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The processing of informationally relevant signals in the cochlea
The Processing of Informationally
Relevant
Signals in the Cochlea
T. W. BARRETT Department of Physiology and Biophysics, Universiv of Tennessee Center for the Health Sciences 894 Union Avenue, Memphis, Tennessee 38163
Communicated by Aage R. Mdller
ABSTRACT The cochlear microphonic potential (CM) and summating potential (SP) response, recorded at locations beyond the point of maximum frequency response and elicited by high intensity elementary acoustical signals with AfAt =f,t,= $, (where Af is signal bandwidth, At is signal duration, fO is signal midfrequency, to is signal midperiod), are of similar shape and duration even when the stimulus dimensions are changed in a compensated way, thus exhibiting a constant response to constant informational relations. The constant CM and SP temporal response indicates that at locations beyond the point of maximum frequency response, a hydrodynamic wavelength-intensity trade in cochlear fluid movement occurs. In amplitude, the negative SP response is spatially distributed with respect to the components of the applied signal. The results of this study provide support for a model of cochlear functioning based on cochlear hydrodynamics and the two hair cell systems of the cochlea.
INTRODUCTION The smallest signal used in visual physiology is the photon. In auditory physiology the smallest signal-or elementary signal-is the logon, an elementary signal or structural “quantum” of information measurement, defined by [l, 14,21,23,24,28]:
AfAt=;,
(1)
where Af is the “effective” signal bandwidth in units of cycles and At is the “effective” signal duration in units of seconds. The requirements for Eq. (1) may be obtained in the time and frequency domains by the following definitions: ~(t)=~-C’(‘--I0)‘~i2nfd, (2) S (f) = e -(n/c)Y-f~Y,-i2nrofe MATHEMATICAL
BIOSCIENCES
29,203-217
(1916)
0 American Elsevier Publishing Company, Inc., 1976
203
T. W. BARRETT
204
To define an elementary signal unambiguously, another bounding condition is called for [ 1,3,8,9], which defines the constant c in (2) as equal to unity, i.e.:
where f. is the signal midfrequency in units of cycles/second or hertz, and t, is the signal midperiod in units of seconds/cycle. An elementary signal defined, then, by the bounding conditions of (1) and (3) is of the form shown in Fig. 1. Given a variable time base, the signal always appears in the form of Fig. 1 at any fo, i.e., with the same number of nodal points, due to the compensatory arrangements defined in (1) and (3). Such a signal is informationally relevant in that it represents the minimum signal, “worth” one “bit” in Shannon’s [29] sense. In other words, such a signal could be used to resolve uncertainty concerning a dichotomous outcome and is the minimum such signal. However, this analysis is concerned with information structure and not with the Shannon theory, which is related but distinct [3,8,9]. We have used such acoustical signals in studies of the auditory cortex [2,4,5,6], inferior colliculus [7] and medial superior olive [lo]. In the present study of the cochlear microphonic potential (CM) and summating potential (SP), the appropriateness of the use of such signals in a description of the auditory pathway is further demonstrated.
FIG. 1. a variable
Elementary
signal defined
by the bounding
conditions:
time base, the signal is of this form at different
fos.
AjAt =f&,=
I. Given
INFORMATION
PROCESSING
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IN THE COCHLEA
In this examination of cochlear potentials, high intensity elementary signals were used so that all four turns of the guinea pig cochlea could be investigated with a wide range of midfrequencies Jo Thus, the cochlear potentials recorded are from locations mainly beyond the point in the cochlea which maximally responds to the midfrequency used. The use of high intensity stimuli to elicit responses from cochlear locations at frequencies not near the resonating frequency for those locations provides an insight into the total cochlear response. Not all the recordings made in these experiments are within the linear range for recording the CM (cf. [18]). However, it should be emphasized that nonlinearity is not synonymous with indeterminism. It is probably the mechanism producing the nonlinearity observed with sinusoidal stimuli which provides the result reported in this paper, i.e., stimulus wavelength lengthening observed when high intensity elementary signals are used. Thus the observations reported here are not at variance with a nonlinear cochlear response demonstrated using sinusoidal signals of frequency range above the best frequencies for the electrode location. The main empirical results of this study have been described in detail [ 11,121. The present paper addresses the conclusions which may be drawn from the empirical findings concerning the total cochlear response. METHODS
F’MMARY
Elementary signals were generated by passing a rectangular wave of duration t, through a bandpass filter set at one-half octave around the midfrequency _/a such that joto= $ [33]. The appropriate Aj and At are also obtained
thereby,
i.e., AfAt = i (see Table
TABLE
Band @Hz) 0.875-1.125 1.750-2.250 2.265-3.375 3.500-4.500 4.375-5.625 5.250-6.750 6.125-7.875 7.000-9.000 7.875-10.125 8.75&l 1.250
*Each elementary
Bandwidth
Aj
(cycles) 250 500 750 1250 1500 1750 2000 2250 2500
signal satisfied
l), as the amplitude
modulation
la
Midfrequencyfe
Duration
A.t
Mid-duration
@Hz)
( psec)
( psec)
1 2 3 4 5 6 7 8 9 10
2000 1000 664 500 400 332 312 252 224 200
500 250 166 125 100 83 78 63 56 50
the two equations:
AjAt = f and for,,= i.
re
T. W. BARRETT
206
due to the nonideal cutoff characteristics of the filter approach a Gaussian waveshape (e --(‘--1~2) at a one-half octave setting around the f. The Af defines two standard deviations in f units, with f. the mid or average frequency. Similarly, the At defines two standard deviations in t units, with t, the mid or average period. A frequency-amplitude plot of the signal is also of Gaussian form. When relayed to a sound driver, these elementary signals are quite similar to the “tone pips” used by Davis, Fernandez and McAuliffe [15] and Goldstein [22], except that the tone pips reach maximum amplitude after a different number of cycles at different f,,s The elementary signals were led through a preamplifier to an ALTEC 808-8A driver which was connected by closed coupling to the auditory canal of the subjects (guinea pigs) anesthetized with Dial in urethane (0.25 cc/kg). The driver gave a linear frequency response up to and beyond 10 kHz. Sound pressure levels were measured with a Briiel and Kjaer 4144 condenser microphone and 2203 sound level meter. Differential electrodes-Teflon coated nichrome steel of 50 pm o.d.were implanted in the Scala vestibuli (SV) and Scala tympani (ST) of the first turn of the cochlea and at least one other turn. The potentials recorded, averaged, and displayed were thus the difference potentials (SV-ST) [ 19,20,30]. In effect, this method cancels the recording of action potentials of the auditory nerve which are negative at both electrodes, and leaves the CM which is in opposite phase in the SV and ST. All signal averaging was achieved with an ORTEC 4620. When recording from any one of the four cochlear turns of the guinea pig, a constant amplitude CM or SP response to all 10 elementary signals (with fOs ranging from 1 to 10 kHz) was maintained by increasing the intensity of these signals if necessary. Thus, it was possible to elicit a response from even the fourth cochlear turn to an elementary signal of fO= 10 kHz, due to the intensity of this signal, even although the fourth turn responds maximally to stimuli of low frequency (less than 500 Hz). As the CM is correlated with movements of the basilar membrane caused by a traveling wave in the cochlear fluids elicited by the stimulus, the results of this study are based on basilar membrane movements caused by a traveling wave which has peaked before the recording location. RESULTS
SUMMARY
At all cochlear turns the CM and SP displayed a temporal constancy which is not present when sinusoidal signals are used [Fig. 2(a) and (b)]. The temporal constancy is apparent from the result obtained from the following procedure: As the signal fO is increased the signal At is decreased (cf. Table 1). However, the CM together with SP distortion components display a lengthening of the temporal wavelength so that the CM and SP At is of constant length even though the signal At is decreased. [Cf. white line
INFORMATION
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PROCESSING IN THE COCHLEA
CM DIF
TURN
1
CM
DIF TURN3
20 uv
12.5MS
FIG. 2. (a) Representative samples of cochlear microphonic potentials elicited by elementary signals and recorded by the differential electrode technique from (i) turn 1 (5 mm from basal end) and (ii) turn 3 in the guinea pig cochlea. The white bar in each record refers to the duration of the signal (At) for ease of comparison with the recording, but does not refer to the time the signal was given. Notice that although the signal At progressively decreases at increasingly higher signal fg (stated in kHz in the left of each record), the CM response remains of approximately the same duration. Each record is the average of 60 responses. in Fig. 2(a) and (b), which this
change
constant.]
with
the
Furthermore,
the Aj components
decreases
duration
as the stimulus
of the
averaged
the CM waveshape of the signal
(t
octave
is changed.
response
is undistorted, around
which
Compare remains
indicating
that
the signal fe) are not
dispersed according to a Fourier-like analysis but are registered at the same place along the basilar membrane as signal fo. Although intense stimuli were used, the stapes volume velocity versus SPL decreases at a rate of only 6 db/octave-thus nonlinearities in the middle ear can hardly be mediating the effects reported here. The relation between the ratio of CM and SP amplitude to signal amplitude (A,/A,) in linear units and the ratio of CM wavelength to signal wavelength (W 0 = output). The trade indicated in Fig. 3 is mirrored in the relation of the wavelength ratio W,,/ Wi to the signal duration At (Fig. 4). Combining the results of Figs. 3 and 4, the relation of signal At to the amplitude ratio A,,/Ai (Fig. 5) is demonstrated to be linearly related to the midfrequency (fe) of the stimulus.
208
T. W. BARRETT SPDIF
TURN
1 80DB
2 N -m
12.5 MS FIG.
2.
(b) Representative
samples
of summating
potentials
recorded
by the differen-
tial electrode technique from turn 1 of the guinea pig cochlea and elicited by elementary signals modified so that the modulated component is non-phase-locked to the modulating envelope. The white bar in each photograph refers to the duration of the signal (At) for ease of comparison with the recording, but does not refer to the time the signal was given. Notice (i) that although the signal At progressively decreases at increasingly higher signal fos (stated in kHz at the left of each record) due to the relations defining an elementary signal, the SP response remains approximately of the same negative component of the SP (indicated by an arrow) reaches Each record is the average of 60 responses.
duration; (ii) that a fast a maximum at jr,= 5 kHz.
DISCUSSION As the lengthening of the stimulus temporal wavelength producing a constant response temporal wavelength occurred in all four turns [Fig. 2(a)(i) and (ii) shows two examples], the effect was not peculiar to an individual location in the cochlea, and was therefore equivalent to a lengthening of the spatial wavelength of the hydrodynamic traveling wave beyond the point of maximum amplitude, causing pressure changes in the cochlea with which the CM and SP are assumed correlated, i.e., change in CM At = W,,/ W, in Figs. 3 and 4. The trade of increasing wavelength for amplitude is a phenomenon well known in the study of the hydrodynamics of a wave on an increasing incline [31,32]. After the wave breaks, the wave amplitude decreases but the wavelength increases. The analogy is then made between waves traveling upon the surface of fluids on an increasing incline with interfacial pressures on a partition, i.e., the basilar membrane, which is of decreasing stiffness from base to apex in the cochlea.
INFORMATION
PROCESSING
IN THE COCHLEA
209
J+
1: 1
3-8
WJW, * ,1
2
s
10
FIG. 3. The response wavelength-change-amplitude-change trade. The data from IO cochleas are plotted. The ordinate is in arbitrary units and is the ratio of the peak-to-peak CM amplitude in PV (A,,) with respect to the linearized intensity of the elementary acoustical signal (Ai). The abscissa is the ratio of the duration (At) of the elicited CM ( W,) with respect to the duration (At) of the elementary signal ( Wi). The circled numbers at each point refer to the center frequency (f,,) of the elementary signal in kHz.
There is no maximum amplitude correlated with signal At at different cochlear turns (Fig. 3). On the other hand, there is a maximum negative SP correlated with signal f. [Fig. 2(b)]. The evidence indicates, therefore, that the wavelength At is registered in the cochlea in a different fashion from center frequency (fe) registration. The increasing wavelength-decreasing amplitude response trade (i.e., a response-response trade) is composed of two stimulus-response relations (Figs. 4 and 5). Since the temporal wavelength At for an elementary signal decreases as the midfrequencyf, increases (Table l), it might be suggested that the relations shown in Fig. 4 and 5 are possibly due to changes in signal midfrequency f0 and not in temporal duration At, to which midfrequency is related by the conditions for an elementary signal: Af At = foto = i. However, previous studies [30] using sinusoidal signals and the same recording methods used here do not report lengthening of the temporal (to) wavelength, nor have we observed this in our own control studies using sinusoidal signals. Therefore, as we report a frequency (fo) dependent negative SP maximum [Fig. 2(b)], the indication is that the trades demon-
210
T. W. BARRETT .L,CX.
200 US 10 KHZ 224
9
252
8
312
7
332
6
400
z
500
+ 4
4
5 2
664
3
1000
2
2000
1 TURN 1-• 23::
1
2
5
10
4-
FIG. 4. The relation between response wavelength change and stimulus Ar. The data are those plotted in Fig. 3. The abscissa is as in Fig. 3. The ordinate in psec indicates the elementary signal’s At. The ordinate in kHz indicates the elementary insignia refer to different turns of the guinea pig cochlea.
signal’s
j,,
The
strated in Figs. 3 and 4 of potential response amplitude and wavelength change are related to the signal At and not the signal_&,. The result of the present study using four-dimensional elementary signals is that at frequencies beyond the resonant frequency for a particular location in the cochlea, a lengthening of the CM and SP temporal wavelength occurs so that a minimum is always obtained of approximately 2 msec for an elementary signal, i.e., CM and SP At =2 msec. On the other hand, both the CM and SP elicited by sinusoids may have durations far less than this. The present result, together with the maximum sensitivity of the SP to the signal midfrequency f0 (Fig. 2), suggests a simplified scheme for the cochlea’s analysis, or reception of acoustical signals (Fig. 6). We shall now elaborate on this scheme. Dallos, Billone, Durrant, Wang and Raynor [ 171 have demonstrated that when the outer hair cells are destroyed by kanamycin, cochlear microphonics cease to follow the basilar membrane displacement but still respond to its motion. This result indicates that the outer hair cells respond to displacement and the inner hair cells to motion or velocity. Using an acoustical stimulus which separates motion components from displacement components, Zwislocki [34] demonstrated two interacting populations of auditory nerve fibers, one following the displacement and the other the velocity of the basilar membrane. Because of Dallos, Billone, Durrant, Wand and Raynor’s [17] result, it is probable that one process is associated with the
INFORMATION
PROCESSING IN THE COCHLEA
211
3
rz-
a0 34
I
FIG. 5. The relation between response amplitude change and stimulus Ar relation. The data are those plotted in Figs. 3 and 4. The abscissae and ordinate are explained in those figures. Each point is the average of ten cochleas.
outer, the other with the inner hair cells. Thus the CM appears to originate from both hair cell systems of the cochlea: the inner and the outer. The two hair cell systems are, however, affected by different stimulus conditions. Furthermore, a recent analysis of cochlear hair cell functioning assigns the inner hair cell system to the role of “phase sensitive” receptors [ 131: that is, these cells are maximally sensitive to a certain stimulus fe. It is significant that the inner hair cells, which do not touch the tectorial membrane, are presumed stimulated by viscous force. Recalling the surface wave analogy to interface wave phenomena: in the terms of the analogy, this inner hair cell system, sensitive to the joto product of the defining conditions of an elementary signal, disperses the frequency (f,) components of an acoustical signal according to the position along the basilar membrane where the wave breaks. At this point [Fig. 6(a)], the velocity of the cochlear fluid is near zero-an assumption also made in an earlier analysis by Peterson and Bogert [26] [Fig.6(d)]. On the other hand, the outer hair cells are presumed stimulated by shear force in Billone and Raynor’s [ 131 analysis. Again in the surface wave analogy to the interface wave phenomena present in the cochlea: the outer hair cell system, sensitive to the AfAt product of the defining conditions of an elementary signal, registers the effect of a hydrodynamic trade between a decreasing intensity and increasing wavelength [Fig. 6(b)]. Both the effects represented in Fig. 6(a) and (b) are elicited by an elementary signal [whereas a sinusoidal signal elicits predominately the
T. W. BARRETT
212 @
f, t,- Longltud~nal Shear-
@I af
.At
Radial Shear-
Inner Hair Cell System
Ou’ter Hair Cell
@
Relatlon
between
k?
Relation
between Veloclti and Basilar Posltlon for Con&ant fO,
v
t
500
Y
Wavelength I,
and
System
Velocity
)ti’ : j\\
Membrane
-
Propagam”
~- ~~ a+renuo+ion
FIG. 6. (a) Theoretical amplitude of basilar membrane displacement elicited by the for,, dimensions of an elementary signal which has a maximum at a certain place along the basilar membrane where the velocity V of the traveling wave has a minimum. The changes m this velocity are indicated by the size of the lettering. This displacement of the basilar membrane is presumed to be in the longitudinal direction and excites the inner hair cell system. (b) Theoretical amplitude of basilar membrane displacement elicited by the Af At dimensions
of an elementary
signal,
i.e., Af= f octave
around
the center
frequency
f.
Changes in the wavelength W of the traveling wave are indicated by the size of the lettering. This displacement of the basilar membrane is presumed to be in the radial direction and excites the outer hair cell system. (c) The hydrodynamic relation of wavelength and velocity. (d) The relation between traveling wave velocity and position along the basilar membrane.
effect illustrated in 6(a)], and both are mediated by the velocity-wavelength relation [Fig. 6(c)] well known in the study of hydrodynamic phenomena [25]. To the left of the line joining the centers of the figures the graph describes capillary waves, i.e., the wavelength is increasing as the velocity is decreasing. To the right of this line the graph describes gravity waves, i.e.,
INFORMATION
PROCESSING
IN THE COCHLEA
213
after the point of maximum registration of the fat,, condition, the velocity increases and the wavelength also increases. The changes in CM and SP reported here are considered to be the result of gravity waves rather than capillary waves, as recordings were made beyond the location of maximum frequency response where wave velocity is zero. We shall now examine another interpretation of cochlear function. The hypothesis here is that the source of the CM is both the inner and outer hair cells. This opinion is at variance with the view that the production of the normal CM is dominated by the outer hair cells [16]. The latter view is based on the observation that the normal CM response to a triangular wave stapes displacement-which results in a square or rectangular wave change in pressure at the oval window-is also a rectangular wave [17]. A further observation is that if, in the region of the recording electrodes, the outer hair cells are destroyed by kanamycin treatment, the inner hair cell dominated CM approximates the derivative of the rectangular wave change in pressure at the oval window. It is, however, possible to offer another interpretation of these data. The input to the cochlea is a rectangular wave change in pressure at the stapes. If, as I suggest, the inner hair cells mediate the response to the midfrequencyf, of the stimulus, then in the basal turn in which the outer hair cells are destroyed, the response should be similar to that of a narrow high frequency bandpass filter in response to a long duration rectangular wave (about 6 msec duration in [17]). This has been demonstrated [17]. But the CM response to this same stimulus recorded from the third or fourth turn, i.e., a turn with low frequency resonance response, should be different. The analogy in this instance is that the bandpass is widened and the inner hair cell response should be greater. This has not been demonstrated, because the majority of the outer hair cells in the third turn of the kanamycin treated animals were not destroyed [17]. My point is thus that the interpretation under discussion [16] concerning the relative contribution of the outer and inner hair cells to the CM production is based on the response of the inner hair cells of the high frequency basal turn to a long duration rectangular wave stimulus. If the duration of the stimulus were shortened, or the position of the recording electrodes changed (assuming outer hair cells could be substantially destroyed in other turns), then the relative contribution of the inner hair cells to CM production should increase. Furthermore, the CM response (elicited by rectangular change in pressure at the stapes) is not identical to that recorded from the normal first turn (cf. [17], Fig. 2). Thus there exists the possibility that the production of the CM in the normal cochlea is based on multiplicative effects from both the inner and outer hair cells. It is also known that in the kanamycin treated animal the threshold for eliciting CM is 30-40 db higher than in the normal animal [18, note 11. This may be interpreted to indicated that the inner hair cells of the kanamycin
214
T. W. BARRETT
treated animal or normal are 30-40 db less sensitive than outer hair cells-if the production of the CM of the normal animal is dominated by the outer hair cells. However, this interpretation is only possible if one presupposes that the normal cochlea is, in fact, dominated by the outer hair cells. If the CM is the result of both inner and outer hair cell activity in the manner of a recruitment effect from both types of hair cells involved in the production of the CM-a mechanism long known in nerve axon physiology-then the 30-40 db decrease in sensitivity of the kanamycin treated cochlea may be interpreted as due to the withdrawal of the contribution from the outer hair cells to the overall recruitment process leading to CM production. The essence of this reinterpretation is that (i) one may not base conclusions concerning the whole cochlea on the response of the basal turn to a long duration stimulus, and (ii) the production of the CM may not be based on the addition of contributions from inner and outer hair cells, but on their multiplication. Finally, it is necessary to contrast the results obtained with sinusoidal signals with those obtained here using elementary signals. If a sinusoidal signal is used which is of a lower frequency than the CM frequencies generally recorded undistorted from a particular turn in the cochlea, and if one considers the cochlea to be a distributed low pass filter, one should expect such a low frequency signal to be recorded without lengthening of the wavelength ratio W,/ Wi. However, Fig. 2(a)(i) shows sample recordings in the first turn (5 mm from the round window) which demonstrate lengthening of the W,,/ Wi ratio for elementary signals of f,=2-10 kHz. On the assumption that the cochlea is a distributed low pass filter for all signals whether sinusoidal or elementary, one should expect no increase in the W,/ Wi ratio for these fes in the first turn. This is because undistorted CMs may be recorded from the first turn for (sinusoidal) frequencies at least as high as 8 kHz. Thus, it might be concluded that the present results, which show lengthening of the W,,/ Wi ratio, are in doubt, as any results obtained using elementary signals must comply with the mechanoelastic properties of the cochlea which were established using sinusoidal signals. This objection, however, misses the point we are stressing, namely, that the mechanoelastic properties of the cochlea brought into use when an elementary signal is used are not the same as those brought into use by a sinusoidal signal. If a sinusoidal signal produces a predominately longitudinal shear force in the cochlea and an elementary signal produces both a longitudinal and radial shear force, then the total force due to each signal (which may be the same) is transduced quite differently in the two cases. Let us suppose a hydrodynamic system which produces longitudinal waves in response to the& and t, parameters of a signal, and torque waves due to
INFORMATION
PROCESSING IN THE COCHLEA
215
the Af and At parameters of a signal. The primary eliciting stimulus for the torque waves we shall assume to be the differential of the amplitude modulating component of the carrier frequency (see Fig. 1). In such a system (which we are not suggesting exists in the cochlea), the response to an elementary signal is quite different from that to a signal consisting of the superposition of frequencies within the bandwidth of the elementary signal (An. Here, then, is a hypothetical case in which the impulse response of a system changes when the stimulus parameters change. The main point I am making, therefore, is that there are four parameters to any acoustical signal [8, Ill, and I suggest that the cochlear response to any signal is unique with respect to the forces defined by those parameters. This uniqueness makes the use of elementary signals in cochlear research most appropriate. A four-dimensional analysis of cochlear information processing ability, therefore, utilizes the availability of two types of hair cells to explain cochlear functioning. The analysis performed on such signals is not only a Fourier analysis of the signalf,, but a secondary and orthogonal analysis of the signal Aft together with temporal analyses of the At and t,, signal parameters. CONCLUSION The CM and SP responses, recorded at locations beyond the point of maximum frequency response and elicited by high intensity elementary signals, are of similar shape and duration even when the stimulus dimensions are changed in a compensated way, thus exhibiting a constant response to constant informational relations. The constant CM temporal response indicates a hydrodynamic wavelength-intensity trade in cochlear fluid movement. In amplitude, the negative SP response is spatially distributed with respect to the components of the applied signal. The results of this study provide support for a model of cochlear functioning based on cochlear hydrodynamics and the two hair cell systems of the cochlea. REFERENCES 1 T. W. Barrett, The information content of an electromagnetic field with relevance to the sensory processing of information, T.-I.-T. J. Life Sci. 1, 129-135 (1971). 2 T. W. Barrett, The response of auditory cortex neurons in cat to various parameters of auditory stimulation, Brain Res. 28, 579-581 (1971). 3 T. W. Barrett, On vibrating strings and information theory, J. Sound and Vib. 20, 407412 (1972). 4 T. W. Barrett, The multiple use of the auditory cortex: interaction at a single point, Exp. Neurol. 34, 1-15 (1972). 5 T. W. Barrett, Interaural stimulation: effects on the Q value of tuning curves and post-stimulus time histograms of cat auditory cortex neurons, Exp. Neural. 34, 4gU96 (1972).
216 6
7
T. W. BARRETT T. W. Barrett, Uncertainty relations in interaural parameters of acoustical stimulation: an evoked potential study of the auditory cortex in the anesthetized cat, B&au. Biol. 8, 299-323 (1973). T. W. Barrett, Information processing in the inferior colliculus of cat using high frequency acoustical stimulation and direct electrical stimulation of the osseous spiral
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laminae, Behao. Biol. 9, 189-219 (1973). T. W. Barrett, Structural information theory, J. Acousr. Sot. Am. 54, 1092-1098 (1973). T. W. Barrett, Comparing the efficiency of sensory systems: a biophysical approach, J. Biol. Phys. 1, 175-192 (1973). T. W. Barrett, Neural information processing in the medial superior olive, 86th
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meeting of the Acoustical Society of America, 1973. T. W. Barrett, Four parameters of information processing
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in the cochlea,
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L. Brillouin, Science and information Theory, 2nd ed., McGraw-Hill, H. Davis, C. Fernandez and D. R. McAuliffe, The excitatory
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cochlea, Proc. Naf. Acad. Sci. 36, 586587 (1950). P. Dallos, Cochlear potentials and cochlear mechanics,
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Experientia
30, 1287-1288 (1974). T. W. Barrett, Information processing in the cochlea, Acustica, 33, 102-l 15. M. Billone and S. Raynor, Transmission of radial shear forces to cochlear hair cells, J. Acoust. Sot. Am. 54, 1143-1156 (1973).
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in
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P. Dallos, M. A. Cheatham and J. Ferraro, Cochlear mechanics, nonlinearities, and cochlear potentials, J. Acoust. Sot. Am. 55, 597605 (1974). P. Dallos, Z. G. Schoeny and M. A. Cheatham, Cochlear summating potentials,
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Science 170, 641-644 (1970). P. Dallos, Z. G. Schoeny and
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descriptive aspects, Acta Oto-Latyngol. Suppl. 302, 146 (1972). D. Gabor, Theory of communication, J. I. E. E. 93, 429-457 (1946). R. Goldstein, Analysis of summating potentials in cochlear responses,
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178, 331-337 (1954). A. A. Kharkevich, Spectra and Analysis, Consultants Bur., New York, 1960. W. E. Koch, On the principle of uncertainty of sound, J. Acoust. Sot. Am. 7, 56-58
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31
The analogy
J. Tonndorf,
surf on sloping
beaches
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fluid motion
and its significance
within
the cochlea
for the mechanism
and formation
of cochlear
of
stimula-
33
tion, Ann. Otol. Rhinol. Laryngol. 65, 498-506 (1956). J. Tonndorf, Cochlear mechanics and hydrodynamics, in Foundations of Modern Audiroy Theory (J. V. Tobias, ed.), Vol. 2, Academic, New York, 1970, pp. 205-254. A. R. Tunturi, Analysis of cortical auditory responses with the probability pulse, Am.
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J. Physiol. 181, 63&638 (1955). J. J. Zwislocki, Cochlear waves:
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Acoust.
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between
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experiments,
J.
Relevant
Signals in the Cochlea
T. W. BARRETT Department of Physiology and Biophysics, Universiv of Tennessee Center for the Health Sciences 894 Union Avenue, Memphis, Tennessee 38163
Communicated by Aage R. Mdller
ABSTRACT The cochlear microphonic potential (CM) and summating potential (SP) response, recorded at locations beyond the point of maximum frequency response and elicited by high intensity elementary acoustical signals with AfAt =f,t,= $, (where Af is signal bandwidth, At is signal duration, fO is signal midfrequency, to is signal midperiod), are of similar shape and duration even when the stimulus dimensions are changed in a compensated way, thus exhibiting a constant response to constant informational relations. The constant CM and SP temporal response indicates that at locations beyond the point of maximum frequency response, a hydrodynamic wavelength-intensity trade in cochlear fluid movement occurs. In amplitude, the negative SP response is spatially distributed with respect to the components of the applied signal. The results of this study provide support for a model of cochlear functioning based on cochlear hydrodynamics and the two hair cell systems of the cochlea.
INTRODUCTION The smallest signal used in visual physiology is the photon. In auditory physiology the smallest signal-or elementary signal-is the logon, an elementary signal or structural “quantum” of information measurement, defined by [l, 14,21,23,24,28]:
AfAt=;,
(1)
where Af is the “effective” signal bandwidth in units of cycles and At is the “effective” signal duration in units of seconds. The requirements for Eq. (1) may be obtained in the time and frequency domains by the following definitions: ~(t)=~-C’(‘--I0)‘~i2nfd, (2) S (f) = e -(n/c)Y-f~Y,-i2nrofe MATHEMATICAL
BIOSCIENCES
29,203-217
(1916)
0 American Elsevier Publishing Company, Inc., 1976
203
T. W. BARRETT
204
To define an elementary signal unambiguously, another bounding condition is called for [ 1,3,8,9], which defines the constant c in (2) as equal to unity, i.e.:
where f. is the signal midfrequency in units of cycles/second or hertz, and t, is the signal midperiod in units of seconds/cycle. An elementary signal defined, then, by the bounding conditions of (1) and (3) is of the form shown in Fig. 1. Given a variable time base, the signal always appears in the form of Fig. 1 at any fo, i.e., with the same number of nodal points, due to the compensatory arrangements defined in (1) and (3). Such a signal is informationally relevant in that it represents the minimum signal, “worth” one “bit” in Shannon’s [29] sense. In other words, such a signal could be used to resolve uncertainty concerning a dichotomous outcome and is the minimum such signal. However, this analysis is concerned with information structure and not with the Shannon theory, which is related but distinct [3,8,9]. We have used such acoustical signals in studies of the auditory cortex [2,4,5,6], inferior colliculus [7] and medial superior olive [lo]. In the present study of the cochlear microphonic potential (CM) and summating potential (SP), the appropriateness of the use of such signals in a description of the auditory pathway is further demonstrated.
FIG. 1. a variable
Elementary
signal defined
by the bounding
conditions:
time base, the signal is of this form at different
fos.
AjAt =f&,=
I. Given
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In this examination of cochlear potentials, high intensity elementary signals were used so that all four turns of the guinea pig cochlea could be investigated with a wide range of midfrequencies Jo Thus, the cochlear potentials recorded are from locations mainly beyond the point in the cochlea which maximally responds to the midfrequency used. The use of high intensity stimuli to elicit responses from cochlear locations at frequencies not near the resonating frequency for those locations provides an insight into the total cochlear response. Not all the recordings made in these experiments are within the linear range for recording the CM (cf. [18]). However, it should be emphasized that nonlinearity is not synonymous with indeterminism. It is probably the mechanism producing the nonlinearity observed with sinusoidal stimuli which provides the result reported in this paper, i.e., stimulus wavelength lengthening observed when high intensity elementary signals are used. Thus the observations reported here are not at variance with a nonlinear cochlear response demonstrated using sinusoidal signals of frequency range above the best frequencies for the electrode location. The main empirical results of this study have been described in detail [ 11,121. The present paper addresses the conclusions which may be drawn from the empirical findings concerning the total cochlear response. METHODS
F’MMARY
Elementary signals were generated by passing a rectangular wave of duration t, through a bandpass filter set at one-half octave around the midfrequency _/a such that joto= $ [33]. The appropriate Aj and At are also obtained
thereby,
i.e., AfAt = i (see Table
TABLE
Band @Hz) 0.875-1.125 1.750-2.250 2.265-3.375 3.500-4.500 4.375-5.625 5.250-6.750 6.125-7.875 7.000-9.000 7.875-10.125 8.75&l 1.250
*Each elementary
Bandwidth
Aj
(cycles) 250 500 750 1250 1500 1750 2000 2250 2500
signal satisfied
l), as the amplitude
modulation
la
Midfrequencyfe
Duration
A.t
Mid-duration
@Hz)
( psec)
( psec)
1 2 3 4 5 6 7 8 9 10
2000 1000 664 500 400 332 312 252 224 200
500 250 166 125 100 83 78 63 56 50
the two equations:
AjAt = f and for,,= i.
re
T. W. BARRETT
206
due to the nonideal cutoff characteristics of the filter approach a Gaussian waveshape (e --(‘--1~2) at a one-half octave setting around the f. The Af defines two standard deviations in f units, with f. the mid or average frequency. Similarly, the At defines two standard deviations in t units, with t, the mid or average period. A frequency-amplitude plot of the signal is also of Gaussian form. When relayed to a sound driver, these elementary signals are quite similar to the “tone pips” used by Davis, Fernandez and McAuliffe [15] and Goldstein [22], except that the tone pips reach maximum amplitude after a different number of cycles at different f,,s The elementary signals were led through a preamplifier to an ALTEC 808-8A driver which was connected by closed coupling to the auditory canal of the subjects (guinea pigs) anesthetized with Dial in urethane (0.25 cc/kg). The driver gave a linear frequency response up to and beyond 10 kHz. Sound pressure levels were measured with a Briiel and Kjaer 4144 condenser microphone and 2203 sound level meter. Differential electrodes-Teflon coated nichrome steel of 50 pm o.d.were implanted in the Scala vestibuli (SV) and Scala tympani (ST) of the first turn of the cochlea and at least one other turn. The potentials recorded, averaged, and displayed were thus the difference potentials (SV-ST) [ 19,20,30]. In effect, this method cancels the recording of action potentials of the auditory nerve which are negative at both electrodes, and leaves the CM which is in opposite phase in the SV and ST. All signal averaging was achieved with an ORTEC 4620. When recording from any one of the four cochlear turns of the guinea pig, a constant amplitude CM or SP response to all 10 elementary signals (with fOs ranging from 1 to 10 kHz) was maintained by increasing the intensity of these signals if necessary. Thus, it was possible to elicit a response from even the fourth cochlear turn to an elementary signal of fO= 10 kHz, due to the intensity of this signal, even although the fourth turn responds maximally to stimuli of low frequency (less than 500 Hz). As the CM is correlated with movements of the basilar membrane caused by a traveling wave in the cochlear fluids elicited by the stimulus, the results of this study are based on basilar membrane movements caused by a traveling wave which has peaked before the recording location. RESULTS
SUMMARY
At all cochlear turns the CM and SP displayed a temporal constancy which is not present when sinusoidal signals are used [Fig. 2(a) and (b)]. The temporal constancy is apparent from the result obtained from the following procedure: As the signal fO is increased the signal At is decreased (cf. Table 1). However, the CM together with SP distortion components display a lengthening of the temporal wavelength so that the CM and SP At is of constant length even though the signal At is decreased. [Cf. white line
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CM DIF
TURN
1
CM
DIF TURN3
20 uv
12.5MS
FIG. 2. (a) Representative samples of cochlear microphonic potentials elicited by elementary signals and recorded by the differential electrode technique from (i) turn 1 (5 mm from basal end) and (ii) turn 3 in the guinea pig cochlea. The white bar in each record refers to the duration of the signal (At) for ease of comparison with the recording, but does not refer to the time the signal was given. Notice that although the signal At progressively decreases at increasingly higher signal fg (stated in kHz in the left of each record), the CM response remains of approximately the same duration. Each record is the average of 60 responses. in Fig. 2(a) and (b), which this
change
constant.]
with
the
Furthermore,
the Aj components
decreases
duration
as the stimulus
of the
averaged
the CM waveshape of the signal
(t
octave
is changed.
response
is undistorted, around
which
Compare remains
indicating
that
the signal fe) are not
dispersed according to a Fourier-like analysis but are registered at the same place along the basilar membrane as signal fo. Although intense stimuli were used, the stapes volume velocity versus SPL decreases at a rate of only 6 db/octave-thus nonlinearities in the middle ear can hardly be mediating the effects reported here. The relation between the ratio of CM and SP amplitude to signal amplitude (A,/A,) in linear units and the ratio of CM wavelength to signal wavelength (W 0 = output). The trade indicated in Fig. 3 is mirrored in the relation of the wavelength ratio W,,/ Wi to the signal duration At (Fig. 4). Combining the results of Figs. 3 and 4, the relation of signal At to the amplitude ratio A,,/Ai (Fig. 5) is demonstrated to be linearly related to the midfrequency (fe) of the stimulus.
208
T. W. BARRETT SPDIF
TURN
1 80DB
2 N -m
12.5 MS FIG.
2.
(b) Representative
samples
of summating
potentials
recorded
by the differen-
tial electrode technique from turn 1 of the guinea pig cochlea and elicited by elementary signals modified so that the modulated component is non-phase-locked to the modulating envelope. The white bar in each photograph refers to the duration of the signal (At) for ease of comparison with the recording, but does not refer to the time the signal was given. Notice (i) that although the signal At progressively decreases at increasingly higher signal fos (stated in kHz at the left of each record) due to the relations defining an elementary signal, the SP response remains approximately of the same negative component of the SP (indicated by an arrow) reaches Each record is the average of 60 responses.
duration; (ii) that a fast a maximum at jr,= 5 kHz.
DISCUSSION As the lengthening of the stimulus temporal wavelength producing a constant response temporal wavelength occurred in all four turns [Fig. 2(a)(i) and (ii) shows two examples], the effect was not peculiar to an individual location in the cochlea, and was therefore equivalent to a lengthening of the spatial wavelength of the hydrodynamic traveling wave beyond the point of maximum amplitude, causing pressure changes in the cochlea with which the CM and SP are assumed correlated, i.e., change in CM At = W,,/ W, in Figs. 3 and 4. The trade of increasing wavelength for amplitude is a phenomenon well known in the study of the hydrodynamics of a wave on an increasing incline [31,32]. After the wave breaks, the wave amplitude decreases but the wavelength increases. The analogy is then made between waves traveling upon the surface of fluids on an increasing incline with interfacial pressures on a partition, i.e., the basilar membrane, which is of decreasing stiffness from base to apex in the cochlea.
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J+
1: 1
3-8
WJW, * ,1
2
s
10
FIG. 3. The response wavelength-change-amplitude-change trade. The data from IO cochleas are plotted. The ordinate is in arbitrary units and is the ratio of the peak-to-peak CM amplitude in PV (A,,) with respect to the linearized intensity of the elementary acoustical signal (Ai). The abscissa is the ratio of the duration (At) of the elicited CM ( W,) with respect to the duration (At) of the elementary signal ( Wi). The circled numbers at each point refer to the center frequency (f,,) of the elementary signal in kHz.
There is no maximum amplitude correlated with signal At at different cochlear turns (Fig. 3). On the other hand, there is a maximum negative SP correlated with signal f. [Fig. 2(b)]. The evidence indicates, therefore, that the wavelength At is registered in the cochlea in a different fashion from center frequency (fe) registration. The increasing wavelength-decreasing amplitude response trade (i.e., a response-response trade) is composed of two stimulus-response relations (Figs. 4 and 5). Since the temporal wavelength At for an elementary signal decreases as the midfrequencyf, increases (Table l), it might be suggested that the relations shown in Fig. 4 and 5 are possibly due to changes in signal midfrequency f0 and not in temporal duration At, to which midfrequency is related by the conditions for an elementary signal: Af At = foto = i. However, previous studies [30] using sinusoidal signals and the same recording methods used here do not report lengthening of the temporal (to) wavelength, nor have we observed this in our own control studies using sinusoidal signals. Therefore, as we report a frequency (fo) dependent negative SP maximum [Fig. 2(b)], the indication is that the trades demon-
210
T. W. BARRETT .L,CX.
200 US 10 KHZ 224
9
252
8
312
7
332
6
400
z
500
+ 4
4
5 2
664
3
1000
2
2000
1 TURN 1-• 23::
1
2
5
10
4-
FIG. 4. The relation between response wavelength change and stimulus Ar. The data are those plotted in Fig. 3. The abscissa is as in Fig. 3. The ordinate in psec indicates the elementary signal’s At. The ordinate in kHz indicates the elementary insignia refer to different turns of the guinea pig cochlea.
signal’s
j,,
The
strated in Figs. 3 and 4 of potential response amplitude and wavelength change are related to the signal At and not the signal_&,. The result of the present study using four-dimensional elementary signals is that at frequencies beyond the resonant frequency for a particular location in the cochlea, a lengthening of the CM and SP temporal wavelength occurs so that a minimum is always obtained of approximately 2 msec for an elementary signal, i.e., CM and SP At =2 msec. On the other hand, both the CM and SP elicited by sinusoids may have durations far less than this. The present result, together with the maximum sensitivity of the SP to the signal midfrequency f0 (Fig. 2), suggests a simplified scheme for the cochlea’s analysis, or reception of acoustical signals (Fig. 6). We shall now elaborate on this scheme. Dallos, Billone, Durrant, Wang and Raynor [ 171 have demonstrated that when the outer hair cells are destroyed by kanamycin, cochlear microphonics cease to follow the basilar membrane displacement but still respond to its motion. This result indicates that the outer hair cells respond to displacement and the inner hair cells to motion or velocity. Using an acoustical stimulus which separates motion components from displacement components, Zwislocki [34] demonstrated two interacting populations of auditory nerve fibers, one following the displacement and the other the velocity of the basilar membrane. Because of Dallos, Billone, Durrant, Wand and Raynor’s [17] result, it is probable that one process is associated with the
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3
rz-
a0 34
I
FIG. 5. The relation between response amplitude change and stimulus Ar relation. The data are those plotted in Figs. 3 and 4. The abscissae and ordinate are explained in those figures. Each point is the average of ten cochleas.
outer, the other with the inner hair cells. Thus the CM appears to originate from both hair cell systems of the cochlea: the inner and the outer. The two hair cell systems are, however, affected by different stimulus conditions. Furthermore, a recent analysis of cochlear hair cell functioning assigns the inner hair cell system to the role of “phase sensitive” receptors [ 131: that is, these cells are maximally sensitive to a certain stimulus fe. It is significant that the inner hair cells, which do not touch the tectorial membrane, are presumed stimulated by viscous force. Recalling the surface wave analogy to interface wave phenomena: in the terms of the analogy, this inner hair cell system, sensitive to the joto product of the defining conditions of an elementary signal, disperses the frequency (f,) components of an acoustical signal according to the position along the basilar membrane where the wave breaks. At this point [Fig. 6(a)], the velocity of the cochlear fluid is near zero-an assumption also made in an earlier analysis by Peterson and Bogert [26] [Fig.6(d)]. On the other hand, the outer hair cells are presumed stimulated by shear force in Billone and Raynor’s [ 131 analysis. Again in the surface wave analogy to the interface wave phenomena present in the cochlea: the outer hair cell system, sensitive to the AfAt product of the defining conditions of an elementary signal, registers the effect of a hydrodynamic trade between a decreasing intensity and increasing wavelength [Fig. 6(b)]. Both the effects represented in Fig. 6(a) and (b) are elicited by an elementary signal [whereas a sinusoidal signal elicits predominately the
T. W. BARRETT
212 @
f, t,- Longltud~nal Shear-
@I af
.At
Radial Shear-
Inner Hair Cell System
Ou’ter Hair Cell
@
Relatlon
between
k?
Relation
between Veloclti and Basilar Posltlon for Con&ant fO,
v
t
500
Y
Wavelength I,
and
System
Velocity
)ti’ : j\\
Membrane
-
Propagam”
~- ~~ a+renuo+ion
FIG. 6. (a) Theoretical amplitude of basilar membrane displacement elicited by the for,, dimensions of an elementary signal which has a maximum at a certain place along the basilar membrane where the velocity V of the traveling wave has a minimum. The changes m this velocity are indicated by the size of the lettering. This displacement of the basilar membrane is presumed to be in the longitudinal direction and excites the inner hair cell system. (b) Theoretical amplitude of basilar membrane displacement elicited by the Af At dimensions
of an elementary
signal,
i.e., Af= f octave
around
the center
frequency
f.
Changes in the wavelength W of the traveling wave are indicated by the size of the lettering. This displacement of the basilar membrane is presumed to be in the radial direction and excites the outer hair cell system. (c) The hydrodynamic relation of wavelength and velocity. (d) The relation between traveling wave velocity and position along the basilar membrane.
effect illustrated in 6(a)], and both are mediated by the velocity-wavelength relation [Fig. 6(c)] well known in the study of hydrodynamic phenomena [25]. To the left of the line joining the centers of the figures the graph describes capillary waves, i.e., the wavelength is increasing as the velocity is decreasing. To the right of this line the graph describes gravity waves, i.e.,
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after the point of maximum registration of the fat,, condition, the velocity increases and the wavelength also increases. The changes in CM and SP reported here are considered to be the result of gravity waves rather than capillary waves, as recordings were made beyond the location of maximum frequency response where wave velocity is zero. We shall now examine another interpretation of cochlear function. The hypothesis here is that the source of the CM is both the inner and outer hair cells. This opinion is at variance with the view that the production of the normal CM is dominated by the outer hair cells [16]. The latter view is based on the observation that the normal CM response to a triangular wave stapes displacement-which results in a square or rectangular wave change in pressure at the oval window-is also a rectangular wave [17]. A further observation is that if, in the region of the recording electrodes, the outer hair cells are destroyed by kanamycin treatment, the inner hair cell dominated CM approximates the derivative of the rectangular wave change in pressure at the oval window. It is, however, possible to offer another interpretation of these data. The input to the cochlea is a rectangular wave change in pressure at the stapes. If, as I suggest, the inner hair cells mediate the response to the midfrequencyf, of the stimulus, then in the basal turn in which the outer hair cells are destroyed, the response should be similar to that of a narrow high frequency bandpass filter in response to a long duration rectangular wave (about 6 msec duration in [17]). This has been demonstrated [17]. But the CM response to this same stimulus recorded from the third or fourth turn, i.e., a turn with low frequency resonance response, should be different. The analogy in this instance is that the bandpass is widened and the inner hair cell response should be greater. This has not been demonstrated, because the majority of the outer hair cells in the third turn of the kanamycin treated animals were not destroyed [17]. My point is thus that the interpretation under discussion [16] concerning the relative contribution of the outer and inner hair cells to the CM production is based on the response of the inner hair cells of the high frequency basal turn to a long duration rectangular wave stimulus. If the duration of the stimulus were shortened, or the position of the recording electrodes changed (assuming outer hair cells could be substantially destroyed in other turns), then the relative contribution of the inner hair cells to CM production should increase. Furthermore, the CM response (elicited by rectangular change in pressure at the stapes) is not identical to that recorded from the normal first turn (cf. [17], Fig. 2). Thus there exists the possibility that the production of the CM in the normal cochlea is based on multiplicative effects from both the inner and outer hair cells. It is also known that in the kanamycin treated animal the threshold for eliciting CM is 30-40 db higher than in the normal animal [18, note 11. This may be interpreted to indicated that the inner hair cells of the kanamycin
214
T. W. BARRETT
treated animal or normal are 30-40 db less sensitive than outer hair cells-if the production of the CM of the normal animal is dominated by the outer hair cells. However, this interpretation is only possible if one presupposes that the normal cochlea is, in fact, dominated by the outer hair cells. If the CM is the result of both inner and outer hair cell activity in the manner of a recruitment effect from both types of hair cells involved in the production of the CM-a mechanism long known in nerve axon physiology-then the 30-40 db decrease in sensitivity of the kanamycin treated cochlea may be interpreted as due to the withdrawal of the contribution from the outer hair cells to the overall recruitment process leading to CM production. The essence of this reinterpretation is that (i) one may not base conclusions concerning the whole cochlea on the response of the basal turn to a long duration stimulus, and (ii) the production of the CM may not be based on the addition of contributions from inner and outer hair cells, but on their multiplication. Finally, it is necessary to contrast the results obtained with sinusoidal signals with those obtained here using elementary signals. If a sinusoidal signal is used which is of a lower frequency than the CM frequencies generally recorded undistorted from a particular turn in the cochlea, and if one considers the cochlea to be a distributed low pass filter, one should expect such a low frequency signal to be recorded without lengthening of the wavelength ratio W,/ Wi. However, Fig. 2(a)(i) shows sample recordings in the first turn (5 mm from the round window) which demonstrate lengthening of the W,,/ Wi ratio for elementary signals of f,=2-10 kHz. On the assumption that the cochlea is a distributed low pass filter for all signals whether sinusoidal or elementary, one should expect no increase in the W,/ Wi ratio for these fes in the first turn. This is because undistorted CMs may be recorded from the first turn for (sinusoidal) frequencies at least as high as 8 kHz. Thus, it might be concluded that the present results, which show lengthening of the W,,/ Wi ratio, are in doubt, as any results obtained using elementary signals must comply with the mechanoelastic properties of the cochlea which were established using sinusoidal signals. This objection, however, misses the point we are stressing, namely, that the mechanoelastic properties of the cochlea brought into use when an elementary signal is used are not the same as those brought into use by a sinusoidal signal. If a sinusoidal signal produces a predominately longitudinal shear force in the cochlea and an elementary signal produces both a longitudinal and radial shear force, then the total force due to each signal (which may be the same) is transduced quite differently in the two cases. Let us suppose a hydrodynamic system which produces longitudinal waves in response to the& and t, parameters of a signal, and torque waves due to
INFORMATION
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215
the Af and At parameters of a signal. The primary eliciting stimulus for the torque waves we shall assume to be the differential of the amplitude modulating component of the carrier frequency (see Fig. 1). In such a system (which we are not suggesting exists in the cochlea), the response to an elementary signal is quite different from that to a signal consisting of the superposition of frequencies within the bandwidth of the elementary signal (An. Here, then, is a hypothetical case in which the impulse response of a system changes when the stimulus parameters change. The main point I am making, therefore, is that there are four parameters to any acoustical signal [8, Ill, and I suggest that the cochlear response to any signal is unique with respect to the forces defined by those parameters. This uniqueness makes the use of elementary signals in cochlear research most appropriate. A four-dimensional analysis of cochlear information processing ability, therefore, utilizes the availability of two types of hair cells to explain cochlear functioning. The analysis performed on such signals is not only a Fourier analysis of the signalf,, but a secondary and orthogonal analysis of the signal Aft together with temporal analyses of the At and t,, signal parameters. CONCLUSION The CM and SP responses, recorded at locations beyond the point of maximum frequency response and elicited by high intensity elementary signals, are of similar shape and duration even when the stimulus dimensions are changed in a compensated way, thus exhibiting a constant response to constant informational relations. The constant CM temporal response indicates a hydrodynamic wavelength-intensity trade in cochlear fluid movement. In amplitude, the negative SP response is spatially distributed with respect to the components of the applied signal. The results of this study provide support for a model of cochlear functioning based on cochlear hydrodynamics and the two hair cell systems of the cochlea. REFERENCES 1 T. W. Barrett, The information content of an electromagnetic field with relevance to the sensory processing of information, T.-I.-T. J. Life Sci. 1, 129-135 (1971). 2 T. W. Barrett, The response of auditory cortex neurons in cat to various parameters of auditory stimulation, Brain Res. 28, 579-581 (1971). 3 T. W. Barrett, On vibrating strings and information theory, J. Sound and Vib. 20, 407412 (1972). 4 T. W. Barrett, The multiple use of the auditory cortex: interaction at a single point, Exp. Neurol. 34, 1-15 (1972). 5 T. W. Barrett, Interaural stimulation: effects on the Q value of tuning curves and post-stimulus time histograms of cat auditory cortex neurons, Exp. Neural. 34, 4gU96 (1972).
216 6
7
T. W. BARRETT T. W. Barrett, Uncertainty relations in interaural parameters of acoustical stimulation: an evoked potential study of the auditory cortex in the anesthetized cat, B&au. Biol. 8, 299-323 (1973). T. W. Barrett, Information processing in the inferior colliculus of cat using high frequency acoustical stimulation and direct electrical stimulation of the osseous spiral
10
laminae, Behao. Biol. 9, 189-219 (1973). T. W. Barrett, Structural information theory, J. Acousr. Sot. Am. 54, 1092-1098 (1973). T. W. Barrett, Comparing the efficiency of sensory systems: a biophysical approach, J. Biol. Phys. 1, 175-192 (1973). T. W. Barrett, Neural information processing in the medial superior olive, 86th
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meeting of the Acoustical Society of America, 1973. T. W. Barrett, Four parameters of information processing
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in the cochlea,
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L. Brillouin, Science and information Theory, 2nd ed., McGraw-Hill, H. Davis, C. Fernandez and D. R. McAuliffe, The excitatory
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cochlea, Proc. Naf. Acad. Sci. 36, 586587 (1950). P. Dallos, Cochlear potentials and cochlear mechanics,
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30, 1287-1288 (1974). T. W. Barrett, Information processing in the cochlea, Acustica, 33, 102-l 15. M. Billone and S. Raynor, Transmission of radial shear forces to cochlear hair cells, J. Acoust. Sot. Am. 54, 1143-1156 (1973).
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in
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P. Dallos, M. A. Cheatham and J. Ferraro, Cochlear mechanics, nonlinearities, and cochlear potentials, J. Acoust. Sot. Am. 55, 597605 (1974). P. Dallos, Z. G. Schoeny and M. A. Cheatham, Cochlear summating potentials,
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Science 170, 641-644 (1970). P. Dallos, Z. G. Schoeny and
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descriptive aspects, Acta Oto-Latyngol. Suppl. 302, 146 (1972). D. Gabor, Theory of communication, J. I. E. E. 93, 429-457 (1946). R. Goldstein, Analysis of summating potentials in cochlear responses,
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178, 331-337 (1954). A. A. Kharkevich, Spectra and Analysis, Consultants Bur., New York, 1960. W. E. Koch, On the principle of uncertainty of sound, J. Acoust. Sot. Am. 7, 56-58
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L. Peterson and B. Bogert, A dynamical theory of the cochlea, J. Acoust. Sot. Am. 22, 369-381 (1950). L. Pimonow, Vibrations en &gime transitoire, Dunod, Paris, 1962. G. W. Stewart, Problems suggested by an uncertainty principle in acoustics, J. Acoust. Sot. Am. 2, 325-339 (1931). C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27, 379423, 623-656 (1948). I. Tasaki, H. Davis and J. P. Legouix, The space-time pattern of the cochlear microphonics (guinea pig) as recorded by differential electrodes, J. Acoust. Sot. Am. 24, 502-518 (1952).
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The analogy
J. Tonndorf,
surf on sloping
beaches
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fluid motion
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within
the cochlea
for the mechanism
and formation
of cochlear
of
stimula-
33
tion, Ann. Otol. Rhinol. Laryngol. 65, 498-506 (1956). J. Tonndorf, Cochlear mechanics and hydrodynamics, in Foundations of Modern Audiroy Theory (J. V. Tobias, ed.), Vol. 2, Academic, New York, 1970, pp. 205-254. A. R. Tunturi, Analysis of cortical auditory responses with the probability pulse, Am.
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J. Physiol. 181, 63&638 (1955). J. J. Zwislocki, Cochlear waves:
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