REGOLAMENTO ANTIDOPING Approvato dal Consiglio Federale nella riunione del 20 settembre 2003 Il presente sostituisce i regolamenti precedenti “REGOLAMENTO ANTIDOPING F.I.Bi.S. - “ CODICE ANTIDOPING – APPENDICE A” 1 Vista la Dichiarazione approvata il 4 febbraio 1999 dalla Conferenza Mondiale sul Doping svoltasi a Losanna, con la quale si è riaffermato il co
Audiolab.usal.esInferred basilar-membrane response functions for listeners
with mild to moderate sensorineural hearing loss
Christopher J. Placka) and Vit DrgaDepartment of Psychology, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, England Enrique A. Lopez-PovedaInstituto de Neurociencias de Castilla y Leo´n, Universidad de Salamanca, Avda. Alfonso X ‘‘El Sabio’’ s/n,37007 Salamanca, Spain ͑Received 3 September 2003; revised 5 January 2004; accepted 17 January 2004͒ Psychophysical estimates of cochlear function suggest that normal-hearing listeners exhibit acompressive basilar-membrane ͑BM͒ response. Listeners with moderate to severe sensorineuralhearing loss may exhibit a linearized BM response along with reduced gain, suggesting the loss ofan active cochlear mechanism. This study investigated how the BM response changes withincreasing hearing loss by comparing psychophysical measures of BM compression and gain fornormal-hearing listeners with those for listeners who have mild to moderate sensorineural hearingloss. Data were collected from 16 normal-hearing listeners and 12 ears from 9 hearing-impairedlisteners. The forward masker level required to mask a fixed low-level, 4000-Hz signal wasmeasured as a function of the masker–signal interval using a masker frequency of either 2200 or4000 Hz. These plots are known as temporal masking curves ͑TMCs͒. BM response functionsderived from the TMCs showed a systematic reduction in gain with degree of hearing loss. Contraryto current thinking, however, no clear relationship was found between maximum compression andabsolute threshold. 2004 Acoustical Society of America. ͓DOI: 10.1121/1.1675812͔ PACS numbers: 43.66.Dc, 43.66.Mk, 43.66.Sr ͓NFV͔ I. INTRODUCTION
erence to derive the BM response to a tone at CF. Oxenhamand Plack ͑1997͒ measured the forward masker level re- Cochlear hearing loss is associated with an increase in quired to mask a brief signal as a function of the level of the absolute threshold, an abnormally rapid growth in loudness signal ͑referred to here as the growth of masking, or GOM, with level, and a loss of frequency selectivity ͑see Moore, technique͒. When the masker was an octave below the signal 1995 for a review͒. These characteristics may result from frequency of 2000 or 6000 Hz, a given change in signal level dysfunction of the outer hair cells ͑OHCs͒ in the organ of required a much smaller change in masker level for the sig- Corti. The OHCs are thought to be involved in an ‘‘active’’ nal to remain at threshold. This is thought to be because the mechanism that effectively applies gain to stimulation at fre- response to the signal is compressive and the response to the quencies close to the characteristic frequency ͑CF͒ of each masker is linear. Indeed, the shallow off-frequency masking place on the basilar membrane ͑BM͒ ͑see Yates, 1995 for a function ͑masker level plotted against signal level͒ is an es- review͒. The gain is greatest at low stimulation levels, and timate of the BM response function to a tone at CF.
decreases with increasing level. This frequency- and level- A different technique was developed by Nelson et al. dependent gain sharpens BM tuning at low to moderate lev- ͑2001͒. The signal was fixed at a level just above absolute els, and also results in a highly compressive BM response to threshold. The masker level required to mask the signal was mid- and possibly high-level tones close to CF ͑Robles et al., measured as a function of the masker–signal interval to pro- 1986; Ruggero et al., 1997͒. Measurements of BM vibration duce a temporal masking curve ͑TMC͒. For an off-frequency in nonhuman mammals have confirmed that interfering with masker, the TMC is assumed to reflect the decay with time of the function of the OHCs, for example by furosemide injec- the internal effect of the masker: As the masker–signal inter- tion ͑Ruggero and Rich, 1991͒, results in a steeper, more val is increased, the masker level has to increase to compen- sate for the decay. For an on-frequency masker, the TMC Psychophysical techniques based on forward masking reflects the decay of masking, and the compression applied have been used to estimate the growth of response of the to the masker: If the response is compressive, a larger change human BM. Forward masking is used to avoid simultaneous in physical masker level will be required to produce a given interactions on the BM ͑e.g., suppression͒ that complicate change in BM excitation. It follows that an on-frequency the interpretation of the results ͑Oxenham and Plack, 1997͒.
TMC that is steep compared to the off-frequency TMC is Most of these techniques have involved comparisons of the indicative of compression. It is also possible to derive re- effects of maskers at and below the signal frequency. Since sponse functions from TMC data. It is assumed that, for a the BM response to a masker well below CF is linear, the given masker–signal interval, the BM excitation level at the off-frequency masking function can be used as a linear ref- signal place in response to the masker is a constant at thresh-old, regardless of the masker frequency. For a given masker– signal interval, the level of the off-frequency masker re- J. Acoust. Soc. Am. 115 (4), April 2004
quired is an estimate of the BM excitation required at the 35 dB. However, the results may have been compromised by signal place ͑give or take an additive constant on a dB scale͒.
the fact that Moore et al. did not use high-pass noise to mask Therefore, a plot of the on-frequency masker level ͑input spread of excitation ͑see above͒. The compression exponents level͒ against the off-frequency masker level ͑output level͒ is estimated by Moore et al. for normal-hearing listeners were an estimate of the BM response function for the on- at least twice as great as those from GOM studies that in- cluded the high-pass noise ͑Nelson et al., 2001; Oxenham The results from the GOM and TMC studies for normal- and Plack, 1997͒. Hicks and Bacon ͑1999a͒, again using the hearing listeners at high frequencies are broadly consistent GOM technique without high-pass noise, found that mild with the rate of growth of BM velocity at high CFs, as mea- temporary hearing loss induced by aspirin was associated sured in other mammals ͑Lopez-Poveda et al., 2003; Nelson with a change in slope, consistent with a reduction in com- et al., 2001; Oxenham and Plack, 1997; Plack and Drga, pression. Two listeners with mild permanent sensorineural 2003͒. Most GOM and TMC studies report compression ex- hearing loss showed similar effects. In a recent study mea- ponents ͑the slopes of the response functions on dB/dB co- suring GOM for simultaneous notched-noise maskers, Baker ordinates͒ in the range 0.15–0.3. This corresponds to com- and Rosen ͑2002͒ reported a reduction in gain and compres- pression ratios ͑the inverses of the compression exponents͒ sion for a listener with a hearing loss of only 20 dB. How- of between 6.7:1 and 3.3:1. Furthermore, the shapes of the ever, compression estimates were generally quite low in this estimated response functions, with linear low-level regions study, possibly because of suppressive interactions between and compressive midlevel regions, are also consistent with the physiology, suggesting that both behavioral techniques In the present study, the TMC technique was used to measure cochlear processes. However, there are two good estimate the BM response to a tone at CF for listeners with a reasons for favoring the TMC technique. As signal level is range of impairments, from no impairment to mild to mod- increased in the GOM technique, the peak of the traveling erate. The aim was to determine how the shape of the re- wave produced by a high-frequency signal will shift basally sponse function changes with severity of hearing loss, and to on the BM ͑McFadden, 1986͒. This means that the GOM test the hypothesis that mild hearing loss is associated with a technique is probably not measuring the response of a single place on the BM, but rather the growth of the peak of thetraveling wave with level. In addition, as signal level is in- II. METHOD
creased excitation will spread to higher CFs. To prevent lis-teners using information from the high-frequency side of the A. Listeners
excitation pattern ͑where the response growth is much more Sixteen normal-hearing listeners and nine listeners with linear than at the peak͒, a high-pass noise needs to be added mild to moderate hearing impairment participated in the to the stimulus ͑Oxenham and Plack, 1997͒. Nelson et al. study. Normal-hearing listeners ͑ten females and six males, ͑2001͒ demonstrated that GOM curves in the absence of a aged 19–37 years old͒ were mostly students from the Uni- high-pass noise exhibit about half the compression of GOM versity of Essex. All had normal audiogram thresholds curves in the presence of the noise. This finding is consistent ͑within 15 dB ANSI, 1996͒ in octave steps from 250–8000 with the greater compression exponents measured in GOM studies that did not include high-pass noise ͑Hicks and Ba- Hearing-impaired listeners ͑five females and four con, 1999b; Moore et al., 1999; Plack and Oxenham, 2000͒.
males͒, were aged 54 – 68 years old, except for listener RD, Selection of the appropriate noise level is problematic, espe- who was 42 years old. Hearing-impaired listeners reported cially for impaired listeners. The TMC technique avoids both the onset of hearing difficulties between 2 and 15 years ago these complications. In the TMC technique the signal is fixed and had mild-to-moderate amounts of hearing loss. This was at a low level, and hence presumably causes excitation above most likely sensorineural hearing loss since it came on detection threshold over a fixed, relatively small, region of gradually and was unrelated to any acute trauma or known the BM. The region of the BM measured does not change disease. It was most likely age related, except for listeners with masker level, and since the spread of excitation is lim- PJ, SG, and RD, who reported repeated exposure to noisy ited there is no need for a high-pass noise.
environments when younger. RD also had a family history of Both the GOM and TMC techniques have been used to hearing loss. On average, audiogram levels for the hearing- estimate the BM response for listeners with cochlear hearing impaired group were higher than laboratory norms for nor- loss. The results suggest that a hearing loss of greater than mal hearing by 20, 30, and 38 dB at 1000, 2000, and 4000 about 50 dB is associated with an almost linear BM response Hz, respectively. Except for ED, the thresholds at lower fre- ͑Nelson et al., 2001; Oxenham and Plack, 1997͒: The slopes quencies were normal or near normal, suggesting that the of the GOM functions and TMCs do not vary with masker impairments did not have a substantial conductive compo- frequency in these cases ͑providing support for the conten- nent. Although bone-conduction tests were not performed, tion that the psychophysical techniques measure cochlear the close spacing of the on- and off-frequency TMCs for the processes͒. For ears with less severe losses, the results are impaired listeners is also inconsistent with a conductive loss mixed. Moore et al. ͑1999͒ used the ratio of the slopes of ͑see Sec. IV A͒. RD had borderline normal hearing at 4000 off- and on-frequency GOM functions as an estimate of com- Hz, but elevated thresholds ͑35– 42-dB loss͒ at 6000 and pression. They found that the compression exponent only 8000 Hz. His absolute threshold for the brief 4000-Hz signal began to increase markedly as hearing loss increased above in the experiment was 5 dB above the highest absolute J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss TABLE I. Absolute thresholds, stimulus parameters, and estimated BM response parameters for normal-hearing ͑upper͒ and hearing-impaired ͑lower͒listeners, ordered according to the absolute threshold for the signal. Listeners were tested in their right ears unless indicated otherwise. Gain estimates are onlyincluded when the low-level portion of the response function is defined by at least two points. Compression and gain could not be sensibly estimated for RGand ES due to the variability of their data. Values marked with asterisks are from response functions generated by interpolation of the off-frequency TMCs.
threshold for the normal-hearing group. Audiogram thresh- hearing listeners and from 33–71-dB SPL for hearing- olds, and absolute thresholds for the signal used in the ex- impaired listeners. Masker level was varied trial by trial.
A low-level notched noise was gated on and off with the All of the listeners were naive except for EK, IY, PP, and masker. This was intended as a temporal cue to help reduce VD. The normal-hearing listeners, except for AC, CN, ES, possible confusion effects ͑Neff, 1986͒ and not as a source of and RB, had 4 – 8 h practice in pilot studies for the current masking. The noise was white except for a notch at the signal experiment. AC, CN, ES, and RB, and all of the hearing- frequency ͑filter cutoffs at 0.883 f s and 1.117 f s , with 90- impaired listeners received 1–2 h practice in blocks used to dB/oct filter slope͒. For normal-hearing listeners and listener determine parameters for them in the main experiment.
RD, the spectrum level in the passband was set 30 dB below There were no systematic improvements in thresholds in the the signal level ͑i.e., 20 dB below signal absolute threshold͒.
experimental sessions. Listeners were paid £5 per hour for For the remaining hearing-impaired listeners the spectrum level was set to either 40, 50, or 60 dB below the signal levelso that it fell in the range Ϫ5 to 11 dB. For most hearing-impaired listeners, setting the spectrum level to 30 dB below B. Stimuli and equipment
the signal meant having spectrum levels almost up to 40 dB, The experiment involved forward masking of tonal sig- resulting in masking due to the noise. Setting the spectrum nals by tonal maskers. The signal had a frequency of f level to a level between Ϫ5 and 11 dB was practical in that ϭ4000 Hz and an absolute duration of 8 ms ͑4-ms raised- hearing-impaired listeners could make use of temporal infor- cosine ramps, 0-ms steady state͒. The masker had a fre- mation at lower frequencies without the noise contributing to masking at 4000 Hz. As described above, most of the ration of 104 ms ͑2-ms raised-cosine ramps, 100-ms steady hearing-impaired listeners had elevated thresholds at 4000 state͒. Silent masker–signal intervals ͑masker envelope off- Hz but normal or near-normal absolute thresholds for fre- set to signal envelope onset͒ ranged from 0–100 ms in steps quencies below 2000 Hz. Notched-noise levels for each in- of 5 or 10 ms, with the set of intervals used dependent on each listener’s performance. The signal level was set to 10 The experiment was run using custom-made software on dB SL, which ranged from 15–27-dB SPL for normal- a PC workstation located outside a double-walled sound- J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss attenuating booth. Stimuli were digitally generated and were except that signal level was varied using a two-down, one-up produced using an RME Digi96/8 PAD 24-bit soundcard set at a clocking rate of 48 000 Hz. The soundcard includes anantialiasing filter. The headphone output of the soundcard III. RESULTS AND ANALYSES
was fed via a patch panel in the sound-booth wall, withoutfiltering or amplification, to Sennheiser HD 580 circumaural A. Temporal masking curves
headphones. Each listener sat in the booth and decisions Individual TMCs are presented in Fig. 1 for normal- were recorded via a computer keyboard. Listeners viewed a hearing listeners and in Fig. 2 for hearing-impaired listeners.
computer monitor through a window in the sound booth.
In general, on-frequency TMCs ͑triangles͒ are steeper, in part Lights on the monitor display flashed on and off concurrently or in whole, than the accompanying off-frequency TMCs.
with each stimulus presentation and provided feedback at the Assuming the BM response to off-frequency maskers is lin- ear at the signal place, then steeper portions of the on-frequency TMC indicate a compressive response to the on-frequency masker. Such results were found for both the C. Procedure
normal-hearing and the hearing-impaired groups.
All stimuli were presented monaurally. Normal-hearing For three impaired ears, RC(l), MB, and PJ, it was not listeners were tested in their right ear. Hearing-impaired lis- possible to reliably measure on-frequency thresholds at the teners were tested in their right ear, or in both left and right longest masker–signal interval. In two successive runs, they ears if their audiogram thresholds at 4000 Hz differed across consistently detected the signal when the 4000-Hz masker ears by more than 10 dB. Those tested in both ears wore an was at 100 dB SPL. The equipment clipped at the next higher earplug in their contralateral ear to prevent the possibility of level in the adaptive track ͑102 dB SPL͒, so the data point for the longest masker–signal interval presented in Fig. 2 for The experiment used a two-interval, forced-choice adap- these three listeners was set at 100 dB SPL, and in each case tive tracking procedure with the interstimulus interval set to this value was used ͑when required͒ in the analyses de- 500 ms. The signal level was fixed at 10 dB SL and the scribed below. Limiting the level in this way resulted in un- masker level was varied adaptively using a two-up, one- derestimates of their thresholds and consequently, based on down rule to obtain the masker level needed to achieve 70.7 linear extrapolation of their off-frequency TMCs, underesti- percent correct ͑Levitt, 1971͒. The masker frequency and mates of the amount of compression ͑overestimates of the masker–signal interval were fixed in any given block of tri- compression exponents͒. For several impaired ears, the off- als. For normal-hearing listeners, the initial masker level was frequency masker levels at the longer intervals also clipped set to 0 dB SPL. The step size of the adaptive track was 8 dB at some stage during the adaptive track on every replication, for the first four turnpoints and 2 dB for 12 subsequent turn- and these measurements were aborted ͓see MB, PJ, DJ(l), points. Data for listeners RD and BH were collected using and BH in Fig. 2͔. However, unlike the on-frequency mea- these settings, but we found it was desirable to slightly surements for the three ears described above, the signal was modify the procedure for the rest of the hearing-impaired only occasionally detected with the masker at the clipping listeners, due to limitations in the equipment’s maximum threshold ͑the adaptive track touched the clipping point be- output ͑102-dB SPL rms͒. The modifications were that the fore retreating͒. It may be assumed that the ‘‘true’’ off- initial masker level was set to 20– 40 dB below estimated frequency masker level for these missing points lies some- threshold, and the step size was 4 dB for the first four turn- points and 2 dB for the 12 subsequent turnpoints. For all A surprising aspect of the data is that the slopes of the listeners, the mean of the last 12 turnpoints was taken as the off-frequency TMCs appear to be different for the normal- threshold estimate for each block of trials. If the standard hearing and hearing-impaired listeners. Two analyses were deviation of the turnpoints was greater than 6 dB the esti- conducted to illustrate and quantify this difference. First, the mate was discarded and the block was later repeated. Data slopes of the straight lines connecting consecutive points on were also discarded and repeated if possible for any blocks in the off-frequency TMCs were calculated for each listener.
which the masker clipped more than twice at levels above The slope values for all the listeners were then combined and ordered by masker–signal interval or by masker level. The Listeners ran blocks of trials lasting 2– 4 min per block upper panels of Fig. 3 show running averages of these val- and spent 15– 60 min in the sound booth at any one time, ues, plotted against running averages of masker–signal inter- taking breaks as needed. A replication consisted of a com- val ͑upper left͒ and masker level ͑upper right͒. The running plete run of 10–20 blocks per listener, depending on the averages were calculated separately for the normal-hearing range of the masker–signal interval at each f m , which was and hearing-impaired groups. The graphs indicate that there determined during each listener’s practice trials. The order of are some trends in the data. First, the off-frequency TMC blocks was randomized across masker–signal interval and f m slopes for the normal-hearing group show a tendency to de- until all blocks in a replication had been completed. Unless crease with increasing masker–signal interval. The correla- otherwise indicated, the mean threshold across four replica- tion between masker–signal interval and slope is significant tions was taken as the threshold estimate for each combina- for the normal-hearing group (rϭϪ0.231, nϭ106, p tion of masker–signal interval and f 0.017). On the other hand, there is little variation in slope for the signal were measured using the same basic procedure, with masker–signal interval for the hearing-impaired group, J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss FIG. 1. TMCs for normal-hearing listeners, showing mean masker level at threshold as a function of masker–signal interval for on-frequency ͑4000-Hz͒maskers ͑triangles͒ and off-frequency ͑2200-Hz͒ maskers ͑circles͒.
and the correlation is not significant (rϭϪ0.155, nϭ48, p absolute threshold and off-frequency TMC slope at a specific ϭ0.293). Second, the off-frequency TMC slopes for the masker–signal interval and at a specific masker level.
normal-hearing group show a tendency to decrease with in- Second-order polynomials were fit to the off-frequency creasing masker level, and the correlation between level and TMCs for each listener, and the slopes of the functions cal- slope is significant (rϭϪ0.271, nϭ106, pϭ0.005). The culated ͑analytically͒ at a masker–signal interval of 30 ms correlation between level and slope is not significant for the and, separately, at a masker level of 85 dB SPL. A slope hearing-impaired group (rϭϪ0.159, nϭ48, pϭ0.282), al- value was only included when the masker–signal interval though the range of levels for this group is much less than ͑either 30 ms, or the calculated masker–signal interval for an 85-dB SPL masker͒ fell within the range of intervals tested A second analysis investigated the relationship between for that listener. The calculated slopes are shown in the lower FIG. 2. As Fig. 1, except showing TMCs for hearing-impaired listeners.
J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss FIG. 3. The upper panels show the slopes of the2200-Hz TMCs, collapsed across listeners and plottedas running averages over 20 consecutive points. Theslopes are shown as a function of masker–signal inter-val ͑upper left͒ and masker level ͑upper right͒. Thelower panels show scatterplots of 2200-Hz TMC slopeagainst signal absolute threshold. The slopes were de-rived by fitting second-order polynomials to the TMCdata for each listener. The slopes at a masker–signalinterval of 30 ms ͑lower left͒ and at a masker level of85 dB SPL ͑lower right͒ were calculated from the fittedfunctions. The lines show linear regression fits, withequations and R2 values displayed on the figure.
two panels of Fig. 3, plotted against the absolute thresholds signal and the masker at threshold should have been unaf- for the signal. There is a significant negative correlation be- fected by the hearing loss, if there was no additional source tween absolute threshold and slope at a 30-ms masker–signal of masking for the normal-hearing listeners.
interval (rϭϪ0.443, nϭ27, pϭ0.021), but no significant At a masker–signal interval of 10 ms, the mean differ- correlation between absolute threshold and slope at an 85-dB ence between signal level and on-frequency masker level is SPL masker level (rϭϪ0.334, nϭ22, pϭ0.129). In sum- Ϫ1.7 dB for the normal-hearing group and 2.0 dB for the mary, the results show that at short masker–signal intervals hearing-impaired group. At an interval of 20 ms, the values the off-frequency TMC slopes are shallower for the hearing- are 6.1 and 5.5 dB, respectively. So, although there is a sug- impaired listeners than for the normal-hearing listeners.
gestion that the noise may have contributed to masking at the However, the difference may be related to the fact that the 10-ms gap, there appears to have been no effect at a 20-ms masker thresholds were at a higher level for the hearing- gap, for which there is a clear difference in off-frequency impaired listeners. There appears to be little difference in slope between the normal-hearing and hearing-impairedgroups when the TMCs are matched for masker level.
B. Response functions
It is conceivable that the results for the shorter masker– signal intervals were influenced by the notched noise that Following the approach of Nelson et al. ͑2001͒, TMCs was presented as a cue to the offset of the masker. The noise for each listener were converted into BM response functions level was generally higher relative to the signal level for the by plotting the off-frequency masker threshold against on- normal-hearing group compared to the hearing-impaired frequency masker threshold, paired according to masker– group ͑see Table I͒. Although in all conditions the signal was signal interval. For several hearing-impaired ears, off- clearly above threshold in the presence of the noise alone, if frequency masker levels were not available at all the the noise had contributed to the masking of the signal at the masker–signal intervals for which on-frequency masker lev- short masker–signal intervals, then the masker level at els were measured. For these ears, it was assumed that the threshold may have been artificially lowered for the normal- slopes of the off-frequency TMCs do not change signifi- hearing group at the short intervals ͑both on and off fre- cantly with masker–signal interval. Given that there was no quency͒ leading to an increase in TMC slope. One way to significant correlation between masker–signal interval and test this hypothesis is to examine the masker levels at thresh- slope for the hearing-impaired listeners ͑see Sec. III A͒, this old for the on-frequency masker. It is assumed that, for a was felt to be a reasonable assumption. For those masker– given masker–signal interval at threshold, the ratio of BM signal intervals missing a measured off-frequency masker velocity in response to the signal to BM velocity in response level, an off-frequency masker level was generated by inter- to the masker is constant. Furthermore, the BM response to a polation, using a linear fit to the off-frequency data.
low-level on-frequency masker should have been affected in The response functions for normal-hearing listeners and a similar way as the response to the 10-dB SL signal by any for hearing-impaired listeners are plotted in Figs. 4 and 5, attenuation ͑or loss of gain͒ resulting from the hearing im- respectively. These show the growth of level with masker– pairment: If the hearing impairment resulted in the response signal interval for the off-frequency masker relative to the to the signal being attenuated by x dB, then the response to growth for the on-frequency masker. Open symbols indicate the masker should also have been attenuated by x dB. It fol- those points that were generated by interpolating the off- lows that the difference between the physical levels of the frequency TMCs. The positive diagonal (y ϭx) is included J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss FIG. 4. Estimated response functions for normal-hearing listeners, showing the 2200-Hz masker level at threshold plotted against the 4000-Hz masker levelat threshold, paired according to masker–signal interval. The positive diagonal ͑straight line͒ indicates the expected response of a passive, linear system. Thevertical line indicates signal absolute threshold (re: the x axis͒. The kinked line shows the piecewise linear fit ͑see the text for details͒.
in Figs. 4 and 5 to indicate the expected response of a linear the response functions with slope less than unity ͑compres- system with 0-dB gain ͑see below͒. Masker–signal intervals over which the on-frequency TMC is parallel to the off- Most of the normal-hearing listeners show evidence of frequency TMC translate to portions of the response func- compression, having shallow portions in their response func- tions with slope unity, implying a linear BM response.
tions in Fig. 4, although this is not so clear for listeners RG Masker–signal intervals over which the on-frequency TMC and ES, whose data are variable. Most of the hearing- is steeper than the off-frequency TMC translate to portions of impaired listeners also show evidence of compression, as FIG. 5. As Fig. 4, except for hearing-impaired listeners. Open circles show points on the response functions that were estimated by interpolation of theoff-frequency data, using straight-line fits to the off-frequency TMCs. Left and right ears are indicated by ͑l͒ and ͑r͒, respectively.
J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss seen in the shallow portions of their response functions in masker͒ are both expressed in dB. The function was fit to the Fig. 5. Indeed, many of the hearing-impaired response func- data using the fminsearch function in MATLAB to satisfy a tions appear at least as compressive as those seen for normal- least-squares regression criterion. The slopes of the lower hearing listeners, although the compression extends over a and upper sections were fixed at unity ͑linear response͒, smaller range of levels for the former. This suggests that BM while the slope of the middle section ͑c͒ and the breakpoints compression is present even when sensitivity is much re- (BP1 and BP2) were varied by the fitting procedure. The duced compared to normal-hearing listeners. Some normal- only constraint on the fitting procedure was that the compres- hearing listeners ͑VD,PP,IG,NB͒ show evidence of a return sion exponent c was not allowed to be negative; otherwise, to linearity at the highest masker levels, with on-frequency the parameters were allowed to vary freely. In some cases TMCs becoming shallow at long masker-signal intervals, and either the lower breakpoint or the upper breakpoint estimated hence the response functions becoming steeper at high lev- by the fitting procedure was beyond the range of the data, so els. This is not the case in general for hearing-impaired lis- that effectively the data were fit using a reduced number of teners. If such a pattern is to be found with hearing-impaired parameters. The fits were first made to the response function listeners, it must occur at very high levels ͑Ͼ100 dB SPL͒.
data without any off-frequency interpolation ͑just the filledsymbols in Figs. 4 and 5͒, and then separately including theinterpolated data ͑i.e., filled and open symbols͒. Fits were C. Estimates of gain and compression
not included when there were less than five points on the The maximum gain of the active mechanism can be es- response function ͓i.e., for DJ(r), MB, RC(l), PJ, and timated using the horizontal distance between the left-most, DJ(l), without interpolated data͔. The lines fit to the re- linear portion of a response function and the positive diago- sponse functions including the interpolated data are shown in nal. This is an estimate of the difference between the levels Figs. 4 and 5. The fits for listeners RG and ES had high rms of a 4000-Hz masker and a 2200-Hz masker required to pro- errors ͑9 and 7 dB, respectively͒ and are not included in the duce the same BM response. If it is assumed that no gain is figures or in subsequent analyses. For the other listeners, applied to the off-frequency masker ͑so that the positive di- however, the fits generally provide a good description of the agonal approximates the off-frequency response even at low input levels͒, then this estimate is equivalent to the difference Scatterplots of maximum gain against signal absolute in the BM response between a low-level masker at 4000 Hz threshold and compression against signal absolute threshold and a low-level masker at 2200 Hz. This measure of gain is are shown in Fig. 6. Gain and compression estimates were similar to that used by others, e.g., Ruggero et al. ͑1997͒, in taken from the three-section fits. A gain estimate was in- that it estimates the difference between the active BM re- cluded only if there were at least two points on the response sponse and the maximum passive response at signal place.
function that were below BP1 . The results are shown sepa- The data of Ruggero et al. suggest that the off-frequency rately for fits to the response-function data without interpo- response to a tone at 0.55ϫCF is slightly less ͑by 2– 4 dB͒ lation ͑left-hand panels͒ and for fits to the data including the than that of the maximum passive response. Since the pas- interpolated off-frequency values ͑right-hand panels͒. The sive response has broad tuning, it is assumed that any dis- fits that involved interpolated values are shown as open sym- crepancy between the off-frequency response and the maxi- bols. Data from both normal-hearing and hearing-impaired mum passive response is approximately constant across listeners are presented together in each graph. A straight-line individuals. If so, this should not affect any correlation of fit to the scatterplot data, and the squared correlation coeffi- gain with absolute threshold in our analyses below.
cient, are also displayed. Individual gain and compression To help quantify gain and compression, a three-section fit was applied to each listener’s BM response function As shown by Fig. 6, the estimated gain of the cochlear ͑Lopez-Poveda et al., 2003; Yasin and Plack, 2003͒. The amplifier decreases systematically with increasing hearing function comprised a linear low-level region ͓Eq. ͑1͔͒, a loss. The correlation is statistically significant both for the compressive mid-level region ͓Eq. ͑2͔͒, and a linear high- data without interpolation (rϭϪ0.930, nϭ16, pϽ0.0005; level region ͓Eq. ͑3͔͒. The three sections were joined by two slopeϭϪ0.736 dB/dB͒ and for the data with interpolation breakpoints, a lower breakpoint (BP1) joining sections 1 and (rϭϪ0.951, nϭ22, pϽ0.0005; slopeϭϪ0.647 dB/dB͒.
2, and an upper breakpoint (BP2) joining sections 2 and 3.
Figure 6 also shows that, although there is a range of com- The equations for the three sections are given by pression values for both normal-hearing listeners ͑left half ofthe data͒ and hearing-impaired listeners ͑right half of the data͒, there is little correlation between compression and ab-solute threshold. The correlations are not significant either for the data without interpolation (rϭ0.101, nϭ21, p ϭ0.662) or for the data with interpolation (rϭ0.284, n ϭ26, pϭ0.159). For some of the more impaired ears the compressive region is defined by only a couple of points where G is the gain ͑dB͒, c is the slope of the compressive ͑often interpolated͒. However, the ears with milder impair- region ͑dB/dB͒ or the compression exponent, k ϭ ments ͓RD, JC, ED(l), SG, DJ(r), RC(r), and ED(r)] have BP2(cϪ1)ϩk1 . Lin input level, level of 4000-Hz well-defined shallow sections in their response functions and compression exponents within the normal range ͑0.29, 0.26, J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss FIG. 6. Scatterplots of maximum gain against signalabsolute threshold ͑upper panels͒, and response-function slope against signal absolute threshold ͑lowerpanels͒, at 4000 Hz. The left-hand panels show the re-sults for response functions generated without interpo-lation. The right-hand panels include the results for re-sponse functions that were generated using interpolatedoff-frequency masker levels ͑indicated by the opensymbols͒. Gain estimates are only included when thelow-level portion of the response function is defined byat least two points ͑see Table I͒.
0.15, 0.29, 0.21, 0.28, and 0.37, respectively, for the interpo- ponent, should all be unaffected by the hearing loss, and lated data͒. The mean compression exponent for the interpo- hence independent of the degree of hearing loss. For an ear lated data is 0.20 for the normal-hearing listeners and 0.26 with purely OHC dysfunction, however, the maximum gain should be strongly related to the absolute threshold. Specifi- There is an issue regarding whether the three-section cally, a plot of gain ͑in dB͒ against absolute threshold ͑in dB͒ straight-line fits provide an accurate characterization of the should be a straight line with a slope of Ϫ1. Turning down response functions. Third-order polynomials have been used the gain by 10 dB should result in an increase in absolute previously to fit response functions ͑Nelson et al., 2001; Plack and Drga, 2003͒. Such fits were attempted on the If the hearing loss experienced by our listeners were present data but gave very inconsistent results, with negative simply a matter of non-frequency-specific attenuation prior slopes in some cases. It was felt that the three-section fits, to the BM, as might result from conductive hearing loss, then although not ideal, do capture the main features of the re- both on- and off-frequency TMCs would increase by the sponse functions for the normal-hearing and hearing- same amount and, consequently, the estimated maximum impaired listeners: The reduction in gain with hearing loss gain would remain unchanged as a function of hearing loss.
͑also reflected in the vertical spacing between the on- and Similarly, pure IHC loss ͑post-BM attenuation͒ should result off-frequency TMCs͒, and the preservation of a shallow in no change in the estimated maximum gain ͑although it is slope in the response function ͑compression͒, even for ears only possible to measure the lower breakpoint on the re- sponse function if it is above absolute threshold͒. These pre-dictions do not seem to describe the present data. The strong IV. DISCUSSION
relation between maximum gain and absolute threshold ͑Fig.
6͒ suggests that the hearing loss in the impaired listeners A. Consequences of inner and outer hair cell
tested here was mainly the result of OHC dysfunction. Off- dysfunction
frequency TMCs were somewhat higher in level for the An elevation in absolute threshold may result from a hearing-impaired compared to the normal-hearing group, but dysfunction of the inner hair cells ͑IHCs͒ or of the OHCs it was the general increase in level for the on-frequency ͑see Moore, 1995͒. IHC dysfunction reduces the efficiency of TMCs relative to the off-frequency TMCs that characterized transduction of BM vibration ͑hence reducing sensitivity͒ but the impaired group, again consistent with OHC damage. In- is not thought to affect the mechanical properties of the BM cluding the interpolated data, the plot of gain against abso- itself ͑Liberman et al., 1986͒. OHC dysfunction affects the lute threshold has a slope of Ϫ0.65, which suggests that most response of the BM, but not the transduction process per se.
of the threshold elevation can be attributed to a reduction in Now, imagine a situation in which a cochlea has damage to gain. The fact that the slope was not Ϫ1 suggests that there the IHCs only. For a given input level, the response proper- may have been some IHC dysfunction among the listeners ties of the BM should be identical to that for a healthy ear.
͑contributing to perhaps 35% of the threshold elevation for According to the measures described earlier, the maximum those ears for which the gain was measurable͒. Indeed, from gain of the active mechanism, the input level at the first the results of other studies examining the relative proportions breakpoint in the response function, and the compression ex- of IHC and OHC hearing loss, it would be surprising if there J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss FIG. 7. BM response functions for normal-hearing andhearing-impaired listeners. The normal response func-tion is an average function generated from the presentdata ͑see the text for details͒. In panels ͑A͒ to ͑C͒ theresponse functions for the hearing-impaired listenersare hypothetical. In panel ͑A͒, the gain for hearing-impaired listeners is reduced equally at all input levelsup to the passive response. In panel ͑B͒, the reductionin gain is greatest at low input levels, with a diminish-ing reduction as level is increased. In panel ͑C͒, thegain is reduced at low input levels, but unaffected athigh input levels. Panel ͑D͒ shows average responsefunctions, impaired listeners, generated from the present data ͑seethe text for details͒. In panel ͑D͒, the thin vertical linesshow the average absolute thresholds for the signal, andthe thin horizontal lines the associated response levels,for the normal-hearing and hearing-impaired listenersused to generate the response functions.
were not some evidence of IHC dysfunction ͑Lopez-Poveda associated with a reduction in the gain at the lower input et al., 2004; Moore and Glasberg, 1997; Moore et al., 1999͒.
levels only, and not across the whole range of input levels IHC dysfunction will raise the output level on the BM re- that are affected by the active mechanism. This is why the sponse function that corresponds to absolute threshold, and slope of the compressive part of the response function did may explain why the low-level linear segment on the re- not vary significantly with absolute threshold ͑see Fig. 6͒.
sponse function is generally shorter for the hearing-impaired In this respect, the present data do not appear to be con- listeners than for the normal-hearing listeners ͑see Figs. 4 sistent with some physiological models of hearing loss. The and 5, and Sec. IV B͒. However, given that OHC dysfunction BM response function of a chinchilla injected 40 min previ- was probably the main cause of the reduction in sensitivity, ously with furosemide showed a reduction in gain at all lev- what do the present results tell us about the effects of OHC els ͑Ruggero and Rich, 1991͒, more similar to option ͑A͒ in Fig. 7. As with the present data, however, BM compressionwas relatively unaffected by this mild hearing loss. Muru- B. Effects of outer hair cell dysfunction on the BM
gasu and Russell ͑1995͒ report guinea pig displacement mea- response
surements during salicylate perfusion. Some of their re-sponse functions show a reduction in gain at all levels, but To aid the discussion of the effects of OHC dysfunction some show an effect only at low levels, similar to the func- on the shape of the BM response function, three different tions reported here. Recent auditory-nerve recordings from hypothetical scenarios are illustrated in Fig. 7. Each panel of cats with noise-induced hearing loss also seem consistent the figure shows the normal response function ͑continuous with the present data ͑Heinz et al., in press͒. For mild hear- black line, generated from the present data as described be- ing loss, a measure of the total auditory-nerve activity low͒, the passive response function with no active mecha- showed a reduction in response at low levels but not at high nism ͑thin dotted line͒, and a hypothetical response for a levels, consistent with a reduction in gain at low levels only.
listener with mild hearing loss ͑alternate dashes and dots͒. In The thin vertical and horizontal lines in panel ͑D͒ of Fig.
the upper left panel ͑A͒ the gain is reduced equally at all 7 show the average absolute threshold for the signal, and the input levels up to the passive response. In the upper right associated response level, for those normal-hearing and panel ͑B͒ the reduction in gain is greatest at low input levels, hearing-impaired listeners used to generate the average re- with a diminishing reduction as level is increased. In the sponse functions. Notice that the BM response level at lower-left panel ͑C͒ the gain is reduced at low input levels, threshold is higher for the hearing-impaired group. This may but unaffected at high input levels. The lower-right panel ͑D͒ be interpreted as a reduction in sensitivity resulting from shows average response functions generated from the present IHC dysfunction. These lines also illustrate the point made in data. These functions were obtained by averaging the x and y Sec. IV A that the linear segment of the response function values of the lower breakpoints and the compression expo- measurable in the experiment ͑threshold to first breakpoint͒ nents derived from the fitting procedure, across the normal- is shorter for the hearing-impaired listeners.
hearing listeners and across the hearing-impaired listeners.
Upper breakpoints were omitted because they often could C. Off-frequency temporal masking curves
not be specified ͑the values from the fitting procedure wereabove the highest points on the response functions͒, and ͑as A surprising incidental finding of the experiment was for the gain estimates͒ the results for ears with less than two that the slopes of the off-frequency TMCs were shallower for points on the response function below the lower breakpoint hearing-impaired listeners than for normal-hearing listeners were also omitted. For those ears that remained, it seems when compared at short masker–signal intervals. Recently, clear that the data are best summarized by option C. Al- Rosengard et al. ͑2003͒ have also reported shallow off- though there are individual differences in the response func- frequency TMCs in hearing-impaired listeners compared to tions, overall it appears that mild cochlear hearing loss is normals. The analysis described in Sec. III A suggests that J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss the difference may be related to the higher off-frequency ACKNOWLEDGMENTS
masker levels for the hearing-impaired listeners. When the The authors thank the Associate Editor and two anony- off-frequency TMC slopes were compared at the same mous reviewers for very helpful comments on an earlier draft masker level ͑or at long masker–signal intervals͒ there was of the manuscript, and especially for spotting that the off- little difference between the groups.
frequency TMC slopes decrease at high levels. The authors According to the interpretation of TMCs outlined in the also thank Andrew Oxenham for comments on an earlier Introduction, the shape of the off-frequency TMC should de- draft of the manuscript, and Ray Meddis for valuable discus- pend only on the internal decay of forward masking, a mea- sions regarding the interpretation of the data. The research sure of temporal resolution. There is little evidence to sug- was supported by EPSRC Grant GR/N07219. Author EALP gest that hearing-impaired listeners in general have a deficit was supported by FIS PI020343 and G03/203.
in temporal resolution, at least as measured by tasks such asgap detection with sinusoidal markers ͑Moore and Glasberg,1988͒ and modulation detection ͑Bacon and Gleitman, 1992; Bacon, S. P., and Gleitman, R. M. ͑1992͒. ‘‘Modulation detection in subjects
with relatively flat hearing losses,’’ J. Speech Hear. Res. 35, 642– 653.
Moore et al., 1992͒. However, it is the case that the hearing- Baker, R. J., and Rosen, S. ͑2002͒. ‘‘Auditory filter nonlinearity in mild/
impaired listeners in the present study were older and re- moderate hearing impairment,’’ J. Acoust. Soc. Am. 111, 1330–1339.
ceived less training than the normal-hearing listeners, and Furukawa, T., and Matsuura, S. ͑1978͒. ‘‘Adaptive rundown of excitatory
this may have influenced temporal processing. If the effects post-synaptic potentials at synapses between hair cells and eighth-nerve
fibers in the goldfish,’’ J. Physiol. ͑London͒ 276, 193–209.
of hearing impairment on the off-frequency TMCs were not a Heinz, M. G., Scepanovic, D., Sachs, M. B., and Young, E. D. ͑in press͒.
consequence of a general temporal resolution deficit, two ‘‘Normal and impaired level encoding: Effects of noise-induced hearing possibilities remain. The first is that the aspect of temporal loss,’’ in Auditory Signal Processing: Physiology, Psychoacoustics, and resolution measured by forward masking is unconnected Models, edited by D. Pressnitzer, A. de Cheveigne´, S. McAdams, and L.
Collet ͑Springer, New York͒.
with the aspect ͑or aspects͒ measured in other tasks, and that Hicks, M. L., and Bacon, S. P. ͑1999a͒. ‘‘Effects of aspirin on psychophysi-
hearing-impaired listeners have a specific deficit in forward cal measures of frequency selectivity, two-tone suppression, and growth of masking. This might be possible if forward masking is a masking,’’ J. Acoust. Soc. Am. 106, 1436 –1451.
Hicks, M. L., and Bacon, S. P. ͑1999b͒. ‘‘Psychophysical measures of au-
consequence of adaptation at the IHC/auditory nerve synapse͑ ditory nonlinearities as a function of frequency in individuals with normal Furukawa and Matsuura, 1978; but see Oxenham, 2001; hearing,’’ J. Acoust. Soc. Am. 105, 326 –338.
Smith, 1979͒, and that IHC dysfunction affects this in some Levitt, H. ͑1971͒. ‘‘Transformed up-down methods in psychoacoustics,’’ J.
way. The second possibility is that the auditory system re- Acoust. Soc. Am. 49, 467– 477.
Liberman, M. C., Dodds, L. W., and Learson, D. A. ͑1986͒. ‘‘Structure–
sponds nonlinearly to an off-frequency masker, either at the function correlation in noise-damaged ears: A light and electron- level of the BM or more centrally. To account for the differ- microscopic study,’’ in Basic and Applied Aspects of Noise-Induced Hear- ence between the normal and impaired ears, the off- ing Loss, edited by R. J. Salvi, D. Henderson, R. P. Hamernik, and V.
frequency compression exponent may be invariant with level Lopez-Poveda, E. A., Plack, C. J., and Meddis, R. ͑2003͒. ‘‘Cochlear non-
but increased in impaired ears ͑leading to a shallow TMC linearity between 500 and 8000 Hz in listeners with normal hearing,’’ J.
slope in impaired ears͒, or the compression exponent may be Acoust. Soc. Am. 113, 951–960.
increased at high levels ͑leading to a shallow TMC slope at Lopez-Poveda, E. A., Plack, C. J., Meddis, R., and Blanco, J. L. ͑2004͒.
high levels͒. The finding that the TMC slopes were similar ‘‘Cochlear nonlinearity between 500 and 8000 Hz in listeners with mod-erate cochlear hearing loss,’’ Abstracts of the Twenty-Seventh Annual for normal and impaired ears at long masker–signal intervals Midwinter Meeting of the Ass. Res. Otolaryngol., Daytona Beach, FL.
McFadden, D. ͑1986͒. ‘‘The curious half octave shift: Evidence for a basal-
ward migration of the travelling-wave envelope with increasing intensity,’’in Basic and Applied Aspects of Noise-Induced Hearing Loss, edited by R.
J. Salvi, D. Henderson, R. P. Hamernik, and V. Colletti ͑Plenum, New V. CONCLUSIONS
Moore, B. C. J. ͑1995͒. Perceptual Consequences of Cochlear Damage
BM response functions derived from on- and off- ͑Oxford University Press, Oxford͒.
frequency TMCs generally show a linear low-level Moore, B. C. J., and Glasberg, B. R. ͑1988͒. ‘‘Gap detection with sinusoids
region and a compressive midlevel region. With hear- and noise in normal, impaired and electrically stimulated ears,’’ J. Acoust.
ing loss the low-level region shifts to the right, re- Soc. Am. 83, 1093–1101.
Moore, B. C. J., and Glasberg, B. R. ͑1997͒. ‘‘A model of loudness percep-
flecting the reduction in sensitivity, but there is little tion applied to cochlear hearing loss,’’ Aud. Neurosci. 3, 289–311.
evidence for a change in the slope of the compressive Moore, B. C. J., Shailer, M. J., and Schooneveldt, G. P. ͑1992͒. ‘‘Temporal
region with losses up to 50 dB or so.
modulation transfer functions for bandlimited noise in subjects with co- The results suggest that mild to moderate sensorineu- chlear hearing loss,’’ Br. J. Audiol. 26, 229–237.
Moore, B. C. J., Vickers, D. A., Plack, C. J., and Oxenham, A. J. ͑1999͒.
ral hearing loss is associated with a reduction in the ‘‘Inter-relationship between different psychoacoustic measures assumed to gain for low-level CF tones, but little change in the be related to the cochlear active mechanism,’’ J. Acoust. Soc. Am. 106,
gain for higher-level tones, and consequently little Murugasu, E., and Russell, I. J. ͑1995͒. ‘‘Salicylate ototoxicity: The effects
on basilar membrane displacement, cochlear microphonics, and neural re- sponses in the basal turn of the guinea pig cochlea,’’ Aud. Neurosci. 1,
frequency TMCs than normal-hearing listeners when measured at short time intervals. However, there is Neff, D. L. ͑1986͒. ‘‘Confusion effects with sinusoidal and narrow-band-
little effect of impairment on TMC slope at long time noise forward maskers,’’ J. Acoust. Soc. Am. 79, 1519–1529.
Nelson, D. A., Schroder, A. C., and Wojtczak, M. ͑2001͒. ‘‘A new procedure
intervals, or if the TMCs are matched for off- for measuring peripheral compression in normal-hearing and hearing- impaired listeners,’’ J. Acoust. Soc. Am. 110, 2045–2064.
J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss Oxenham, A. J. ͑2001͒. ‘‘Forward masking: Adaptation or integration?’’ J.
from growth-of-masking functions and temporal masking curves,’’ Ab- Acoust. Soc. Am. 109, 732–741.
stracts of the Twenty-Sixth Annual Midwinter Research Meeting of the Oxenham, A. J., and Plack, C. J. ͑1997͒. ‘‘A behavioral measure of basilar-
Ass. Res. Otolaryngol., Daytona Beach, FL.
membrane nonlinearity in listeners with normal and impaired hearing,’’ J.
Ruggero, M. A., and Rich, N. C. ͑1991͒. ‘‘Furosemide alters organ of Corti
Acoust. Soc. Am. 101, 3666 –3675.
mechanics: Evidence for feedback of outer hair cells upon the basilar Plack, C. J., and Drga, V. ͑2003͒. ‘‘Psychophysical evidence for auditory
membrane,’’ J. Neurosci. 11, 1057–1067.
compression at low characteristic frequencies,’’ J. Acoust. Soc. Am. 113,
Ruggero, M. A., Rich, N. C., Recio, A., Narayan, S. S., and Robles, L.
͑1997͒. ‘‘Basilar-membrane responses to tones at the base of the chinchilla
Plack, C. J., and Oxenham, A. J. ͑2000͒. ‘‘Basilar-membrane nonlinearity
cochlea,’’ J. Acoust. Soc. Am. 101, 2151–2163.
estimated by pulsation threshold,’’ J. Acoust. Soc. Am. 107, 501–507.
Smith, R. L. ͑1979͒. ‘‘Adaptation, saturation, and physiological masking in
Robles, L., Ruggero, M. A., and Rich, N. C. ͑1986͒. ‘‘Basilar membrane
single auditory-nerve fibers,’’ J. Acoust. Soc. Am. 65, 166 –178.
mechanics at the base of the chinchilla cochlea. I. Input–output functions, Yasin, I., and Plack, C. J. ͑2003͒. ‘‘The effects of a high-frequency suppres-
tuning curves, and phase responses,’’ J. Acoust. Soc. Am. 80, 1364 –
sor on tuning curves and derived basilar-membrane response functions,’’ J.
Acoust. Soc. Am. 114, 322–332.
Rosengard, P. S., Oxenham, A. J., and Braida, L. D. ͑2003͒. ‘‘Estimates of
Yates, G. K. ͑1995͒. ‘‘Cochlear structure and function,’’ in Hearing, edited
basilar-membrane compression in listeners with normal hearing derived by B. C. J. Moore ͑Academic, San Diego͒, pp. 41–73.
J. Acoust. Soc. Am., Vol. 115, No. 4, April 2004 Plack et al.: Nonlinearity and hearing loss
The New Testament Greek term for “church” is ekklesia, which means an assembly of believers, called out by God (1Pet. 2:9-10). The Bible speaks of the church in two distinct ways: the universal church and the local church, with the majority of references to local churches. Grudem simply defines the church as, “the community of all true believers for all time.” The church consists of