neurons,

- or finally of a mixed deficit by peripheric neuro sensorial alteration. This latter - the most frequent - results from secondary degeneration of auditory neurons. The location of the lesion is changeable: either scattered or most often located at the base of the basilar membrane.


In all these cases, these sensori-neural hearing losses may result from a widening of the cochlear sampling span, either from a spatial sampling of Corti cells or from a neuronal temporal sampling, or from a spatio-temporal sampling.



1. IMPAIRMENT OF A PERIODIC COMPLEX SOUND.


Supposing a periodic complex sound with its fundamental Fo and its harmonic components F1, F2, F3, and supposing that the maximal frequency of sampling corresponds to F3 (which means a sampling performed with a number of captors equal to the double of frequency F3 x 2). For a normal sampling interval, all the frequencies FO, F1, F2 and F3 can be detected. On the contrary, if the interval is partially destroyed with a random rarefaction of the captors, the span of the sampling is enlarged and F3 cannot be detected. The more enlarged the span is, the lower the detected harmonic frequency is, whatever spatial or temporal the sampling may be (fig. 40).


These data are keeping with a decreasing of the upper limit of auditory range for pure tones which is observed in sensorineural presbycusis and hearing loss due to ototoxic drugs.





Fig. 40. Periodic complex sound sampling.

When the interval of the sampling is enlarged, which corresponds to a rarefaction of the cell captors, the upper limit of frequency is decreasing.




2. IMPAIRMENT OF TRANSIENT SOUNDS PERCEPTION.


Most of surrounding sounds are transient sounds and evolving sounds. Their duration is shorter than the time constant of the ear. These transient sounds carry the maximum of speech information. On the basilar membrane, a transient signal produces a traveling wave which includes forced vibrations, and this traveling wave is damping more or less quickly according to the impedance of each inner ear. As for sustained oscillations which are obtained with long time of pure tones, these damped oscillations can be sampled with hair cells and the closer the captors are, the better the sampling is.


If the space interval of sampling is enlarged, some of the oscillations contained in the traveling wave cannot be detected. Then the result of the sampling will be the same as the one of a normally sampled transient vibration including a smaller number of oscillations (fig. 41).


These data allow to understand why the perception of transient sounds persists in spite of the damage of the hair cells. However, the shape of this transient sound seems to be modified and produces a sensation like the one produced by a more damped vibration (like an aliasing process). Then the impaired hearing exhibits sound distorsions and concerning the speech these distorsions result in a difficulty of perception of its components such as the plosive consonants, and at last in more or less severe intelligibility trouble .






Fig. 41. Transient sound sampling.

The enlargement of the interval of sampling modifies the parameters of the sampled transient: note the decreasing amplitude plus the occultation of some waves, and the increasing of wave length. When considering the psycho-acoustic level, a decreasing hearing level sensation and a shift of pitch towards low frequencies (aliasing) are occuring. On this figure the sampling is supposed to be carried out through the comblike scale n°4.











3.2. DEAFNESS AND COCHLEAR SAMPLING


3 types of sensorineural hearing loss can be observed:


- 1. first, a real hearing loss with elevation of the threshold sensitivity of all the frequencies,

- 2. second, an auditory distorsion with a tonal audiometric curve which is practically unchanged, but with a more or less important impairment of speech intelligibility (the maximum intelligibility score is reduced). "I can hear but I can't understand a thing".


- 3. at last a hearing loss associated with an auditory distorsion. An elevation of the auditory threshold is mixed with an impairment of the recognition of spoken transient sounds.


About the anatomo-pathologic lesions, it can be found:


- 1. a random rarefaction of HC for internal cells and external cells as well, and a rarefaction of afferent nervous fibers,


- 2. a significantly rarefaction of HC most often located at the basal coil. Beyond this area the sensorineural range is usually preserved,


- 3. the association of these two above groups of lesions.


There is no compulsory relationship between the location of the lesions and the impaired frequencies. On the contrary, thanks to the Sampling Cochlear Theory, three types of hearing loss may be linked to the anatomo-pathologic data:


- Type 1: the random rarefaction of hair cells causes a widening of the space interval sampling and results in:

= a decreasing of the superior limit of frequency range. The tonal audiometric curve falls towards the upper frequencies,

= a difficulty to recognize only the quickest transient sounds. The intelligibility is then very slightly disturbed.


- Type 2: a basal area of HC completely destroyed with normal remaining coils. The sampling cannot be performed at the basal part of the BM whereas this sampling remains possible beyond the basal area. Then:

- the sampling of the upper frequency can be possible. The tonal audiometric curve remains normal,

- the sampling of spoken transient sounds is disturbed except for the most energic transient sounds which can reach the functional area. An important impairment of intelligibilty occurs with a vocal sloping down curve.


- Type 3: the association of a destroyed basal area with a sensorineural rarefaction of HC on the other parts of the cochlea results in:

- an impairment of transient sounds sampling at the basal part, with a poor intelligibility,

- a widening of the space interval of sampling with decreasing of perception of high frequencies.

The two tonal and vocal audiometric curves are altered.


In short, the type and the degree of the hearing loss depend on the spatial distribution of the sensorineural lesions (fig. 42).






Fig. 42. Sensori-neural Hearing Loss. The different types of hearing loss depend on the location of the cochlear lesions. A scattered alteration of IHC can generate a sensitivity loss beginning at the highest frequencies. A located destruction at the base of the BM can result in an alteration of the maximum of the speech intelligibility performance. Therefore these data can explain the presence of a normal intelligibility with a normal sensitivity loss to the highest tones, the presence of an altered intelligibility with a normal tonal audiometric curve, and the presence of a great variety of hearing loss degrees when these two types of impairment are mixed.








3.3. AUDIOMETRIC PATTERN AND AUDITORY PHYSIO-PATHOLOGY



Assuming that:

- on the one hand, the different alterations of cochlea (deficit in hair cells, stria vascularis atrophy, loss of neurons, impairment of the physical characteristics of the cochlear duct)

provide specific deficits,

- on the other hand, the different types of lesions can be additive, the audiometric pattern should reflect the underlying pathologic changes in the cochlea and auditory pathway. Moreover, the audiometric scale should be the combination of the different deficits from these different alterations.

With Cochlear Sampling Theory, interesting and original suggestions on the functional significance of the different parts of auditory system can be deducted. On the other hand, it may also allow to reveal meaningful relationships between audiometric abnormalities and corresponding cochlear disorders.

Six pure tone threshold audiometric profiles can be recognized by clinical experience and six corresponding types of specific deficit can theorically be described (fig. 43). These are:


- Type 1: a gradual decreasing threshold in case of internal sensorineural lesion (IHC losses, presbycusis, ototoxic hearing loss,...)[54]


- Type 2: a bowl shaped curve centered at 2 KHz in case of external sensori-neural deficits, (OHC lesion, hereditary hearing loss, congenital hearing loss)


- Type 3: a flat threshold pattern or slightly descending pure tone threshold audiometric pattern, corresponding to a strial alteration (hypotension, sclerotic drugs, hypoxia,...)[54]


- Type 4: an abrupt high tone loss usually starting with 1 KHz (meningitis lesions...)


- Type 5: a 4 KHz dip (acoustic trauma succeeding to a mechanism of excessive vibration of the cochlear resonator)[10],


- Type 6: an ascending curve observed with conductive cochlear lesion (bone dysplasia, Meniere's disease...).

The audiometric curve is rarely pure. The combination of the different types of pure tone threshold provides a wide spectrum of the functional expression of hearing loss (fig. 44).



Fig. 43. Cochlear Sampling and Hearing Loss Classification.





Fig. 44. Addition of pure tone sensitivity curves. Note that numerous pure tone sensitivity curves are actually the result of two superposed typical tonal patterns. These curves represent the additive effect of different pathologic types of hearing loss.





3. 4. ACOUSTIC TRAUMA


On the one hand, a persistent exposure to moderate intensity noise levels usually produces a noise-induced hearing loss. On the other hand, a single or repetitive short-term exposure and a high-intensity impact noise level may cause a hearing loss which is usually referred to as acoustic trauma. A sudden impulsive noise exposure is thought to produce partial or complete destructions in cochlear duct, probably because of the high amplitude traveling wave. Human temporal bones studies reported maximal damages which were approximately 5 to 15 mm far from the oval window [31]. Simultaneously, the audiogram reveals a decrease in threshold sensitivity at /or close/ to 4 000 Hz. With further noise exposures, the 4 000 Hz notch may become deeper and wider. But the reasons of these psychoacoustic effects are still unclear (fig. 45).


Data on cochlear mechanics and Theory of Cochlear Sampling suggest that two pathogenical mechanisms just appear to be mingled [10] :

- on the one hand, a high and short incident noise is a transient sound which causes direct mechanical lesions on basal part of the basilar membrane by a strong travelling wave beyond the physiologic limits,

- on the other hand, this high intensity impact induces spontaneous vibrations of the cochlear resonator whose resonance frequency is about 6 KHz (°). These forced oscillations may cause visible or non microscopic detectable alterations of hair cells all along the basilar membrane and thus may prevent the sampling when there is a 6 KHz frequency.


These two mechanisms may explain the constant threshold sensitivity loss around 4 KHz whatever the blast spectrum of frequencies may be. Clinicians should routinely test high-frequency sensorineural hearing-impaired listeners at mid-octave frequencies. The audiogram obtained through octave-interval threshold testing should provide additional information in detecting an acoustic trauma notch around this 6 KHz frequency (chart VI).

(°) Note that a value of 5357 Hz is obtained through calculation [24].



With reference to Bernouilli Law, the resonant frequency of a resounding tube with a closed extremity is obtained with the following formula:

 C
f =------
 4 L

As the velocity C of a sound into the water is about 1,500 m per s, and if the tube is 70 mm long as it is in the inner ear (scala vestibuli, helicotrema and scala tympani), the resonant frequency lies as follows:

f # 5 000 Hz ( 5 357 Hz )

Whatever the input frequency is - especially when a transient sound with a wide frequency spectrum is concerned - the resonant frequency lies the same.



Chart VI

















Fig. 45. Noise-induced hearing loss (A & B), (C & D).


= Concerning the acoustical point of view (A & B):

1. the theorical spectrum of a transient sound is a continuous spectrum (A),

2. paradoxically, the maximum threshold sensitivity loss occurs at about 4,000 - 6,000 Hz (B). This noise-induced hearing loss may be explained with an impairment of the basilar membrane due to a mechanism of forced resonance.


= Concerning the mechanical point of view (C & D):

1. a transient provides an impairment at the basal part of the basilar membrane (C),

2. this altered space of the membrane leads to a difficulty with the sampling of the speech transients,

3. as a result, the maximum speech intelligibility score is reduced when identifying the words.




3.5. HEARING LOSS, AUDITORY THRESHOLD WITH WHITE NOISE

AND COCHLEAR SAMPLING



1. As it has been proved in my first publication (18), the ear has a high sensitivity to variations of white noise intensity. Though the waveform graph of a white noise shows high variations around an average amplitude, the auditory threshold is very accurate and can be determined nearly 1 dB.


2. According to my own research (19), there is no correlation between the threshold with white noise and the distributuion of deafness in the frequency range. The threshold with white noise is approximatively equal to the threshold for a 1 KHz tone, whatever the shape of the tonal audiometric curve may be.


3. At last, there is no "tonality" at the neigbourhood of the threshold with a white noise. Experiments have shown that a white noise gives rise to vibrations more or less energetic on the whole basilar membrane. Even if the white noise is filtered by low pass filter or high pass filter, it remains impossible to notice a tonotopic pattern as it has been previously described.


These data can only be explained when assuming that:


- the neural systematization depending on OHC leads to a summation of the random responses of the vibration of the basilar membrane. If every OHC were linked to an only fiber, there would be high variations of loudness.


- the random spatial excitation of IHC carries a spatial sampling with a random step or interval. This random sampling prevents any "tonality" and pitch.



3.6. IMPAIRED SPEECH PERCEPTION WITH NORMAL TONAL AUDIOGRAM


Many patients with a normal hearing acuity are complaining of impaired speech perception, particularly in noisy conditions. On the one hand, this auditory dysfunction has no specific relation with an increased speech reception threshold in noise or with an abnormal central test result such as dichotic discrimination test or filtered speech reception test [25].


On the other hand, this phonemic regression seems related to a loss of cochlear neurons in these patients. This loss of cochlear neurons located in the 15 to 22 mm region has been positively correlated with a loss of words discrimination whereas there has been no significant correlation between losses of cochlear neurons in other areas and this very loss of words discrimination [54].

Such auditory defects and anatomo-pathology data could be linked by cochlear sampling theory and by taking into account that sampling which is impaired at the base but still undamaged in the other parts of the basilar membrane (fig. 46).


Consequently:

- as the sampling of the highest frequency limit remains possible, therefore the tonal audiometric curve is normal;

- the detection of transients at the base is impossible except for the more energetic transient signals which induced damped membranary oscillations which can reach the undamaged part of the cochlea.


As the acoustic transient signals of the speech carry the greatest part of semantic information, the impaired sampling of these transients is able to explain the decreasing of the recognition score of the words.





SILENT AREA REMAINING AREA OF SAMPLING



Fig. 46. Hearing loss with intelligibility score trouble without significant frequency selectivity impairment may be explained by sampling difficulties of transient sounds whereas the sampling of pure tones remains feasible.

The acoustical environment is essentially composed of transients and provides a main impairment of the basal part of the basilar membrane by numerous and repeated mechanical pressures in this area. Note that the forced vibrations by strong transients may not involve an impairment of cells situated at the nearest area of the MB (the amplitude of the early vibrations during the signal onset being lower). This view is in agreement with the histological data observed in the cochlea after acoustic trauma.



3.7. COCHLEAR ALIASING


It is well known that an error can be introduced in the analysis of a continuous data with a discrete sampling. This effect is illustrated when looking at a sinusoidal pressure waveform with sampled points uniformly spaced on the time axis. Several waves with all the same peak amplitude and which are all going through the same points cannot be separated from one another by the selected set of points. These waves are called aliases and this effect of sampling process is known as aliasing (fig. 47).


If the sampling rate for the incoming signal is not higher than twice the highest frequency of any component in the signal, then some of the high-frequency components of the signal are effectively translated down to be less than one-half of the sampling rate.

The frequencies of components that are aliases are related by the equation F1 = F2 + k Fs where F1 and F2 are the alias frequencies, k is an integer, and Fs is the sampling frequency.


The analysis of a vibration of a membrane by transducers which are uniformly spaced on the length axis, may be compared to the sampling of a waveform. The same effects of aliasing can then be observed when the density of transducers (IHCs) is decreasing. When this interference effects are observed in electronics, they can be avoided by a sampling at a high enough rate (or by adding a low pass filter). On the contrary concerning cochlear sampling, it is not possible to interfere to increase the density of the transducers or the number of neural fibers. "Ghost" vibrations which are not contained in the incoming acoustical signal can appear there. They introduce an element of noise which can provide difficulties to recognize the patterns of membranary vibration. However, they are a natural coding which can be helpful because of its translating down the non detected vibrations.


This aliasing process could explain that:

- during a tonal audiometric test some patients can hear a sound without any tonality, without any pitch, on the upper frequency limit before the "disappearance" of the sound sensation,

- when all frequencies are amplified - even the non perceived frequencies - better results can be obtained with hearing aid for a deaf person. The aliasing process then provides a natural and helpful coding of these non perceived frequencies within the residual auditory range,

- it appears to be unrecommanded to use a pass-band filter or a cut-off frequency in a hearing aid device.



Fig. 47. Aliasing. An interfering signal may occur and introduce an error into analysis through a signal sampling. If the sampling rate (SR) for an incoming signal (IS) is not greater than twice the highest frequency of any component in the signal, then some of the highest frequency components of the signal are effectively translated down into frequencies (A1 or A2) which will be less than one-half the sampling rate. These frequencies are called aliases. There are false frequencies which take the place of genuine high frequencies.



3.8. COCHLEAR SAMPLING THEORY AND HEARING AID


The improvement of deafness by hearing aid involves two main purposes:

- on the one hand, it consists in rising the sound level of the acoustical signal above the auditory threshold of the deaf person,

- on the other hand, it has to transmit the informative components of the acoustic message without any distorsion and it has to rise the flow of information (in bit/sec) up to its maximum.


These purposes are respectively evaluated:

- the first by the measurement of the prosthetic gain (qualitative aspect),

- the second by comparing the score of intelligibility of words or sentences with and without the prosthesis. A spectrogram can be used to detect the distorsions on the image of the acoustic signal after crossing the device.


To date, hearing aids are able to transmit a wide band of sustained sound frequencies and to perform a very high amplification of the sound level. On the opposite, great difficulties occur when acoustical transients are transmitted through the device.


These difficulties are depending on two modifications of the acoustical signal:

- first the delay imposed to the signal when it passes through the

device. This difference of time can reach from 7 to 10 msec;

- second the distorsions due to the time-constant of the different components of the prosthesis and which induces a time display of transients. So, the device disturbs the transfer of the shortest phenomenons of speech and it can even suppress them totally. For instance, this mechanism can occur when a transient sound appears whereas the fall time of the previous transient has not disappeared yet. Consequently, the percentage of intelligibility may significantly decrease with this device.


Lastly, after the passage of the sound signal through the hearing aid, the percentage of intelligibility depends on the sampling ability of the sensori-neural cochlear transducer. The results reach the best degree for conduction deafness (drum and ossiculary injuries, otosclerosis, etc) even though a delay occurs for acoustic signal and even though this very signal contains some distorsions. Anyway this signal can then be entirely sampled by

the inner ear.


On the contrary, the results vary for perception deafness. In this case, the enlarged sampling step and the damaged area of the ciliar cells at the base of the cochlea prevent the shortest signals from being correctly sampled. A compensation may be supplied when raising the level, but unfortunately it is limited by the highest sound levels which can be harmful. An arrangement is found when using peak-clipping process. In the same way, it is admitted that compression amplification by inducing attack and recovery times modifies transient signals and has some effects upon the quality and intelligibility of speech signals through the hearing aid.


In addition, it seems that the pass-band of a hearing aid has not to be limited, even if the frequency range of the deaf person is narrowed. This option enables the perception of frequencies which, - according to our own new theory of cochlear sampling - are ghost frequencies induced by aliasing and which may prove to be useful for the identification of acoustical messages.




Fig. 48. Hearing losses and sound pattern identification.

The values of differential threshold concerning level, frequency and duration allow to define the smallest sound volume which can be perceived and called as a phonon. However, since the measure of DT is not a current practice yet, the assessment of this elementary sound volume is presently reduced to a two-dimensional pattern. So any sound volume can be represented in a two-dimensional graph by juxtaposition of pixels. These pixels are white squares without information and black squares with a sound information. According to the hearing loss degree (light, medium, severe or profound deafness) and according to the frequential impairment (auditory scale narrowing or selectivity trouble), the outlines of this sound pattern will appear more or less clear and more or less blurred. On the whole, the sound pattern assessment will depend on the accuracy of the cochlear sampling and will range from a perfect clearness to a complete blurred image.




Fig. 49. Rehabilitation of hearing losses by hearing aids and sound pattern recognition.


The recognition of a sound pattern depends on the ability to discriminate the elementary patterns they are made of. Except DT whose measure is difficult and still inaccurate to date, sound pattern can be performed by a gathering of elementary patterns having two dimensions DI and DF.


Concerning conduction hearing losses (with DI and DF unmodified), the increase of the level by amplification is sufficient to recognize all the elementary sound patterns entering the global pattern. So, the contrast is maintained but note that moreover it is amplified.


On the contrary, when there are hearing losses, the size of elementary patterns is increased and the amplification is not able to improve neither the contrast nor the accuracy of the discrimination of the sound pattern. As the sampling span is not modified by the hearing aid, the sound pattern remains blurred.










3.9. PARADOXICAL AUDIOMETRIC CURVES IN PROFOUND DEAFNESS


a) In profound deafness, the perception is close to a tactile sensitivity. But note that if the patient has already memorized auditory sensations, he will then be able to recognize low sounds.


b) On the contrary if it is a sensorineural hearing loss, audiometric curves may be observed like those of conductive hearing loss. In this very case, a false Rinne is observed and the tympanometric curve is normal. The best response is then obtained through bone conduction and may be considered as a tactile response instead of a pure auditory one with a coded tactile information carried by the auditory nerve (fig 50).






Fig. 50. Profound deafness.





3.10. SOME IMPLICATIONS OF THE COCHLEAR SAMPLING THEORY


REGARDING COCHLEAR IMPLANTS


The recovery of hearing by cochlear implant in case of profound deafness consists of a stimulation of the remaining auditory nervous fibers by electric impulses through the inside or outside cochlea implanted electrodes, when a hearing aid cannot be used. Apart from anatomical, psychological and social problems, plus the possible reeducation, a great deal of problems should be solved.


They are linked to three different fields:


1. THE ELECTROPHYSIOLOGICAL DATA.


= the on-off principle concerning the response for the single nervous fiber (to trigger a response, the electrical stimulus should have a sufficient energy),


= the unvarying response of the fiber through a membranary depolarization, which is translated on the monitor or on the recording by a spike,


= the limited rate of the spikes which cannot be theorically higher than 1000 c/sec (the monitoring of spikes cannot reach over 1000 c/sec because of the refractory period),


= the possibility of a tissue destruction by electrolysis. So an electrical positive phase is needed after the negative phase in each stimulus, but unfortunately this positive phase is increasing the refractory period,


= the production of a relatively extended electrical field around each electrode. Therefore this electrical field does not stimulate only one fiber, but a set of them,


= the impossibility to get electrical areas which are close but separate in the inner ear (because of electrical diffusion in conductive tissues and liquids),


= the junction point between one electrode and the fibers is not as thin as the sensorineural synapse is,


= the limited number of electrodes (about 10 to 20) . Over 20 electrical fields may overlap on each other.



2. SPEECH ANALYSIS.


= speech is an acoustical redundant signal,


= it carries along two types of information:

- an aesthetic information,

- a semantic information which is the most important,


= the average flow of speech information is about 100 bits/s [50]. However, it can be reduced to 50 bits/s without any loss of understanding of the message [30]. But this flow is still too high when considering the possible information that the remaining fibers are able to carry (about 5 to 50 bits/s).


= the speech analysis must sort out the main significant components and reject all the other ones,

= the analysis-synthesis techniques of speech have shown that the greatest part of semantic information is supported by the formants F1, F2, F3, and by their frequential variation and their frequential reciprocal ratio [26],

= presently, most of the speech analysis technique consists of a frequential analysis like the VOCODER principle. Some other techniques focus on F0 or F2.

= These above choices favour the aesthetic information and suppose that the functional modeling of the ear is based on the acoustical and electrical tonotopy.


3. THE ELECTRICAL CODING OF SPEECH.


= since the acoustical signal coming from speech is shunted in the inner ear and since it is caused by a direct electrical stimulation, a conversion of acoustical information into an electrical information must be carried out.

= the main purpose is to conceive an electrical coding which might be the closest possible to a mechanical conversion into an electrical signal.


= two parameters can be both used for this coding:

- 1. the rate of the stimulus, with a maximal which cannot exceed about 600 to 700 c/s,

- 2. the place of stimulation, which depends on the implanted electrode number.


= if the rate of discharges upon the fibers is used for the intensity coding, a single spatial coding upon the basilar membrane can only be avalaible.


= as for this spatial coding, two possibilities occur according to the chosen model of ear functioning:


1. - on the one hand , according to the classical conception of the frequency localisation on the basilar membrane (theory of tonotopy). a stimulating electrode can be alloted to each band of the auditory frequency scale. In this coding the major information support of the speech is thought to be a frequential one, and moreover there may be an electrical tonotopy. Finally, it has been assumed that when increasing the number of implanted electrodes the very best information flow is increasing as well.


Unfortunately, this coding will raise some objections:

- the part of speech information supported by transitory phenomenons is not sufficiently taken into account.


- the electrical Savart images which are obtained are as a result inaccurate compared with the acoustical membranary images. Therefore it can only be a new but poor nervous coding.


- these electrical Savart images are not stable. On the one hand, it is due to the variation of the intensity of the voice in the same speaker. This variability triggers the setting of a very variable number of channels of the vocoder analyser coming from a same word or sentence. On the other hand, it depends on the speaker's register of the voice (male, female, child) who consequently can produce a set of different electrical images coming from a same speech information. It results in an extreme high number of electrical possibilities for a same speech information, which leads to learn, memorize and recognize a difficult new language.


2. - on the other hand, when taking into account the Cochlear Sampling Theory, another conception of coding may be suggested as follows:


= as a deaf person's channel of information is narrowed, the entire information of the speech cannot be transmitted. Consequently a choice among the speech components is needed to select the most informative of them (fig. 51).


= as experiments of speech synthesis have proved, the semantic information is more important than the aesthetic one. This semantic information is mainly supported by the frequential variations of formants and by their reciprocal frequential relations. The major formant is the second formant F2, which owns the highest energy.


= so detecting the formants may be suggested (or intensity peaks when frequency bands are concerned) from a spectral analysis of speech, and their frequential evolution in time may be followed (fig. 52)[11];


= two or three formants (F1, F2 and F3) could be easily detected and the frequential variations determined between these formants. Unfortunately, the Cochlear Sampling Theory showed that a great number of closed electrodes is needed to code these frequential variations between the formants, and to code at least two steps of sampling.


= the easiest possible method could be to detect only the F2 and to code the frequential evolution of this formant in a variation of the place of the electrical stimulation. It would be supposed that there is another virtual formant (F0 or F1) which is fixed and that the interval of the stimulated electrodes corresponds to a step of sampling. The decreasing of the spatial step might represent an increasing of frequency of the formant and conversely. In this coding, the spreading of acoustical transients on the basilar membrane should be translated by a more or less important electrical step. Moreover, the speed of the frequential variation of the formant should be suitably performed. However, it is obvious that the coding is bound to be relatively poor.


3. - At last another coding could be imagined: it would be different from the model of functioning cochlear described in the Sampling Cochlear Theory. It would consist of selecting the three more energic formants in the acoustical signal of the speech and in coding them on three fixed electrodes. The frequential variations of these formants might be coded in a rhythmic variation of electrical impulses. In this coding, the intensity of the acoustical signal is not represented. On the opposite, the reciprocal variations of the formants are suitably represented. It is obvious that this coding should be limited to subjects who have never heard before. Whereas for people who have already heard, the coding would disturb their memorization of sounds. The use of only three stimulating electrodes should be considered as an advantage in the technical choice of implantation (fig. 53).




Fig. 51. Diagram of the auditory channel in deafness. Whereas the flow of information through the transmitter and the conduction channel is normal, there is a decrease of the flow induced by the narrowing of the cochlear channel.







Fig. 52. Coding of the frequential position of the formants through an acoustical shift on white noise bands which can be discriminated by the impaired ear.




Fig. 53. Detection of the formant peaks of the speech and a possible coding through electrical pulses.




3. 11. TINNITUS and COCHLEAR BACKGROUND NOISE



17 to 30 per cent of people have experienced episodes of tinnitus and this proportion increases with age. This sensation of abnormal sound appears usually insidiously but can be attributed by patients to definite causes (noise, ototoxicity, ...).


The pitch can variate, but low pitch to is usually associated with conductive or consequent hearing loss whereas high pitch is linked to sensorineural deafness. In this last case, tinnitus is often compared to a buzzing, the murmuring of the wind, or a hiss noise. Sometimes, tinnitus offers a pulsating characteristic like in a conductive deafness. At times, it has a continuous aspect like in sensorineural deafness and can generate an obsessive aspect with a possible psychological repercussion. Their loudness greatly varies: faint from very loud. Tinnitus is always notified in silent conditions and is masked by noisy background. Some of these abnormal auditory sensations are objective and can be recognised by the investigator, but in most cases they are subjective.


Tinnitus generally occurs as linked to impairment of the auditory system (traumatisms, ototoxicity, presbycusis). However it can appear without hearing loss and with a strictly normal tonal audiometric curve. Without an obvious local cause, it usually offers a bilateral localization. Tinnnitus has generally a wrong response to treatment (masking, medication, electric stimulation) and sometimes justifies a psychotherapy.


In the other hand, when a subject with a normal hearing and who does not suffer from tinnitus stands in a silent background, he quickly feels a dizziness located in the ears. This auditory sensation can be called cochlear background noise: it is a physiological noise.


The cause and the pathophysiological mechanism of tinnitus are rarely known. However a pathogenic model can be advanced when 3 parameters are taken into consideration: the production of spontaneous spikes onto the nervous fibers, a disturbance of the cochlear feedback nervous system, and lastly, the absence of a cochlear tonotopic localization.


1. Like any nervous fibers, the auditory nervous fibers at rest support a spontaneous depolarization with a production of spikes in a slow rate, without any synchronization between themselves. When a sound stimulus arises, the rate of spikes which travel through each fiber increases and leads to a rythmic manner when the signal is periodic.


2. The efferent cochlear system has the anatomic and functional features of a brake feedback system (negative response). This systematization suggests a brake regulation of the rate of spikes which spread to the cochlear cortical areas. As a result the impairing of this feedback system releases the rate of this spikes. (compared to vertebral circle of pain)


3. When retaining the theory of sound cochlear localization (tonotopy), it would be admitted when high pitched tinnitus is present that the fiber depolarization is solely and strictly located at the base of the basilar membrane. In fact, this condition is incompatible with the moaning of tinnitus by a normal auditory subject. Conversely, the Cochlear Sampling Theory points out for the same high pitched tinnitus, that the pattern shall be spread onto the basilar membrane. This pattern is similar to the one of a random stimulation of auditory cells and fibers, similar to the pattern of a random noise. Moreover, this random noise consequently can have more or less high pitches, depending on the density of depolarized fibers.


When adding a pure tone to the acoustical signal, the Cochlear Sampling Theory suggests the superposition to this diffused pattern by a pattern composed of bands which progressively arises as tone loudness increases (emergence and recognition of the pattern on a bakground in the Gestalttheory).


At last, this same concept gives an original model to the physiological cochlear background noise.







CONCLUSION



All things considered, the inner ear mechanics does not reveal to be as elaborate as we might have thought up to now.


Actually, the function of a spectral analysis by the cochlea inducing for preliminary analysis of the acoustical signal is not needed. In fact, an analysis of the membranary patterns generated by an acoustical signal thanks to a digital mechanism should be sufficient. The main point is that a given acoustical signal always results in an identical membranary cochlear pattern.

Moreover the cochlear bone need not have a regular and perfect geometrical aspect. Besides the inner ear need not be exactly the same from a person to another. Note that the efficacy of this mechanism depends on the sharp accuracy of the spatial analysis and on the temporal analysis - especially on the diameter of the sensorial system network and on the number of nervous fibers linked to each hair cell.


The new auditory theory proposed and demonstrated in this very issue is compatible with the extensive data concerning the cochlear microanatomy, micromechanics and neurophysio logy. This theory favours the integration of the ear in the general scheme of communication. Thus, this new theory is able to link psychoacoustics, neurophysiology and audiology as well.


The use of this proposed cochlear model appears to be helpful to explain psychoacoustic paradoxes and to interpret some difficulties in clinical data. For instance, it enhances an original reading of the audiometric tonal curves. This proposed Cochlear Sampling Theory has been used for about fifteen years in our clinical practice and we have been able to assess its advantages when dealing with difficulties on auditory pathology.


Moreover it is important to mention that a short period of adjustment is only needed to be quite familiar with it.


In short, we can only hope that the purpose of this new theory of auditory function will draw much attention from the concerned laboratories and will favour dramatic progress in the research and treatment of hearing impairment in a wider range of deaf patients.






ACKNOWLEDGMENTS




We would like to express our deepest gratitude to many people who have contributed to the realization of this project. Many of them entered the working group created in 1976 with the name of Audiophonology Institute; we intended them to extend our research in hearing physiology, particularly in cochlear mechanics, and also in deafness. We were already associated with the "Centre Régional d'Audiophonologie Infantile" (*) and with the specialized school for children with impaired hearing "Beau Site".(**) in TOURS.


We wish to acknowledge our close friends Lionel Joncheray, as electronics engineer, and Max Plessis, as signal treatment specialist for their enthusiastic support and technical contributions. Without their active participation, we could not have been able to complete our experiments on perfect mechanical models. Moreover we thank them for the innumerable and incentive discussions and comments we had after our experiments.

We are greatly indebted to Jean Louis Thillier, M.D., electrophysiologist, for his valuable criticisms that arose from his most diligent and painstaking review of the evolving manuscript from the first book published in Paris in 1986.


We would like to pay special tribute to our close friend Jack Durivault, audiologist and hearing aid practitioner, and to Alain Enard, teacher for deaf children, for their talented help in organization and experiments.

A particular gratitude should be expressed to Mrs Michele Jomaron who assumed the fearsome responsability to translate the contents of this book in English. Without her long and patient help and her encouragement, this project could not have become a reality.


Finally we wish to express our deepest gratitude to our family and especially to Marie Josèphe Carrat for her unflagging patience and for her loving support in spite of many difficulties during the long and arduous development period of this entire enterprise.



(*) 16 rue de la Pierre. 37 100 Tours. France.

(**) 12 rue de la Loire. 37 100 Tours. France.



SELECTED REFERENCES




1. Békésy G. von. Zur Theorie des Hörens. Die Schwingungsform der Basilarmembran. Physic. Z., 1928; 29: 793-810.


2. Békésy G. von. Experiments in Hearing. 1960; McGraw-Hill Book Company. New York.


3. Békésy G. von., Rosenblith, W.A. The Mechanical Properties of the Ear. Handbook of Experimental Psychology. John Wiley & Sons, New York. 1951; 1O75-1115.


4. Bosquet J. Un modèle synthétique linéaire de la fonction auditive monaurale. Rev. Acoust., 1977; 42: 209-225.


5. Brownell W.E. Microscopic observation of cochlear hair cell motility. Scann. Electron. Microscopy. 1984; III: 1401-1406.


6. Brownell W.E. Observations on a motile response in isolated outer hair cells. In: Webster W.R., Aitk L.M., Eds. Mechanisms of Hearing. Clayton, Australia: Monash University Press, 1983: 5-10.


7. Carrat R. Réponse d'une membrane dans un modèle mécanique cochléaire à des sons purs, transitoires ou bruit blanc. C.R. LXXII Congr. Fr. Oto-rhino-laryng., Paris, 1975; Arnette édit., Paris, 1976, 189-197.


8. Carrat R. Influence des paramètes expérimentaux sur la réponse de modèles mécaniques cochléaires. Implications dans la physiologie de l'audition. Rev. Acoust. (Paris), 1979; 12:189-196.


9. Carrat R. Mécanique cochléaire: nouvelles données expérimentales. Ann. Oto-Laryngol., Paris, 1979; 96:23-48.


10. Carrat R. Traumatisme sonore et scotome auditif: proposition d'un modèle pathogénique. Rev. Acoust., Paris, 1981; 14: 110-114.

11. Carrat R. Analysis and Synthesis of Speech Regarding Cochlear Implant. Acta Otolaryngol (Stockh) 1984; Suppl. 411:85-94.


12. Carrat R. Théorie de l'échantillonnage cochléaire. Arnette édit. Paris. 1986.


13. Carrat R, Carrat X., Enard A., Durivault J. La reconnaissance des formes sonores dans les surdités de perception. Comm. LXXXVIII Congr. Fr. d'Oto-Rhino-Laryngologie. Paris, 1991.


14. Carrat R., Carrat X., Enard A., Durivault J. La correction prothétique des surdités et la reconnaissance des formes sonores. Comm. LXXXVIII Congr. Fr. d'Oto-Rhino-Laryngol., Paris, 1991.


15. Carrat R., Durivault J. Cochlée et bruit blanc: approches expérimentales. Comm. 12° Ass. Nat. Proth. Audit., Tours, 1974.


16. Carrat R., Durivault J. Influence des conditions expérimentales sur le signal délivré par un diapason à un modèle mécanique cochléaire. Rev. Acoust., 1978; 11:22-24.


17. Carrat R., Thillier J.L. Réponse d'une membrane dans un modèle cochléaire à des sons entretenus et à des transitoires. C.R. Soc. Biol., 1976; 170:900-903.


18. Carrat R., Thillier J-L., Durivault J. Le seuil auditif au bruit blanc. Ann. Oto-Laryng., Paris, 1975; 92:585-600.


19. Carrat R., Thillier J-L. La mesure de l'acuité auditive par le bruit blanc. Ann. Oto-Laryng., Paris, 1976; 93:487-500.


20. Chocholle R., Botte M.C., Da Costa L. Largeurs de bande nécessaires pour une perception non déformée du caractère tonal d'un bruit blanc à divers niveaux de ce dernier. Audiology, 1974; 13:140-146.


21. Deol M. S., Gluecksohn-Waelsch S. The role of inner cells in hearing. Nature, 1979; 278: 250-252.


22. Escarpit R. Théorie générale de l'information et de la communication. Hachette Université. Partis.1976.


23. Evans, E.F. Place and Time coding of frequency in the peripheral auditory system: some physiological pros and cons. Audiology, 1978; 17: 369-420.


24. Evans, E.F., Wilson, J.P. The frequency selectivity of the cochlea. Basics Mechanisms in Hearing. A.R. Moller. Academic Press, New York, 1973; 519-554.


25. Ferman L., Vershuure J., Van Zanten B. Impaired Speech Perception in Noisein Patients with a Normal Audiogram. Audiology, 1993; 32:49-54.


26. Flanagan J.L. Speech Analysis Synthesis and Perception. Springer-Verlag. New York. 1983.


27. Flock, A., Brestcher A., Weber, K. Immuno-histochemical localization of several cytoskeletal proteins in inner ear sensory and supporting cells. Hearing Res., 1982; 7: 75-89.


28. Gold, T. Hearing II. The physical basis of the action of the cochlea. Proc. Roy. Soc., 1948; B 135: 492-498.


29. Goldstein, J.L. Mechanisms of signal analysis and pattern perception in periodicity pitch. Audiology, 1978; 17: 421-445.


30. Guibert J. La parole. Compréhension et synthèse par les ordinateurs. P.U.F. Paris.1979.


31. Hawkins J.E, Johnsson L-G. Patterns of Sensorineural Degeneration in Human Ears Exposed to Noise. in Effects of Noise on Hearing. Edit. by Henderson D., Raven Press, New York, 1976; 91-110.


32. Huggins, W.H. Phase principle for complex-frequency analysis and its implications in auditory theory. J. A. S. A., 1952; 24: 582-589.


33. Husson R. La physiologie de la phonation, du langage oral et de l'audition, de Helmholtz à nos jours. Rev. Soc. Fr. Etudes correction audit., 1970; 14:19-32.


34. Iurato S. Efferent fibers to the sensory cells of Corti's organ. Exp. Cell. Res., 1962; 27:162.


35. Kemp D.T. Stimulated acoustic emissions from the human auditory system. J. Acoust. Soc. Am., 1978; 64: 1386-1391.


36. Kemp, D.T. Otoacoustic emissions, travelling waves and cochlear mechanisms. Hearing Res., 1986; 22: 95-104.


37. Kimura R.S., Wersall J. Termination of the olivocochlear bundle in relation to the outer hair cells of the organ of Corti in guinea pig. Acta Otolaryngol., (Stockh.), 1962; 55:11-32.


38. Korn T.S. La notion de la fréquence du son. Acoustica, 1968; 20: 55-61.


39. Korn T.S. Theory of audioinformation. Acoustica, 1969-1970; 22: 336-344.


40. Lafon, J.Cl. Sur la théorie impulsionnelle de la phonation et de l'audition. Bull. Audioph., 1962; 6: 3-16.


41. Lafon J-Cl. Etude microtemporelle de l'audition. Bull. Audiophonol., 1976; 6:75-78.


42. Leipp E. La machine à écouter. Essai de psyschoacoustique.

Masson Edit., Paris, 1977.


43. Loeb G. Le remplacement des organes fonctionnels de l'oreille. Pour la Science, 1985; 90: 32-39.


44. Mercier J. Traité d'acoustique. P.U.F. Paris, 1962.


45. Moles A. La communication. Retz édit., Paris, 1971.


46. Morrison D., Schindler R.A., Wersall J. A quantitative analysis of the afferent innervation of the organ of Corti in guinea pig. Acta Otolaryngol., (Stockh.), 1975; 79:11-23.


47. Nomura Y. Nerve fibers in the human organ of Corti. Acta Oto Laryngol. (Stockh.), 1976; 82:317-324.


48. Osborne, N.P., Comis, S.D., Pickles, J.O. Morphology and cross-linkage of stereocilia in the guinea pig labyrinth examined without the use of osmium as a fixative. Cell tissue res., 1984; 237: 43-48.


49. Pierson A. Déficits auditifs produits par certaines stimulations sonores. Rev. Acoust., Paris, 1977; 9: 301-318; 10: 147-158.


50. Pimonow L. Vibrations en régime transitoire. Dunod édit., Paris, 1962.


51. Pujol, R. Neuropharmacology of the cochlea and tinnitus. Tinnitus 91, Proc. of the Fourth Intern. Tin. Sem., Kugler Pub. Amsterdam/New york., 1992; 103-107.


52. Russel, I.J., Sellick, P.M. Intracellular studies of hair cells in the mammalian cochlea. J. Physiol., 1971; 284: 261-290.


53. Schouten, J.F. The perception of pitch. Philips Tech. Rev., 1940;, 5: 286-294.


54. Schuknecht H.F., Gacek M.R. Cochlear pathology in presbycusis. Ann. Otol. Rhinol. Laryngol., 1993; 102:supp 158.


55. Shannon C.E. A mathematical theory of communication. Bell Syst. Tech. J., 1948; 27:379-343, 623-656.


56. Shannon C.E., Wever W. The Mathematical Theory of Communication. Urbana, University of Illinois Press, 1949.


57. Smith C.A., Rasmussen G.L. Recent observation on the olivocochlear bundle. Ann. Otol. Rhinol. Laryngol., 1963; 72:489-505.


58. Spoendlin H. The Organization of the Cochlear Receptor. Karger S., Basel, 1966.


59. Spoendlin H. Ultra structure and peripheral innervation pattern of the receptor in relation to the first coding of the acoustic message. Hearing Mechanisms in vertebrates. J & A. Churchill LTD, London, 1968; 89-118.


60. Spoendlin H. Innervation pattern in the organ of Corti of the cat. Acta Otolaryngol., (Stockh.), 1969, 67:239-254.


61. Spoendlin H. Innervation densities of the cochlea. Acta Otolaryngol., (Stockh.), 1972, 73:235-248.


62. Spoendlin H. Neuroanatomy of the Cochlea. In Facts and Models in Hearing, Springer Verlag, Berlin, 1974; 18-36.


63. Spoendlin H. Retrograde degeneration of the cochlear nerve. Acta Otolaryngol., (Stockh.), 1975; 79:226-275.


64. Spoendlin H. Neuroanatomical Basis of cochlear coding mechanisms. Audiology, 1975; 14:383-407.


65. Spoendlin H. Organization of the auditory receptor. Rev. Laryngol., Bordeaux, 1976; 97:453-462.


66. Spoendlin H, Gacek R. Electron microscopic studies on the efferent and afferent innervation of the organ of Corti in the cat. Ann. Otol. Rhinol. Laryngol., 1963; 72:660-684.


67. Tonndorf J. The mechanism of hearing loss in early cases of endolymphatic hydrops. Ann. Otol., 1957; 66:766-784.


68. Walby A.P., Barrera A., Schucknecht H.F. Cochlear Pathology in chronic suppurative otitis media. Annals of Otol. Rhinol. Laryngol., 1983; 92: 2, suppl. 103.


69. Weaver, W., Shannon C.E. Théorie mathématique de la communication. Retz édit., Paris, 1975.


70. Wever, E.G. Theory of hearing. John Wiley & Sons, New York. 1949.


71. Wever, E.G., Bray, C.V. Present possibilities for auditory theory. Psychol. Rev., 1930; 37:365-380.


72. Wightman, F.L. The pattern transformation model of pitch. J. Acoust. Soc. Am., 1973; 54: 406-416.


73. Winckel F. Vues nouvelles sur le monde des sons. Dunod, Paris, 1960. (french traduct. of Klangwelt unter der Lupe, Verlag, Berlin).




Download the PDF version

Back