Acoustic reflexes to Schroeder-phase harmonic complexes in normal-hearing and hearing-impaired individuals

Hearing Research 202 (2005) 1–12 www.elsevier.com/locate/heares

Acoustic reflexes to Schroeder-phase harmonic complexes in normal-hearing and hearing-impaired individuals Lina R. Kubli *, Marjorie R. Leek, Laura E. Dreisbach

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Army Audiology and Speech Center, Walter Reed Army Medical Center, 6900 Georgia Avenue NW, Washington, D.C. 20307-5001, USA Received 15 July 2002; accepted 17 August 2004 Available online 6 November 2004

Abstract Harmonic complexes generated with positive or negative Schroeder-phases may result in differences in cochlear excitation, even though their long-term spectra and amplitudes are equal. As a measure of possible differences in cochlear excitation resulting from these harmonic complexes, thresholds and growth of the acoustic reflex were assessed in normal-hearing and hearing-impaired subjects. Harmonic complexes with fundamental frequencies of 50, 100, and 200 Hz were constructed with positive and negative-Schroeder phases. In normal-hearing subjects, acoustic reflex thresholds for the 50- and 100-Hz fundamental waveforms were typically lower for negative Schroeder-phase complexes than for positive Schroeder phase stimuli. At the highest fundamental frequency of 200 Hz, there were no significant threshold differences due to phase. Hearing-impaired subjects showed a similar pattern for thresholds between the two phase selections, but with smaller differences than those observed in normal-hearing subjects. At levels above reflex threshold, the magnitude of the acoustic reflex was greater for the negative-phase than the positive-phase stimuli for the lowest fundamental frequency, but no significant differences were observed at fundamental frequencies of 100 and 200 Hz. These results are consistent with generally greater cochlear excitation in response to negative than to positive Schroeder-phase stimuli when the fundamental frequency is sufficiently low. Increased excitation may reflect a synchronization of response across a wide band of frequencies in the cochlea when the rate of frequency sweep within periods of these harmonic complexes is appropriately matched to timing characteristics of the traveling wave.
2004 Elsevier B.V. All rights reserved. Keywords: Acoustic reflex; Cochlear excitation; Harmonic complexes; Schroeder phase

1. Introduction The purpose of this study was to evaluate the threshold and growth characteristics of the acoustic reflex in response to complex activating stimuli with monotonically increasing or decreasing frequencies in normalhearing and hearing-impaired subjects. The stimuli were harmonic complexes with equal amplitude components and three different fundamental frequencies, presented *

Corresponding author. Tel.: +1 202 782 8611; fax: +1 202 782 9228. E-mail address: [email protected] (L.R. Kubli). 1 Present address: San Diego State University, San Diego, CA USA. 0378-5955/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.heares.2004.08.012

to subjects at several levels. The phases of the components were selected such that within each harmonic period, frequencies swept upward or downward. The acoustic reflexes in response to these stimuli were measured to assess possible differences in activation strength as a function of both fundamental frequency and component phases. Harmonic complexes with monotonic changes in component phase have been used to explore several aspects of cochlear processing. Patterson (1987) assigned phases to each component of a harmonic complex with the goal of providing equal time shifts across auditory filters. He was searching for a ‘‘super pulse train’’ that would have the effect of simultaneous firing of all neurons within the frequency region of the complex.

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Patterson concluded from his study of harmonic phase discrimination using these stimuli that phase shifts across cochlear channels were discriminable, so long as the phase changes were large. However, he also argued that there is a phase alignment mechanism within the auditory system that serves to reduce across-channel phase differences. Consistent with earlier investigators, Patterson also reported that the best discrimination of smaller component phase changes occurred when the components fell within auditory channels or filters. Presumably, such discriminations among harmonic complexes were cued by differences in within-channel temporal waveform shapes, and therefore were at least partially reliant on the spacing of harmonic components relative to auditory filter bandwidths. Monotonic changes in phase across the frequencies of a harmonic complex produce a systematic upward or downward sweep in instantaneous frequency within each period of the complex. Upward sweeping stimuli have been used by Shore and Nuttall (1985) to synchronize firing in the auditory nerve across frequency in order to maximize the compound action potential in guinea pigs. Their logic was that a broadband stimulus with exponentially increasing frequency (i.e., low frequencies appearing first followed by higher frequencies) could compensate for the increasing delay time in neural firing as the traveling wave moves from the base to the apex in the mammalian cochlea. Dau et al. (2000) followed similar logic in determining the most effective time waveform of a click-like stimulus in measures of the auditory brainstem response (ABR), which relies on synchronous neural firing in the auditory nerve. They used a chirp stimulus that increased in frequency to compensate for the phase delays of the traveling wave along the length of the basilar membrane. Dau et al. reported that the response to this chirp stimulus was a markedly enhanced Wave V in the ABR, suggesting synchronized excitation of the high and low frequency regions in the cochlea. The monotonic changes in frequency produced by the Shore and Nuttal glides and the Dau et al. chirps are also observed within the periods of harmonic complexes with systematically decreasing or increasing component phases, similar to the stimuli used by Patterson (1987). Schroeder (1970) developed an algorithm for component phase selection in order to produce a very flat-envelope temporal waveform hn ¼
pnðn þ 1Þ=N ;

ð1Þ

where hn represents the phase of the nth harmonic, and N is the total number of harmonics. Harmonic complexes constructed with a negative sign have component phases that are monotonically decreasing with harmonic number, while those generated using a positive sign have increasing phases, as shown in Fig. 1(a). These monotonic changes in component phase produce a sweep in

frequency occurring within each period of the waveform. That is, over the frequency extent of the harmonic complex, a positive Schroeder-phase waveform, with phases increasing with increasing frequency, produces a downward frequency sweep once each period, while the negative Schroeder-phase waveform has an upward frequency sweep once each period (Fig. 1(b) and (c)). It should be noted that the positive and negative Schroeder complexes have identical long-term magnitude spectra, but one waveform is the time-reverse of the other. Smith et al. (1986) first reported the interesting finding that by using the Schroeder-phase harmonic complexes constructed with either increasing (‘‘positive Schroeder phase’’) or decreasing (‘‘negative Schroeder phase’’) component phase, large differences in masking were observed. Given an appropriate choice of frequencies and stimulus levels, there may be as much as 20–25 dB more masking resulting from the negative Schroeder complex than from the positive complex in normal-hearing listeners. While these harmonic complexes may produce different amounts of tone masking for normalhearing listeners, similar masking by the two complexes has been observed in listeners with hearing loss (Summers and Leek, 1998). Further investigation of these masking differences led Kohlrausch and Sander (1995) to suggest that the masking differences between the positive and negative Schroeder maskers occurred in part because the phase characteristic of the auditory filters interacted with the phase characteristics of the stimuli to alter the within-channel waveform shape. To the extent that the stimulus phase characteristic compensated for the phase change across an auditory filter, the internal within-channel waveform would become more highly modulated, thereby reducing its effectiveness as a masker. The increasing or decreasing instantaneous frequencies may also compensate or enhance the traveling wave in successive regions of the basilar membrane as the harmonics in the complex are dispersed from base to apex. An increasing frequency sweep should lead to more synchronous firing of neurons along the cochlea, while a decreasing frequency sweep would result in a more dispersed pattern of firing over time. The predicted changes in synchrony of neural firing of these within-period sweeps might be reflected in differences in threshold and growth characteristics of the acoustic reflex. The acoustic reflex in humans is a contraction of the stapedius muscle in the middle ear that normally occurs in the presence of loud sounds. Although the middle ear acoustic reflex is bilateral in that a sufficiently intense stimulus presented to one ear results in a contraction of the stapedius muscles in both middle ears, the threshold for the reflex is typically lower when measured in the same ear as the stimulus than when measured in the contralateral ear. Both the ipsilateral and contralateral neural pathways pass through early nuclei in the central

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(a)

(b)

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Fig. 1. (a) Phase spectra for the positive and negative Schroeder-phase harmonic complexes for three fundamental frequencies. The phase is shown in radians for each harmonic component. (b) Five periods (50 ms) of the negative Schroeder-phase waveform with a fundamental frequency of 100 Hz. (c) Five periods (50 ms) of the positive Schroeder phase waveform with a fundamental frequency of 100 Hz.

auditory system as far up as the superior olivary complex (SOC), and involve only a small number of synapses. From the structures in the SOC, motor neurons in facial nuclei are stimulated, innervating the stapedius muscles by way of the VIIth (Facial) nerves (Borg, 1973; see Møller, 2000, for review). The reflexive contraction of the stapedius muscle in response to sounds of sufficient intensity may be measured by noting the increase in stiffness of the ossicular chain, reflected as changes in transmission of sound through the middle ear to the cochlea. This type of measurement is a routine part of audiological assessment, assisting in the evaluation of the integrity of the middle ear as well as other structures along the reflex arc involving both the VIIIth nerve (sensory) and VIIth nerve (motor), the cochlea, and some brainstem nuclei. Acoustic reflexes are typically elicited at sound levels from approximately 85–100 dB SPL for tones and about 65–95 dB SPL for broadband noise (BBN) stimuli (Silman et al., 1987). The acoustic reflex threshold, defined as the lowest intensity of a given sound that is sufficient to produce a contraction of the stapedius muscle, is affected by frequency, bandwidth, and duration of a stimulus (Silman and Gelfand, 1982), with generally lower thresholds for long-duration, broadband sounds like

noise (Dallos, 1964; Flottorp et al., 1971; Silman et al., 1987). The measurement is fast and non-invasive, and the magnitude of the acoustic reflex measure is related to the intensity of the activating stimulus (Silman et al., 1978; Wilson and McBride, 1978). Given that the strength of the acoustic reflex directly relates to the intensity of the activator stimulus, it is clear that a greater reflex magnitude points to a more intense activating signal on the VIIIth nerve side of the reflex pathway. Just as observed by Dau et al. (2000) in measures of ABR response, greater synchrony of neural firing of an acoustic reflex activator might produce a stronger response, or a response at a lower stimulus level. If the within-period frequency sweeps in the Schroeder-phase waveforms produce differences in internal excitation because of increased or decreased synchronization of neural firing along the basilar membrane, there may be differences in the thresholds, magnitudes, and rate of growth of acoustic reflexes. Further, changes in cochlear function resulting in hearing loss may alter the dynamics of the interaction between the harmonic complex stimuli and temporal aspects of cochlear processing. This possibility will be evaluated by including subjects with hearing loss in this study.

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to Eq. (1), with either an initial positive or negative sign, resulting in a total of six stimuli (two phase selections · three fundamental frequencies). All stimuli were 500 ms in duration, including 10 ms rise/fall times. To reduce possible edge pitches associated with the spectral limits, an amplitude ramp was imposed on the first two and last two harmonics in each stimulus. This ramp was generated by attenuating the first and last harmonics by 6 dB and the second and next-to-last harmonic by 3 dB, relative to the remaining harmonics, which had equal amplitudes. Spectral and waveform characteristics of the stimuli were verified at the output of the transducer using a Hewlett Packard 35665A spectrum analyzer.

2. Materials and methods 2.1. Subjects Acoustic reflexes were measured in nine normal-hearing and nine hearing-impaired subjects. The age ranges were 31–55 years for the normal-hearing subjects and 31–79 years for the hearing-impaired subjects. All of the subjects had normal middle ear function as determined by type A (normal) tympanograms and acoustic reflexes for pure tones at frequencies of 0.5, 1, and 2 kHz at or below 100 dB HL (ANSI S3.39 1987). In addition, each participant had acoustic reflex thresholds below 100 dB SPL in response to each stimulus used here. The normal hearing subjects had audiometric thresholds of 25 dB HL (ANSI S3.6 1996) or lower at octave frequencies from 0.5k to 6 kHz, with the exception of one subject with a threshold of 30 dB HL at 6 kHz. Hearing-impaired subjects had sensorineural hearing losses as determined by acoustic immittance results and bone conduction testing. The hearing losses were of various configurations and severity. Mean audiometric thresholds for the subjects are shown in Fig. 2. Subjects who were eligible under federal regulations were compensated $25 per hour for their participation.

2.3. Apparatus The stimuli were presented through a 16-bit D/A converter (TDT DD1) at a rate of 40,000 samples per second, attenuated, and fed to the external input of a Grason-Stadler GSI-33, Version 2, middle ear analyzer. Upon manual initiation of a trial, the stimulus was played through the GSI-33 to an insert earphone (ER3A), which was placed in the test ear of the subject. An immittance probe tip was placed in the other ear to measure tympanograms and acoustic reflex responses. For all stimuli, contralateral acoustic reflexes were measured using a probe frequency of 226 Hz at 85 dB SPL.

2.2. Stimuli Reflex activator stimuli were created off-line and stored in computer files for presentation during the experiment. These stimuli were harmonic complexes, with components ranging in frequency from 0.2–5 kHz, with fundamental frequencies of 50, 100, and 200 Hz, resulting in 97, 49, and 25 components, respectively. The phase of each component was calculated according

2.4. Procedure The subject was seated comfortably in a reclining chair in a sound-attenuating booth during the acoustic reflex measurements. One of the experimenters was also in the booth monitoring the graphical displays and

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Frequency ( kHz) Fig. 2. Average audiograms for nine normal-hearing subjects and nine hearing-impaired subjects. Error bars are standard deviations.

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numerical data during the testing. Listeners were asked to limit movement (including swallowing) during presentation of the stimuli to prevent excessive artifact during data collection. Subjects could relax with eyes open or closed during data collection. They were allowed to fall asleep, but were awakened if they began to snore. If excessive changes in breathing or snoring were observed during sleep, then the subject was instructed to stay awake during subsequent testing. Contralateral acoustic reflex thresholds to the Schroeder phase harmonic complexes were obtained for one ear for each subject. Usually the ear with the lower acoustic reflex threshold for pure tones was selected. When subjects had no difference between acoustic reflex thresholds to pure tones, the ear with the lower audiometric thresholds was selected. If the audiometric thresholds were the same, then the right ear received the activator stimulus unless excessive artifact was observed, in which case the left ear received the stimulus. At the beginning of data collection, an acoustic reflex threshold was obtained for each of the six stimuli. The activator signal was presented with a starting level of 65 dB SPL, and then changed in 5 dB increments and decrements until an acoustic reflex could be observed. Threshold was defined as the minimum level of the activating signal that produced a repeatable time-locked shift in compliance of 0.02 ml of equivalent volume or greater. The experimenter viewed the graphical display on the middle ear analyzer for a detectable change as indicated by a deflection and a numerical change of at least 0.02 ml of equivalent volume in the probe ear. The lowest level for each stimulus that produced a repeatable criterion response was taken as the reflex threshold. The order of presentation of the six possible stimuli was randomized for each subject. After measuring acoustic reflex thresholds for each stimulus, acoustic reflex growth functions were obtained by presenting each of the six stimuli at levels starting from 3 to 6 dB below the acoustic reflex threshold up to a maximum of 110 dB SPL, in 3 dB steps. The order of presentation was randomized across stimuli, and, within each stimulus block, the presentation levels were also randomized. Each level was tested three times, with replications presented randomly within the trial block. The average of the replicates at each level was taken to generate growth functions for each of the six stimuli (reflex amplitude as a function of stimulus intensity). Not all listeners heard the same set of levels for each stimulus (because levels were linked to the individualÕs reflex threshold), but each listener heard at least five levels, sufficient to estimate the pattern of reflex growth with level. Randomizations of stimulus set and levels within the sets were controlled by computer. The experimenter monitored the graphical display of the response after each stimulus presentation. Unless there was an obviously invalid response (e.g., due to subject move-

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ment), the reflex waveform was transferred to a database in numerical form. Also included in the data transfer for each trial were the compliance and maximum deflection values after onset and before offset of the stimulus. Time intervals between presentations ranged from 5 to 10 s and were determined by the time required to save data from each trial and the subsequent manual presentation of the next stimulus. Because the ear canal containing the probe might be sealed over a relatively long period of time, it was possible that the normal canal air pressure might change. Further, sometimes the probe might shift in position, changing the ear canal volume in front of the probe. Either of these occurrences could alter the reflex magnitudes, so at the beginning and end of each stimulus set, tympanograms were measured to monitor any changes in air pressure that had occurred in the sealed canal or movement of the probe tip. If the ear canal pressure or volume had changed during the course of the previous stimulus set, the probe was re-seated, taking care to re-establish a similar ear canal volume and initial pressure reading for the next stimulus set. This happened rarely, and it was assumed that a significant effect on the measurement would be reflected in the preliminary analysis of outliers described below, so no additional measures were taken. Testing time for the entire experiment was approximately one and a half to two hours. 2.5. Data reduction and initial analyses For each of the six stimuli, the data consisted of an acoustic reflex threshold estimate, and three replications each of responses to several stimulus levels. For most conditions, the response estimate was the mean of the three replicates. However, upon inspection of the data it was noted that in a few cases, the standard deviations across the three replicates were large, suggesting that at least one of the responses might be an outlier. In order to avoid effects of such spurious data, an analysis of outliers was undertaken. For each subject, the normal range of variability was established by calculating the average standard deviations across the three replicates for each data point. The standard deviation of that average (of the replicate standard deviations) was then computed. Finally, each set of three replicates for that subject was examined to determine if any response was more than two standard deviations from the mean of the three. If so, that response was excluded as an outlier, and the data point was recalculated as the mean of two replicates. In rare cases where more than one datum of the three-trial average exceeded two standard deviations from the mean, no data were excluded. This outlier determination resulted in 26 of 1299 responses for the hearing-impaired subjects being excluded (2.0%), and 12 of 1443 responses for normal-hearing subjects

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excluded (0.83%). The outliers were spread across all levels, stimuli, and subjects. All data points reported here are means of either two or three replicates. 2.6. Use of human subjects The study was conducted in accordance with the Declaration of Helsinki. The experiment was approved by the Institutional Review Board of Walter Reed Army Medical Center, and all subjects provided written informed consent before participating.

3. Results Three components of the acoustic reflexes were evaluated: (1) reflex thresholds, (2) reflex magnitudes at different stimulus levels, and (3) rate of growth of the acoustic reflex response with increasing levels (slopes of the reflex growth functions). 3.1. Reflex thresholds Mean reflex thresholds were obtained for each group of subjects for the six stimuli and are shown in Fig. 3. The left-hand panel shows data from normal-hearing subjects, and the right-hand panel shows mean thresholds from hearing-impaired subjects. In normal-hearing subjects, the thresholds for 50- and 100-Hz fundamental frequencies are lower for the negative Schroeder-phase waveforms than for the positive Schroeder-waveforms. At the highest fundamental frequency, the average thresholds are identical. Thresholds for the hearing-impaired subjects show a similar pattern, but the differences between the positive and negative Schroeder are considerably smaller than observed in the normal-hearing data. The thresholds are similar in level across both subject groups for the positive Schroeder phase stimuli,

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but occur at reduced levels for the negative-phase waveforms in normal-hearing subjects. A repeated measures ANOVA on the data in Fig. 3 indicated that there was a significant effect of phase (F(1,16) = 17.8, p < 0.001) and fundamental frequency (F(2,32) = 10.7, p < 0.001), as well as a significant interaction of these two factors (F(2,32) = 15.7, p < 0.0001). Group membership was not significant (p > 0.05), reflecting the similar overall threshold levels for the two groups, but the interaction between group membership and phase was significant (F(1,16) = 7.1, p < 0.02). Post-hoc t-tests with the Bonferroni correction indicated that the negative Schroeder-phase produced lower reflex thresholds than positive-phase stimuli in normal-hearing subjects for fundamental frequencies of 50 and 100 Hz. The hearing-impaired subjects also showed a significant difference in reflex thresholds between the two phases for waveforms with a fundamental frequency of 50 Hz, but differences at 100 and 200 Hz were not significant. Stimulus phase did not significantly affect reflex threshold for either of the subject groups for a fundamental frequency of 200 Hz. Comparing across subject groups, the positive phase waveforms resulted in similar thresholds. Although both groups had lower thresholds for the negative than the positive Schroeder waveforms, this difference was considerably greater for the normal-hearing group. 3.2. Reflex magnitude For each stimulus condition and across both subject groups, the average magnitude was calculated for each stimulus level above the reflex threshold, and these are shown in Fig. 4. Data from the three fundamental frequencies are shown in separate panels, and the parameters on each panel are the subject group and stimulus phases. For most of the stimulus levels shown, the number of subjects included in each average is nine, with the

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Fig. 3. Average acoustic reflex thresholds for the positive and negative Schroeder waveforms at three different fundamental frequencies. Error bars are standard errors.

Reflex Magnitude (ml)

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Stimulus Level (dB SPL) Fig. 4. Average acoustic reflex magnitudes at different stimulus levels for the three different fundamental frequencies. Each panel shows mean magnitudes for each subject group for the two phase conditions.

exception of the very low levels, where some subjects had not yet achieved reflex threshold. Acoustic reflex magnitudes are shown as ml of equivalent volume at each measured stimulus level. Fig. 4 shows that differences in magnitude of the acoustic reflex in response to the two phase conditions were observed primarily at the lowest fundamental frequency tested, 50 Hz. Both groups of subjects showed

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mean magnitudes of the reflexes that were larger for the negative phase than for the positive-phase stimuli. The hearing-impaired subjects also show a slightly greater magnitude for the negative phase for higher-level stimuli at the 100-Hz fundamental frequency, but there were no differences due to phase selection for either group for the highest fundamental frequency. Group differences are clearly apparent for all three fundamental frequencies, with reflex magnitudes of the hearing-impaired subjects greater than those of the normal-hearing group. Two statistical analyses were carried out to evaluate the differences in reflex magnitudes shown in Fig. 4: one estimated the effects of the experimental conditions and group membership on a global estimate of magnitude for each subject, averaging magnitudes across levels for each condition, while the second assessed the mean difference between data from the two phase conditions at each fundamental frequency for each subject. First, a three-way ANOVA, with group membership as a between-subjects factor, and repeated measures on the factors of phase condition and fundamental frequency, was carried out on the magnitude measures for each subject. These values were calculated by computing a mean magnitude for each phase and fundamental frequency condition for each subject. This metric addresses the question of whether, in general, the phase and/or fundamental frequency factors resulted in differences in overall reflex responsiveness. The ANOVA indicated no significant main effects (all p > 0.05), but the interaction of group and fundamental frequency, as observed across the panels in Fig. 4, was significant (F(2,32) = 5.58, p < 0.01). This results from the larger differences between groups with increases in fundamental frequency. There was also a fundamental frequency-by-phase interaction (F(2,32) = 5.31, p = 0.01), reflecting the phase difference observed at the 50 Hz fundamental, but not at the higher fundamentals. This analysis supports a conclusion that reflex magnitudes in response to the negative Schroeder-phase waveforms were greater than for the positive-phase waveforms for the lowest fundamental frequency tested for both subject groups. For all fundamental frequencies, reflex magnitudes from the hearing-impaired listeners at the highest stimulus levels tended to be greater than those observed for normal-hearing subjects, particularly for fundamentals of 100 and 200 Hz. A second ANOVA evaluated the differences between the phase conditions across fundamental frequency for the two groups. For this analysis, the differences in reflex magnitude in the two phase conditions were averaged across level for each subject. There was no effect of group membership (p > 0.60), but there was a highly significant effect of fundamental frequency on the amount of difference in magnitude due to phase (F(2,32) = 6.94, p = 0.004). For both groups, there was

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a reduction in the phase difference with increasing fundamental frequency. As may be seen in Fig. 4, the response difference between positive and negative stimuli is only notable at a fundamental frequency of 50 Hz. 3.3. Slope of the reflex growth functions As indicated by the average data shown in Fig. 4, the magnitude of the acoustic reflex increased in response to increasing stimulus levels, and the hearing-impaired subjects tended to have greater magnitudes than observed for normal-hearing subjects. The rate of increase in reflex magnitude is reflected in the slope of the growth function. There was considerable variability across subjects in the slopes of the reflex growth functions within both subject groups, but individual subjects tended to have characteristic growth functions across the stimuli. For example, one of the normal hearing listeners consistently showed a relatively steep growth, increasing to the highest magnitudes among this group of subjects, on each of the six stimulus conditions. In contrast, another normalhearing subject always showed the lowest responses within the group across all stimuli, with relatively shallow growth. Among the hearing-impaired subjects, a similar pattern emerged. For example, two of the hearing-impaired subjects had relatively steep functions, but one was offset from the other by 25–30 dB, and this pattern between these two subjects repeated across all stimuli. The functions relating reflex magnitude to stimulus level typically spanned about 20–30 dB, from acoustic reflex threshold to the highest level tested, 110 dB SPL. In some cases, the reflexes showed no evidence of saturating at the highest levels tested, but showed a linearly increasing magnitude with increasing level. In many cases, however, the reflex magnitudes reached a maximum at about 20 dB or so above reflex threshold, and then showed no further increase with higher levels. A normalization procedure described by several investigators (e.g., Borg, 1977; Møller, 2000) was applied in order to compare the slopes of reflex growth functions across conditions. Each reflex magnitude was converted to a percentage of the maximum magnitude observed across all stimulus conditions for a given subject. Thus, the greatest magnitude observed within a subject was given a value of 100%, and every other reflex measurement for that subject was referenced to that value. Each of these growth functions (percent of maximum magnitude as a function of stimulus level) was fit with a straight line, and with two intersecting best-fitting lines. To determine whether there was a significant improvement (p < 0.05) in the fit for the two-line versus the linear fit, taking into account the greater number of parameters in the former, an F-test was computed using the sums of squared deviations from each of the two fits. Degrees of freedom were determined by the number of points in each fitted line and the number of parameters

in the fits (i.e., two parameters for the linear fit; five parameters, including the intersection point, for the two-line fit). Fig. 5 shows an example of two growth functions, one that was better fit with two lines than with one, and the other represented adequately by a single straight line. The abscissa on this figure is the stimulus level above reflex thresholds. The rate of growth of the reflex magnitudes for each subject and stimulus type was taken as the slope of either the linear fit, or the slope of the first of the twoline fits, if that fit was significantly better than the single line. There were 54 functions for each group of subjects (six conditions · nine subjects). For the normal-hearing group, the selection of fit was split exactly evenly, with each of the two candidates assigned to 27 functions. The hearing-impaired group had 37 functions best represented with the two-line fits, and 17 with the single-line fits. A chi-square analysis (with the Yates correction for continuity) indicated, however, that these two distributions were not significantly different (v2 = 3.107, df = 1, p > 0.05). Fig. 6 shows the mean slopes extracted from the individual fitted reflex growth functions. Slopes for normalhearing subjects ranged from 0.44 to 7.73, whereas the slopes for the hearing-impaired listeners ranged from 1.37 to 8.99. A repeated-measures ANOVA indicated a significant main effect of group membership (F(1,16) = 4.67, p < 0.05), and of fundamental frequency (F(2,32) = 3.333, p < 0.05), but neither the main effect of phase nor any interactions were significant (all p > 0.05). These results indicate that the slopes of the reflex growth functions were significantly steeper for hearing-impaired listeners than for normal-hearing listeners. Although statistically significant, the differences due to fundamental frequency are not systematic across 100 Reflex Magnitude (% of Maximum)

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Fig. 6. Average slopes of the fitted acoustic reflex growth functions across individual subjects. Error bars are standard errors.

frequency, showing a significant quadratic trend, with the mean at the 100-Hz fundamental being steeper than at 50 or 200 Hz.

4. Discussion The range of acoustic reflex thresholds of normalhearing subjects over all conditions in this study was from 50 to 95 dB SPL. This is well within the range typically reported for wide band stimuli, such as broadband noise, and is lower than has been observed in response to tonal stimuli (Silman et al., 1987). Summation across frequency is thought to underlie the lower acoustic reflex thresholds for noise than for tones, and is probably also responsible for the lower thresholds resulting from the broadband harmonic complexes used here. According to Cacace and Margolis (1985), the acoustic reflex threshold occurs as sufficient excitation spreads across frequency in response to a broadband stimulus. Kawase et al. (1997), among others, have argued that the summed activity across frequency in a noise activator is the reason acoustic reflex thresholds in response to noise are typically lower than thresholds in response to tonal activators. Kawase et al. reported lower acoustic reflex thresholds when a facilitator tone was added to a reflex activator. This was taken as further evidence that the acoustic reflex threshold occurs as a result of summed excitation across frequencies. Summation of excitation across frequency has even been implicated in acoustic reflex thresholds to tonal stimuli. Borg et al. (1990) noted that the level of the acoustic reflex threshold in rabbits was highly correlated with the level of the tails of high frequency tuning curves, and suggested that the ‘‘recruitment’’ of high frequency neurons

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into the total sum of neural firing was the determinant of the reflex at that level. The normal-hearing subjects showed lower thresholds for the negative Schroeder waveforms than the positive Schroeder waveforms at fundamental frequencies of 50 and 100 Hz, with at least a 5-dB difference between the two types of waveforms. Further, they showed greater magnitudes in response to negative Schroeder waveforms than the positive Schroeder for the 50 Hz fundamental, but not for higher fundamentals. The differences in both reflex thresholds and suprathreshold magnitudes for one or more fundamental frequencies used here suggest differences in internal excitation resulting from the two Schroeder-phase waveforms. Hypothesized interactions between stimulus characteristics and phase responses of the cochlear filters have been implicated in masking studies showing that the negative Schroeder complex can be a more effective masker than the positive (e.g., Kohlrausch and Sander, 1995; Summers and Leek, 1998). These studies suggest that masking differences due to the positive and negative phase selections are a result of the interaction between the external phases of the harmonic components in the frequency region around the probe signal and the internal phase characteristic of the auditory filter in the signal region, resulting in two different internal waveform shapes within auditory channels. The Schroeder masking differences are observed when sufficient adjacent components are passed by individual auditory filters, and thus, for widely spaced components, masking by harmonic complexes may be less affected by the polarity of the Schroeder phase selection (Kohlrausch and Sander, 1995). However, for sufficiently low fundamental frequencies, the negative-phase masker typically provides more masking than the positive Schroeder masker. Recio and Rhode (2000) reported measurements of chinchilla basilar membrane motion in response to the two Schroeder-phase waveforms that are consistent with these psychophysical measures. Localized basilar membrane responses to the negative Schroeder-phase waves were greater in overall magnitude than responses to the positive Schroeder waves, indicating greater excitation for negative Schroeder waves. Further, Recio (2001) reported that the negative Schroeder waveforms resulted in greater rates of firing and greater synchronization of firing in cochlear nucleus and in the auditory nerve. There is therefore good evidence that, in mammals at least, within-channel cochlear processing of Schroeder-phase harmonic complexes may result in more excitation for the negative than the positive phase selections. The summation across frequency for effective activation of the acoustic reflex may reflect greater within-channel excitation in a number of overlapping channels, producing more overall excitation in response to a negative-Schroeder complex.

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The hearing-impaired subjects also had lower reflex thresholds for the negative than the positive Schroederphase stimuli, though these differences in thresholds were smaller than those obtained for the normal-hearing group. The magnitude differences between the two phase conditions were similar for the two groups. However, the growth of reflex magnitude with increasing stimulus level was greater for hearing-impaired than normal-hearing subjects. Silman et al. (1978) also found that hearing-impaired subjects produced steeper-than-normal reflex growth functions in response to noise stimuli, at least for stimuli within about 14 dB of reflex thresholds. The larger-than-normal responses to complex stimuli, particularly at the higher stimulus levels might be due to greater overlap of channel outputs of broad auditory filters, and to more excitation summed across channels. Although normal auditory filters broaden with stimulus level, they may not be as broad as those of hearingimpaired listeners (Leek and Summers, 1993; Moore, 1995). The assignment of monotonically increasing or decreasing phase to components of the harmonic complexes results in systematic time delays associated with each frequency. Each period of these stimuli has a rapid frequency glide upward (negative Schroeder) or downward (positive Schroeder), and responses to the harmonics are not initiated simultaneously in the cochlea. However, there is some indication that the spacing in time of the responses to the harmonics interacts with the timing characteristics of basilar membrane motion. Traveling waves are initiated for each component frequency on the basilar membrane, each beginning with its own time delay (phase). The traveling waves move along the basilar membrane with a velocity that begins to slow and amplitudes that grow to a peak at the characteristic place associated with each component frequency. Thus, it might be expected that a set of harmonically related frequency components that have an increasing phase delay with increasing frequency would stimulate the cochlea from low-to-high frequencies, but be compensated by the high-to-low-frequency direction of the traveling wave. The result might be a stronger temporal coherence of stimulation along the length of the cochlea, and therefore lower acoustic reflex thresholds and greater magnitude of the reflex (i.e., greater summation across simultaneously responding frequency regions). Such interactions in timing between the stimulus and cochlear processing might be responsible for differences in simultaneity of firing across component frequencies for the two types of Schroeder stimuli. The positive Schroeder stimulus, whose phases produce earlier initiation of high frequencies relative to low frequencies, would interact with temporal properties of the traveling wave by increasing the temporal disparity, such that there is less simultaneous firing across cochlear neurons. The result of the most effective combination of stimulus timing

and characteristics of the traveling wave might be many fibers recruited simultaneously, and therefore a stronger stimulation of the acoustic reflex, for the negative-Schroeder-phase wave than for the positive. However, a frequency glide rate that is too fast, even if in the ‘‘correct’’ direction to compensate for the traveling wave, might result in a phase dispersion that is inappropriate for the timing characteristics of the basilar membrane, and the across-frequency simultaneity of stimulation might be disrupted. This may underlie the difference observed here in acoustic reflex thresholds and magnitudes, depending on the fundamental frequency (which determines the sweep rate for these stimuli), consistent with an enhancement due to simultaneous firing across frequency. Given a sufficiently low fundamental frequency, the amplitude characteristics of the acoustic reflex (threshold and magnitude) provide evidence that harmonic waveforms with negative Schroeder-phases produce greater excitation than those with positive Schroeder phases. Because of the direction of the traveling wave on the basilar membrane, with high frequencies processed earlier than low frequencies, this particular stimulus phase selection would counteract the traveling wave, resulting in enhanced synchrony of neural firing at many points along the basilar membrane, and thereby produce greater excitation relative to that resulting from the positive Schroeder wave. The positive Schroeder stimulus, with frequencies occurring from high to low over the fundamental period, would reinforce and extend the normal timing of the traveling wave, and increase the time dispersion along the basilar membrane. Similar logic was developed by Dau et al. (2000) in their study optimizing stimuli for ABR. Using a model of traveling wave motion, these investigators calculated an upward-sweeping frequency-modulated ‘‘chirp’’, meant to just compensate for the traveling wave in the human cochlea. They also tested the reverse waveform, a downward chirp. The low-to-high sweep in frequency in the negative Schroeder-phase harmonic complexes used here is analogous to the frequency modulation of the upward chirp, while the positive Schroeder-phase stimuli parallel the frequency sweep in the downward chirp. Differences in acoustic reflex thresholds and magnitudes between negative and positive Schroeder-phase complexes, and the reduction in those differences for the 200-Hz fundamental frequency stimuli, point to a synchronization of neural firing that results from an appropriate compensation of frequency dispersion of the traveling wave. Fig. 7 2 shows the upward sweep in frequency over time within the fundamental periods of each of the three negative Schroeder-phase waveforms (positive Schroeder waveforms are not shown: frequencies resulting from those waveforms sweep from high fre2 We thank Dr. Van Summers for suggesting this figure and performing these calculations.

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Instantaneous Frequency (kHz)

10

8

Dau et al.(2000)

6 Negative 200 Hz Negative 100 Hz 4

2

Negative 50 Hz

0 0

5

10

15

20

Time (ms)

Fig. 7. Instantaneous frequencies as a function of time within the periods for three negative Schroeder-phase waveforms with fundamental frequencies of 50, 100 and 200 Hz. The solid line is the upwardsweeping glide described by Dau et al. (2000).

quency to low frequency, opposite to the direction needed to compensate for the traveling wave). For this figure, instantaneous frequencies were calculated for each of the Schroeder-phase waveforms using a procedure described in Appendix C of deBoer and Nuttall (1997). These frequencies are plotted as a function of time within the fundamental period. The instantaneous frequencies of the upward chirp developed by Dau et al. (2000) are shown on the figure as a dark line. Recall that the Dau et al. chirp was designed to optimally synchronize firing along the basilar membrane by compensating for the delay associated with the traveling wave in each frequency region. It is clear that the 50-Hz fundamental frequency Schroeder-phase wave follows the Dau et al. chirp closely for a significant portion of time, suggesting that the greatest degree of synchronization of firing across frequency would result from that stimulus as an acoustic reflex activator. The 100-Hz fundamental stimulus produces a faster sweep (i.e., change in frequency across time), and the 200 Hz fundamental is even more inappropriate as a compensation for the frequency sweep of the traveling wave. Therefore, just as Dau et al. argued for their ABR stimulus, the lowest fundamental stimulus used here to activate the acoustic reflex would create a greater synchronized firing of auditory neurons across frequency, probably producing a greater total excitation.

5. Conclusions 1. Acoustic reflex thresholds at fundamental frequencies from 50 to 200 Hz are similar for hearing-impaired and normal-hearing subjects when harmonic complexes are constructed with a positive Schroederphase algorithm. For both groups of subjects, the negative-phase complex produced lower acoustic reflex thresholds than the positive-phase for a funda-

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mental frequency of 50 Hz. The normal hearing subjects also demonstrated lower reflex thresholds for a fundamental of 100 Hz. 2. These acoustic reflex threshold patterns are consistent with greater cochlear excitation for the negativephase complexes, as long as the fundamental frequencies are sufficiently low. The greater excitation may be a differential response to an appropriate rate of frequency sweep along the basilar membrane that adequately compensates for the cochlear delays associated with the traveling wave. 3. Reflex magnitudes were generally greater for hearingimpaired subjects than for normal-hearing subjects, and the slopes of the growth functions were greater as well. For both groups of subjects, at the lowest fundamental frequency, reflex magnitudes in response to the negative Schroeder-phase stimuli were greater than for the positive phase stimuli. 4. All of these results suggest that there is a summation of excitation across frequency for these harmonic complexes, and that the summation is influenced by the rate of change of frequency within the stimuli. When the sweep rate is in the opposite direction but of similar rate of frequency change as the traveling wave along the basilar membrane, the strongest acoustic reflexes are observed as lower reflex thresholds and greater reflex magnitudes at suprathreshold levels.

Acknowledgements Thanks to Brian C.J. Moore and an anonymous reviewer for their helpful comments on the manuscript. This work was supported by grant DC 00626 from the National Institutes of Health and was carried out under Work Unit #2567 at Walter Reed Army Medical Center. A preliminary report of this work was presented at the Midwinter meeting of the Association for Research in Otolaryngology, February 2000, St. Petersburg Beach, Florida. All subjects participating in this research provided written informed consent prior to beginning the study. We are grateful to Ken Grant, Van Summers, and Michelle Molis for stimulating discussions of the issues addressed here. The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the Department of the Army or the Department of Defense.

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