The effect of stimulus-frequency ratio on distortion product otoacoustic emission components

The effect of stimulus-frequency ratio on distortion productotoacoustic emission components

Sumitrajit Dhara)

Hugh Knowles Center, Department of Communication Sciences and Disorders, Northwestern University,Evanston, Illinois 60208

Glenis R. LongGraduate Center, City University of New York, New York, New York 10016

Carrick L. TalmadgeNational Center for Physical Acoustics, University of Mississippi, University, Mississippi 38677

Arnold TubisInstitute for Nonlinear Science, University of California—San Diego, La Jolla, California 92093

~Received 25 January 2005; revised 11 March 2005; accepted 11 March 2005!

A detailed measurement of distortion product otoacoustic emission~DPOAE! fine structure wasused to extract estimates of the two major components believed to contribute to the overall DPOAElevel in the ear canal. A fixed-ratio paradigm was used to record DPOAE fine structure from threenormal-hearing ears over a range of 400 Hz for 12 different stimulus-frequency ratios between 1.053and 1.36 and stimulus levels between 45 and 75 dB SPL. Inverse Fourier transforms of theamplitude and phase data were filtered to extract the early component from the generator region ofmaximum stimulus overlap and the later component reflected from the characteristic frequencyregion of the DPOAE. After filtering, the data were returned to the frequency domain to evaluate theimpact of the stimulus-frequency ratio and stimulus level on the relative levels of the components.Although there were significant differences between data from different ears some consistentpatterns could be detected. The component from the overlap region of the stimulus tones exhibits abandpass shape, with the maximum occurring at a ratio of 1.2. The mean data from the DPOAEcharacteristic frequency region also exhibits a bandpass shape but is less sharply tuned and exhibitsgreater variety across ears and stimulus levels. The component from the DPOAE characteristicfrequency region is dominant at ratios narrower than approximately 1.1~the transition variesbetween ears!. The relative levels of the two components are highly variable at ratios greater than1.3 and highly dependent on the stimulus level. The reflection component is larger at all ratios at thelowest stimulus level tested~45/45 dB SPL!. We discuss the factors shaping DPOAE-componentbehavior and some cursory implications for the choice of stimulus parameters to be used in clinicalprotocols. © 2005 Acoustical Society of America.@DOI: 10.1121/1.1903846#

PACS numbers: 43.64.Bt, 43.64.Ha, 43.64.Jb@BLM # Pages: 3766–3776

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I. INTRODUCTION

Kim’s ~1980! initial prediction of two sources for thedistortion product otoacoustic emission~DPOAE! at the fre-quency 2f 12 f 2 ( f 1 and f 2 are the frequencies of the stimulus tones andf 1, f 2) has undergone considerable develoment and formalization over the last decade. The DPOAE2 f 12 f 2 , as well as other~apical! DPOAEs wheref dp, f 1

, f 2 , are understood to be a vector sum of~at least! twocomponents, each generated at disparate locations onbasilar membrane due to distinct mechanisms. The nonlininteraction between the stimulus tones around the tonotregion of the higher-frequency stimulus tone (f 2) generatesthe distortion or generationcomponent. Thereflectioncom-ponent, on the other hand, is due to linear coherent refltions from a randomly distributed roughness about the totopic region of the DPOAE. Detailed analytic descriptions

a!Corresponding author: Sumitrajit Dhar. Electronic [email protected]

3766 J. Acoust. Soc. Am. 117 (6), June 2005 0001-4966/2005/1

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the above model, or parts thereof, have been presenteseveral groups~e.g., Zweig and Shera, 1995; Talmadgeet al.,1998; Mauermannet al., 1999! along with several lines ofsupporting experiments. Although these models apply toapical DPOAEs, we will use the term DPOAE synonmously with the DPOAE at the frequency 2f 12 f 2 in thispaper. Evidence in support of such a two-source, twmechanism model has come from suppression experim~e.g., Kummeret al., 1995; Heitmannet al., 1998; Talmadgeet al., 1999; Kalluri and Shera, 2001!, results in thepseudotime domain following Fourier analysis of frequencdomain data~e.g., Kalluri and Shera, 2001; Konrad-Martet al., 2001, 2002; Knight and Kemp, 2001; Dharet al.,2002!, as well as true time-domain recordings of DPOA~Talmadgeet al., 1999!. An important consequence of thinteraction of energy from two sources is the DPOAE fistructure~a pseudoperiodic variation of the DPOAE levand phase as a function of frequency!.

In a view parallel to that of the two-source, twomechanism dichotomy, the two DPOAE components ha

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also been referred to asplaceandwavefixed. Initially pro-posed as two sources of DPOAEs originating at the salocation on the basilar membrane~Kemp, 1986!, the place-/wave-fixed description has embraced the mechanistic ancation differences between DPOAE components; withwave- and place-fixed components equated to the geneand reflection components, respectively~Knight and Kemp,2000, 2001!.

A third view has also recently emerged, driven primarby experimental comparisons of delay measures of otoactic emissions and basilar membrane recordings~Ruggero,2004; Ren, 2004!. Here, otoacoustic emissions~OAEs! areproposed to~i! be generated from a distributed area exteing toward the base of the cochlea similar to that associawith cochlear microphonics; and~ii ! propagate via acousticompression waves in the cochlear fluids rather than asditional traveling waves on the basilar membrane. Argumefor this view come from the presence of OAEs in basilmembraneless ears of frogs and limited sets of data fgerbils, guinea pigs, and chinchillas~Ruggero, 2004!. Whilethese are interesting developments, regularly observedtures of OAEs such as phase behavior and fine structureyet to be explained using this new model. The significanceRen’s ~2004! report is also unclear, given his choicestimulus-frequency ratios for which the propagationDPOAE energy from thef 2 CF region is known to be predominantly in the apical direction~Schneideret al., 2003!.Moreover, evidence in support of this model is yet topresented from human ears. Our work here, representingperimental results from normal-hearing human ears, is psented using the theoretical framework of the traditio‘‘two-source’’ model of apical DPOAEs.

Talmadgeet al. ~1998! provide a detailed derivation of‘‘two-source’’ model of the DPOAE recorded in the ear can(Pe) at the angular frequency (vdp). Two components of thedistortion product~DP! are initially generated in the cochlearegion of maximum overlap of the waves from the twstimulus tones. One component (Pl) travels basally~back-ward! toward the cochlear base and into the ear canal whit gives a DPOAE contributionPl(vdp). The other generatedDP component in the cochlea travels apically~forward! tothe DP characteristic frequency~CF! region, where it is par-tially reflected toward the cochlear base into the ear canacoherent scattering from assumed cochlear inhomogene~Zweig and Shera, 1995; Talmadgeet al., 1998!. This re-flected energy results in an ear-canal signal contributionPr(vdp)Ra(vdp), wherePr(vdp) is related to the initial api-cal moving DP component in the cochlea andRa is the apicalreflectance. In a simplified version of the model it is assumthat all of the reflected energy leaves the cochlea and isreflected back into the cochlea from the junction of thechlea and the middle ear. Consequently the DPOAE pressignal recorded in the ear canalPe at the frequencyvdp canbe represented as

Pe~vdp!5Pl~vdp!1Ra~vdp!Pr~vdp!. ~1!

Later versions of the model~supported by experiments! in-clude multiple internal reflections between the stapes andDPOAE CF region~Dharet al., 2002!. However, for the pur-

J. Acoust. Soc. Am., Vol. 117, No. 6, June 2005

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poses of this paper we assume that the reflectance at thewidow (Rb in our models! equals zero. We will refer to therepresentation ofPl in the ear canal as thegeneratorcom-ponent and that ofRaPr as thereflectioncomponent.

In this paper we evaluate the relative contributions ofgenerator and reflection components to the ear-caDPOAE. Specifically we wish to examine the behaviorthese two components as a function of stimulus-frequeratio. The most comprehensive work in this area has bpresented in a series of three articles by Knight and Ke~1999, 2000, 2001!. In the first of the series, they demonstrated similarity between the characteristics of transievoked OAEs~TEOAEs! and DPOAEs generated for sma~narrow! stimulus-frequency ratios, alluding to concordanbetween their generation processes. In the second pubtion, a detailed analysis of the phase behaviors of multiorders of DPOAEs was used to demonstrate that the menism for DPOAE generation was dominantly place- awave-fixed for narrow and wide stimulus-frequency ratiorespectively. In the third publication, these authors confirmthese results using the same data transformed into thedomain using inverse Fourier transformation. The essencthe Knight and Kemp findings can be summarized as~i!DPOAE generation is predominantly place fixed at narrratios; ~ii ! the wave- and place-fixed components demostrate a bandpass shape as a function of stimulus-frequratio; ~iii ! the bandpass shape of the place-fixed componis asymmetrical, the ‘‘drop-off’’ being much steeper at thwide ratios; and~iv! the change in dominance of one mechnism over the other occurs approximately around a stimufrequency ratio of 1.1. Note that we refer to the place- awave-fixed components as the reflection and generator cponents, respectively.

Schneideret al. ~2003! investigated the dominance othe components in the guinea pig by examining the DPOgroup delay. In contrast to the work reported by Knight aKemp, where DPOAE recordings were done with fixstimulus-frequency ratios, Schneideret al. varied the fre-quency of one stimulus tone while keeping the other fixedfrequency. The transition in dominance from place- to wafixed mechanisms occurred at a stimulus-frequency rwider than that observed in human ears, consistent withdifference in the sharpness of basilar-membrane tuningtween guinea pigs and humans as well as wider fine-strucspacing in rodents~Long et al., 1999; Withnellet al., 2003!.Schneideret al. ~2003! demonstrate the relationship betwethe two components at stimulus-frequency ratios greater t1.35 to be ambiguous.

In sharp contrast to the somewhat extensive experimtal work presented in this area to date, a theoretical exanation of the mechanistic implications of these findings hbeen limited. Knight and Kemp~1999! base the explanationof their results on the rapid phase variation of the 2f 12 f 2

wave near thef 2 peak region asf 2 / f 1 approaches 1. Thisvariation, the authors point out, will cause a reduction ofmagnitude of the backward traveling wave as DPOAE walets will fail to combine in phase. While these phase-relaarguments may be valid, amplitude effects as a functionchanging stimulus-frequency ratio cannot be neglect

3767Dhar et al.: Distortion product components and f2/f1

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Shera~2003! has included amplitude effects in his treatmeof the subject and provided a more complete analyticscription of the interplay between the generator and refltion components as a function of the changing stimulfrequency ratio. These issues, in light of our data,presented in detail in Sec. IV.

In this paper we extend previous findings by evaluatDPOAE component behavior as a function of stimulufrequency ratio in normal-hearing human ears. We repnovel behavior of DPOAE components at wide stimulus fquency ratios. Our study also differs from previous reportsthe use of lower level stimulus tones, which reveals featuof DPOAE components not reported previously. We wconclude by providing a theoretical analysis of our resuand preliminarily comment on the implications of these finings on the clinical application of DPOAEs.

II. METHODS

A. General methods

The methods used to record and analyze data were slar to those reported by Dharet al. ~2002!. In brief, high-resolution DPOAE data were recorded from three normhearing subjects recruited from the Purdue Universcommunity. These three subjects were selected from aof approximately ten subjects screened. Subject selecwas based on a negative family history of hearing loss, nmal middle ear function as determined by type-A tympangrams, hearing thresholds better than 10 dB HL at hoctave frequencies measured using tracking audiombetween 250 and 8000 Hz, and a ‘‘desirable’’ OAE profiOAE screening involved recording of spontaneous OA~SOAEs! as well as DPOAEs recorded using stimulus levof 65 dB SPL and a stimulus-frequency ratio (f 2 / f 1) of1.225; DPOAE results were considered ‘‘desirable’’ whensignal-to-noise ratio between DPOAE-level maxima andnoise floor was approximately 20 dB or greater and distifine structure was observed in some frequency ranges.presence or absence of SOAEs was not used to detereligibility, but the frequency of the SOAE~s! when presentwas considered during an examination of the DPOAE fistructure. Subjects were seated comfortably in a reclinerside a double-walled IAC sound chamber for the experimtal sessions, that lasted approximately 2 h each.

All experiments were conducted using custom desigsoftware developed in the laboratory running on a Neworkstation. Signals generated on the computer were pathrough a set of TDT PA4 programmable attenuators anHB6 headphone buffer before being fed to a set of ER2 tphones. The signals were delivered to the subjects ear cfrom the tube phones through a ER10B microphone prassembly. Signals recorded in the ear canal by the ERmicrophone were passed through the microphone’s prea

3768 J. Acoust. Soc. Am., Vol. 117, No. 6, June 2005

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lifier and a battery-operated Stanford Research SR560 lnoise amplifier/filter. The output of the SR560 was digitizusing a Singular Solutions AD64x at a sampling rate44 100 Hz before being stored on the hard disk of the Necomputer for offline analysis. The ER10B probe was fittedthe subject’s ear using a GSI emittance probe tip matchesize to the ear canal. Stimulus levels were calibrated iZwislocki coupler and system distortion, measured in an aminum 2 cm3 coupler, was generally below230 dB SPL inthe frequency range of interest for the highest stimulus levused.

Extensive DPOAE recordings were obtained at variostimulus levels and frequency ratios from three subjects wsatisfied the above mentioned inclusion criteria. The folloing stimulus frequency ratios were used: 1.053, 1.065, 11.11, 1.14, 1.18, 1.22, 1.26, 1.30, 1.32, 1.34, and 1.36. Thequal-level stimulus pairs (L15L2545, 65, 75 dB SPL!were used to record data. Additionally, severalL2 ~45, 50,55, and 60 dB SPL! were used in conjunction with anL1 of65 dB SPL. The choice of stimulus levels was made to coa range of input levels. A comprehensive range of stimulfrequency ratios were chosen consistent with our princiaim—examination of DPOAE-component characteristicsa function of stimulus-frequency ratio. The choice of stimlus levels was less rigorous, and was made simply to prova range of unequal and equal level inputs. A resolution0.025 mm based on the Greenwood map~Greenwood, 1990!was used for frequency spacing. This resulted in approximfrequency resolutions of 4 Hz around 1500 Hz and 8around 2500 Hz. Each fine structure period was sampled16 data points. The fixed-ratio data sets were converted fthe frequency domain to the time domain using a custdesigned IFFT algorithm and the DPOAE components wisolated using time windowing~Stoveret al., 1996; Knightand Kemp, 2001; Kalluri and Shera, 2001; Konrad-Maret al., 2001!. The reader is directed to Dharet al. ~2002! fora complete description of the IFFT algorithm and the timwindowing protocol. An example of the transformations usin estimating DPOAE-component magnitudes for subjectis displayed in Fig. 1.

Frequency domain amplitude and phase data~Fig. 1;panel A! were processed through an IFFT protocol to yieldtime-domain representation~Fig. 1; panel B!. These datawere time windowed to isolate the generator and reflectcomponents. Each component was then converted bacthe frequency domain~Fig. 1; panel C!. Note that the limitsof our time-domain filters were chosen to isolate the prinpal DPOAE components only. Specifically, the upper limitthe second window was carefully selected, thereby atteming to eliminate any ‘‘contamination’’ of the reflection component by subsequent intracochlear reflections. In pracsubsequent reflections, when present, were analyzed uindependent filters; those data, irrelevant to the current isare not presented here. The magnitudes of the componobtained from the reconstructed frequency spectra, wsampled every 24 Hz to yield an average value for estimulus condition.

Dhar et al.: Distortion product components and f2/f1

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FIG. 1. An example of the process followed to determine magnitudes oDPOAEs components. DPOAE amplitude, phase, group delay, and noisfloor are displayed in panel A for subject AE (L15L2565 dB SPL; f 2 / f 1

51.22). These data were processethrough an IFFT algorithm to transform them to the time domain. The results of the IFFT analysis for thesedata are presented in panel B. Thcomponents were isolated in time anconverted back to the frequency domain ~panel C!. DPOAE componentmagnitudes were estimated from thesfrequency-domain data.

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B. Statistical Methods

A repeated measures multifactor analysis of varia~MANOVA ! was performed to evaluate the effect of stimulparameters on component magnitudes. While the magnituof the individual components served as dependent variabstimulus level and frequency ratio were the independent v


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ables. Frequency was used as an observational variable arecorded data over different frequency ranges for the thsubjects to maximize the observation of fine structure, ahence was not included in the model. Separate analysesperformed for the generator and reflection componentsavoid interfering with the orthogonality of the models


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independence of the two components could not be eaestablished. DPOAE-component magnitudes were stubetween 2250 and 2650 Hz for subject AE, between 1and 1950 Hz for subject CZ, and between 1800 and 2200for subject KT.

III. RESULTS

A. General results

The main effects of subject (F5125.9,d f52), stimuluslevel (F5483.89, d f56), stimulus-frequency ratio (F5198.27,d f511) and the interaction of level and ratio (F513.19,d f563) on the generator component (Agen) wereall highly significant (p,0.0001). A similar analysis for thereflection component (Aref) also showed highly significan(p,0.0001) main effects of subject (F5597.99, d f52),stimulus level (F5171.68,d f56), stimulus-frequency ratio(F5109.16,d f511), and the interaction between level aratio (F59.34, d f563). Note that data recorded with astimulus conditions with the exception ofL15L2545 dBSPL, f 2 / f 1.1.3 were included in these statistical analysEach subject showed differences in the relative amplitudethe two components across frequency. Interactions betwthe variable subject and other independent variables wereincluded in the model as different subjects contributed dfrom different frequency ranges. Thus, the effects of fquency and subject could not be isolated in this model.

B. Effects of stimulus frequency ratio

The results of a Tukey Studentized Range~HSD! ~Inc.,1999! test comparing mean values ofAgen and Aref for dif-ferent stimulus-frequency ratios are presented in Table I.top and bottom halves of the table present comparisonsAgen and Aref , respectively. While the last two columns oTable I present the computed means for each ratio andthem in descending order, the initial columns show thTukey letter groupings. Means sharing the same letter groing were not significantly different~a50.05!. Thus, the meanvalues ofAgen for stimulus ratios 1.22, 1.18, and 1.26diddiffer significantly from each other as they have differeletter groupings~A, B, and C in this case!. However,Agen

means for 1.14, 1.32, and 1.11 share the same letter grou~D! and hencedo notdiffer significantly. This is suggestiveof a fairly symmetrical bandpass shape.Agen was highest fora ratio of 1.22, whileAref was highest for 1.11. Additionallythe ratios generating the four highest values ofAre f did notdiffer significantly from each other, consistent with an asymetric bandpass shape and/or greater variability betwears and across frequency within a given ear. The lowvalues ofAgen and Aref were generated at narrow and widratios, respectively. The strong statistical overlap betwratios generating highAref contrasted with the significant differences between 1.22, 1.18, and 1.26 forAgen provides anindication of distinct differences between the magnitufunctions for the two components.

Mean values forAgen and Aref for different ratios, col-lapsed across subjects, frequency, and stumulus levelspresented in Fig. 2. The solid lines representAgen, while thedashed lines representAref . The error bars represent61


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standard error. The lighter lines represent means calculfrom the entire dataset, while the darker lines represmeans calculated from the dataset after excluding datastimulus levels ofL15L2545 dB SPL. Data could not berecorded at all ratios for stimulus levels of 45/45 dB SPwhich resulted in a disparity in cell sizes for different ratioConsequently, data acquired for stimulus levels ofL15L2

545 dB SPL were excluded from subsequent plots whdata were collapsed across stimulus levels. Data withwithout DPOAEs recorded with stimulus levels ofL15L2

545 dB SPL are presented in Fig. 2 to enable a comparisAn examination of Fig. 2 reveals that the exclusion

data for stimulus levels of 45 dB SPL causes an upward sof the traces at the ratios where we were able to recordat 45 dB, without significantly altering the slopes or the peratios for eitherAgen or Aref . The inclusion of DPOAEs re-corded with stimulus levels of 45 dB SPL affected the curfor Agen to a greater degree. TheAgen ratio function appearsnarrower and more peaked than that ofAref . Aref is higherthan Agen at narrow ratios and the two functions cross btween the ratios of 1.11 and 1.14. TheAgen ratio functionpeaks around a ratio of 1.22. The two functions approeach other at ratios of greater than 1.3.

AgenandAref for individual subjects are displayed in Fig3. In keeping with the general trend seen in Fig. 2,Aref is

TABLE I. Results of the Tukey Studentized Range~HSD! test for generator(Agen) and reflection (Aref) components for the independent variable ratThe results are in accordance with the following parameters:a50.05, d f52724, MSE533.234 91 (Agen) and 36.228 47 (Aref), Minimum significantdifference51.7495 (Agen) and 1.8266 (Aref). Ratios at the extema(1.053, 1.36)and midpoint~1.22! of the distribution are specially markednote the different positions of these ratios in the rank hierarchy.

Results for generator componentAgen

Tukey grouping Mean Ratio

A 22.8184 1.22B 24.6063 1.18

C 27.4451 1.26D 210.0574 1.14

E D 210.3632 1.32E D 211.7540 1.11E 211.8192 1.30

F 214.3388 1.34G F 216.0069 1.08G 216.1129 1.36

H 219.0315 1.065H 219.3439 1.053Results for reflection componentAref

Tukey grouping Mean Ratio

A 28.6516 1.11A 28.8938 1.18

B A 29.9972 1.14B A 210.1653 1.22

C B 211.3941 1.08C 212.0360 1.065C 212.2809 1.053

D 214.5252 1.32D 215.7227 1.26

E D 216.2043 1.30E 217.8815 1.34

F 220.8783 1.36


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FIG. 2. Magnitude of DPOAE components as a funtion of the changing stimulus-frequency ratio. The soand dashed lines indicate the magnitude of the genetor (Agen) and reflection (Aref) components, respectively. The lighter lines represent means calculatedthe entire dataset. The darker lines represent meansculated after excluding data points recorded with stimlus levels ofL15L2545 dB SPL. The error bars on altraces represent61 standard error.

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FIG. 3. Component magnitudes for subjects AE, CZ and KT with changstimulus-frequency ratio. Data panels are marked with the subjects’ initSolid and dashed lines representAgen andAref , respectively. Data used fothese plots do not include those obtained with stimulus levels of 45 dB SThe error bars signify61 standard error.


higher thanAgen at narrow ratios and theAgen exhibits abandpass characteristic in all subjects.Aref is bandpass forsubjects AE and CZ, but low pass for subject KT. Somadditional differences between subjects can be observecomparing the three panels of Fig. 3. In subject CZ,Aref ismore peaked compared to the other subjects. This resultsshift in the ratio at which the two traces cross over. While tcrossover occurs around 1.11 for subjects AE~top panel! andKT ~bottom panel!, the crossover ratio is around 1.14 fosubject CZ ~middle panel!. Agen and Aref show relativeequivalence at high ratios for subjects AE and CZ, in keepwith the general trend seen in Fig. 2. WhileAref is larger thanAgen in subject CZ at these ratios~>1.3!, Agen remains sub-stantially larger thanAref at high ratios for subject KT. Acomparison of the three panels of Fig. 3 also reveals relaequivalence in the pattern and level ofAgen between the sub-jects. However,Aref is very different for the three subjectswith Aref being largest for subject CZ, followed by subjeAE and KT.

Agen andAref for different stimulus levels are presentein Fig. 4. Data for equal stimulus levels are presented inleft column, while the panels in the right column display dafor unequal stimulus levels (L1565 andL2545, 50, 55, 60,and 65 dB SPL!. While the general trends observed in thprevious two figures are present, some significant variatiwith the stimulus level are noticable. The differences btween Agen and Aref are less pronounced across the entratio range for stimulus levels of 65/55 and 65/60. BothAgen

and Aref appear less peaked for stimulus levels of 45/4Finally, Aref remains consistently higher thanAgen across theentire ratio range for the lowest stimulus levels used~45 dBSPL!. In contrast, little change is observed inAref at thehighest stimulus levels used~75 dB SPL!, with Agen remain-ing higher thanAref at wide ratios.

IV. DISCUSSION

By separating the ear-canal DPOAE signal into its twmajor components, we have been able not only to investigthe relative levels of the two components, but also to be

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FIG. 4. Agen andAref for different stimulus-level com-binations as a function of the changing stimulufrequency ratio. Solid and dashed lines representAgen
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understand the properties of each component. While theerator component (Agen) when plotted as a function of thstimulus-frequency ratio showed a distinct bandpass shwith a peak nearf 1 / f 2'1.2 for all stimulus levels excep45/45 dB SPL, the pattern for the reflection component (Aref)was more variable with the stimulus level and across eOne of the most striking characteristics of the results isstability of the generator component and the variability ofreflection component across ears. The influence of stimlevel on absolute and relative component levels is also foto be significant. We begin with a discussion of our datathe context of previous DPOAE publications and thenplore the relationship of these data with basilar membrmechanics. We conclude with some observations aboutchoice of stimulus parameters for the current clinical apcations of DPOAEs.

A. Comparison with previous DPOAE results

The pattern we see inAgen is similar to previous reportsof the magnitude of the ear-canal DPOAE signal, when pted as a function of the stimulus-frequency ratio~Harriset al., 1989; Gaskill and Brown, 1990; O’Mahoney anKemp, 1995; Stoveret al., 1999!. Another notable feature inthese reports was the presence of a notch in the DPOlevel around a stimulus-frequency ratio of 1.1 in human e~e.g., Stoveret al., 1999!. This notch has been interpretedbeing due to the cancellation between the two DPOAE co


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ponents when they are roughly equal in magnitude butmost 180° out of phase. In the few studies where amplituof the generator and reflection components,Agen and Aref ,respectively, were extracted, the former exhibited bandpbehavior as a function off 2 / f 1 and the latter a low-pass oasymmetric bandpass behavior~Knight and Kemp, 1999,2000, 2001!. Aref was .Agen for f 2 / f 1,1.1 in humans~Knight and Kemp, 1999, 2000, 2001! and '1.2 in guineapigs ~Schneideret al., 2003!.

Before making more in-depth comparisons of our dwith previous studies, some significant differences in meodology should be pointed out. While our recordings wemade using repeated measures withf 2 / f 1 fixed for each re-cording, Schneideret al. ~2003! used a fixed-f 2 paradigmand estimated the relative dominance of the two componfrom group delay. Similarly, Konrad-Martinet al. ~2001!also used a fixed-f 2 paradigm but extracted DPOAE component levels using an IFFT algorithm from the ratio functioresulting in data collapsed across frequency as wellstimulus-frequency ratio. This methodology served the ppose of their work—the examination of DPOAE componelevels as a function of the stimulus level; but poses problein direct comparison with our data. Perhaps most similarour work in DPOAE-recording methodology are the repoby Knight and Kemp~2000, 2001!, who also used IFFTanalyses of results from fixed-ratio sweeps. However, sign


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cant differences in stimulus levels used and the implemetion of time-domain filters exist even here. Knight and Kemuse a narrow time window to isolate the~early latency! gen-erator component and associate the reflection compowith the accumulated signal that occurs after the ealatency one. In contrast, we use narrow time windowsisolate both the generator and the shortest-latency refleccomponents. This difference in approach influences the emate of the reflection component significantly, since the wtime window used by Knight and Kemp allows the inclusiof secondary reflection components due to multiple interreflections between the stapes and the DP CF region~Dharet al., 2002!. The behavior ofAgen, observed here to be simlar across subjects, is in close agreement with KnightKemp. However, we report much greater variability in tbehavior ofAref across subjects and demonstrate intereseffects of stimulus level on DPOAE components that hanot been reported before.

Our results indicate a significant influence of stimullevel on the absolute and relative levels of the two comnents. Although Konrad-Martinet al. ~2001! and Mauer-mann and Kollmeier~2004! have examined the effect ostimulus level on DPOAE component behavior in the pasis difficult to isolate the effect of the stimulus-frequency rafrom that of the stimulus level in these studies. Both thegroups use the ‘‘scissor’’ approach where the level differebetween the stimulus tones is governed by a linear regresmodel ~Kummer et al., 1998; Janssenet al., 1998!, the dif-ference decreasing with an increasing overall level. Adtionally, Konrad-Martin et al. ~2001! also report data recorded with a fixed level difference (L12L2510). Knightand Kemp~2000, 2001! used stimulus levels of 75 dB SPonly. In contrast, we have reported results for both equal-unequal-level stimulus tones over a wide range~45–75 dBSPL!. Our results are consistent with previous reports in tthe reflection component is shown to be dominant at lstimulus levels only. Furthermore, we have also showndominance ofAref to be consistent across the entire rangestimulus-frequency ratios tested at these levels.

Our results are loosely consistent with the previous msurements cited above forf 2 / f 1,1.3 ~Fig. 2!. However, theydiffer from those of Knight and Kemp forf 2 / f 1.1.3 in thatAgen andAref do not ‘‘roll off’’ together @see Fig. 5 of Knightand Kemp~2001!#. The relative behavior ofAgen andAref atthese ratios is heavily dependent on the subject in our~Fig. 3!. Aref is significantly lower thanAgen for subject KT,and the two component levels are more or less equivalwith Agen being slightly larger for subject AE. In subject CZAref is larger thanAgen at ratios.1.3. Thus, we see greavariability in Aref across subjects at these ratios.Agenexhibitsa bandpass behavior—with symmetric behavior on bsides of a peak around a ratio of 1.2, while the behaviorAref in most cases is asymmetric if bandpass or evenpass, with very little rolloff at narrow ratios. It is also notworthy that our results are in close agreement with thattained by Knight and Kemp, when data recorded wequivalent stimulus levels~e.g., 75/75 dB SPL! are com-pared.

The time-intensive experiments necessary to prod


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data on DPOAE components has limited the number of pticipant ears in our as well as previous reports. It is nsurprising then that the variety of behavior inAref has goneunreported in the past. Our purely fortuitous sampling of eappears to show greater diversity in this area as compareprevious subject pools. It is curious that the rank orderobserved inAref is consistent with other measures suchhearing thresholds and fine-structure depth. Althoughthree subjects demonstrated hearing sensitivity within nmal limits, CZ had the best thresholds~coarsely measuredusing 5 dB steps and a clinical protocol!, followed by AEand then KT. Fine-structure depth was the greatest in CZleast in KT.

B. Comparison with psychophysical and physiologicalresults

Insight into the behavior of DPOAE components malso be obtained by examining psychophysical and phological data. The DP at 2f 12 f 2 , often referred to as thecubic distortion tone~CDT! in the physiological literature,has been examined by recording basilar membrane vibraat the CF place for 2f 12 f 2 ~see Robles and Ruggero, 200for a recent review!. Termed thecubic distortion toneor thecombination toneat 2f 12 f 2 in the psychophysics literaturethis DP has also been studied using cancellation as weloudness-matching techniques~see Plomp, 1976!. Record-ings of basilar-membrane motion of the CDT have beenported from guinea pig@basal turn and hook, Cooper anRhode~1997!# and chinchilla@apical turn, Cooper and Rhod~1997!; basal turn Robleset al. ~1997!# ears. The results depend on the stimulus level as well as the location ofpreparation along the length of the cochlea. General obvations from these data include a plateau in DP level afunction of increasing stimulus-frequency ratio up to a ‘‘coner ratio’’ and a sharp rolloff as stimulus-frequency ratioincreased beyond this critical ratio. The ‘‘corner ratio’’approximately dependent on stimulus level and the locain the cochlea. On occasion, a rolloff in the DP level asstimulus-frequency ratio approaches 1 is observed. Trolloff is perhaps most-prominent in the hook and basegions as well as for higher stimulus levels~Cooper andRhode, 1997!. The reader is directed to Figures 4g–i of Coper and Rhode~1997! and 6 and 7 of Robleset al. ~1997!.Note that these figures appear contrary at first glance, wthe discrepancy resolved by accounting for the fact that Cper and Rhode~1997! display the level of the DP relative tothat of the lower-frequency stimulus tone. The cutoff rawas highest and the slope the least steep for the recordfrom the apical turn of the chinchilla cochlea.

The results from psychophysical experiments appeabe largely dependent on the method used for an estimatiothe combination tone. A monotonic low-pass shape isserved with the use of the cancellation method~Goldstein,1967!, where the stimulus and cancellation tones are psented simultaneously. However, with the use of a nonsimtaneous pulsation technique, the combination tone appeadisplay an asymmetric bandpass shape~Smoorenburg, 1974Siegel and Borneman, 1999!, much akin to that observed inDPOAE and physiological data.


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Prior to the emergence of DPOAE-component data,discordance between the magnitudes of DPOAEs and bamembrane motion as a function of the stimulus-frequeratio was a source of concern. Indeed, Robleset al. ~1997!contrast the lack of reduction in the level of 2f 12 f 2 as f 2 / f 1

approaches 1 in basilar-membrane measurements withobserved for DPOAEs. However, the more appropriate coparison of the DPOAE level with physiological or psychphysical data is made usingAref rather than the ear-canaDPOAE level. Once the appropriate comparison is madata from the basilar-membrane, psychophysical, and Odomains appear to be in approximate qualitative agreemIt should be noted that to expect exact correspondencetween data from these three domains is unrealistic dudifferences in experimental conditions, and perhaps moreportantly, the actual variables being measured. WhetherCDT measured directly on the basilar membrane, or the cbination tone measured psychophysically, is equivalent toreflection component of the DPOAE at 2f 12 f 2 is an inter-esting question in itself. Even after the simplifying assumtion of a transparent middle ear is made, the equivalebetween these quantities would depend on the exact natuthe mechanism by which the incident DPOAE energy‘‘turned around’’ at the DPOAE-CF region. For examplKemp’s recent proposal of dichotomousactive and passivereflectance mechanisms~Kemp, 2002! would alter whetherthe reflection term is ‘‘accounted for’’ in physiological anpsychophysical measurements. However, it can be saidsome confidence that measurements in all three domainsresent some common aspects of peripheral auditory phyogy.

C. Component magnitudes and basilar membranemechanics

We discuss here the behaviors of bothAgen and Aref interms of cochlear models of DPOAEs@see Sec. V of Tal-madge et al. ~1998!; and Shera~2003! for much greatermodel detail#. In the following greatly simplified discussionwe ignore details such as mutual suppression of the stimfrequency waves whenf 2 / f 1 is close to 1, and focus on othefactors that determine the gross variation ofAgen and Aref

with stimulus frequency ratio. A comparison with data wousuggest that mutual suppression of the stimulus frequewaves mostly influence the behavior ofAref for ratios closeto 1.

For the case of a simple cubic nonlinearity,Agen will beapproximately proportional to the magnitude of an integover the 2f 12 f 2 sources. The integrand of the integralproportional to the square of the apical-movingf 1 cochlearwave times the complex conjugate of the apical-movingf 2

cochlear wave times the 2f 12 f 2 apical-moving cochlearwave @see Eqs.~130! through ~136! in Talmadge et al.~1998!#. The expression forAref involves the magnitude othe product ofRa ~the apical reflectance that results frocoherent reflection of a cochlear wave due to cochlear rouness around the DP tonotopic site! times an integration ovesources that is essentially the same as the one forAgen, ex-cept that the basal-moving DP wave replaces the apimoving one in the integrand. For largef 2 / f 1 , bothAgen and


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Aref decrease with increasing frequency ratio largely duethe decrease of overlap between the activity patterns oftwo stimulus waves.

When f 2 / f 1 is close to 1, the magnitude of the sourintegrations forAgen andAref are mainly determined by contributions from around thef 2 tonotopic site (x̂2). The fre-quency ratio that will give the largest value ofAgen will thenbe approximately the value that minimizes the variationthe phase of the integrand with distancex along the BM inthe region ofx' x̂2 ~the principle of the stationary phase!.This phase condition can be simply expressed as~Talmadgeet al., 1998!:

k̂22k~ x̂2 , f 1!2k~ x̂2,2f 12 f 2!50, ~2!

wherek̂ is the wave number of a cochlear wave in its peregion ~constant in a scale-invariant cochlea! and k(x, f ) isthe wave number of a cochlear wave of frequencyf at loca-tion x. The dependences ofk( x̂2 , f 1) and k( x̂2,2f 12 f 2) onf 2 / f 1 are estimated in Talmadgeet al. ~1998!, where it isalso shown that

Agen'¯exp$2~sx2/2!@ k̂22k~ x̂2 , f 1!2k~ x̂2,2f 12 f 2!#2%,

~3!

wheresx is a measure of the spatial width of the peak of tcochlear activity pattern. Asf 2 / f 1 increases from 1, the expression on the left side of Eq.~2! starts out negative andincreases through zero. These considerations then implyAgen as a function off 2 / f 1 has bandpass behavior, in agrement with data presented previously as well as here.

Now considerAref . Using an approach similar to the onjust discussed, it can be shown that

Aref'¯uRauexp$2~sx2/2!@ k̂22k~ x̂2 , f 1!

1k~ x̂2,2f 12 f 2!#2%. ~4!

As f 2 / f 1 increases from 1, the quantity,

k̂22k~ x̂2 , f 1!1k~ x̂2,2f 12 f 2!, ~5!

in Eq. ~4! can be shown to start out positive or negative aincrease with increasing ratio. If the value is initially postive, Aref will monotonically decrease with increasingf 2 / f 1 ,resulting in a low-pass shape~similar to that observed forsubject KT in Fig. 3!. On the other hand, when the valueinitially negative, it is still greater than the quantity on thleft-hand side of Eq.~2!. In this case,Aref will assume anasymmetric bandpass shape with the peak at a ratio lessthe peak ratio forAgen ~similar to that observed for subjecCZ in Fig. 3!. Additionally, this relationship leads to thprediction ofAref.Agen as f 2 / f 1 increases from 1, given areasonable magnitude ofRa . Aref is predicted to be equal toAgen ~and possibly give rise to a notch behavior in tDPOAE amplitude under the requisite phase-cancellaconditions! for a ratio ~typically around 1.1 in our data!smaller than the peak ratio forAgen ~typically around 1.2!, inagreement with the data of Figs. 2, 3, 4.

From Eqs.~3! and ~4!, we see that

Aref /Agen'uRauexp$~2sx2!k~ x̂2,2f 12 f 2!

3@ k̂22k~ x̂2 , f 1!#%. ~6!


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It should be emphasized thatRa , according to the coherenreflection model~Zweig and Shera, 1995; Talmadgeet al.,1998; Shera, 2003!, depends mainly on the sharpness of tuing of the BM around the DP CF region and the strengthcochlear inhomogeneities around that region.Ra will gener-ally be significant only if both of these factors are preseThusRa is expected to fluctuate significantly across healears due to differences in the degree of cochlear roughacross such ears. It is therefore not surprising that the relalevels ofAgenandAref are found to change from ear to ear ff 2 / f 1.1.3 and across frequency within a given ear~see Fig.1!.

In sumAref.Agen at narrow ratios, overcoming the suppressive effects of the stimulus tones onRa . This observa-tion is in contrast to the assumption of bidirectional distribtion of energy from the generation region~e.g., Allen andFahey, 1992!. Thus, Shera’s~2003! assertion that phase appears to ‘‘win’’ in the battle between amplitude and phasethe overlap region can perhaps be confidently extended;only does phase win, it appears to win by a landslide. Tbehavior ofAref at wide stimulus-frequency ratios is stronginfluenced byRa . We provide two lines of evidence in support of Ra being the driving force behind the behavior ofAref

at wide ratios. First, with an~assumptive! correlation be-tween cochlear health and reflectance, we argue that theordering ofAref , hearing thresholds, and fine-structure dein our three subjects is not coincidental but due to varydegrees of reflectance in these ears. Second, the influenRa on Aref is evident in Fig. 4 whereAref remains larger thanAgen for all stimulus-frequency ratios for stimulus levels45 dB SPL, due to reduced suppression by the lower-lestimulus tones. The influence of stimulus level onAref hasalso been demonstrated elsewhere~Mauermann and Koll-meier, 2004; Konrad-Martinet al., 2001!.

We have thus seen that most of the characteristictures ofAgen and Aref that we find are at least qualitativeldescribed by cochlear models that incorporate a nonlingeneration process around thef 2 CF region combined withthe coherent reflection of the initial apical-moving DP coponent.

D. Clinical implications

We conclude by making some observations aboutrelationship betweenAgen and Aref when stimulus levels(L1 /L2 in dB SPL! of 65/50 and 65/55 are used. A stimululevel combination of 65/55 at a stimulus-frequency ratio1.2 is often used in clinical applications of DPOAEs. Thehas been some recent work speculating that DPOAEstructure is~at least partially! responsible for the failure oDPOAEs in predicting hearing thresholds with accura~Shafferet al., 2003; Shera, 2004; Dhar and Shaffer, 200!.If this speculation was valid and the goal of a clinical procol was to record DPOAEs with the minimum possible fistructure, stimulus conditions that lead to the biggest difence betweenAref andAgen should be chosen. More specifically, the ideal stimulus conditions should bias the ear-caDPOAE signal towardAgen to the greatest extent possible,the goal is to monitor cochlear health around thef 2 CF re-gion. Our data appear to suggest that stimulus-frequency


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tios around 1.22 satisfy these demands to a great extent,the exception that a stimulus-frequency ratio of 1.26 leadsimilar if not greater bias toward the generator componwhen stimulus levels of 65/50 are chosen. Consideratisuch as a good signal-to-noise ratio and the separationtween normal and impaired populations also influencechoice of stimulus conditions in a clinical protocol. However, our results indicate that the current choice of stimuparameters in clinical protocols mostly satisfies the conseration of relative component levels.

ACKNOWLEDGMENTS

Part of this work was completed when all four authowere affiliated with Purdue University. This research wsupported in part by the NIH/NIDCD Grant No. R2DC03094 to CLT and R03 DC0005692 and a grant fromDRF to SD. We thank Professors Christopher Shera, PFahey, Jonathan Siegel, and Robert Withnell for ththoughtful comments on an earlier version of the papThanks are also due to Professor Brenda Lonsbury-Maand two anonymous reviewers. Feedback received frthem made this a better manuscript.

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The effect of stimulus-frequency ratio on distortion product otoacoustic emission components

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