EMANUELEBIONDIand FERDINANDO GRANDORI Center of Systems Theory of CNR (Italian National Research Council), Electrical and Electronic Institute of Mikzn Polytechnic, Via Ponzio 3415, Milan 20133 (Italy)

(Received: 28 November, 1975)


The aim of this work is to critically review some of the classical electrocochleographic methods in accordance with the systems theory: (a) in describing, by means of mathematical models, the different parts of the auditory system concerned in the generation of stimulus-evoked signals; and: (b) in comparing the outputs of these models with the measurements of the corchlear potentials. It must be stated clearly that we realise that many of the conclusions drawn could be criticised; it is hoped that future research in the field will be stimulated by this work.


Le but de ce travail a ete de revoir, d’unefacon critique et en fonction de la thtorie des systemes, quelques unes des methodes classiques d’electrocochleographie: (a) en decrivant, par des modeles mathematiques, les differentes parties du systeme auditif qui sont concern&es dans la generation des signaux tvoques, (b) en comparant les predictions de ces modeles avec les mesures exptrimentales des potentiels cochleaires. Ii doit Ctre dit clairement que les conclusions des auteurs pourront elles aussi faire l’objet de critiques. De toute faron on peut souhaiter que leur travailpuisse etre te point de depart de nouvelles recherches. ht. J. Bio-Medical Computing (7) (1976+0

Printed in Great Britain


Applied Science Publishers Ltd, England, 1976










Let us briefly recall the basic physiological knowledge available on the auditory system (in relation to this paper), giving at the same time a description in terms of mathematical models. Some of these models are largely accepted in the scientific literature while others are at present only in the initial stages of assessment. As is well known, the auditory system can be subdivided into three essential constituents, as follows: (a) Mechanical part (external and middle ear, basilar membrane). (b). Peripheral nervous part (auditory receptors and primary neurons). (c) Central nervous part (superior nuclei up to the cortex). A schematic representation of the system is given in Fig. 1.








acoustic stimulus

unique signal EFFERENT

ensemble of signals


Fig. 1.



of the peripheral




It should be noted that only the mechanical part and the peripheral nervous part play a role in the process of generating the cochlear signals; thus, a detailed description of the superior nervous part will not be given. Actually, in a complete description of the subject one could not neglect the presence of the efferent fibres system (see, for example, Klinke and Galley, 1974). In this paper, however, we feel it sufficient to mention the system and to take its presence into account, as shown in Fig. 1 (blocks A and B). 1.1. The mechanical part As is well known, the mechanical part is made up of the outer ear, the middle ear



and the basilar membrane; the acoustic stimulus at the eardrum is the input of the system, while the displacements of any single point of the basilar membrane can be considered as outputs. Let us now make the following assumptions and/or simplifications: (a) No feedback signal acts on the stapedius muscle or on the tympanic membrane. (b) The system is linear (this assumption can hardly be accepted for the lowest stimulus intensities (see, for example, Dallos, 1973) or for high stimulus amplitudes (see, for example, Rhode, 1971)). (c) Only thevertical displacements of basilar membrane single points are taken into account, and, in addition, their motion is dependent on the spatial cofeedback



e (1) acoustic stimulus (input)







from the superior nuclei

on muscles

’ x=0

w d (0 ,t)



- d(x,t)






I I middle ear



1 membrane displacements


I basilar membrane

Fig. 2. A model for the mechanical part of the peripheral ear. It provides any single point motion along the basilar membrane.

ordinate, x, the distance from the oval window. (This holds true only as a first approximation, because the two lateral edges of the membrane are bent to the surrounding cochlear structures). Following these assumptions, a scheme for establishing the behaviour of the mechanical part (see, for example, von Bekesy, 1960; Johnston and Boyle, 1967; Rhode, 1971) is shown in Fig. 2. A suitable starting point for the simulation of the mechanical part seemed to be the transfer functions proposed by Flanagan (1965): G,(S) represents the dynamic behaviour ofthe middle ear, and the transfer functions H(x, S) reproduce the peculiarities of the motion of the basilar membrane single points.




These functions satisfactorily match most of the experimental data regarding the motion of the mechanical parts; hence it is possible to evaluate, by means of a digital computer, any single point displacement, d(x, t) as a function of time, t, in response to any acoustic stimulus, e(t). Recently, other models have been presented (see, for example, Schroeder, 1973; Hall, 1974) to reproduce the basilar membrane motion (see Fig. 3). These can be considered to be second-order approximation models in which the non-linear behaviour of the cochlear partition is also accounted for.







Fig. 3. Comparison between frequency response of Schroeder-Hall Model and of basilar membrane (adapted from Hal/1974). Light lines: Frequency response of points on basilar membrane, as determined by MBssbauer-effect measurements. Heavy lines: Frequency response of model.

1.2. The peripheral nervous part Cochlear potentials originate,mainly from the peripheral nervous part which will therefore be described in detail. (We shall define the ensemble constituted by hair cells and primary neurons as the peripheral nervous part, for the sake of simplicity). The adequate excitation of the synaptic-like junctions existing between hair cells and afferent nervous endings causes a variation of the post-synaptic potential which, in turn, elicits a spike as soon as it exceeds a threshold value. The following points are known: (a) There are two different populations of hair cells (outer and inner cells) whose behaviour is probably different.



(b) A system of efferent fibres (crossed and uncrossed olivocochlear bundle) ennervates the hair cells and its r6le is still under investigation; there is a widespread opinion that it has an inhibitory effect on the afferent fibres (see, for example, Klinke and Galley, 1974; Biondi and Grandori, 1974; Geisler, 1975). Several theories have been proposed for the transduction mechanism of hair cells and the related formation of the stimulus-evoked electric field (see, for example, Dallos, 1973). The so-called ‘battery theory’ (Davis, 1956) is only recalled here because it is widely accepted. It will be used in the following sections. According to this theory, the

strla vascolarls

Fig. 4.

The schematic


of the cochlear circuit, 1956).

based upon the ‘battery

theory’ (Davis,

deflection of hair causes a variation of the resistance, R,in the electric circuit shown schematically in Fig. 4 (for a more detailed version of the circuit describing the electrical features of a narrow portion of the cochlea see Fig. 5). As a consequence of these resistance variations, the potentials of every point of the net vary with time. As regards the electric field measurable within the cochlea, any variation of R can be looked upon as avai-iation.of the emf E2 (provided thevalues of all the resistances are known). This concept is shown schematically in Fig. 6. In the following sections it will be useful to consider the entire cochlea as being subdivided






Fig. 5. Electric circuit for any zone of the cochlea (adapted from Cattaneo et al., 1975). The resistances R7, R8, R9 and RlO represent the longitudinal resistances along the pathways between two neighbouring zones. The resistance R4 and the capacitance C4 represent the impedance given by the Reissner membrane; the resistance R6 and the capacitance C6 represent the impedance of the basilar membrane. The impedances RI-Cl, R2-C2, R3-C3 resume the influence of the medium respectively existing between the vestibular, media and tympanic scalae and ground. The two generators 4, and ‘A,,,are equivalent to the effects of the Stria Vascolaris and of the hair cell generators.

into a certain number of sections so arranged that any point within each zone can be considered subject to the same mechanical excitation. On the basis of the above considerations we shall define the microphonic generators, ei(l), as functions of the zone, i, and of time, t.

5 -=d Rc



i tdt 1

f t-


iariable hair cells resistance

Fig. 6.


microphonic generators

The figure shows the equivalence between R-variations and emf-variations.



It must be emphasised that the assumptions made previously in describing the mechano-to-electric processes and the schematisation of the cochlea shown in Fig. 5 are a suitable starting point for the simulation of the electric field generated within the cochlea.


5 msec




1Omsec H Fig. 7. Cochlear Microphonics and Summating Potentials generated by the computer simulations ofthe Cattaneolef al. (1975)jmodel. At the top the acoustic stimulusl(tone-burst) is shownlhavingone period of rise time, four full cycles and one period of fall time. The four traces are the potentials in the Scala Media at a fixed point, in response to var&us frequencies. The growth ofthe Summating Potential iswell marked.

Without going into further details about this model, which was described in an earlier paper (Cattaneo et al., 1975), the computer simulation of the complete electric net reproducing the inner ear potential distribution gives satisfactory results and confirms thevalidity of our assumptions. As an example, in Fig. 7 the time course of the cochlear microphonic and of the summating potential are plotted at a given point. The stimuli were tone bursts of different frequencies.




If we take into account: (a) the genesis of this equivalent emf (the electric field is actually generated by a variation of a resistance), and (b) many direct and indirect neurophysiological data, it can be stated that the dependence of ei(t) on the displacements d,(t) is non-linear (see also Fig. 5-27 in Dallos, 1973). In particular, the resulting characteristic is non-symmetric with respect to the origin. It is at present an open question if the potential variation generated internally at the hair cells can be considered to be responsible for spike generation on the primary afferent neurons (in addition to the generation of the electrical field in the surrounding space). It must be pointed out that the input-output relationship (stimulus d(x, t)-spikes in a fibre u;(t)) of the system shown in Fig. 8 could be determined by means of direct experiments; on the other hand, ei(t) is not directly measurable. d(x,t

) 4 basilar-membrane

ei (t ) Amlcrophonic u?(tIeaction afferent




displacement generators

potential fiber

on j-th




Fig. 8. Schematic drawing of the model for the generation of a single microphonic generator (ei(t)) and of the action potential (u,*(l)) on a single auditory nerve fibre.

The problem of the interpretation of electrocochleograms becomes significant on the basis of this consideration. For this reason the distinction made in Fig. 8 between the non-linear characteristics of blocks C and D is theoretically important. A number of extensive investigations describe the activity patterns on auditory nerve single fibres (see, for example, Kiang, 1965; Rose et& 1967; Pfeiffer and Kim 1972). The most salient results are as follows. (a) Some fibres are spontaneously active; others have a definite threshold of firing; in any case, this part of the system is notably non-linear. (b) All fibres show stochastic inherent properties and the driving signal modifies their parameters (see also (d) below on the phenomenon of ‘phase-locking’). (c) There is an overall good correspondence between single fibre activity and the mechanical properties of the basilar membrane.



(d) In response to sinusoidal stimuli, up to frequencies of 4 + 5 KHz the distribution of intervals between spikes exhibits the well-known phenomenon of ‘phase-locking’. In order to solve the problem of determining the electrical field, action potentials on single fibres can be considered as generators of potential variations; they will be defined as spike generators and expressed by u:(t), where j ranges all over the set of afferent fibres. Some models describing the input-output [d(x, t) - u:(t)] behaviour of the system in Fig. 8 have been proposed and a generally good agreement can be seen between their outputs and the experimental data (see, for example, Weiss, 1966; Hall, 1974). An even better agreement is reached if the presence of efferent fibres on the auditory receptors is taken into account (Biondi and Grandori, 1974). Consider now the ensemble of all the nervous fibres originating in the same zone (as previously defined); it is possible to introduce the concept of an Equivalent Neuron as that element whose output, q(t), produces the same electrical field as that generated by the entire set of fibres of the zone. This definition is based upon the following considerations. Remember that the neuron is a non-linear, time variant, stochastic system and that many thousands of neurons are excited when an acoustic stimulus is applied to the system. It is easily understood that it is impossible to simulate every receptor and every neuron of the spiral ganglion. Assume now that the behaviour of all the fibres of a zone is represented by a much simpler component, which sends the same pieces of information to the central part of the nervous system. A Compound Action Potential would be obtained by summing all the Equivalent Neuron contributions at any instant. A mathematical model accounting for the generation of single zone contributions to the Action Potential (AP), based upon the concept of the Equivalent Neuron was presented elsewhere (Biondi et al., 1975; Biondi and Grandori, 1975a). On the basis of these preliminary considerations, the following problem arises (direct problem):

Suppose that all the generators ei(t) (microphonic generators) and ui(t) (spike generators) are known. Determine the potentials V(P, t) at every point, P, within the cochlea or in the neighbouring structures. Apart from some computational difficulties and some neurophysiological uncertainties, this problem should be solved in the near future. 2.


2.1. Individualisation of the problems As was mentioned previously, the acoustic stimulus acts on a certain number of emf generators which give rise to an electrical field within the cochlea and in the neighbouring structures.




Assume that the medium in which the field arises is linear (this approximately holds true: the non-linearity is found at the level of emf generation); it is thus possible to apply the principle of superposition of the effects as follows: UK 0 = V,,(P, t) + K,(C t) (1) where: V,,,,(P, t) = potential at point P due to the microphonic generators; V,,(P, t) = potential at point P due to the spike generators. The assumption made about the linearity of the medium makes it possible to write, again utilising the superposition principle: xl

V,,(P, t> =










where the coefficients ai and pi are dependent on the point P and on any single generator. It must be pointed out that these coefficients are merely scalar parameters in the case of a purely resistive medium; on the other hand, they are complex operators if the capacitative properties of the tissues are also taken into account. For any fixed section, i.e. for any x, the potentials will vary only with the places to be considered, and no dependence on the,other spatial co-ordinates will be assumed. Referring eqn. (1) to tympani, media and vestibuli, we can write:

w,, t) = w,,

0 = vmg(xm~ ‘1 + vsg(xmf ‘1






V(x,, t) =


vmg(xc5 ?>+ vsg(xc, ?)







In the literature on this subject, three.distinct problems, closely interconnected, are concerned with the determination of some of the variables previously introduced. Problem 1 (Separation problem): ‘By means of measurements of V(P, t), determine V,,,,(P, t) and V,,(P, t). The solution of this problem strictly depends on the point P and, in general, gives no information about the generators. Problem 2 (Problem of the individualisation of the generators): By means of measurements of V(P, t), determine the generators ei(t) and u,(t). Problem 3 (Problem of the characterisation of the behaviour of the generators): By means of measurements of V(P, t), determine the normal or abnormal functioning of the generators. 2.2. Actual methods and their criticism A. Methods regarding Problem 1: The usual procedures are basically as follows:



A 1 Simultaneous measurements at different points (see, for example, Tasaki et al., 1952; Teas et al., 1962). A2 Measurements at the same point, but relative to the proper sequence of stimulation (see, for example, Portmann and Aran, 1971; Yoshie, 1971; Eggermont et al., 1974). Method A 1: One of the adopted procedures is as follows: V(x”, t) and V(x,, t) are recorded, and are supposed to measure: K&, t) = A VX,, t) + WX”, t) VJX, t) = CV(x,, t) + DV(x, t)

(4) (5)

where A, B, C and D are suitable numerical coefficients. But, in order for eqns. (4) and (5) to hold, the following conditions must be satisfied (eqns. (7) and (8)). Actually, if V&, given by: V&(x, t) = A V(xl, t) + BV(x,, t) (64 and V& defined by: V,*,(x,.t) = CV(x,, t) + DV(d, t) (6’4 are the results obtained by method Al, then: V&(X, t) = AK&,, 1) + AJ’,,(x,, t) + BV,,,,(x,, t) + BV,,(x, t) Recalling eqn. (2a), it follows: V&(x, t) = A



+ A


+ B


+ B





and, similarly: V,*,(x,t) = CK,,,(x,, t) + CK,(x,, 0 + DV,,,,(x,, t) + DV,,(x,,, t) Then : vgx,

t) = c T


+ C


+ D


dx,)ei(t) J

+ D c


so that:

v*&, t) = v!l&, t) v:&? 1) = V&, t)

(7) (8)

it must be: A


Pi(x,)ui(t) = -B




and, in addition: C

cli(x,)ei(t) = -D c




But it seems very unlikely that these last equations should, in general, hold true. Moreover, it should be remembered that the medium has dielectric properties: eqns. (9) and (10) could be satisfied with much more difficulty. Since this is, in fact, the case, A, B, C and D should be complex operators and not simple coefficients.









Fig. 9. Potential distribution along the cochlear partition in the Scala Vestibuli (SV) and Scala Tympdni (ST), at a fixed time response to a continuous tone. Abscissa: Points along the cochlea. Ordinate: Arbitrary units. Only within the’zone marked A are eqns. (9) and (IO) satisfied (see text).

In addition, some experimental findings directly suggest that eqns. (9) and (10) cannot be considered (see, for example, Weiss et al., 1971). A computer simulation of the problem clearly shows that the results are inconsistent with th’e available knowledge about the distribution of the electrical field within the cochlea (see, for example, Strelioff, 1973; Cattaneo et al., 1975); only in some regions along the cochlear partition can eqns. (9) and (10) be satisfied, as shown in Fig. 9.. Method A2: This method is usually adopted in clinical electrocochleography. A sequence of pairs of stimuli of opposite signs (clicks or tone bursts) is delivered to the system and the potential recorded at a point near the inner ear (for instance, at the promontory or the oval window). The signals usually adopted as stimuli are: (a) Clicks unfiltered or conveniently filtered. (b) Tone bursts having a fixed rise-and-fall time. For the sake of simplicity, the method will be discussed in a general form, without going into detail about the possible implications deriving from the use of procedures (a) or (b). Let s’(t) and s-(t) be the elements of the pair of signals envoyed with an inter-stimulus time of T seconds. If the following equation holds true: ei[t;s+(t)] = -e,[t + T;s-(t)] (11) then: V[xyt;~+(t)]








+ ui[t + T;s-(t)]]) (12)

If we make the further assumption that: u,[t;s+(t)] = Z&Jr + T;s-(t)]




Then VJx, t) could be derived from eqn. (12) and, by subtraction, V&x, t) from eqn. (1). This method, even though based upon safer assumptions than method Al, nevertheless has to be criticised, mainly for the following reasons. (1) It is based on thevalidity of eqn. (9): therefore it is based upon the assumption that the system is linear at this level; more specifically, the characteristic shown in Fig. 8 (input d(x, t) - output e,(r)) should be symmetrical with respect to the origin. This probably holds true for low stimulus intensities, but not for moderate-to-high amplitudes. It must be pointed out that the Summating Potential (at least on the basis of the ‘battery theory’) is due to the presence of this non-linearity.

500 nscc Fig. 10. Stimuli s’(r) and s-(l) (top) and Cochlear Microphonics CM’ and CM-. At the bottom the sum CM’ + CM- shows that CM is not completely cancelled out. The fundamental component of the summed outputs has a frequency which is twice the frequency of the input.

In order to give further support to these considerations we wanted to test this stimulation condition on a simplified version of a mathematical mode1 (Cattaneo et al., 1975) able to reproduce the cochlear potentials in response to tone bursts of opposite polarity. The stimulus adopted and the output obtained are shown in Fig. 10. It can be easily seen that for stimuli with sufficiently high amplitudes, because of the non-linearity of the system, the Cochlear Microphonic is not completely cancelled out and gives rise to a complex waveform in which a sinusoidal component is clearly seen with a frequency twice the frequency of the stimulus. This same




,2msec, Fig, 11. Action potentialwaveform in response to a tone-burst of 500 Hz. The second-order harmonic is quite appreciable (redrawn from Eggermont et al., 1974).

component is probably present in many recordings, superimposed on the AP response; an example, adapted from Eggermont et al. (1974), is given in Fig. 11. This phenomenon also finds another, more obvious, explanation (see, for example, Eggermont et al., 1974). (2) Equation (13) is clearly not satisfied in any stimulus conditions: therefore this method only provides a mean response of ‘spike generators’ to the two kinds of stimuli (see, for example, Fig. 10 in Aran, 1971). The simulation of a mathematical model accounting for the compound electrical activity of eight nerve fibres gives the opportunity for verifying this behaviour from

Fig. 12. Action Potentials derived from a model of the peripheral auditory system (Biondi et al., 1975),in response to clicks of opposite polarities.



another point of view. In Fig. 12 the responses to the stimuli s’(t) and s-(t); AP+ and AP- respectively, are shown. (3) Any further processing of the electrocochleograms obtained by using this method (as, for instance, the separation between Action Potential and Summating Potential) must be examined in the light of the two previous considerations. BASILAR-MEMBRANE case



displacements (a 1)




to the noise




Fig. 13. Methods regarding Problem 2 (see text).

B. Methods regarding Problem 2: These techniques only recently appeared in the literature on electrocochleography (see, for example, Eggermont ,et al., 1974; Elberling 1974). The stimulus adopted consists of filtered masking noise and pairs of stimuli of opposite polarity. In Fig. 13 some representations of the problem are shown schematically. In panel (a. 1) the case of a sinusoidal stimulus and single point displacement is shown, making imaginary assumptions about localised displacements; in (a.2) the case of real displacement envelopes is’shown for different stimulus amplitudes.





Panels (b. 1) and (b.2) show a sinusoidal stimulus with a white noise superimposed, filtered by reject-band filter. From now on, the filters will be considered to be ideal, since the effects caused by real filters can be separately computed. In (b.l), the displacements due to the sinusoidal stimulus are real, while the displacements caused by noise are schematised. In this case (unreal) the procedure could give satisfactory results. In the real case (b.2), on the other hand, one might clearly see: (i) A zone characterised by a complete masking (M). (ii) A zone in which there is no masking (N.M.) at all. (iii) A third zone in which the masking is incomplete (U.M.): this causes uncertainty in interpreting the results obtained by using this method. The case of a sinusoidal stimulus masked by a high-pass filtered white noise is shown in the panel (c. 1); in the figure, the real displacements are plotted. Using the same symbols as before, the various zones, M., N.M. and U.M., are shown. e(t)1-;“‘“;a!



+r--l +






Somevery simple systems showing the so-called ‘adapt?tion’ pheaomenon; in the three cases it has completely different ongms.



The contribution of the zone to be explored is computed by making the difference between two measurements obtained with two different filters. Assuming that the contribution to the compound activity given by the U.M.+ zone is almost equal to the contribution of the U.M.- zone, and therefore that they are cancelled out by making the difference, this latter method can give better results than the former. Experimental results, too, seem to confirm the theoretically predicted ones (see. for example, Eggermont et al., 1974). C. Methods regarding Problem 3: No standard unified procedures can be found in the literature about this problem. Therefore only some non-exhaustive indications about the methodological aspects of the problem are suggested: actually, what will be discussed in the following section is the contribution of a systemic point ofview on neurophysiological investigations to be performed on the peripheral auditory system. Cl. Adaptation: This is often used improperly and with many different meanings. Actually, whenever a biological system presents output changes at the arrival of a series of identical stimuli, the process is called adaptation. A few examples of systems showing this phenomenon are: (i) time-variant systems; (ii) feedback systems; (iii) systems inwhich the transient has not yet died out, after the 6th stimulus, at the arrival of the (i + I)-th stimulus.

mset 2.5-

Stimulus50dB oS/N=+5dE ?? S/N= -5dE

o .


St N.G. N.w.H



E Fig.

15. A,, (a) and 5N1 (b) variations the end of a white noise masker




2048 msec

in forward-masking experiment as functions of the delay between and a short tone-burst. (Adapted from Eggermont, 1974.)




As an example, in Fig. 14, some systems showing the so-called adaptation are illustrated. Consider, for instance, the results (obtained by forward masking-tone burst electrocochleography) shown in Fig. 15. In this figure, for the increasing of inter-stimulus intervals (ISI), the response changes markedly. In the light of the available knowledge of the system, it is easily understood that all the above-mentioned causes act in determining such behaviour. At present, a quantitative separation of these effects is not possible. (An interesting paper on the mathematical modelling of AP adaptation can be found in Eggermont (1974)); on the other hand, further investigations about these problems are believed to be able to contribute decisively to the solution of Problem 3.

P”’ 15-



0 0


I 100 dB*

Fig. 16. Amplitude of the first peak of AP, A,, as a function of stimulus intensity of a normal cochlea and for two recruited ears (A and 9).

C2. Cochlear pathologies: Some typical characteristics showing the first peak amplitude of the Action Potential (tone-burst responses) as a function of stimulus intensity are given in Fig. 16 for two abnormal subjects, A and B. It is believed that only by using physiologically oriented models for AP generation can these results be interpreted. Among the many possible suggestions, one could also take into account the effect of the efferent fibres (olivocochlear bundle) on the peripheral receptors (see, for example, Biondi et al., 1973).

3. CONCLUDING REMARKS: PROPOSAL FOR A NEW METHODOLOGY (1) The present knowledge of the behaviour of the auditory system allows a qualitative interpretation of the most salient features of electrocochleography (in



contrast, for instance, to what happens in nystagmography; on this subject there has been, until now, a lack of knowledge about the genesis of a signal and its fundamental characteristics). (2) On the other hand, what is known about the system is not yet sufficient for a quantitative description of all the results. (3) The investigations which are now being currently made for diagnostic purposes are at an early stage (see, for instance, Biondi and Grandori, 1975~; Biondi and Grandori, 1975b; Elberling, 1974).


stirnull acoustics_,





results of the simulation


(or other perlormed

results of different on the subject)







Fig. 17. Schematic representation of a possible bio-medical engineering approach to computer-aided diagnosis.

The usefulness of carrying out research with the aim of quantifying the available knowledge of the system is clearly evident. These studies should be mainly based upon the bio-medical engineering approach shown in Fig. 17 (see also Biondi and Grandori, 1975b). It must be emphasised that there are at present a great number of simulation programs; all of them fit, in varying degrees, the available physiological knowledge. In our opinion, better diagnostic procedures, based upon mathematical modelling techniques, could arise from a closer co-operation between bio-medical engineers, physicians and neurophysiologists. REFERENCES AJZAN,I. M., L’kleclro-cochlkogr-e, Compagnie Francaise d’Audiologie, Paris, 1971. B~KBsY,G. van, Experiments in hearing, McGraw-Hill, New York, 1960. BIONDI,E. and GRANDORI,F., Modelling stimulus processing by peripheral auditory system. In R. Trappl and V. Pinchler (Eds) Progress in cybernetics, Hemisphere Publ. Co., London, 1974.





DACQUINO,G. and GRANDORI, F., Compound Action Potential and Single Auditory nerve fibers activity generation: An Equivalent Neuron approach, Inr. J. Eio-Medical Computing, 6 (1975) pp. 157-66. BIONDI.E. and GMNDORI. F.. Mathematical modeline of cochlear electrical activitv and its oossible applications to a diagnosiic methodology, J. Acoist. Sot. Amer., Suppl. 1, 57 (i975a) p. 76. BIONDI,E. and GRANDORI,F., Computer-aided techniques in objective audiometry, Inr. J. Clinical Compufing (19756). (In press.) BIONDI, E., DACQUINO,G., MIILLER,A. and OTTAVIANI,A., Auditory recruitment in man. Paper presented at Symposium on Regulation and Control in Physiological systems; Portland, 1973. CATTANEO, R., DACQUIN?,G. and GRANDORI,F., Cochlear responses to acoustic stimuli: A model to interpret Cochlear Mcrophonic (CM) and Summating Potential (SP). Paper presented at the Third International Congress of Cybernetics and Systems, Bucharest, August, 1975, Editura Technica, Bucharest, 1976. DALLOS,P., The auditory periphery, Academic Press, New York, 1973. DAVIS,H., Initiation of nerve impulses in the cochlea and other mechano-receptors. In T. H. Bullock (Ed.) Physiological triggers and discontinuous rate processes, Amer. Physiol. Sot., Washington, DC., 1956. EGGERMONT, J. J., ODENTHAL,D. A., SCHMIDT,P. H. and SPOOR,A., Electrocochleography. Basic principles and clinical application, Acra Otoluryngol. Suppl., 316 (1974). ELBERLING, C., Action Potentials along the cochlear partition recorded from the ear canal in man, &and. Audiol., 3 (1974) pp. 13-19. FLANAGAN,J. L., Speech analysis, synthesis and perception: Springer-Verlag, Berlin, 1965. GEISLER,C. D., Hypothesis on the function of the crossed ohvocochlear bundle, J. Acousr. Sot. Amer., 56 l(1975) pp. 1908-9. HALL,J. L., Two tone distortion products in a nonlinear model of the basilar-membrane, J. Acoust. Sot. Amer., 56 (1974) pp. 1818-28. JOHNSTON, B. M. and BOYLE,A. J. F., Basilar-membrane vibration examined with Mijssbauer technique, Science, 158 (1967) p. 389. KLINKE,R. and GALLEY,N., Efferent innervation of vestibular and auditory receptors, Physiol., Rev., 54 (1974) p. 316. KIANG,N. Y.-S., Dischargepatterns of singlefibers in the cat auditorynerve,MIT Press, Cambridge, 1965. PFEIFFER,R. R. and KIM, D. O., Response patterns of single cochlear nerve fibers to click stimuli: Description for cat, J. Acousf. Sot. Amer., 47 (1972) pp. 1669-80. PORTMANN,M. and ARAN, J. M., Relation entre ‘pattern’ &lectrochleographique et pathologie rttrolabyrintique, Acta Oto-Laryng., 73 (1971) pp. 19&205. RHODE,W. S., Observations of the vibration of the basilar-membrane in squirrel monkeys using the Mijssbauer technique, J. Acousf. Sot. Amer., 49 (1971) p. 1218. ROSE,J. E., BRUGGE,J. F., ANDERSON, D. J. and HIND,J. E., Phase locked response to low frequency tone in single auditory nerve fibers of the squirrel monkey, J. Neurophysiol., 30 (1967) p. 402. SCHy2F;2 M. R., An integrable model for the basilar-membrane, J. Acousr. Sot. Amer., 53 (1973) pp. STRELIOFF,‘D., A computer simulation of the generation and distribution of cochlear potentials, J. Acousr. Sot. Amer., 54 (1973) pp. 62&31. TASAKI,I., DAVIS,H. and LEGOUIX,J. P., The space-time pattern of the cochlear microphonics (guinea pig), as recorded by differential electrodes, J. Acoust. Sot. Amer., 24 (1952) pp. 502-18. TEAS,D. C., ELDREDGE, D. H. and DAVIS,H.,Cochlear responses to acoustic transients: An interpretation of whole-nerve action potentials, J. Acoust. Sot. Amer., 34 (1962) pp. 1438-59. ZEISS, T. F., A model of the peripheral auditory system, Kybernetik, 3 (1966) pp. 153-80. WEISS,T. F., PEAKE,W. T. and SOHMER,H. S., Intracochlear potential recorded with micropipets. II. Responses in the cochlear scalae to tones, J. Acoust. Sot. Amer., 50 (1971) p. 587. YOSHIF,, N., Clinical cochlear response addiometry by means of an average computer: Non-surgical technique and clinical use, Rev. De Luryngol. (Bordeaux) Suppl. 646 (1971).

Electrocochleography by mathematical modelling.

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