Annals of BiomedicalEngineering, Vol. 16, pp. 35-51, 1988 Printed in the USA. All rights reserved.

0090-6964/88 $3.00 + .00 Copyright 9 1988 Pergamon Press plc

USE OF PSEUDORANDOM NOISE IN STUDIES OF AUDITORY EVOKED POTENTIALS A a g e R. M r

R i c h a r d M. A n g e l o *

Department of Neurological Surgery University of Pittsburgh School of Medicine Pittsburgh, Pennsylvania

The extent to which sensorineural systems such as the auditory system are nonlinear depends on the type o f stimulus that is used, and the part o f the system from which recordings are made. An estimate o f the first-order Wiener kernel o f the evoked response from the inferior colliculus to amplitude-modulated tones and noise was obtained by cross-correlating the response with the same pseudorandom noise as was used to amplitude modulate the sounds that were used as stimuli, in order to characterize the linear portion o f the system. The shape o f these cross-correlograms resembled the potentials evoked to short bursts o f the unmodulated tones and noise. The degree o f nonlinearity in the response to amplitude-modulated tones and noise was determined, and information about the type o f nonlinearity was obtained using the inverse-repeat feature o f the pseudorandom noise. Recordings both from the surface and from deep in the nucleus o f the inferior colliculus revealed nonlinearities that were predominantly o f an even order, but the magnitude o f the nonlinearities depended on what stimulus was used, the stimulus intensity, and from which neural structure the recording was made. Keywords--Nonlinear analysis, Amplitude-modulated sounds, Auditory evoked potentials, Inferior colliculus, Pseudorandom noise.

INTRODUCTION The stimuli traditionally used in studies of the auditory nervous system have been transient stimuli such as clicks and tonebursts. The responses from single nerve fibers in the auditory nerve and from cells in the various nuclei of the ascending auditory pathway have been studied in numerous investigations using transient stimuli, and the responses to similar stimuli have been recorded with gross electrodes placed at various locations on the ascending auditory pathway. The results of such studies have provided important information about the function of the auditory system. However, interpretations of the results of such studies are hampered by the fact that senAcknowledgment-This study was supported by Grant R01-NS21378-03from the National Institutes of Health. Address correspondence to Aage R. Moller, Ph.D., Department of Neurological Surgery, 9402 Presbyterian-University Hospital, 230 Lothrop Street, Pittsburgh, PA 15213. *Present address: Richard M. Angelo, Ph.D., Navy Hall, BloomsburgState College, Bloomsburg, PA 17815. 35

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Aage R. Mr

and Richard M. Angelo

sorineural systems are generally nonlinear. However, it is known that many nonlinear systems can be described adequately by a series of linear models that may be arrived at by testing with small perturbations of the input signal. Different models are likely to emerge at different levels of the input signal. Studies in which responses are recorded from the auditory system to steady tones (or noise), amplitude modulated with sine waves (19,20,40), or steps (26), are examples of how a series of different linear models can be used to approximate description of a nonlinear system. The traditional way to obtain a complete description of a nonlinear system is to use random noise as test signals and then to obtain estimates of not only the firstorder Wiener kernel, but also higher-order kernels (17). However, the great complexity of biological systems and the difficulties in interpreting higher-order kernels makes this method less attractive in studies of such systems, and few studies have attempted such a complete description of sensorineural systems. In the auditory system, several studies have used either noise as test signals (2,3,24,25,30,31), or signals that were amplitude modulated with noise to obtain estimates of the first-order Wiener kernel (8,9,20-23,27,28,36,39,44). In these studies true Gaussian noise has usually been substituted by pseudorandom noise, i.e. noise that is generated by the digital technique and which repeats itself after a certain time. The methods used in these studies are largely developments that are based on the work by Wiener (45), Lee and Schetzen (15,16), Marmarelis and Marmarelis (17), French and Holden (6), French (7), de Boer (2), de Boer and Kuyper (3), Johannesma (12), and O'Leary and Honrubia (37). (For reviews, see (5), (17), and (34).) Information about the degree of nonlinearity and its character in the responses of such a system can be estimated by first obtaining an estimate of the first-order Wiener kernels by cross-correlating the response with the noise that was used as a test signal and then comparing the actual responses with the responses of a linear filter that has the obtained cross-correlogram as its impulse response. This presumes that the first-order cross-correlation obtained in a nonlinear system is a valid estimate of the impulse response of the linear portion of the system. This is so, provided that the higher-order autocorrelations of the noise that is used as the test signal are zero (see (4,13,34,43)). The difference between the actual response and the response o f such a model represents the nonlinearities of the system and uncorrelated signals (17,34-36). The pseudorandom noise differs from true Gaussian noise in several ways, and the noise used earlier by many investigators was based on binary sequences. The secondand higher-order autocorrelations of such noise are thus substantially different from zero, while all higher-order autocorrelations of Gaussian noise are zero(43). The use of such noise in studies of nonlinear systems may therefore imply a certain degree of error. It has been shown that these problems are less when the noise used is based on ternary sequences instead of binary sequences, because all even-order autocorrelations of such noise are zero. However, third-order autocorrelations suffer from anomalies (10,11,38,43), and these anomalies may affect the accuracy of the determination of the first-order kernel (34,43) in a system that contains third-order (or higher odd-order) nonlinearities. Because of the way it is generated, pseudorandom noise that is based on ternary sequences becomes of the inverse-repeat type, which means that the latter half of one noise period is equal to the first half multiplied by - 1 . If the latter half of the response to one period of the noise is subtracted from the former half, all even-order nonlinearities in the response are cancelled; however, the first-order response (linear

Use o f Pseudorandom Noise in A E P

37

portion), as well as all odd-order nonlinearities, are unchanged. The difference between the model response and such "folded" responses thus reflects odd-order nonlinearities. Comparing this with the difference between the unfolded responses provides an estimate of the magnitude o f the nonlinearities t h a t are of even order, and comparing that with the total magnitude of nonlinearities gives a measure of the degree of odd-order nonlinearity in the system being tested (34-36). Nonlinearities that are of even order indicate an asymmetry in the response waveform, and typically occur because the response to an increment is different from the response to a decrement in the stimulus intensity. Studies of the responses from single nerve cells in the cochlear nucleus to a tone stimulus, the intensity of which was increased and decreased in a stepwise fashion, have shown such an asymmetry (26). A slightly different use of these techniques in studies of the auditory nervous system involves recording evoked potentials from nerves and nuclei. Such recordings are made by using relatively large electrodes placed in, or on, the surfaces of nerves or nuclei. Evoked potentials f r o m the nerve tracts and nuclei of the ascending auditory pathway recorded in animal experiments by placing recording electrodes on exposed portions of the ascending auditory pathway have traditionally been studied using transient stimuli such as click sounds or tonebursts as stimuli. The responses obtained to such stimuli are the sums of the activity in m a n y neurons. When recording f r o m nerves or fiber tracts in the brain the potentials are the sum of individual discharges, whereas recordings from nuclei also contain slow synaptic potentials (EPSP or IPSP). When evoked potentials are recorded from the cochlear nucleus and the same type o f stimulus is used, the cross-correlograms obtained resemble the response obtained to short tonebursts, but the decrease in latency with an increase in stimulus intensity is less for the cross-correlograms than it is for the response to tonebursts (27,28,33). It has been shown earlier that the response recorded from the surface of the cochlear nucleus in an anesthetized rat to a continuous tone that is amplitude modulated with pseudorandom noise is nonlinear, but that this nonlinearity is mainly of even order (35). In the present paper we present the results o f using similar methods to study the responses from the inferior colliculus of the rat to stimulation of the ear with tones or noises that are amplitude modulated with pseudorandom noise. The contralateral inferior colliculus receives input that has passed through the cochlear nucleus, and also input that has been processed in the nuclei of the superior olivary complex. The contralateral inferior colliculus, therefore, contains third- and fourth- and probably higher-order auditory neurons, and the responses from the inferior colliculus are therefore much more complex than those obtained from the cochlear nucleus. METHODS White Sprague-Dawley rats were anesthetized with urethane (1.5 g / k g bodyweight). After the outer ears were deflected, the animal's head was placed in a headholder with hollow earbars, through which sound generated by a condenser microphone (Type 4131, Bruel & Kjaer, Naerum, Denmark) was led to one ear (18). The skull bone overlying the inferior colliculus was removed and portions of the cerebrum overlying the inferior colliculus were removed by suction. A metal electrode with a tip diameter of about 50 #m, insulated except for 200/~m o f its tip, was advanced in a dorso-ventral direction through the inferior colliculus. The recorded potentials

38

Aage R. MOiler and Richard M. Angelo

were amplified by AC amplifiers (Type P51 lk, Grass Instrument Co., Quincy, MA) with a high impedance probe (Type HP51 l, Grass Instrument Co.). The potentials were filtered (highpass 3 Hz and lowpass 3,000 Hz) and sampled and digitized for processing by an LSI I 1/73 processor. The pseudorandom noise used in this study was the same as that used in previous studies (27,29,30,34,35). It was generated by simulating a nine-stage shift register that had feedback from its output to different stages. The signals were added modulo 3 to form 19,682 steps of a ternary signal 00,28,30); this signal was digitally lowpass filtered at l0 kHz and the number of samples reduced to 2,048 by linear interpolation. An analog signal was produced by a 12-bit digital-to-analog converter with a sampling interval of 80 /zs. The output was lowpass filtered (3.4 kHz cutoff, 18 dB/octave). The duration of each period of the pseudorandom noise was 163.8 ms. This signal was then fed into an analog multiplier, together with a tone or highpassfiltered noise (3.9 kHz cutoff, 36 dB/octave), to generate an amplitude-modulated signal (27). The modulation depth was 25% when tones were used as carrier, and 35% when noise was used as carrier. The same computer that generated the modulation signal also averaged the recorded potentials. The averager was locked to the periodicity of the pseudorandom noise, and the averaged response therefore represented the response to one period of the pseudorandom noise. When amplitude-modulated sounds are used, it is the modulation waveform that is regarded to be the signal. Therefore, an estimate of the impulse response of the system being tested was obtained by computing the circular cross-correlation between the averaged response and one period of the pseudorandom noise that was used as modulation (21,34). Assumi.ng sampled data, the circular cross-correlation was 1

1 K--n--I

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,

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(1) where x is the recorded responses and y is the pseudorandom noise, n = 0,1,2 . . . . . K-1. The model response was obtained by convolving the pseudorandom noise with the obtained cross-correlation of the response: 1 K--n--1

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where Z is the model response, Rxy is the cross-correlation, and Y is the noise. The model response is then subtracted from the actual response, after the mean values of the model response and the actual response were subtracted to remove any DC components. The root mean square (RMS) values of the actual response, the model response, and the difference were obtained. (For computational details see (17,30,33,34).) The ternary noise as well as the technique described above for analyzing physiological data have been tested on linear as well as on nonlinear models to show the accuracy of the method compared with traditional testing methods (30).

Use o f Pseudorandom Noise in A E P

39

RESULTS The cross-correlograms of the response recorded from an electrode placed deep in the central nucleus of the inferior colliculus while the contralateral ear was stimulated with a 5-kHz tone that was amplitude modulated with pseudorandom noise are shown in Fig. l (CC); also shown is the response to 1-ms long bursts of the same tone, but unmodulated at these different sound intensities (EP). In Fig. 1 the waveshapes of the evoked potentials and the cross-correlograms are similar, but there are certain important differences. Thus, the evoked potentials show small peaks that are not discernible in the cross-correlograms, and the peaks in the evoked potentials tend to be sharper than the corresponding peaks in the cross-correlograms. For comparison, Fig. 2 shows recordings made from the round window in a rat. These potentials are characterized by two negative peaks, the earliest of which represents neural activity in the distal portion of the auditory nerve, while the second negative peak originates in the cochlear nucleus (32). It is seen that the waveshapes of the evoked potentials (EP) are nearly a replica of the cross-correlograms, but there is a slight difference in the latency of the peaks in the cross-correlograms compared to that of the evoked potentials: the latency of the cross-correlograms is slightly shorter and less dependent on the stimulus intensity than that of the evoked potentials. Figure 3(A) shows the averaged response to a tone that was amplitude modulated by pseudorandom noise, representing one period of the pseudorandom noise. Figure 3 also shows the response of a model that has the cross-correlogram as its impulse response (B). The difference (C) between the model response (B) and the actual response (A) is a measure of the nonlinearities of the system. There is a relatively large discrepancy between the recorded response and the model, which indicates that the system under test does not behave as a linear system. When the last half of the averaged response to one noise period (shown in Fig. 3A) is subtracted from the first half (D), all of the components of the response that are generated by even-order nonlinearities are cancelled out, leaving the components that are results of the linear portion of the system, as well as all odd-order nonlinearities, unchanged. The difference (F) between the response "folded" in that way and the likewise "folded" response of the model (E) is smaller than when the "unfolded" responses are compared. This means that a large proportion o f the nonlinearities in the response from the cochlear nucleus are o f even order, and since such nonlinearities are typical for a system in which the response to a (small) increase in the stimulus intensity is of a different amplitude than the response to an equivalent decrease in the stimulus intensity, we may assume that the main nonlinearities of these responses were due to asymmetry in the way the response altered with small increases and decreases in stimulus intensity. The RMS value of the averaged response to amplitude-modulated tones is shown as a function o f stimulus intensity in Fig. 4. Also shown is the RMS value of the model response, and the RMS value o f the difference between the actual response and the model response. It is seen that the RMS value of the response increases with stimulus intensity, but the difference between the actual response and the model response increases less steeply than does the actual response. The RMS values were calculated after the mean value was subtracted, and these values represent the sensitivity to small changes in the amplitude of the stimulus sound.

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Aage R. MOiler and Richard M. Angelo

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FIGURE 1. Comparison of the waveform of the response to tonebursts (EP) with cross-correlograms of the response to 5-kHz tones that were amplitude modulated with pseudorandom noise. The responses were obtained from the central nucleus of the inferior colliculus to stimulation of the contralateral ear at about 20 dB above threshold (upper graph), 40 dB above threshold {middle graph), and 60 dB above threshold (lower graph). The amplitude scales for the individual recordings were different, but were normalized so that waveforms on the individual records could be compared.

Use o f Pseudorandom Noise in A E P

41

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TIME IN MILLISECONDS FIGURE 2. Results similar to those in Fig. 1 9 but showing a comparison of the waveform of the responses recorded from the round w i n d o w of the cochlea of a rat to stimulation with 15-kHz tonebursts of 0.3 ms duration (solid lines) with cross-correlograms of the responses to 15-kHz tones that were amplitude modulated with pseudorandom noise. The stimulus intensity is given in dB above threshold for stimulation with tonebursts (from (33)).

42

Aage R. MOiler and Richard M. Angelo

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FIGURE 3. A: average of responses during one period of the pseudorandom noise obtained from the central nucleus of the inferior colliculus to stimulation with a continuous 5-kHz tone that was amplitude modulated with pseudorandom noise. The sound was presented for 5 minutes at a level of about 6 0 dB above threshold. CC: cross-correlation between one period of the pseudorandom noise and the average response. B: output of a model that has the cross-correlogram (CC) as its impulse response, and the pseudorandom noise used to amplitude modulate the stimulus as its input. C: difference between model response and actual response. D: folded actual averaged response obtained by subtracting the latter half of the response s h o w n in A from the first half. E: model response folded in the same way as in D. F: difference between folded average response and folded model response, using the same amplitude scale as in the other recordings (upper curve), and with an amplitude scale that was expanded 10 times (lower curve).

Figures 5 to 7 show results similar to those shown in Figs. 1 to 4, but when highpass-filtered noise was used as a carrier. The cross-correlograms of the responses to amplitude-modulated noise are similar in shape to those obtained when amplitudemodulated pure tones are used as stimuli, and their shapes resemble the shapes of the responses to short bursts o f the same noise, but unmodulated. However, as seen in Figs. 6 and 7, nonlinearities are of a smaller magnitude than they are when the stimulus is an amplitude-modulated tone. The recordings shown in Figs. 5 and 6 were obtained from the central nucleus of

Use o f Pseudorandom Noise in A E P

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dB A B O V E T H R E S H O L D FIGURE 4. RMS value o f the average response from the central nucleus of the inferior colliculus to a 5-kHz tone that was amplitude modulated with pseudorandom noise, as a function of stimulus

intensity (filled circles, solid lines), together with the model response (open circles, dashed lines). The dashed lines and filled squares show the RMS value of the difference between the actual response and the model. The dashed lines and open squares show similar differences between the " f o l d e d " actual response and the "folded" model response.

the inferior colliculus in response to stimulation of the contralateral ear with amplitude-modulated noise of an intensity that was about 40 dB above threshold. When recordings are made from the surface of the exposed inferior colliculus, the correlograms, as well as the responses to tonebursts, are more complex than when recording f r o m the center of the main nucleus. The reason for this is that a surface electrode, in addition to recording the potentials from the nucleus of the inferior colliculus, also records potentials that are generated by the nerve tract that terminates in the inferior colliculus (lateral lemniscus), as well as more peripheral nuclei (such as the superior olivary nucleus and the cochlear nucleus), and the nerve tracts that connect these nuclei to the auditory nerve. The electrical events that are generated by the more peripheral structures of the ascending auditory pathway occur with shorter latencies than those generated by the inferior colliculus, as can be seen from Fig. 8, in which the cross-correlograms of the responses to a 5-kHz tone that is amplitude modulated with pseudorandom noise are compared with the responses obtained when short bursts of the same, but unmodulated, tones were used as stimuli. The amplitude of the sharp peaks that occur with short latency in the response to tonebursts is larger relative to the later and slower potentials, and even in this case there is a reasonably good agreement between these two measures. Figure 9 shows the response f r o m the same location to a 5-kHz tone that was amplitude modulated with p s e u d o r a n d o m noise, together with the response to a model that has the cross-correlogram as its impulse response, similar to the situation shown in Fig. 3, That the nonlinearity in this case is mainly of second order is evi-

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Aage R. MOiler and Richard M. Angelo

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FIGURE 5. Graphs similar t o t h o s e s h o w n in Fig. 1, b u t s h o w i n g responses f r o m t h e central nucleus o f t h e inferior colliculus t o highpass-filtered noise bursts (EP) and cross-correlograms o f t h e response t o t h e same noise presented as a c o n t i n u o u s s o u n d t h a t w a s a m p l i t u d e m o d u l a t e d w i t h pseudorand o m noise.

Use o f Pseudorandom Noise in A E P

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dent from inspection of the response, each half of which contains two peaks with the same polarity. Because the second half of the pseudorandom noise that was used to modulate the tones is equal to the first half but inverted, it is evident that components that have the same polarity in both halves of the response must be the result o f an even-order nonlinearity. Although these two peaks appear more clearly in the graph of the difference between the actual response and the response o f the model, they are cancelled out when the response is "folded" by the process in which the latter half of the response is subtracted f r o m the first half; consequently, the difference between the folded actual response and the folded model response becomes small, indicating that the degree o f odd-order nonlinearities is small. Figure 10 shows the RMS values of the response to noise-modulated tones (A) and noise (B). These graphs are similar to those showing the results obtained when amplitude-modulated tones were used as stimuli. The nonlinearities are of a smaller magnitude when amplitude-modulated noise, rather than pure tones, is used as the stimulus.

46

Aage R. MOiler and Richard M. Angelo 2.0

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FIGURE 7. Results similar to those shown in Fig. 4, but obtained using noise-modulated noise as the stimulus.

DISCUSSION It is interesting that the waveforms of the cross-correlograms of the response from the inferior coUiculus to amplitude-modulated tones and noise so closely resemble the responses to short bursts of the same sounds when unmodulated. In this way, the results from the inferior colliculus resemble results obtained from a more peripheral, and presumably less complex, nucleus (the cochlear nucleus) (27,28,35) and from the auditory nerve. It was shown in previous studies (27,28,33) that the latencies of the peaks in the cross-correlograms were less dependent on the stimulus intensity than those of the peaks in the evoked potentials to transient sounds. This is presumably because the latencies o f the components o f the cross-correlograms are independent of the time it takes for the E P S P to climb to the threshold of firing in individual neurons. The latencies of the peaks in the evoked potentials to transient sounds also include the time it takes for the EPSP to rise to the level where the neurons discharge. This means that the latencies of the various components of the cross-correlograms mainly represent axonal conduction time and synaptic delays together with the time it takes for the stimulus to reach the sensory receptor, the latencies of which are all largely independent of the stimulus intensity. The cross-correlograms therefore provide a more accurate measure of neural conduction delay than do evoked potentials to transient stimuli. This is one important advantage in using continuous sounds compared to using transient sounds in studies of the auditory nervous system. The differences in latency of the evoked response and the cross-correlograms are clearly seen when recording from the periphery o f the auditory system (auditory nerve and cochlear nucleus), as seen in Fig. 2, but not nearly as apparent when recording from the inferior colliculus because o f the broader peaks in the response and longer latencies.

Use o f Pseudorandom Noise in AEP

47

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FIGURE 8. Graphs similar t o t h o s e s h o w n in Fig. 1, b u t s h o w i n g results o b t a i n e d f r o m t h e surface o f t h e inferior colliculus. The stimulus w a s 5-kHz tones presented to t h e contralateral ear at the same t h r e e d i f f e r e n t s t i m u l u s intensities as in Fig. 1.

48

Aage R. MOiler and Richard M. Angelo

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Another advantage in using noise-modulated continuous sounds is that it offers the possibility to study nonlinearities in the system. The value of nonlinear analysis o f biological systems has recently been demonstrated in studies in which a random train of impulses was used as stimuli (14) in connection with a simplified display of second- and third-order kernels (41). Thus, the nonlinearities were studied and the effect o f responses of neurons in the hippocampus of long-term potentiation (LTP) were examined by Berger and Sclabassi (1). These investigators found that LTP changed the nonlinear behavior of this system in a characteristic way. They also showed that it is the spike generator that contributes most to the nonlinearities of this system, and that the EPSPs and IPSPs contribute little to the nonlinearities. Other studies have shown that the feedback from the somatosensory cortex to the dorsal column nuclei affects the nonlinear components in the somatosensory evoked potentials elicited by median nerve stimulation (42). The nonlinearities in the responses from the inferior colliculus are generally of an even order, and thus similar to the nonlinearities that were found in the cochlear nucleus (35); however, the degree o f nonlinearity found in the responses from the inferior colliculus is greater than that found in the recordings from the cochlear nucleus. This, in fact, is not unexpected because of the more complex nature of the

Use o f Pseudorandom Noise in A E P

49

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nucleus of the inferior colliculus and because its input already has been processed in the cochlear nucleus, which means that the information has already been processed in a nonlinear neural network before it reaches the inferior colliculus. The RMS value of the response recorded from the inferior colliculus increased monotonically over the range of stimulus intensities studied. This is slightly different from the RMS values o f the responses from the surface of the cochlear nucleus in anesthetized rats; the latter first increased and then decreased as the stimulus intensity was increased from threshold to physiological sound intensities, indicating an increased sensitivity to changes in stimulus intensity as the stimulus intensity is increased from threshold up to a certain stimulus level, above which it decreases (35). In a way similar to what was seen in the cochlear nucleus, the RMS value of the difference between the response of the model and the actual response from the inferior colliculus usually increased only slightly with increasing stimulus intensity and did not show a maximal value within the stimulus intensity range that was studied. Further, the response from the inferior colliculus to amplitude-modulated noise showed less degree of nonlinearity than did responses obtained to amplitude-modulated tones, thus similar to what was found in studies of the cochlear nucleus (see (34)). Thus, the possibility of studying nonlinearities in these systems is likely to provide important information about the function of these systems, although the interpretation of such findings may not be simple. However, it shows the possible superiority of using noise in such studies rather than using the traditional test stimuli. That such methods for studies of nonlinearities in neural systems are n o t i n more general use may be due to the relative complexity of this type o f analysis and possibly also to the difficulties in interpreting higher-order Wiener kernels. The methods used in the present study in which information about the nature of the nonlinearities is obtained

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Aage R. Mr

and Richard M. Angelo

without computing higher-order Wiener kernels may offer an attractive alternative to a complete description using higher-order Wiener kernels. Finally, the fact that amplitude-modulated sounds are more similar to natural sounds suggests that the responses to such test sounds may reflect the properties of the auditory system that are more relevant to the normal function of the system than a r e t h o s e p r o p e r t i e s t h a t a r e r e f l e c t e d w h e n t r a d i t i o n a l t e s t s t i m u l i s u c h as click sounds or tonebursts are used.

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NOMENCLATURE CAP EPSP IPSP MTF RMS LTP AEP

= = = = = = =

Compound action potentials Excitatory postsynaptic potentials Inhibitory postsynaptic potentials Modulation transfer function Root mean square Long term potentiation Auditory evoked potentials