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Detailed f1, f2 Area Study of Distortion Product Otoacoustic1 Emissions in the Frog

2 SEBASTIAAN W. F. MEENDERINK,1,2 PETER M. NARINS,3 AND PIM VAN DIJK1,2

3 1Department of Otorhinolaryngology and Head and Neck Surgery, University Hospital Maastricht, 5800, 6202 AZ, Maastricht,4 The Netherlands

5 2Institute for Brain and Behaviour, Maastricht University, Maastricht, The Netherlands

6 3Department of Physiological Science, University of California, Los Angeles, Los Angeles, CA 90095-1606, USA

7 Received: 11 March 2004; Accepted: 12 October 2004; Online publication: 2 February 2005

9 ABSTRACT

10 Distortion product otoacoustic emissions (DPOAEs)11 are weak sounds emitted from the ear when it is12 stimulated with two tones. They are a manifestation13 of the nonlinear mechanics of the inner ear. As such,14 they provide a noninvasive tool for the study of the15 inner ear mechanics involved in the transduction of16 sound into nerve fiber activity. Based on the DPOAE17 phase behavior as a function of frequency, it is18 currently believed that mammalian DPOAEs are the19 combination of two components, each generated by a20 different mechanism located at a different location in21 the cochlea. In frogs, instead of a cochlea, two22 separate hearing papillae are present. Of these, the23 basilar papilla (BP) is a relatively simple structure24 that essentially functions as a single auditory filter. A25 two-mechanism model of DPOAE generation is not26 expected to apply to the BP. In contrast, the other27 hearing organ, the amphibian papilla (AP), exhibits28 a tonotopic organization. In the past it has been29 suggested that this papilla supports a traveling wave30 in its tectorial membrane. Therefore, a two-mecha-31 nism model of DPOAE generation may be applicable32 for DPOAEs from the AP. In the present study we33 report on the amplitude and phase of DPOAEs in34 the frog ear in a detailed f1, f2 area study. The result35 is markedly different from that in the mammalian

36cochlea. It indicates that DPOAEs generated by nei-37ther papilla agree with the two-mechanism traveling38wave model. This confirms our expectation for the39BP and does not support the hypothesized presence40of a mechanical traveling wave in the AP.41Keywords: distortion product otoacoustic emis-42sions, amphibian, frog, traveling, wave, two-mecha-43nism DPOAE model44Abbreviations: AP – amphibian papilla; BP – basilar45papilla; DPOAE – distortion product otoacoustic46emission47

48

49INTRODUCTION

50Distortion product otoacoustic emissions (DPOAEs)51are an acoustic phenomenon that can be observed in a52healthy ear that is stimulated with two stimulus tones53with properly chosen frequencies ( f1, f2, with f1 G f2)54and levels (L1 and L2, respectively). It is currently55believed that in the mammalian, lower-sideband56DPOAEs (with fdp G f1, f2) are the result of two57DPOAE components, each originating from a differ-58ent location on the basilar membrane (Kim 1980;59Kemp and Brown 1983; Brown et al. 1996; Talmadge60et al. 1999; Shera and Guinan 1999).61Shera and Guinan (1999) postulate that the62fundamental distinction between these two compo-63nents is not the different location but the different64mechanism involved in their generation. Hence, they65use the term two-mechanism model of DPOAE66generation. Here, nonlinear distortion generates67the initial DPOAE component (at the overlap region

Correspondence to: Sebastiaan W. F. Meenderink & Department ofOtorhinolaryngology and Head and Neck Surgery & UniversityHospital Maastricht & 58006202 AZ, Maastricht, The Netherlands.Telephone: (31) 43-6884251; fax: (31) 43-3877598; email:b.meenderink@kno.unimaas.nl

JARO 6: 37–47 (2005)DOI: 10.1007/s10162-004-5019-0

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68 of the two stimulus tones) that may travel both in69 basal and apical directions in the cochlea. The70 apically traveling DPOAE energy may be reflected71 because of local irregularities in the fine structure of72 the basilar membrane (around the characteristic73 frequency place of the distortion product) resulting74 in a second DPOAE component traveling to the base75 of the cochlea. The combination of the two basally76 traveling components, together with multiple inter-77 nal reflections (Stover et al. 1996), results in the78 DPOAE that can be recorded in the ear canal.79 The frog ear is an interesting model for studying80 DPOAEs because, instead of a cochlea, it contains81 two distinct papillae that respond to airborne sound.82 The amphibian papilla (AP) consists of an elongated83 strip of sensory epithelium. It exhibits tonotopic84 organization (Lewis et al. 1982), and the presence85 of traveling waves in the tectorial membrane has86 been proposed (Lewis and Leverenz 1983; Hillery87 and Narins 1984; Lewis 1984). Hair cells are inner-88 vated by both afferent and efferent nerve fibers, the89 former having tuning characteristics similar to those90 found in mammals (Lewis 1992). The AP may91 generate both spontaneous and distortion product92 OAEs (Van Dijk and Manley 2001). The analogy of93 this papilla with the mammalian cochlea, i.e., the94 presence of tonotopic organization, suggests that a95 traveling wave mechanism, with separate emission96 sources, may underlie DPOAE generation.97 The basilar papilla (BP) is a much simpler98 structure. It consists of a small patch of sensory99 epithelium which is covered by a tectorial membrane100 (Lewis and Narins 1999). In Rana catesbeiana, hair101 cells in the BP are only innervated by afferent nerve102 fibers (Robbins et al. 1967; Frishkopf and Flock103 1974). In individual frogs, the vast majority of nerve104 fibers is tuned to a single frequency (Ronken 1991;105 Van Dijk et al. 1997). Also, in ranid frogs the hair106 bundles are oriented in parallel (Lewis 1978). These107 properties indicate that this papilla functions essen-108 tially as a single auditory filter (Ronken 1990; Van109 Dijk and Manley 2001), which makes it unlikely that110 DPOAE generation involves two different emission111 sources or a traveling wave mechanism.112 Recently, Knight and Kemp (2000) reported an f1,113 f2 area study of human DPOAEs. They showed that114 patterns in the amplitude and phase data, when115 represented in an f2/f1 versus fdp plot, are oriented116 either horizontally or vertically. The patterns are117 consistent with the two-mechanism model of DPOAE118 generation. A similar method to analyze the phase119 data was presented by Schneider et al. (2003).120 Although these methods offer no technique to study121 the two components separately, they do provide a way122 to study which component dominates the recorded123 DPOAE.

124In the present study, we report an f1, f2 area study125of amplitude and phase of DPOAEs in the leopard126frog, Rana pipiens pipiens. The patterns observed127deviate considerably from those observed in mam-128mals. We conclude that a cochlear-like, two-source129DPOAE model does not apply to the amphibian130inner ear. This confirms our expectations for the BP,131but does not support the hypothesized presence of a132mechanical traveling wave in the AP.

133METHODS

134Distortion product otoacoustic emissions were re-135corded from Northern leopard frogs (Rana pipiens136pipiens): n = 5 females, body mass = 20.8Y31.9 g137(mean, 27.2 g), snout-vent length = 7.11Y7.84 cm138(mean, 7.42 cm). Animals were anesthetized with an139intramuscular injection of pentobarbital sodium140solution (Nembutal, 60 mg/ml; 1.0 ml/g body mass)141in one of the hindlimbs. Measurements were per-142formed in a sound-attenuating chamber, with the143frog placed on a vibration isolation table. During the144experiments, the animal was covered by gauze soaked145in tap water to prevent dehydration and to facilitate146cutaneous respiration. In each subject the left ear was147tested.148DPOAEs were recorded with a probe assembly149that contained two miniature transducers (ER-10C;150Etymotic Research) for stimulus generation, and one1511/2-in. condenser microphone (Bruel and Kjær type1524134) for emission recording. The open end of the153probe assembly was carefully placed against the skin154surrounding the frog’s tympanic membrane. A tight155seal between probe and skin was obtained by using156silicone grease.157DPOAEs were evoked by two stimulus tones, with158frequencies f1 and f2 (where f2/f1 9 1) and levels L1

159and L2, each of which was played from a separate160miniature speaker. The stimulus tones were generat-161ed from two separate D/A channels (RP2; Tucker162Davis Technologies, Gainesville, FL, USA) and the163level of each tone was adjusted with a separate164programmable attenuator (PA5: Tucker Davis Tech-165nologies). The microphone signal was amplified to16660 dB with a preamplifier (Bruel and Kjær type 2609)167and recorded on computer disk using an A/D168converter (RP2; Tucker Davis Technologies). During169the experiments, the amplified microphone signal170was also fed into a spectrum analyzer (Stanford171Research Systems SR770) in order to monitor the172DPOAEs online. Customized software, written in173Matlab (The MathWorks, Inc.) and RPvds (Tucker174Davis Technologies) were used to control stimulus175tone generation and signal recording.

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176 For each frog, recordings were made in a series of177 fixed-frequency ratio (fixed f2/f1) sweeps from low to178 high f1, starting with the lowest frequency ratio f2/f1 =179 1.02 and ending with a ratio of 1.70. In each sweep,180 f1 varied from 213 to 2774 Hz in approximately 30 Hz181 steps. The levels of the stimulus tones, L1 = L2 = 76182 dB SPL, were kept constant for all stimulus frequency183 combinations. These relatively large stimulus ampli-184 tudes were used in order to evoke DPOAEs over a185 wide enough stimulus frequency ( f1, f2/f1) area to186 reliably unwrap the phase data. At the start and at187 regular intervals during the experiment, a calibration188 procedure was performed to set the levels of the189 stimulus tones. In addition, the condition and the190 position of the animal were checked, and the gauze191 covering the animal remoisturized. To determine the192 nonlinear distortion of the DPOAE recording setup,193 experiments were performed with the open end of194 the probe pressed against a solid surface. This195 resulted in no detectable system distortion for any196 of the stimulus conditions used.197 At each frequency pair ( f1, f2), stimulus tones198 were played continuously for 50,000 sample points199 ($4.10 s with a sample frequency of 12.2 kHz).200 Frequency f1 was chosen such that 100 periods of201 this stimulus tone matched exactly an integer num-202 ber of sample points. By performing the experiments203 in the form of fixed-ratio sweeps, where the ratio204 f2/f1 was chosen with a maximum of two significant205 digits (e.g., f2/f1 = 1.04 or f2/f1 = 1.30), all other206 frequencies of interest (i.e., stimulus frequency f2 and207 all DPOAEs) were also exactly periodic over the same208 integer number of sample points. This method has209 two advantages in the analysis of the recorded signal.210 First, the total recorded signal (50,000 sample points)211 can be divided into a series of blocks that all have the212 same starting phase of the stimulus tones and213 DPOAEs. These blocks can be averaged in order to214 reduce the noise floor, without affecting the ampli-215 tude and phase of the tones of interest. Second, the216 exact periodicity of all tones of interest ensures that217 in the Fourier analysis the corresponding frequencies218 each fall exactly in the center of a frequency bin. This219 abolishes spectral smearing, and provides an accurate220 estimate of the amplitudes and phases of the221 DPOAEs.222 In the analysis of the digitized microphone signal,223 the first periodic block was omitted to exclude onset224 phenomena. The remaining signal was used to225 calculate the amplitudes (L1, L2) and phases (�f1,226 �f2) of the stimulus tones using Fourier analysis. The227 parameters thus obtained were used to subtract the228 stimulus tones from the microphone signal in the229 time domain. For the remaining signal, containing230 only the DPOAEs and system noise, each periodic231 block was subjected to a level-crossing artifact rejec-

232tion method. Artifact-free blocks were subaveraged in233two buffers, A and B. The average (A + B) / 2 was234used to estimate the DPOAEs’ amplitudes and235phases, whereas the difference A j B provided an236estimate for the noise levels. As with the stimulus237tones, the amplitudes and phases of the DPOAEs238were calculated using Fourier analysis.239The BPrinciples of Animal Care^ (NIH publication24085-23, revised 1985) and US regulations were fol-241lowed throughout this study, and the protocols were242approved by the University of California Animal243Research Committee.

244Data analysis and representation

245For each distortion product, amplitude and phase246data were arranged in an ( f1, f2/f1) area matrix. Only247data points for which the emission amplitude248exceeded the noise floor by 6 dB were included in249the matrices. Phase data are represented relative to250the phase of the stimulus tones. That is, for the251distortion product at fdp = (n + 1)f1 j nf2, the relative252phase is: �fdp

¼ �fdp� n þ 1ð Þ�f1 þ n�f2 . Subsequently,

253the phase data were unwrapped in two dimensions254(constant f1 and constant f2/f1) by removing 2p255discontinuities.256Phase slope delay (group delay) is defined as:

D ¼ � 1

2�

d�dp

dfdpð1Þ

257where Fdp is the relative phase of the distortion258product and is considered as a function of f1 for a259constant ratio f2/f1. The slope dF/df of the phase was260calculated by fitting a straight line to three points, f1261and the two neighboring points. This was only262performed when all three points had a DPOAE263amplitude exceeding the noise floor by 6 dB. To pre-264vent contamination of the results, only slopes with a265correlation coefficient exceeding 0.988 (corre-266sponding to p = 0.10) are considered in this paper.

267RESULTS

268Distortion product otoacoustic emissions could be269detected in each individual frog investigated. We270systematically analyzed the recorded data for distor-271tion products at frequencies 2f1 j f2, 2f2 j f1, 3f1 j

2722f2, and 3f2 j 2f1.273The dependence of DPOAE amplitude on the274stimulus frequencies follows a complicated pattern.275Some of these patterns are illustrated by the contour276lines in Figure 1. In each panel of Figure 1, the277bottom half refers to the DPOAE at 2f2 j f1, and the278top half illustrates DPOAE at 2f1 j f2. In general,

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279 DPOAE amplitudes were relatively large in two broad280 frequency ranges. Separating these two peak regions281 is a well-defined valley where DPOAE amplitudes282 dropped considerably. As is obvious from the figure,283 the orientation of these DPOAE peak and valley284 regions depends on the parameter plotted on the285 abscissa. When the DPOAE at 2f1 j f2 is plotted as a286 function of stimulus frequency f1 (Fig. 1b, upper287 half), these DPOAE amplitude peaks and valleys give288 rise to a vertical pattern in the contour lines. In con-289 trast, when the amplitude of this DPOAE is plotted290 as a function of either DPOAE frequency (Fig. 1a,

291upper half) or stimulus frequency f2 (Fig. 1c, upper292half), a diagonal pattern in the contour lines appears.293Inspection of the lower halves of the panels in294Figure 1 makes it clear that for the DPOAE at 2f2 j f1295the situation is similar, but slightly more complex.296Here, the peaks and valleys in DPOAE amplitude297result in an approximately vertical pattern in the298contour plots when either the DPOAE frequency299(Fig. 1a) or the stimulus frequency f2 (Fig. 1c) is on300the abscissa. With the stimulus frequency f1 on the301horizontal axis (Fig. 1b), the pattern in the contour302plot is diagonal.

FIG. 1. Amplitude at 2f1 j f2 and2f2 j f1 in dB SPL, evoked withL1 = L2 = 76 dB SPL, recorded in onefrog. The different panels representthe same data set with f2 /f1 versuseither (a) distortion productfrequency, (b) stimulus frequencyf1, or (c) stimulus frequency f2.In each panel, the same color-codingis used. Individual contour lines aredrawn at 2-dB intervals. The shadedarea represents the (f1, f2) areastudied. For DPOAEs at 2f1 j f2,amplitude peaks and valleys result inpatterns that are vertical when dataare plotted as function of primaryfrequency f1 (panel b, upper half). Incontrast, for DPOAE at 2f2 j f1, asimilar vertical pattern occurs whenthe data are plotted as a functionof either primary frequency f2 (panelc, lower half) or DPOAE frequency(panel a, lower half). Note that twobroad frequency regions can be seenwhere emission amplitudes show arelative maximum. These two regionsare separated by a notch regioncentered around f1 = 1250 Hz (for 2f1j f2) or fdp slightly below 1250 Hz(for 2f2 j f1), where emissions areconsiderably lower in amplitude oreven undetectable. This frequency of1250 Hz corresponds with theseparation in characteristic frequencyranges of nerve fibers from theamphibian and basilar papilla(Ronken 1991).

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303 DPOAEs at 2f2 j f1 could be detected for much304 wider stimulus frequency ratios than those at 2f1 j f2.305 For example, at the largest ratio studied (f2/f1 = 1.7;306 i.e., the horizontal boundaries of the panels),307 DPOAEs at 2f2 j f1 were still as large as 26 dB SPL,308 while for the same ratio DPOAEs at 2f1 j f2 were309 indistinguishable from the noise floor.310 DPOAE audiograms recorded in the frog typically311 show a bimodal dependence on frequency (Van Dijk312 and Manley 2001; Van Dijk et al. 2003; Meenderink313 and Van Dijk 2004). They exhibit two frequency314 regions with elevated DPOAE amplitudes which are315 separated by a clear notch in DPOAE amplitude. The316 area representations in Figure 1 show that this317 bimodal dependence is observed irrespective of the318 stimulus frequency ratio f2/f1 used. At the same time,319 these representations show that whether the notch320 shifts in frequency for DPOAE audiograms recorded321 with different frequency ratios f2/f1 depends on the322 parameter plotted on the x -axis. For DPOAEs at323 2f1 j f2, the notch in DPOAE audiograms does not324 shift position when stimulus frequency f1 is on the325 x-axisVit is centered around approximately f1 = 1250326 Hz. For DPOAEs at 2f2 j f1 the notch is observed at a327 fixed frequency slightly below fdp = 1250 Hz when328 distortion product frequency is on the abscissa.329 Compared to the amplitude, the pattern observed330 in the DPOAE phase is simpler. Figure 2 illustrates331 the phase data accompanying the amplitude data332 presented in Figure 1. Again, the bottom half of the333 panel illustrates DPOAEs at 2f2 j f1, and the top half

334refers to DPOAEs at 2f1 j f2. For DPOAEs at both3352f1 j f2 and 2f2 j f1, contour lines, i.e., lines of equal336relative phase of the DPOAEs, are (nearly) vertical337when plotted as a function of DPOAE frequency338(Fig. 2). These vertical contour lines indicate that339DPOAE phase primarily depends on DPOAE fre-340quency, and is nearly independent of the stimulus341frequency ratio f2/f1.342The distance between the contour lines in the343phase data showed a bimodal dependence on344DPOAE frequency, similar to the bimodal depen-345dence observed in the DPOAE amplitude. This is346reflected in the group delays of the DPOAEs.347Figure 3a shows the combined group delays (average348T SD of all frogs and all frequency ratios) for DPOAEs349at 2f1 j f2 plotted as a function of primary frequency350f1. For f1 G 1250 Hz, the group delays were larger351(corresponding to more closely spaced contour lines352in Figure 2) compared to the group delays for

FIG. 2. Phase data (in rad) for 2f1 j f2 and 2f2 j f1 plotted as afunction of distortion product frequency. The phase data correspondto the amplitude data represented in Figure 1. Contour lines aredrawn at p rad intervals. The shaded area represents the (f1, f2) areastudied. The vertical contour lines indicate that the relative phase ofthe DPOAEs depends on the frequency of the distortion productitself, and is independent of both the absolute and relativefrequencies of the two stimulus tones.

FIG. 3. Group delays calculated for a fixed-ratio recordingparadigm plotted as a function of primary frequency f1. The twopanels represent group delays for (a) 2f1 j f2 and (b) 2f2 j f1. Eachpoint gives the combined average over all frogs and all f2 /f1 ratios.The error bars denote the standard deviation (T1 SD). Points lackingan error bar represent single observations.

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353DPOAEs recorded with f1 9 1250 Hz. A similar plot is354given for DPOAEs at 2f2 j f1 in Figure 3b. Here, the355group delays are relative constant for f1 9 800 Hz.356Below 800 Hz, the group delays decrease with in-357creasing stimulus frequency.358The presence of DPOAEs was not restricted to the359frequencies 2f1 j f2 and 2f2 j f1. In all frogs studied,360DPOAEs were also detectable at 3f1 j 2f2 and 3f2 j

3612f1. However, the frequency areas in which these362DPOAEs could be observed were restricted to both363smaller relative (i.e., f2/f1) and absolute stimulus364frequency ranges. This was attributable to the smaller365amplitudes of these DPOAEs. Figure 4 shows ampli-366tudes of DPOAE at 3f1 j 2f2 and 3f2 j 2f1 in a similar367representation as Figure 1. For DPOAE amplitude at3683f1 j 2f2, i.e., the upper halves of Figure 4, the peaks369and valleys do not shift in frequency with varying370stimulus frequency ratio when stimulus frequency f1371(Fig. 4b) is on the abscissa. In contrast, in the lower372halves of Figure 4, i.e., DPOAE at 3f2 j 2f1, the373amplitude peaks and valleys give rise to an approxi-374mately vertical pattern in the contour plots when375either DPOAE frequency (Fig. 4a) or stimulus376frequency f2 (Fig. 4c) is on the horizontal axis.377In only one frog were these higher-order DPOAEs378observed over a large enough stimulus frequency379area to reliably unwrap the phase data. The phase380data obtained in this frog are shown in Figure 5. This381figure corresponds to the amplitude data shown in382Figure 4. For both of the higher-order DPOAEs,

FIG. 4. Amplitude of DPOAEs at 3f1 j 2f2 and 3f2 j2f1. Thedifferent panels are different representations of the same set ofamplitude data in dB SPL. The data are plotted with f2 /f1 versuseither (a) distortion product frequency, (b) stimulus frequency f1, or(c) stimulus frequency f2. In each panel, the same color-coding isused. For clarity, individual contour lines are drawn at 3-dB intervalsrather than at 2-dB intervals as was used in Figure 1. For DPOAEs at3f1 j 2f2, a vertical pattern occurs when plotted as a function of f1(panel b). In contrast, for DPOAEs at 3f2 j 2f1 patterns are onlyclose to vertical when either primary frequency f2 (panel c) orDPOAE frequency (panel a) is on the horizontal axis. Although theamplitudes are reduced, these results are qualitatively the same asthose observed for DPOAEs at 2f1 j f2 and 2f2 j f1 (Fig. 1).

FIG. 5. Relative phase of DPOAE at 3f1 j 2f2 and 3f2 j 2f1 plottedas a function of distortion product frequency. Data correspond toamplitude data represented in Figure 4. Contour lines are drawn at prad intervals. The vertical contour lines indicate that the relativephase of the DPOAEs depends on the frequency of the distortionproduct alone, and is independent of both the absolute and relativefrequencies of the two stimulus tones. This dependence on distortionproduct frequency is similar to that observed for the relative phasedata for DPOAEs at 2f1 j f2 and 2f2 j f1 (Fig. 2).

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383 phase showed vertical contour lines when the384 DPOAE frequency is plotted on the horizontal axis385 (Fig. 5). These observations in both the amplitude386 and phase data for DPOAE at 3f1 j 2f2 and 3f2 j 2f1387 are similar to those made for DPOAE at 2f1 j f2 and388 2f2 j f1.

389 DISCUSSION

390 In the present study, DPOAEs were only found over a391 limited range of stimulus frequencies. This range is392 within the frequency range to which nerve fibers393 from the frog ear are tuned (100Y2300 Hz in R.394 pipiens pipiens; Ronken 1990). This frequency range395 could be divided in two broad frequency subregions396 where DPOAEs exhibited relatively large amplitudes.397 These subregions were separated by a frequency398 notch where relatively small DPOAE amplitudes were399 found. Based on the bandwidth of neural tuning400 curves recorded in R. pipiens pipiens, Ronken (1991)401 estimated that nerve fibers tuned to frequencies less402 than 1250 Hz innervate the amphibian papilla, while403 nerve fibers tuned to higher frequencies innervate404 the basilar papilla. The correspondence between the405 DPOAE data and the nerve fiber data suggests that406 frog DPOAEs originate from both of the papillae407 present in the inner ear. A similar observation was408 made by Van Dijk and Manley (2001), Van Dijk et al.409 (2003), and Meenderink and Van Dijk (2004). At the410 stimulus levels used here (L1 = L2 = 76 dB SPL),411 DPOAE amplitude was larger in the BP than in the412 AP for all frogs.413 The phase, obtained when recording these414 DPOAE audiograms, varies with varying stimulus415 frequencies. For DPOAEs from the AP, the rate of416 phase change decreases for increasing frequency,417 resulting in the observed frequency dependence of418 the group delay (Fig. 3). For DPOAEs generated in419 the BP, group delays are relatively constant, signifying420 a nearly linear change in phase with changing421 frequencies. This dependence of group delay on422 frequency (in the AP) is not only similar to the423 frequency dependence of response delays reported424 for neural data in frogs (Hillery and Narins 1984,425 1987), but also to neural delays reported for all426 vertebrate classes (see Manley et al. 1990 for an427 overview). In mammals, these delays have been428 attributed to the delay time of the traveling wave on429 the basilar membrane. In fact, the close correspon-430 dence between mammalian delays and those found431 in the coqui frog (Hillery and Narins 1984) led to the432 hypothesis of a traveling wave in the tectorial433 membrane that covers the frog amphibian papilla.434 However, in the bobtail lizard no traveling wave on

435the basilar membrane is present (Manley et al. 1988),436while the neural delays again show a similar depen-437dence on frequency (Manley et al. 1990). It seems438that the relatively similar neural delay patterns found439across nonmammalian vertebrate classes arise from440similarly tuned filter arrays. Thus, despite the very441different auxiliary structures in the inner ears of the442different vertebrate classes, filter mechanisms may be443similar across species.444The patterns in DPOAE amplitude and phase445described here deviate considerably from those446reported for mammals (Knight and Kemp 2000;447Schneider et al. 2003). In the mammalian cochlea,448the patterns observed in the amplitude and accom-449panying phase data are oriented parallel to each450other: when plotted in an f2/f1 versus fdp area map,451both amplitude and phase display either a vertical or452a horizontal orientation. A vertical orientation of the453patterns occurs when the recorded DPOAE is dom-454inated by a reflection component. This component is455thought to arise via a mechanism of linear reflection456occurring at irregularities of the cochlea around the457characteristic place of the DPOAE (Shera and458Guinan 1999). Consequently, DPOAE amplitude and459phase primarily depend on the distortion product460frequency, which results in the observed vertical461patterns for both amplitude and phase. In contrast, a462horizontal orientation of the patterns in amplitude463and accompanying phase data is found if not the464reflection component, but rather the nonlinear dis-465tortion component dominates the recorded DPOAE466signal. This component is thought to arise via nonlin-467ear distortion at that region along the basilar mem-468brane where the response envelopes of the two469stimulus tones overlap maximally, i.e., around the470tonotopic location of primary frequency f2. By assum-471ing a scale-invariant cochlea with respect to frequen-472cy, the relative phase of the two stimulus tones473depends only on the ratio f2/f1 and is independent474of DPOAE frequency, resulting in the observed475horizontal orientation of the patterns in amplitude476and phase.477The close link between the patterns in DPOAE478amplitude and phase, as seen in the mammalian479cochlea, was not present in the frog. This is seen most480clearly for lower sideband DPOAEs (with fdp G f1, f2),481i.e., DPOAEs at 2f1 j f2 and 3f1 j 2f2. Here, the482relative phase of the DPOAEs shows a dependence483on only the DPOAE frequency, i.e., vertical contour484lines in the upper halves of Figures 2 and 5. However,485in the corresponding area maps of the amplitude, the486observed patterns are clearly diagonal (Figs. 1a and4874a, upper halves). This diagonal orientation of the488patterns in amplitude data when represented in an489f2/f1 versus fdp map indicates that the DPOAE490amplitude does not exclusively depend on either

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491 the relative stimulus frequencies or the DPOAE492 frequency. Rather, the observed patterns are oriented493 vertically when the primary frequency f1 is plotted on494 the horizontal axis (Figs. 1b and 5, upper halves).495 For upper sideband DPOAE (with fdp 9 f1, f2), i.e.,496 2f2 j f1 and 3f2 j 2f1, similar differences between497 mammalian and frog DPOAEs were present. Again,498 the vertical contour lines in the phase data (Figs. 2499 and 5, lower halves) indicate a dependence of500 DPOAE phase on distortion product frequency501 alone. On the other hand, the patterns in amplitude502 data are slightly diagonal when DPOAE frequency is503 on the horizontal axis. A similar diagonal orienta-504 tion is observed when amplitude is plotted as a505 function of stimulus frequency f2 (Figs. 1 and 4,506 lower halves).507 Knight and Kemp (2001) describe their results,508 obtained in the cochlea, with a transmission line509 model. The model is not a physical description of the510 cochlea, but it incorporates some generic cochlear511 properties, such as the traveling wave on the basilar512 membrane. The difference in the amplitude and513 phase patterns observed in mammals and frogs514 indicate that the model does not apply to the frog515 inner ear. In other words, our results do not provide516 any evidence for cochlear-like traveling wave mechan-517 ics in the frog inner ear.518 But if no cochlear-like traveling wave mechanics519 are involved in the sound transduction in the frog520 inner ear, what kind of mechanism is?521 Of the two hearing organs present in the frog inner522 ear, the basilar papilla is the simplest in structure and523 function. It consists of a small patch of hair cells,524 which is embedded in a solid surface and covered by a525 tectorial membrane. The papilla essentially functions526 as a single auditory filter. Evidence for this is provided527 by tuning curves obtained from nerve fibers innervat-528 ing this organ: in individual frogs almost all nerve529 fibers are tuned to a single frequency, with the shapes530 of all tuning curves being remarkably similar (Ronken531 1990). Obviously, a traveling wave model is not532 applicable here.533 Based on the notion that the BP functions as a534 single auditory filter, we will consider a single resona-535 tor, the Duffing oscillator, as a simple model for536 DPOAE generation in this papilla (see also Van Dijk537 and Manley 2001). The Duffing oscillator is described538 by the nonlinear second-order equation

m€xx þ R _xx þ k xð Þx ¼ F tð Þ ð2Þ

539 where m is a mass, whose movement is driven by an540 external force F(t). The linear resistance R impedes541 this movement, while a nonlinear stiffness k xð Þ ¼542 k 0 1þ x2

x20

� �tries to restore the mass’ position x to its

543 equilibrium position x = 0.

544When the oscillator is driven by a two-tone force

F tð Þ ¼ A1 sin 2�f1tð Þ þ A2 sin 2�f2tð Þ ð3Þ

545cubic distortion products are present in the response546x(t). We simulated the oscillator using a range of547absolute and relative stimulus frequencies: f1 varied548between 0.2 and 2.0 in 0.01-steps, with the resonance549frequency of the oscillator being 1, while f2/f1 was550between 1.04 and 1.7 in steps of 0.01. This allowed551for a qualitative comparison between the model and552the DPOAEs recorded in the frog. The results of the553model are shown in Figure 6 for m = 1, r = 1, k0 = 4p2,554x0 = 1, and A1 = A2 = 1. In this figure, the amplitude555and phase data are plotted as a function of inter-556modulation product frequency, similar to what was557performed for the DPOAEs recorded from the frog558ear (Figs. 1a and 2).559The amplitude contour lines, drawn at 10-dB560intervals (Fig. 6a), show a pattern that is very similar561to that observed in the recorded DPOAEs (Fig. 1a).562For intermodulation products at 2f1 j f2 (Fig. 6a,563upper half) this pattern has a diagonal orientation,564following lines of fixed f1. In contrast, for intermod-565ulation products at 2f2 j f1 (Fig. 6a, lower half) the566pattern in the contour lines is approximately vertical.567Notice that in both the lower and upper halves of the568panel contour lines exhibit three more or less569pronounced lobes. These arise whenever f1, f2 or fdp

570coincides with the resonance frequency of the571oscillator.572The phase of the intermodulation products pro-573duced by the model are shown in Figure 6b. It can be574seen that the phase obtained with a single fixed-ratio575sweep remains largely unchanged. Only when the576intermodulation product frequency varies from577slightly below to slightly above the resonance fre-578quency does phase change rapidly by p rad. The579contour lines in Figure 6b follow lines of equal580intermodulation product frequency, resulting in a581vertically oriented pattern which is similar to that582observed in frog DPOAE.583The qualitative good agreement between the584patterns in DPOAE and intermodulation products,585both in amplitude and phase, provides further586support that the frog basilar papilla functions as a587single (nonlinear) resonator.588DPOAEs from the amphibian papilla, the other589hearing organ in the frog ear, behave similar to those590from the BP: the patterns of DPOAE amplitude and591phase (Figs. 1 and 2, respectively) are similar below592(AP) and above (BP) the notch frequency of 1250593Hz. Consequently, as with the BP, emissions from the594AP can be described by the simple oscillator model595given in Eq. (2). However, the AP is not a single596auditory filter, but functions as a tonotopically orga-597nized array of auditory filters (Lewis and Leverenz

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5981983). How can the simple BP-like DPOAE character-599istics be reconciled with the structural and functional600properties of the AP? We will discuss various factors601which may contribute to the answer of this question,602but at present we are unable to provide a definitive603answer.604The AP is situated in a short chamber which runs605from the periotic canal to the saccular recess. A606contact membrane separates the perilymph in the607periotic canal from the endolymph in the papillar608space. The sensory hair cells are situated in the roof609of the chamber, and are embedded in a rigid support610structure. Hanging from the hair cells is an acellular611structure, the tectorial membrane. Approximately612halfway along the papilla, a tectorial curtain projects613from the tectorial membrane to the floor of the614papillar chamber. Because of its positioning within615the chamber, any fluid movement along the principal616axis of the papilla will result in movement of this617tectorial curtain.618By tracing auditory nerve fibers with known619characteristic frequencies to their point of innerva-620tion within the AP, Lewis et al. (1982) showed that621the tonotopic organization is along the principal axis622of the papilla. Here, the highest frequencies are at623the caudal part of the AP (close to the contact624membrane that separates the peri- and endolymph),625while toward the rostral end (closer to the sacculus)626the characteristic frequency of nerve fibers decreases.627Although acoustic energy enters the papillar cham-628ber from the saccular space (Purgue and Narins6292000), it seems that the excitation moves from high630to low frequencies, similar to the cochlea. This is631manifest in the first-spike latency for auditory nerve632fibers, which is longest for low-frequency fibers and633shortest for fibers tuned to the highest frequencies634within in the AP (Hillery and Narins 1987). Neural635tuning curves from the AP, show shallow slopes below636the characteristic frequency, and steep slopes above637(Narins and Hillery 1983). Therefore, Lewis and638Leverenz (1983) concluded that the AP, like the639cochlea, may be modeled as a transmission-line low-640pass filter: each section of the papilla absorbs high-641frequency acoustic energy, but passes lower frequen-642cies to the subsequent sections in the structure.643Although such a model describes the functional644behavior of the papilla, Lewis and Leverenz (1983)645were unable to reconcile it with the known anatom-646ical gradients in the papilla.647They emphasized that the implementation of such648a low-pass filter mechanism in the amphibian papilla649must be very different from that in the cochlea. The650basilar membrane in the cochlea is between two fluid-651filled scalae, and is excited by a pressure difference652between these scalae. The mechanical coupling653between the different sections of the basilar mem-

FIG. 6. Intermodulation products at 2f1 j f2 and 2f2 j f1 obtainedfrom a single nonlinear resonator used to model the frog basilarpapilla. The model consisted of a Duffing oscillator which wasdriven by a two-tone force. a) Amplitude in dB plotted as a functionof intermodulation product frequency, similar to the presentation ofDPOAE amplitude in Figure 1a. Individual contour lines are drawnat 10-dB intervals. The pattern formed by the contour lines is verysimilar to that observed in the recorded DPOAE. For 2f1 j f2 (upperhalf of the panel), the pattern is oriented diagonally, following linesof fixed f1. In contrast, for 2f2 j f1 (lower half of the panel) thepattern is closer to vertical. The individual contour lines for bothintermodulation products all exhibit three more or less distinctlobes, which is not observed in the DPOAE data. These lobes occurwhenever f1, f2 or fdp coincides with the resonance frequency of theoscillator. Apart from these lobes, the pattern of the contour linesdisplayed here is similar to that in Figure 1a for the basilar papilla(91250 Hz). b) Phase, in rad, accompanying the amplitude data inpanel a. It is plotted relative to the f1 and f2 stimulus frequencycomponents in the response x(t) (see Eq. (2)), rather than the forceF(t). This compensates for the nonlinear phase response of themodel. Individual contour lines are drawn at 0.1p rad intervals.Again, the data are plotted as a function of intermodulation productfrequency. As for the DPOAE phase (Fig. 2), the contour lines arevertical, irrespective of the intermodulation frequency (i.e., 2f1 j f2or 2f2 j f1). This indicates that the phase primarily depends on thefrequency of the intermodulation product, and not on the twostimulus frequencies.

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654 brane is provided through the fluid within the scalae:655 when the basilar membrane moves down at a656 particular location, it pushes away fluid within the657 scala tympani. This fluid has to push up (toward scala658 vestibuli) the basilar membrane at a different loca-659 tion in the cochlea. This fluid coupling contributes660 to the traveling wave propagation on the basilar661 membrane. Consequently, it contributes significantly662 to the DPOAE patterns, as observed by Knight and663 Kemp (2000) and Schneider et al. (2003), because664 these patterns reflect both forward and reverse travel665 of acoustic excitation along the basilar membrane.666 In contrast with the cochlea, the AP is not between667 two fluid-filled canals. Therefore, coupling between668 the different sections of this papilla must be differ-669 ent, where some sort of coupling via the tectorial670 membrane is most likely to occur. As sound enters671 the AP from the saccular space, it moves along the672 principal axis of the papilla. Two modes of excitation673 of the tectorial membrane can be considered (Lewis674 and Leverenz 1983): (1) fluid flow in the recess of675 the AP may move the tectorial curtain that spans the676 recess. This excitation may travel down the rest of the677 tectorium and may thus stimulate the entire papilla.678 Alternatively, (2) frictional coupling between fluid679 flow and the tectorial membrane may excite the680 papilla along its entire length. Because both the681 tectorial membrane mechanics and the coupling682 between subsequent sections in the papilla are683 different from that in the cochlea, it is not surprising684 that the observed DPOAE patterns (this work) differ685 from those in the cochlea (Knight and Kemp 2000;686 Schneider et al. 2003). However, at present, it is687 impossible to decide what mechanism describes the688 observed behavior in the AP, as no data are available689 on the mechanics of the tectorial membrane.690 It is important to note that the differences be-691 tween the amphibian and the mammalian DPOAEs692 need not reflect a difference in the emission gener-693 ation mechanism itself. In frogs, the dependence of694 DPOAE amplitude on stimulus levels is similar to that695 in mammals (Meenderink and Van Dijk 2004). This696 strongly suggests important similarities between697 DPOAE generation in frogs and mammals. Note that698 the broad similarities across vertebrate species also699 include similar neural delays (reviewed in Manley et700 al. 1990) and similar frequency selectivity in neural701 tuning (reviewed in Manley 1990). In conclusion, we702 showed that the dependence of DPOAE amplitude703 and phase on the stimulus frequencies is conspicu-704 ously different from that in mammals. Our DPOAE705 measurements did not give any evidence for a706 mammalian-like traveling wave in the frog inner ear.707 For the frog’s basilar papilla, this is not surprising708 and our results are consistent with the view that this709 papilla essentially functions as a single auditory filter.

710For the amphibian papilla, a traveling wave on the711tectorial membrane has been hypothesized in the712past. This hypothesis is not supported by our results.713The differences described here need not reflect714fundamental differences between DPOAE generation715mechanisms, but presumably reflect the different716mechanical properties of the auxiliary structures717between the amphibian and basilar papillae and the718mammalian cochlea.

719ACKNOWLEDGMENTS

720This work was supported by grants from the Netherlands721Organization for Scientific Research (NWO), and the722Heinsius Houbolt Foundation to S.W.F.M. and P.v.D., and723NIH grant DC-00222 to P.M.N.

724REFERENCES

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AUTHOR QUERY

AUTHOR PLEASE ANSWER QUERY.

Q1. Please provide publisher location for Kemp and Brown 1983.