Research ArticleHydromechanical Structure of the Cochlea Supports the BackwardTraveling Wave in the Cochlea In Vivo

Fangyi Chen ,1,2 Dingjun Zha ,2,3 Xiaojie Yang,1 Allyn Hubbard,4 and Alfred Nuttall2,5

1Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China2Oregon Hearing Research Center, Department of Otolaryngology and Head and Neck Surgery, Oregon Health and ScienceUniversity, Portland, OR 97239, USA3Department of Otolaryngology-Head and Neck Surgery, Xijing Hospital, Fourth Military Medical University, Xi'an,Shaanxi 710032, China4Department of Electrical & Computer Engineering, Boston University, Boston, MA 02215, USA5Kresge Hearing Research Institute, The University of Michigan, Ann Arbor, MI 48109, USA

Correspondence should be addressed to Fangyi Chen; chenfy@sustc.edu.cn and Dingjun Zha; zhadjun@fmmu.edu.cn

Received 21 March 2018; Accepted 12 May 2018; Published 17 July 2018

Academic Editor: Jian Wang

Copyright © 2018 Fangyi Chen et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The discovery that an apparent forward-propagating otoacoustic emission (OAE) induced basilar membrane vibration has createda serious debate in the field of cochlear mechanics. The traditional theory predicts that OAE will propagate to the ear canal via abackward traveling wave on the basilar membrane, while the opponent theory proposed that the OAE will reach the ear canalvia a compression wave. Although accepted by most people, the basic phenomenon of the backward traveling wave theory hasnot been experimentally demonstrated. In this study, for the first time, we showed the backward traveling wave by measuringthe phase spectra of the basilar membrane vibration at multiple longitudinal locations of the basal turn of the cochlea. A localvibration source with a unique and precise location on the cochlear partition was created to avoid the ambiguity of the vibrationsource in most previous studies. We also measured the vibration pattern at different places of a mechanical cochlear model. Aslow backward traveling wave pattern was demonstrated by the time-domain sequence of the measured data. In addition to thewave propagation study, a transmission line mathematical model was used to interpret why no tonotopicity was observed in thebackward traveling wave.

1. Introduction

Ears not only hear sound but also generate sound, which iscalled the otoacoustic emission (OAE) and was discoveredin 1978 [1]. There are currently two competing theoriesestablished to explain the propagation of sound from theplace where it is produced inside the cochlea towards the exitof the cochlea. The backward traveling wave theory, whichpostulates that OAE-induced waves travel slowly along thebasilar membrane (BM), is widely accepted as an explanationof the propagation of the OAE [1, 2]. However, thispredominant backward slow-wave theory cannot explainsome experimental phenomena [3–6] favoring the fast com-pression wave theory that would exist in the lymph fluidssurrounding the BM. In the compression wave theory, the

slow-speed propagation of the backward transversal wavemotion of the BM is replaced by a fast-fluidic compressionwave and experimental time/phase differences are accountedfor by mechanisms independent of the wave. To date, it is stillan open question about the OAE path. Resolving this ques-tion is important because the OAE has become a useful andnoninvasive clinical tool for hearing screening. To utilizethe OAE for more precise diagnoses, it is necessary to under-stand how it propagates backward to the ear canal. In relationto the backward propagation of the OAE, von Békésy discov-ered that the wave on the BM always traveled from the baseto the apex, even the stimulus (the stapes vibration) wasplaced at the apex of the cochlea. This so-called paradoxicalwave was a hurdle that prevented people from believing thatthe OAE can propagate along the BM backward at the time

HindawiNeural PlasticityVolume 2018, Article ID 7502648, 11 pageshttps://doi.org/10.1155/2018/7502648

when OAE was just discovered. In a few years since then, theseeming contradiction to the paradoxical phenomena wasexplained by stating that the vibration source of OAE wason the BM rather than in the fluid by the stapes as in theparadoxical wave. Hence, the theory of backward travelingwave was widely accepted.

One critical issue that causes the uncertainty in determin-ing the wave propagation mechanism is that the actual loca-tion of the OAE source is uncertain. Most of the previousstudies used nonlinear, intrinsic vibration to the organ ofCorti to generate organ vibration at the intermodulationfrequency of two tones. This intrinsic vibration initializesthe backward wave propagation, but the spatial location ofthe vibration along the BM is still debated. This caused theanalysis of the experimental data to be difficult because thegeneration mechanism of the OAE is complicated [2], andthe origin of the OAE could be multiple sites. Although thewidth and location of the generation site are so important,they cannot be ascertained. The uncertainty of the sourcelocation also makes it difficult to estimate the wave propaga-tion speed, which is a critical data for distinguishing thepropagation forms and testing which theory explains thesound propagation mechanisms. Such an uncertainty hasoften resulted in interpretations of the same experimentalresults [6–8] using both competing theories. Thus, it is criti-cal to study the backward wave propagation from a vibrationsource at a unique and precise location in the cochlea.

In addition, although as a widely accepted theory, thebackward traveling wave theory has not been validateddirectly using an experiment where the vibration on theBM is measured [3]. The evidence used to support this theoryis mostly from mathematical modeling [7, 9–14] and indirectmeasurements [15, 16]. Attempts have been made to experi-mentally generate local vibration on the BM via optical [17]and direct mechanical [18] methods but with limited success.The optical method [17] does not provide enough mechani-cal vibration until the light is strong enough to cause damageto the organ of Corti. The mechanical stimulation in Richteret al. [18] did provide an accurate vibration source withenough energy, but the hemicochlea preparation in this studydestroyed the integrity of the basic hydromechanical struc-ture of the cochlea. Also, the poor sensitivity (~10 nm) ofthe vibration measurement method limited its capability todetect the small vibration on the BM.

Since the hypothesized backward traveling wave is atransverse vibration on the BM, these indirect measurements[15, 16] have also been criticized to not truly represent theBM vibration [19, 20]. Moreover, other structures (e.g., tecto-rial membrane and Reissner’s membrane) in the cochlea havealso been suggested to be capable of supporting wave propa-gation inside the cochlea [21, 22], but their contribution tothe cochlear mechanical dynamics has not been thoroughlystudied and determined. Therefore, a direct measurement ofthe BM vibration using an experiment is necessary to deter-mine the wave propagation mechanism of OAE in cochlea.

In the present study, we designed a novel method using amechanical/piezoelectric stimulator to drive the BM at aprecisely known location; thus, the location of the vibrationsource initiating the backward wave was accurately known.

The BM vibration was then directly measured at multiplelocations in an in vivo cochlear preparation. We found thatthe phase of the measured BM motion showed a consistentlag with the increase of the distance from the vibrationsource. The speed of the wave propagation was shown inthe order of tens of meters per second, much less than thespeed of a compression wave in water. This study, for the firsttime, used directly an experiment to prove that there was aslow backward traveling wave on the BM of the cochleain vivo. The computer simulation of the experimental resultsin a mechanical model, termed “artificial cochlea,” also con-firmed that the hydromechanical structure of the cochleasupported the backward traveling wave.

2. Methods

2.1. Specimens. A total of 6 young guinea pigs weighted at250 g–400 g were used in this study. After an animal wasanesthetized by intramuscular injection of a mixture of keta-mine (30mg/kg) and xylazine (20mg/kg), the temporal bonewas opened using the dorsal-ventricle approach as describedby Zheng et al. [23]. During the experiment, the animal wasanesthetized with regular supplements of anesthetics. Tra-cheotomy was performed, and a ventilation tube was insertedinto the trachea for natural breathing. The guinea pig’s headwas then mounted on a heated head holder. A surgical oper-ation was performed to expose the left bulla, which was thenopened for access to the cochlea. During the experiment, thecore temperature of the animal was maintained at 37°C-38°C by a heating blanket and a rectal thermometer, whichwas controlled by a servo temperature controller (FHC,Bowdoinham, ME, USA) [23]. After the bulla was openedto expose the cochlea, an oblong window of about 2mmlong and 0.5mm wide was opened on the bony wall atthe cochlear basal turn to expose the BM. As shown inFigure 1(a), the basal turn of the cochlea was cut to openand the BM was exposed over almost the whole basal turn.Reflective beads assigned names of basal, middle, and api-cal were placed on the BM along the longitudinal direc-tion. The tip of stimulator touched the BM at the apicalend of the basal turn and delivered the vibration to initiatethe backward wave. The wave propagation along the BMwas recorded by focusing the laser of the vibrometer ontothe reflective beads.

In the preparation, the joint between the incus and stapeswas dislocated so that the middle ear chain was disrupted,significantly reducing any possible middle-ear-conductedacoustic stimulation. The ossicular dislocation was donebecause the piezo stack used to stimulate the BM also radiatesacoustic energy. This sound will propagate to the adjacenttympanic membrane, initiating a normal acoustic stimulusto the cochlea and thus producing a forward traveling wavein the cochlea if the ossicular chain is intact. That forwardtraveling wave would interfere with the backward waveinitiated by the stimulation probe on the BM. The fluidlevel of the perilymph in the scala tympani was carefullylowered using cotton wicks so that only a very small amountof fluid (~30μm thick based on visual comparison with the

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known diameter of the probe tip) was left to moisten theexposed BM.

The study was approved by the Institutional AnimalCare and Use Committee of Oregon Health and ScienceUniversity.

2.2. Piezo Stimulator Design and Mounting. The accuratelocation of the vibration source was a problem in almost allof the previous studies designed to measure the backwardwave propagation in the cochlea. In our study, the directmechanical driving method was adopted with a different

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Figure 1: BM and stapes vibration spectra induced by a point stimulation of the BM. (a) The opened cochlea with stimulator and reflectivebeads in place. The stimulator probe is a blunt pipette driven by a piezoelectric stack. Reflective beads are placed on the BM, labeled as apical,middle, or basal, in the direction away from the stimulator. A bead was also placed on the stapes for recording its vibration. Vibrationamplitude (b) and phase (c) of the middle (solid), basal (dash), and the stapes (circle) beads, relative to that of the apical bead. (d) Phasedifference (solid) between the middle and basal beads and the calculated group delay (dash). (e) Wave velocity and the wavelength,calculated from the phase difference in D. The negative delay value at lower frequencies (<14 kHz) in both (d) and (e) is likely due to alocal disturbance, such as the local reflection with the insertion of the stimulator. The wave speed is high at lower frequencies, and thedistance between these two beads is small. Both effects make it vulnerable to the disturbance. For a wider range, apical to stapes, this smallnegative delay is absent (g). (f) Phase difference (solid) between the middle and basal beads and the calculated phase delay (dash). (g)Phase of the stapes vibration (solid) relative to the apical bead and the calculated phase delay (dash).

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design. The tip of a pulled pipette when heated with anelectrical cautery, melted into a sphere of about 50μm indiameter. This rounded tip was appropriate in size comparedto the BM width for the delivery of a local vibration. Thena ~2 cm piece from the tip end of the pipette was cut offand attached to a piezo stack (AE0203D04F from Thorlabs,Newton, New Jersey) using cyanoacrylate cement. The driverwas then cemented onto a steel bar, which was mounted on amicromanipulator. Figure 2 shows a view of the assembledprobe. The overall size of the piezo stimulator allowed it tofit under the objective lens of the laser Doppler vibrometer(LDV). During the experiment, the piezo stimulator wasadvanced in about a 60-degree (relative to the horizon) angleby the micromanipulator into the opened scala tympani andto get contact with the BM by the tip. This process is visuallyguided under a surgical microscope. Careful attention wastaken to avoid significant deformation or perforation on theBM. After placing the stimulator, the surgical microscopewas moved away and the LDV with the objective lens wasthen moved in for vibration measurement. The piezo stackand the steel bar were held in such a way as to reduceinterference caused by the laser beam of the velocimeter.The contact of the probe tip to the BM was also verified bymeasuring the vibration of the bead that is closest to theprobe on the BM.

2.3. Calculation of the Delays. Two kinds of delays, groupdelay and phase delay, were calculated from the phase spectrain this study. The group delay is the derivative of the phasedifference. To avoid the influence of the noise, the phase datawas firstly fitted with a 4th-order polynomial to smooth thecurve before performing the differentiation.

Group delay = −dφ2πdf , 1

where d is the differential operator, φ is the phase in radius,and f is the frequency.

Group delay has been used in most OAE studies [2, 5, 15,16, 24] to quantify the delay for determining the direction ofthe wave propagation.

Besides group delay, another method to quantify thedelay from the phase response is to calculate the phasedelay by

Phase delay = −φ

2πf 2

This method has been adopted in previous studies by Renand his colleagues [3–6, 17, 19].

2.4. The Mechanical Cochlear Model. In this study, a mechan-ical model of the cochlea was used to verify the backwardwave propagation. This mechanical device consisted of afluid channel, a membrane section, and an artificial BM tosimulate the basic hydromechanical structure of the cochlea[25]. The artificial BM was constructed from a polymermembrane with 32 copper beams deposited on it. Thelengths of the copper slots increased gradually from one(basal) end to the other (apical) and resulted in a stiffness

gradient for simulating that in the cochlea. Vibration mea-surement on this mechanical model demonstrated the travel-ing wave-like features, that is, tonotopicity, the frequency-to-place map, unsymmetrical filtering (the shallow slope at thelow-frequency side of the peak but steep slope at the high-frequency side), and slow traveling wave phase. Therefore,it is a valid model of the cochlear hydromechanical structurefor verifying the backward wave propagation.

2.5. Transmission Line Model of the Cochlea. A mathematicalmodel, lumped transmission line model, was created andsimulated in a circuit simulator LTSPICE (Linear Technol-ogy, Milpitas, CA) based on acoustic-electrical analogy. Thebasic structure of the model is shown in Figure 3(a) andreviewed by Ni et al. [26]. This circuit model was firstly devel-oped by Peterson and Bogert [27] and represented the basichydromechanical property of the cochlea. Rather than aone-dimensional structure, our model includes a two-dimensional matrix of mass and dampers to represent thefluid channel. The cochlear partition was modeled as 400sections of dampened mass-spring resonators and coupledwith the fluid channel. No active component (outer haircell) was included since the experimental preparation waspassive. By placing a vibration source at the very basal endof the fluid channel, we simulated the stapes driving thecochlea; by placing the source inside a more apical sectionon the BM, we simulated the backward wave case where theglass probe stimulates the BM directly. The BM stiffnesswas taken from Puria and Steele [28], and the cochleartonotopicity was taken from Greenwood [29].

3. Results

3.1. In Vivo Data Demonstrated a Slow Backward Wave onthe BM. For this experiment, the cochlea of a young guineapig was surgically exposed and the basal turn of the cochleawas widely opened. Reflective beads were placed on the BMat different longitudinal locations and on the head of stapes,as shown in Figure 1(a). In a typical experiment, vibrationspectra were measured from three beads (named apical,middle, and basal, according to their relative longitudinallocations) and from the stapes. Vibration spectra measuredat the middle and basal beads were scaled by the spectrameasured at the apical bead, the closest one to the vibration

Piezo stackMicromanipulator

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Figure 2: Construction of the piezo stimulator. Glass pipette withmelted tip was glued on a piezo stack and then on a steel bar,which was fixed on a micromanipulator.

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source, in order to calculate the transfer functions.Figure 1(b) shows the amplitude responses. In this plot, theamplitude of all the transfer functions demonstrated peaksat about 16 kHz and a gradually decreasing roll-off frequencyin the direction away from the stimulus. This peak is likelydue to the standing wave that was introduced by inserting

the probe. In absolute units, the maximum vibration velocitymagnitudes are 1.3mm/s, which correspond to a displace-ment of 12nm at the 16 kHz peak of the middle locationresponse. As indicated by the arrows in Figure 1(b), in addi-tion to the 16 kHz peak and the roll-off after, the amplituderesponses showed higher-frequency roll-offs from about

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Figure 3: Model of the cochlear passive hydromechanical structure. (a) Schematic of the model structure. The thick solid lines represent thefluid channel and the open rectangles represent the cochlear partition, or simply BM. In this lumped model, the fluid channel and the cochlearpartition (or simply BM) were divided into a series of sections. The rectangle is wider and shorter at the base and thinner and longer at theapex, representing the BM stiffness gradient: stiffer at the base and softer at the apex. (b) Circuit analogy of each section. The fluid mass isanalogous to a series of inductors; the fluid viscosity is analogous to a series of resistors; the stiffness of the partition is analogous to acapacitor. (c) At each section, the forward and backward waves experience the same low-pass filtering. (d) Schematic shows the low-passfilters that the traveling wave experiences during the forward and backward propagation. Note that the forward direction is towards thelow frequency. The roll-off frequency at the basal, middle, and apical locations decreases.

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23 kHz for the middle location to about 20 kHz for the basallocation and about 17 kHz at the stapes. Corresponding tothe gradually decreasing roll-off frequencies, the phase ofthe spectra demonstrates a significant phase lag from themiddle to the basal bead and then the stapes, indicating aslow wave propagating backward in the cochlea. The phaselag from the apical location to the stapes is more than onecycle (Figure 1(c)).

Phase difference between two neighboring—middleand basal—beads was used to calculate values of the wavepropagation parameters: delay, wave velocity, and wave-length. The phase data were smoothed and fitted with poly-nomial before calculating the delay and velocity, as stated inMethods. The group delay between the middle and basalbeads gradually increased with an increasing vibrationfrequency. It amounted to 62μs at 20 kHz (Figure 1(d)). Cor-respondingly, the wave velocity and wavelength decreased.The wave velocity was about 6.4m/s at 20 kHz for thedistance of 400μm between the two beads (Figure 1(e)).

Another method used to estimate the delay from thephase response was to calculate the phase delay. InFigure 1(f), we show that the phase delay value also increaseswith increasing frequencies but was smaller than the groupdelay, about 10μs at 20 kHz. This resulted in a higherestimated speed of 38m/s, as compared with using group

delay. However, both speed values were much smaller thanthe estimated compression wave speed of approximately1500m/s. The calculated phase delay from the apical beadto the stapes is about 40μs at 20 kHz.

3.2. BM Vibrations from Conventional Acoustic StimulationValidated the Preparation. In this preparation, the sound-conduction system (i.e., the tympanic membrane and theossicular chain) inside the middle ear was maintained to beintact and functional. The basal turn of the cochlea waswidely opened, and the fluid at the scala tympani of the basalturn was maintained only at a level to moisten the BM. Thecochlea thus became a single-channel hydrodynamic struc-ture. To verify that this single-channel preparation preservedthe forward traveling wave feature of the normal cochlea, theBM vibration was measured at the same longitudinal loca-tions under normal acoustic conditions, that is, the soundwas delivered to the ear drum. Rather than scaled by thevibration spectrum of the apical bead, here, the vibrationspectra of three beads were scaled by the stapes vibration toobtain the forward cochlear-transfer functions. The ampli-tude plotted in Figure 4(a) shows a tonotopic map. The vibra-tion spectrum rolled off at 28 kHz at the basal location; itrolled off at about 25 kHz at the middle location and at about20 kHz at the apical location. Correspondingly, the phase

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Figure 4: BM responses induced by normal acoustic stimulation at the ear drum. Vibration amplitude (a) and phase (b) of the beads on theBM. They are labeled as basal (dotted), middle (solid line), and apical (open cycle). Arrows in (a) indicates the roll-off of the amplituderesponses. (c) Calculated phase and group delay between basal (dotted) and middle (solid line). (d) Calculated velocity (solid line) andwavelength (dashed line).

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plotted in Figure 4(b) shows gradually the increasing phaselag from the basal to the middle and then to the apical loca-tions. These are expected traveling wave-like features underconventional acoustic stimulation. The phase and groupdelay increased with the increasing frequency (Figure 4(c)).The phase delay amounted to about 1/5 of the group delay,similar to what they were in the backward direction asshown in Figures 1(d) and 1(f). The velocity and wavelengthdecreased with the increasing frequency (Figure 4(d)). Thevelocity ranged from about 10m/s to 40m/s. Correspond-ingly, the wavelength ranged from 0.3mm to 2mm. Thetrend and the values of the delay, velocity, and the wave-length all indicated a slow forward traveling wave. Thisexperimentally verifies the wave propagation function ofthe single-channel cochlea.

3.3. Forward and Backward Traveling Waves Were Observedin the Mechanical Model of the Cochlea. To better understandthe role of the hydromechanical structure of the cochlea inthe backward wave propagation, we studied a mechanical

model of the cochlea. This artificial device was composed ofa fluid channel to simulate the scala vestibuli and amembrane to simulate the BM. Figure 5(a) shows the topschematic view of the device. Thirty-two copper beams aredeposited on a membrane to form an artificial BM. The beamlength varies gradually from beam #1 to beam #32, simulat-ing the BM stiffness gradient from the base to the apex. Thesingle fluid channel is underneath the BM (detailed construc-tion of the device can be found in Chen et al. [25]). In aprevious study, we showed that this hydromechanical struc-ture could demonstrate cochlea-like features and its capabil-ity to support the forward cochlear traveling wave [25].

Figure 5(b) shows the time-domain response of thebeam vibration, when the artificial cochlea was driven atthe base, just before beam #1. About 1ms delay wasdemonstrated between the onset responses of beam #1and beam #25. The distance of these two beams wasabout 15mm, so the speed of the wave propagation wasabout 15m/s. Figure 5(c) shows the results when thedevice was driven at the apex, on Beam #32. A clear

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Figure 5: Vibration responses of a mechanical model of the cochlea. (a) Schematic view of the artificial BM. The length of the copper beamvaries from 4mm at the base (narrower) to 8mm at the apex (wider). A total of 32 beams are placed on a membrane. The distance betweenbeam #1 and #32 is about 20mm. (b) BM vibration of the model while it was driven at the base, the narrowest, and thus the stiffest end. Thedriver was placed on the membrane right next to beam #1 at the base. Note that the scale of y-axis decreases from the top to the bottom,showing that the vibration amplitude was attenuated during the propagation. (c) BM vibration while it was driven at the apex. The driverwas placed on the membrane at beam #29, close to the apex.

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backward delay was demonstrated in the plots. The amountof the delay was similar to its forward counterpart and so asthe speed. This slow wave propagation implies that abackward traveling wave exists in this artificial device.

3.4. Simulation Results from a Mathematical Cochlear ModelWhere a Point Vibration Source Reproduced Features of theExperimental Data. In addition to the in vivo data andthe experimental results from the mechanical model, wealso studied the backward traveling wave in a mathemati-cal model. This model has a traditional transmission linestructure for simulating the hydromechanical structure ofthe cochlea. With this model, we simulated the backwardresponses. This was done by placing a vibration sourceat about 1/3 of the length of the cochlear model fromthe base and computing the BM vibration responses atmore basal places towards to the stapes. BM vibration atthree locations was computed to simulate the measuredresults at the apical, middle, and basal beads. As in theexperimental results, the vibration spectra of the middleand basal beads were scaled by that of the apical bead,as shown in Figure 6. Features in the experimental results,as shown in Figures 1(b) and 1(c), were also demonstrated inthe simulation results. The spectra can be viewed at twodifferent frequency ranges. At lower frequencies (about<15 kHz), the amplitude response in Figure 6(a) shows apeak at about 12 kHz for both middle and basal locations.Correspondingly, the phase plotted in Figure 6(b) shows asteep roll off at the peak frequency. This could be due toreflection between the point source and the stapes. Atfrequencies lower than the peak, the phase responses of bothlocations almost overlap. This can be interpreted as a fasttraveling wave at lower frequencies. The amplitude responserolled off at about 25 kHz for the middle location and atabout 20 kHz for the basal location. Correspondingly, thephase response showed a clear delay from the middle to thebasal location. This indicates a slow backward wave.

4. Discussion

4.1. Direction of the Wave Propagation. It has been hypothe-sized [1] that the OAE, generated as vibration at the organ of

Corti, will propagate backward toward the stapes via a travel-ing wave on the BM. Although this theory is widely acceptedand used to interpret the OAEs [2], the backward travelingwave has never been demonstrated with direct evidence ofthe BM vibration. Analysis of the OAE phase [9, 15] andcochlear microphonic signal that were measured at the roundwindow [16] was used as indirect evidence of backward prop-agation. In this present study, the organ of Corti was set intovibration at a specific point location. This produced the firstdirectly observed in vivo backward wave propagating on theBM. The phase plotted in Figure 1(c) has a gradual increaseof phase lag at the vibration spectra measured at the apical(used as the reference; not shown) to the middle, the basalbead, and then the stapes. The velocity and delay calculatedfrom the phase plot were within the same order of magnitudeof their forward counterpart (Figure 4). These results are alsoevidence of a slow transverse wave propagating backward onthe BM. In addition, we found a slow reverse wave propaga-tion in a mechanical model of the cochlea (Figure 5). Sincethe cochlea prepared through the surgical procedure becamea passive one (surgical damage removes the amplification bycochlear outer hair cells), this wave propagation appears to bea fundamental property of the hydromechanical structure ofthe cochlea. The artificial cochlea, which mimics the basichydromechanical structure of the cochlea, confirms andsupports the essential nature of the slow transverse waves,that is, they exhibit bidirectional propagation.

4.2. Interpretation of No Tonotopicity in Backward WavePropagation. Although the experimental results in Figure 1demonstrated the correct phase in reverse propagation, theamplitude response did not show the expected cochleartonotopicity: the peak-frequency-to-place map [29]. Incontrast, there was a slight inversion or reversal of themap, that is, the roll-off frequency is higher at the moreapical location and lower at the more basal location. Theseseemly controversial reverse wave features are simulatedby the transmission line model of the cochlea, as shownschematically in Figure 3.

The hydromechanical theory of the cochlea asserts thattonotopicity is achieved with the combination of fluidcoupling in the scalae and a local resonance at the BM,

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8 Neural Plasticity

the so-called critical-layer resonance [30]. For a passivecochlea, as used in this study, the hydromechanical structureis the dominant contributor [31]. The passive responses lacksharp tuning and diminish at high frequencies. Therefore, thelocal resonance is simplified in the model to a capacitorbecause the resonator is stiffness dominant at the lowerfrequencies. Acoustic energy in the fluid couples to the BM,whose stiffness decreases from the base to the apex.

Although the stiffness gradient is the most importantfeature for the tonotopicity [32], a small amount of frequencyselectivity can be achieved without it. This process is mosteasily explained with an electric circuit analogy. The cochlearhydromechanical structure is analogous to a lossy transmis-sion line, as originally proposed by Zwislocki [31]. In alumped model, the cochlea is divided into a series ofconnected repeating sections (Figure 3(a)). At each section(Figure 3(b)), the fluid coupling effect was modeled as a seriesof inductors and resistors, representing the fluid mass andviscosity, respectively [33]; the mechanical impedance ofthe cochlear partition was modeled as a capacitor, represent-ing the stiffness of the BM. Although the BM is usuallymodeled as a second-order resonator to account for the sharptuning of the cochlea, generality is maintained with thesimplification to a spring (capacitor in a circuit analogy) tomodel the passive responses. This simplification is funda-mental to Zwislocki’s transmission line theory [31] to inter-pret the passive vibration data observed by von Békésy [34].With this simplification, the propagation of the BM vibrationwas described using a wave equation [31]. Each section of thestructure applies a low-pass filtering effect onto the vibrationof the BM, attenuating the high-frequency components andproducing propagation delay. Vibration, originated fromeither a basal or apical location, will experience the samelow-pass filtering sections (Figure 3(c)), but from differentdirections. Therefore, the high-frequency components ofthe BM vibration are continuously attenuated, and the phasedelay is continuously accumulated during the propagation,no matter which end the wave originates.

Figure 3(d) explains why no cochlear tonotopicity isachieved in reverse propagation. In the forward direction,the stiffness of the cochlear partition decreases in the direc-tion of the propagation. Therefore, the roll-off frequency ofthe low-pass filtering, implemented by the fluid mass andthe stiffness of the partition, becomes lower and lower.Therefore, the high-frequency components of the travelingwave are cut off gradually during the propagation, resultingin the passive cochlear tonotopicity. In the reverse direction,the traveling wave encounters the low-pass section with thelowest roll-off first. Most of the high-frequency componentsare attenuated at this early section. During the propagation,although the traveling wave will still experience low-pass sec-tions, its already low-passed components will not be furthercut off because the roll-off frequencies of the later sectionsare all higher. The result is that no clear tonotopicity is pro-duced, but the high-frequency components are still slightlyattenuated along the direction of propagation.

Despite the significant difference in the amplituderesponses, the transmission line-like structure of the cochleaproduces a propagation delay in the direction of away from

the vibration source, no matter where the vibration sourceis located. This is shown in both the experimental data inFigure 1(c) and the simulation results in Figure 6(b).

4.3. Validation of the Preparation. Since we opened thecochlea widely and drained the fluid in the scala tympaniat the base, we need to ensure that this preparation canstill support the wave propagation as a normal cochlea.The single-channel preparation for the measurement of bas-ilar membrane vibration has been used previously [35, 36]and has theoretically been proven to be able to produceforward traveling wave features [37]. LePage [36] used acapacitive probe to measure the BM motion, which requiredthe fluid in the scala tympani to be removed. It was shownthat the BM vibration showed similar responses as itsdual-channel counterpart. The acoustic driving results inFigure 4 also showed traveling wave features. Therefore,this preparation still maintains the basic hydromechanicalstructure of the cochlea. The in vivo physiological environ-ment in the cochlea is maintained stably so that the mechan-ical properties provided by the cellular structure of the organof Corti do not deteriorate during the experiments. Althoughthis preparation is designed to verify the backward travelingwave, it does not preclude the existence of the compressionwave, as the intact scala vestibule can still support thecompression wave propagation. The open channel at thescala tympani could influence the speed of the compressionwave. However, this influence is minimal considering thatthe speed of the compression wave is two orders of magni-tude higher than that of the traveling wave. The BM vibrationmeasurement method used in this study is also essentially thesame as that used by He et al. and Ren et al. [3–5]. Therefore,if the compression wave does exist in this preparation, weshould be able to observe its effect, as a transverse wave inthe forward direction in our experiments.

To ensure that the vibration source in this study is on theBM, we drained the perilymph at the opened portion of thescala tympani and then maintained the fluid at a very lowlevel (~30μm) with a cotton wick. According to the currenttheory, it is the vibration generated in the organ of Corti onthe BM that initiates the backward traveling wave. TheOAE is also generated in the organ of Corti. The stimulusin the fluid may result in a similar effect as the stimulationby the stapes, producing a forward wave. This phenomenonhas been demonstrated by von Békésy [38] and termed asthe paradoxical wave, where even if the stapes is placed atthe apex of the cochlea, a forward traveling wave was stillobserved, moving towards the source.

4.4. Passive or Active Preparation. In this study, the extensivesurgery on the cochlea resulted in a loss of sensitivity, sothat the preparation was essentially passive. Although lossof cochlear amplification would influence the generation ofthe OAE, the passive preparation is an advantage in studyingthe wave propagation. The wave propagation inside thecochlea is mostly determined by the hydromechanical struc-ture, and our preparation preserves the basic hydromechan-ical components of the cochlea.

9Neural Plasticity

The advantage in the use of the passive preparation is thatit avoids any phase delay introduced by the active tuning ofthe cochlea. In a sensitive preparation, active tuning of thecochlea contributes strongly to the measured group delay[20]. Tuning-induced group delay is primarily responsiblefor the enhancement of the propagation delay in theforward-propagation condition, because the tuning fre-quency of the cochlea decreases in the forward directionand this frequency gradient produces a phase lag in the samedirection. In a sensitive cochlea, artificially driven to producea backward wave, tuning-induced forward delay may maskthe possible backward traveling wave delay. The propagationdelay increases while traveling away from the source. How-ever, the tuning delay is determined by the cochlearfrequency map and it always increases from the base to theapex, no matter where the source is. Therefore, in the mea-sured phase responses in a backward-traveling-wave study,there are two components that can contribute oppositely tothe total delay. This tuning-induced delay could be one wayto explain the results of He et al., Ren et al., and Ren [3–6],in which the measured phase delay increased from the baseto the apex and thus indicated the absence of a detectablebackward traveling wave. In those experiments, however, avery sensitive preparation was usually required by thevibration-source-generation method (acoustically produceddistortion product or electrically stimulated emission). Thetuning delay may be significant, especially when the vibrationat two close locations is compared to determine the directionof the wave propagation [3]. In their study, the measurementrange was narrow, and thus, the propagation delay wasrelatively small, compared to the tuning delay.

5. Conclusions

In this study, we investigated the backward wave propagationinside the cochlea. By creating a vibration source at a preciselocation, we avoided the uncertainty of the place where thevibration was originated in most previous studies. Withmeasurements at multiple longitudinal locations along thecochlea, we, for the first time, demonstrated a slow backwardtraveling wave towards the stapes. This result was also con-firmed in a mechanical model of the cochlea and interpretedwith a traditional transmission line mathematical model.

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

Fangyi Chen and Dingjun Zha designed the experiments;Fangyi Chen analyzed the data; Fangyi Chen, XiaojieYang, Allyn Hubbard, and Alfred Nuttall wrote the paper;

and all authors helped with the manuscript preparationand revision.

Acknowledgments

The authors would like to thank Drs. Egbert DeBoer,Anders Fridberger, and Sripriya Ramamoorthy for theircomments on the manuscript. This work was funded bythe National Natural Science Foundation of China (Grantnos. 81470701 and 81771882), the Fundamental Research(Discipline Layout) Foundation from Shenzhen Committeeof Science, Technology and Innovation (Grant no.JCYJ20170817111912585), and Deafness Research Founda-tion for Fangyi Chen; the National Natural ScienceFoundation of China (Grant nos. 81271077 and 81470695)for Dingjun Zha; and NIDCDR01 (Grant nos. DC000141and DC010399) for Alfred Nuttall.

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