Nonlinear phenomena as observed in the ear canal and at the auditory nerve

[Pages:15]Nonlinear phenomena as observed in the ear canal and at the auditory nerve

P.F. Fahey AT& T BellLaboratoriesM, urray Hill, NewJersey07974andDepartmentofPhysicsU, niversityofScranton, ScrantonP, ennsylvania18510

J.B. Allen AT& T Bell LaboratoriesM, urray Hill, New Jersey07974

(Received11,April 1983;acceptedfor publication5 September1984)

We reporthereseveralmeasuresof nonlineareffectsin the mammalianearmadein the external auditorymeatusandin singleneuronsof the auditorynerve.We havemeasuredthe 2f? --f2 and thef: -f? distortionproductsandwehavefoundthat (a}theneuraldistortionproductthreshold curvefor 2f? -f2 mirrorsthelow-frequencysideof the frequencythresholdcurve,(b}whenthe neuraldistortionproductthresholdcurveof 2f? -f: isplottedversuslog{f:/f?}itsslopeisabout 50 dB/oet andits interceptis 10-20 dB abovethe frequencythresholdat the characteristic frequencyCF, (e}substantia2lf? -f: distortionwasseenin all animalsstudiedwhilethef: --f? distortionproductwasonlyrarelyfoundat substantiallevels,and(d}the distortionproduct pressureobservedin theearcanalwasat a levelequalto that detectedat thresholdby theneural unitsunderstudy.We havealsomademeasurementosf two-tonerate suppressionthresholds usingtwo newandconsistentthresholdparadigmsW. e findthat (a}for highandintermediate characteristifcrequencyneuralunitsthesuppressiotnhresholdisindependenot ffrequencyandat alevelofabout70dBSPL,(b}thesuppressioanboveCF ismuchlessthanbelowCF, and(e}thetip of the frequencytuningcurvecanbesuppressebdy up to 40 dB by a low-frequencysuppressor.

PACS numbers: 43.63.Pd, 43.63.Hx

INTRODUCTION

In thispaperwestudytwo separatemeasuresof ?ochlear nonlinearresponsen, amely,distortionproductsand two-tonesuppressionF.irst, we reporton measurementosf two-tonedistortionproductsdetectedat theauditorynerve of theeat.We thencomparethesethresholddistortionproduetmeasurementws ith theacousticdistortionpressurelevels as detectedin the external auditory meatus.We shall restrictourselvesto the two largestobservabledistortion products(DPs)whichareat frequencie2sf? --f? andf? --f? (wheref: isthehigherfrequencyof two inputtonefrequeneiesf? andf2}.For a recentreviewof psyehophysicalmlyeasured DPs seeGoldstein et al., 1978 and for discussionof physiologicasltudiese,specialliyn eats,seeKim etal., 1980; BuunenandRhode,1978;Buunenetal., 1977;Smoorenburg et al., 1976;GoldsteinandKiang, 1968.

The approachtakenhereisto useneuronsin theauditory nerveof theeatasthresholddetectorsof thedistortion products2f? --f2 andf: -fl. By makingourmeasurements

at the neural rate threshold we have avoided the nonlinear

saturation of the neural rate level function as a function of

soundpressurelevel.Hence,we havebeenableto measure distortionproductscloseto the lowestpossibledetectable levelsand to extensivelymeasurethe dependenceof their generationuponthefrequencieosftheprimariesM. oreover, we havemademeasurementsof the distortionproductsin the ear canalpressureeontemporaneouswlyith the neural measurementsT.hisapproachhasallowedusto measurethe distortionproductamplitudein theearcanalunderthecon-

straint of a neural iso-threshold DP stimulus. We have

found, for this ease,that the level of the acousticdistortion

productmeasuredin the earcanalissufficiento accountfor

the observedexcitationof the neuralunit understudy.The levelof nonlinearacousticdistortionproductseenin the ear canalismuchgreaterthanthat seenwhentheacousticdriver is terminatedwith a 1-era3 acousticavity.In severaal nimalsweobservedthe 2f? --f: DP at rathersubstantia(lbut reduced}levelsup to 1 h postmortem,but we did not study the lability of the DP in a systematicway.

In parallel with the distortionproduct measures,we havemeasuredneuraltwo-toneratesuppressiotnhresholds. In our studiesof two-tonesuppressiona,subthresholdtone ofonefrequencyisusedto reduceor removethedetectability

of a tone at the CF. Here we have determined the level of the

input of a subthresholdtone (which,by itself, would not drive the neuralunit aboveits spontaneousrate}which reducestheneuralresponseto a suprathresholdCF toneto the neuron'sspontaneoursate response{.For a reviewof twotonesuppressionand othernonlinearphenomena,seeHall, 1981.)

We have made extensivemeasurementsu, sing our modifiedcriterion,of thefrequencydependencoef two-tone suppressiotnhresholdsa, ndtheseresultsappearto besomewhat differentthan the resultspreviouslyreportedin the literature.For suppressorasbovethecharacteristicfrequency, wehavefoundonlysmallamountsof two-tonesuppression.For CFsabove3 kHz andsuppressofrrequenciebselow CF, wefindupto 40 dB of ratesuppressioant theunit'sCF. Moreover,we havemeasuredtwo-tonesuppressionon the sameunitsasourmeasurementosfdistortionproductsin the hopethat onenonlinearphenomenoncouldberelatedto the other.No quantifiablecorrelationshaveasof yet beenob-

served between these two nonlinear measures.

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I. METHODS

A. General

The data presentedin this studyhavebeenobtained

from 20 cats. From each animal we have characterized fre-

quencythresholdcurves(FTCs)for morethan 100 neural unitsalongtheauditorynerveduringthe24-to 36-hexperimental run. We are presentingdata here that have come from animalswith goodthresholds(= 15-?30dB SPL re: 20 /?Pa).Due tolimitationsoftheupperfrequencycutoffofour acousticdriver (25 kHz), our distortionproductmeasurementswere obtainedonly on units with characteristicfrequencies(CFs)oflessthan 13kHz.

Both the surgerynecessaryto gainaccessto the auditory nerveand the mechanical,electronic,and computing apparatususedin thisstudy,havebeendescribedin detailby Allen (1983).Briefly,theanimalswereadultsofbodyweight 2-5 kg, which were free of ear mites and middle ear infections.Accessto theauditorynervefollowedretractionof the cerebellumT. he cochlearmicrophonic(CM) wasmonitored with a silverball electrodeapposedto the round window bothbeforeandafterthe skullopeningandbeforeandafter

the retraction of the cerebellum. Anesthesia was maintained

with sodiumpentobarbitoal ndwasadministeredintraperitoneallyasrequiredto suppresas pinchreflex.

Boththe electricalinput to the acousticdriver(Sokolich, 1977)and the responsme easurement(sfromthe calibratedprobemicrophone,from the CM electrodea, ndfrom theneuralelectrodew) ereunderthecontrolof a Data GeneralS/200 EclipseminicomputerT. hissystemallowedusto measurea neuralFTC, usingthe Kiang and Moxon paradigm(Liberman,1978)in under1min. Moreover,we interleavedear canalpressuremeasureswith neuraldistortion productthresholdmeasuresin under2 min. Under nocondition were SPLs greaterthan 110 dB ever deliveredto the

animal.In fact,onlybrieflywastheinputgreaterthan80dB

SPL, as measured in the ear canal.

OurneuralmeasuremenptsroceedeadsfollowsA. glass micropipettefilled with 3M KC1 {resistancebsetween10 M/2 and30M/2 )wasinsertedbymanuaml icrometeardjustmentintotheauditorynerve.Thereaftert,hepositionofthe micropipettewasunderthe controlof a Burleigh"inch worm"PZT drive.Neural unitswerefoundby inputinga gatedwidebandnoisesearchstimulus.Oncefound,the unit FTC wasmeasurebdyscanningfromhighto lowfrequency while changingthe input amplitudeof a windowed50-ms tonepipuntilthenumberofneuralspikesgenerateduring thetoneintervalwas0nlyonemorethanthenumberof spikesduringanadjacent50-mssilentinterval.The locusof the pointssoobtainedi,n frequency-amplitudspeaced, e-

fines the FTC.

B. Distortion products

GiventheFTC and,hence,the CF frequencyoecvw, e theninputan acoustictonepip comprisedof twofrequencies,f?andf2, wheref2 >f?, suchthateither2f? -f? oralternativelyf?--f? wasat or slightlybelowthefcv. The two toneshavegivenpressurelevels`4? and`4v Again,weused the Kiang and Moxon paradigmto determinethe locusof acousticstimuluspointsin thefrequency-amplitud{fe?,A?) planesuchthattheunitrespondewdithonemorespike?uringthe drivenintervalthan duringthe silentinterval.This locusof pointsdefinesa distortionthresholdcurve(DTC). For mostof thedatacurvespresentedherethepressureamplitudeoffl andf2 wasapproximateleyqual(A1= '42= ?4).

Effectively,our procedureis to calibratean auditory neuron(bymeasuringitsFTC) andthento usetheresponse

of this "calibrated" neuron to determine the acoustic level at

eachfrequencyto maintainaniso-rateneuralDP response.

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FIG. 1.ThisfigureshowseightFTCs (solid lines)for cat41 with the respectiveraw distortiondataDTCs (dashedlines)oftheunit.

The DTC is defined in the text. With most

unitsmultipleDTC runsareshownA. lsoon the DTCs there is a triangleat the DTC-

FTC intersection. Points on the DTC of

lowerfrequencythan the intersectionpoint are not consideredpart of the DTC because thefl primaryratherthedistortionproduct is drivingthe unit.

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In Fig. 1weshowseveraFl TCs (solidlines)alongwith the units'2fl -f2 DTCs (dashedlines).In eachpanelof thefigure the amplitudeof the distortionproducthas'beenheld constantat the CF threshold(.If Wewereto shiftthedistortionproductfrequencyfromCF, wecouldthenchangethe gainof ourneuraldetectorandhencechangetheamplitude of the distortionproductthat we aremeasuring.W) e define thedistortionproductratethresholdasthesmallespt rimary levelwhichcangenerateadetectablDe P responseN.otethat foranyfl belowthefrequencyofintersectionoftheDTC and the FTC, both the stimuluscomponenat tfl andthe distortionproductdrivetheunit.In eachof theunitsof Fig. 1the FTC-DTC intersectionis marked with a triangle. In the figuresthatfollowwecallthelevelof theFTC-DTC intersectionthedistortionproductratethreshold(DPT). Several of the unitsin Fig. 1showmultiplepassesof the DTC.

The curvesin ourFig. 1aresimilarto curvesin Buunen andRhode{1978)(theirFig. 3)that definedthe "maximum frequencyseparatiofnordetectabilitoyfa CDT." Generally,

their measure contains information that is similar to our

DTCs, althoughthe precisemannerin whichtheir ampli-

tudes are measured differs.

Figures2 and 3 showseveraFl TCs with splinefitted DTCs. We averagedmultipleDTC passesonthesameunit by leastsquaresfittedsplines(Fox, 1976)to thetotalsetof DTC points.In Fig. 2 weshowcubicsplinefitsof 2fl --f2 DTCs.Shownin Fig.3 aresplinefitsoff2 --fl DTCsforthe

same animal.

C. Ear canal pressure measurements

The carcanalpressurewasmeasuredwith a calibrated Bruel and Kjaer 1/2-in. microphoneterminatinga 2-cmlongprobetube.Thetip oftheprobetubewaspositionedto within 2-4 mm of the umbo.The sameprobemicrophone

was used to ascertain the level of distortion in the external

auditory meatusand in a closed1-ccacousticcavity. In the acousticcavitythe levelof the distortionproductwasalways more than 70 dB below the primaries(nearthe distortion floor of the driver).

II. RESULTS

A. Neural

Because our detectors are neurons at threshold, the gainsof thesedetectorsare various.In orderto accountfor thesedifferentgains,wecanexpressthe DTC relativeto the gainof the detector(i.e.,in mostcaseshere,relativeto the valueof the FTC at CF). In Fig. 4(a)and (b)are two FTCs

with DTCs in which the thresholds at CF are different. In

Fig. 4(c)theDTCs arenormalizedby theirrespectiveFTCs

at CF. We call the normalized DTC the relative distortion

thresholdcurve (RDTC). Note that were we measuringa linearphenomenonthepresentationof the datain thisnormalizedwaywouldbenatural.For aphenomenonthat isnot linear,onemightexpectthat a normalizationbythedetector

threshold to some nonlinear function of that threshold

would be the natural normalization.For example,if the 2fl -- f2 werecompletelyaccountedforbythecubictermofa powerseriesexpansionin inputamplitude.4,thentheproper

normalization for us to use would be relative to the cube root

of the thresholdat CF. As can be seenfrom Fig. 4(c) and from previousworksof others(Goldsteinand Kiang, 1968 and Buunenand Rhode, 1978),the normalizationby the thresholdat CF thatwechoseseemsto bestreflecttheamplitudedependencoef the2f? --f2 signal.In Fig. 4(d),we show the effectof changingthe gainof the detectorby displacing the 2f? -f2 tonefromtheCF. Noticethat theDTC generatedundertheseconditionsisseveraldB higherthantheDTC generatedat a frequencyequalto CF. Likewise,the threshold (thevalueof the FTC) of the detectoris alsohigher.In

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FIG. 2. For cat 47 the spline fit DTC (dashedcurve)is plottedwith the FTC for eightunits.The splinefit wasusedto providea leastsquaresaveragefor multiple DTC runs. The distortion product is 2A -A.

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FIG. 3. SameasFig. 2 excepthedistortion producitsf? -- f?. Thedashedcurvesarethe f? --f] DTCswhilethesolidcurvesarethe

FTCso

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everyanimalthat wehavestudied,changingthegainbyx dB usuallyresultsin anincreaseof at leastx dB in theDTC and not in an increaseof x/3 dB as one would expectfrom a purelycubicnonlinearity.Shownin Fig. 4(e)areDTCs measuredwith threedifferentratiosof,41to,42.Onesetof DTCs ismeasuredin the usualway with,41 = ,42;oneis measured with,41= 3,42a; ndthethirdismeasuredwith,42= 3,41'The superpositioonf thesecasessuggesttshat thenonlinearityis

notoftheform,4?1?. TheobservatioonfFig.4(e)hasbeen foundin all animals.The DTC isindependenot ftheratio of ,41/,42untilthatratiobecomesgreaterthan4 or 5orlessthan

0.2 or 0.25.

Besidesnormalizationby detectorthreshold,we found that the transformationof the frequencyaxisfrom logf] to

log(f2/gfle)neraulnlyifiethse2fl--f2datacrofsrsequen-

cies.In Fig. 5, weseetheresultsofthistransformationF.igure5(a)isthecompletesetofRDTCs for oneanimal;in Fig. 5(b)theseRDTCs arereplottedwithabscisslaog?/fl). Figure5(c)and(d)showsthesameforanotheranimal.For frequenciesof 2fl--f? above3 kHz, we foundthat boththe normalizationby detectorthresholdand rescalingthe frequencyaxisto log0e2/flw) eremosteffectivein unifyingthe data.Thesetransformationswereunifyingin fourof thefive animalsfor which we had extensivedata acrossmany fre-

quencies. In Figs.1,2, 4, and5 it isapparentthat nonmonotonic

featuresof the DTCs are commonplaceF. urthermore,it is generallyevidentthat at highCFsthedetectabledistortion

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