FOUR COUNTER-ARGUMENTS FOR SLOW-WAVE OAEs

Transcription

1 FOUR COUNTER-ARGUMENTS FOR SLOW-WAVE OAEs CHRISTOPHER A. SHERA Eaton-Peabody Laboratory, Boston, MA 02114, USA ARNOLD TUBIS Institute for Nonlinear Science, La Jolla, CA 92093, USA CARRICK L. TALMADGE National Center for Physical Acoustics, University, MI 38677, USA Introduction A recent paper [6] presents measurements of basilar-membrane (BM) motion to argue against the slow-wave model of OAEs, in which emissions propagate back to the stapes primarily via transverse pressure-difference waves (often simply called reverse-traveling waves ). The experimental evidence adduced against slow-wave DPOAEs is two-fold: (1) group-delay measurements indicate that the stapes vibrates earlier than the BM at the distortion-product (DP) frequency and (2) longitudinal measurements of BM phase find no evidence for reversetraveling waves. These two experimental results, interpreted using the schematic illustrated in the bottom panel of Fig. 1, have been taken to confirm the suggestion [13,8] that the reverse propagation of OAEs occurs via fast compressional (i.e., sound) waves [6]. The diagram posits that DP fast waves generated near x 2 propagate nearly instantaneously to the stapes, where the asymmetric movements of the oval and round windows create a slow (pressure-difference) wave that propagates to x dp, driving the transverse motion of the BM en route. Here, we present two pairs of counter-arguments against these claims [6]. The first pair critique the evidence against slows waves outlined above; the second pair argue that the fast-wave model contradicts other well established facts of OAE phenomenology, thereby countering the conclusion that compression waves play the dominant role in the production of otoacoustic emissions. Counter-Argument #1 The group-delay argument against slow waves fails when the DPs are generated near the point of measurement rather than remotely. The group-delay argument 449

2 Phase lag Phase lag f 2 f 1 middle ear f 2 f 1 f 2 f 1 f 2 f 1 middle ear D x 2 x 2 Distance from stapes nonlinear distortion and slow-wave generation R x dp coherent reflection nonlinear distortion and fast-wave generation x dp fast-wave generation Figure 1. Schematic illustrating the generation of slow-wave (top) and fastwave (bottom) lower-sideband DPs. The panels show wave phase lag (increasing downward) vs cochlear location. In each case, slow waves (solid lines) at f 1 and f 2 produce nonlinear distortion near x 2, creating either slow or fast (dashed line) waves at. Reverse waves travel to the stapes, where the fast wave creates a slow forward wave that then drives the BM at. In the top panel, distortion near x 2 also creates a forward wave that is partially reflected near x dp. In the bottom panel, the slow wave launched from the stapes creates a fast reverse wave near x dp. Empty boxes in the lower panel indicate unknown biophysical mechanisms. For simplicity, the diagram ignores multiple internal reflections. Adapted from [10,6]. against slow waves [6] follows from the contradiction between the group-delay data and the predictions of the schematic diagram shown in the top panel of Fig. 1. The argument hinges on a crucial feature of the diagram: Namely, that the region of strong distortion that generates the wave (denoted D in the diagram) is localized at some distance from the stapes. In other words, the argument assumes that the distortion measured in the motion of the stapes did not originate close to the stapes but has propagated to the point of measurement from a remote generation site located elsewhere in the cochlea. Although this assumption presumably holds under many experimental conditions, no evidence of its validity has been presented for the measurements in question [6]. On the contrary, given the relatively high levels of stimulation ( 70 db SPL) and the proximity of x 2 to the base ( 2 mm), it seems likely that the DP generation site encompasses a considerable stretch of the basal turn of the cochlea. What does the slow-wave framework predict when measurements are made inside the region of strong distortion, D? Under such circumstances, the framework indicates that DP measurements are typically dominated not by propagated distortion, but by distortion generated close to the point of measurement. Group-delay data of the sort reported in [6] then reveal nothing about DP propagation delays or the relative time ordering of events at the DP frequency within the cochlea. Rather, group-delay measurements reflect changes in the output 450

3 of the local DP source, whose phase varies as the local phases of the primary tones change with frequency. When f 2 is fixed, as it was in the measurements [6], the framework predicts that the phase of a locally generated DP varies with the phase of the f 1 wave at the site of generation. Measurements of BM transfer functions at two different points in the cochlea show that phase slopes at any given frequency below CF are shallower at the more basal location [7], and similar results presumably apply to intracochlear pressures that drive the stapes [3]. Viewed in this way, the finding that group delays controlled by the f 1 wave are smaller at the stapes than they are near x 2 is thus entirely consistent with the predictions of the slow-wave framework. The observation that the group-delay data can be explained within the slowwave framework obviates the need to postulate novel biophysical mechanisms to account for the results. Since the generation of compressional (sound) waves requires the vibration of a sound source (OHC somata? hair bundles?), the fastwave interpretation of the group-delay data evidently requires that the vibrating sound source be both (i) strongly coupled to the BM in one direction, since its vibration is presumed to be driven by forward-traveling BM waves at f 1 and f 2 ; and (ii) weakly coupled to the BM in the other direction, since BM motion at occurs significantly after stapes motion (i.e., only after the fast wave has generated a forward-traveling slow wave at the stapes). These two conflicting requirements appear difficult to reconcile with cochlear biophysics. Current understanding of the cochlear amplifier, for example, makes it hard to imagine synchronous volume changes in the hair cells, as proposed by Wilson [13], that are not also accompanied by forces that couple strongly into the transverse motion of the BM. 1 Counter-Argument #2 The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather than remotely. At the DP frequency, the measured BM phase vs position data have negative slopes, as expected for forward- but not reverse-traveling waves. Curiously, three of the four longitudinal measurements presented as evidence against slow waves (see Fig. 1a c in [6]) were made at BM locations largely apical to x 2, the presumed center of the 1 One theoretical possibility is that the cochlear amplifier (CA) operates not by generating forces that couple into BM motion locally near the OHC, but by generating compressional waves that couple into BM motion at the stapes via the impedance asymmetry between the cochlear windows. However, without considerable ad hoc manipulation this model for the CA cannot be made to amplify forward-traveling waves except at certain special locations in the cochlea determined by round-trip phase shifts. (de Boer [personal communication] has independently analyzed this model for the CA and uncovered other deficiencies.) 451

4 region of DP generation. Since both the slow- and fast-wave frameworks predict forward-traveling waves in the region x 2 <x<x dp, the measurements cannot distinguish the two alternatives. The fourth measurement (Fig. 1d) was made basal to x 2, but its interpretation suffers from the same limitation as the group-delay data: The argument breaks down when applied inside the region D of strong distortion, where local rather than propagated distortion dominates the measurement. 2 The phase of the local distortion follows that of the DP source, which has the form φ src (x) =2φ 1 (x) φ 2 (x) + constant, (1) where φ 1 (x) is the phase of the f 1 wave, etc. Since the measurements indicate that φ src (x) defined above has a negative slope, the experimental results again appear consistent with the predictions of the slow-wave framework. Interlude Counter-arguments #1 and #2 indicate that recent measurements claimed to refute the existence of slow-wave OAEs [6] fail to provide compelling tests of the slow-wave model. The failure of an argument, however, does not imply that its conclusion is incorrect: It remains possible that slow-wave OAEs really are negligible or non-existent and that fast-wave mechanisms dominate the production of otoacoustic emissions, as claimed. To address this possibility, counter-arguments #3 and #4 discuss two additional OAE measurements. Both measurements contradict simple predictions of the fast-wave model but have natural explanations in the slow-wave framework. Counter-Argument #3 The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and upper-sideband DPOAEs. In the fast-wave model, DPs couple directly to the stapes via compressional waves whose propagation is unaffected by the properties of the BM. Once they couple into the fluids, fastwave DPs unlike their slow-wave counterparts undergo no BM-related filtering prior to their appearance in the ear canal. It therefore makes no difference whether fast-wave DPs are generated at cochlear locations whose CFs are above or below their own frequency. The fast-wave model thus indicates that both lower- and upper-sideband DPs are generated in the overlap region near x 2 by identical wave-fixed mechanisms. As a consequence, the model predicts that 2 Even if the experiments [6] had established that the measurements were dominated by propagated rather than local distortion, interpretation of the data would still be enormously complicated by wave reflection from the stapes. 452

5 both DPOAE types should manifest nearly constant phase when measured using frequency-scaled stimuli (fixed f 2 /f 1 ). This prediction of the fast-wave model is contradicted by experiment: Whereas the phase of lower-sideband DPOAEs (e.g., 2f 1 f 2 ) at near-optimal primary ratios remains almost constant (as predicted), the phase of upper-sideband DPOAEs (2f 2 f 1 ) varies rapidly with frequency [4]. 3 The different phase gradients of lower- and upper-sideband DPOAEs can, however, be understood in the slow-wave framework. When DPs couple into BM pressure-difference waves they become subject to filtering by the BM. For lower-sideband DPs, the overlap region near x 2 is basal to the BM cutoff for waves, and DPs generated in this region propagate freely. At near-optimal ratios, the multiple reverse-traveling DP wavelets created in the distortion region D combine coherently to produce a large reverse-traveling wave whose phase behavior is wave-fixed. For upper-sideband DPs, however, the region near x 2 is apical to the BM cutoff for waves, and DPs generated in this region are strongly attenuated. As a result, place-fixed mechanisms at x dp become dominant [4]. For example, upper-sideband DPs generated at x<x dp create slow waves propagating in both directions. Because of phase interactions among the wavelets arising from the distributed DP source, those wavelets initially traveling toward the stapes tend to cancel one another out, whereas those traveling toward x dp tend to reinforce one another. The result is a forward-traveling slow wave, which as with any forward-traveling wave undergoes partial coherent reflection near its characteristic place. Since the dominant reverse-traveling wave is generated by scattering off place-fixed perturbations, upper-sideband DPOAEs (like SFOAEs) have a rapidly rotating phase. Counter-Argument #4 The fast-wave model cannot account for the results of experiments performed using the Allen Fahey paradigm. The Allen Fahey paradigm [1] consists of measuring the ear-canal DPOAE as a function of r f 2 /f 1 while the intracochlear DP response is held constant at x dp (e.g., by monitoring the response of an auditory-nerve fiber tuned to ). Aside from possible suppressive effects, the predictions of the fast-wave model can be deduced immediately from the bottom panel of Fig. 1. Fixing the DP response at x dp is equivalent to fixing the fast wave at the stapes, which is equivalent to fixing the DPOAE in the ear canal. How does suppression modify this prediction? As r decreases towards 1, the primaries draw closer to x dp and their suppressive action reduces the response to 3 Although characteristic of mammalian DPOAEs, striking differences between the phasegradient delays of upper- and lower-sideband DPOAEs are not found in the frog [5]. 453

6 the DP at x dp. To maintain the constant response mandated by the paradigm, the DP source output must be increased (e.g., by boosting the levels of the primary tones). When the source output is increased, the fast-wave pressure at the stapes and the DPOAE in the ear canal both increase correspondingly. For the Allen Fahey paradigm, the fast-wave model therefore predicts that the ear-canal DPOAE will increase at close ratios. This prediction, however, is contradicted by experiment: Studies performed using the Allen Fahey paradigm all find that the ratio of ear-canal to intracochlear DPs falls as r 1 [1,9,2]. The results of Allen Fahey and related experiments can, however, be understood in the slow-wave framework, where they reflect changes in the effective directionality of the waves radiated from the distortion-source region [11]. Slowwave calculations explain the Allen Fahey experiment by showing that at close ratios the distortion region D radiates much more strongly toward x dp than it does back toward the stapes. As a result, and despite the countervailing effects of suppression, fixing the response at x dp causes the corresponding ear-canal DPOAE to fall as r 1. [Note that in the top panel of Fig. 1 the forward- and reverse DP waves emanating from D need not maintain the same amplitude ratio at all values of r; contrast this with the bottom panel, where the ratio of reverse fast wave to forward slow wave is determined, independent of r, by impedance relationships at the stapes.] Conclusion The counter-arguments presented here indicate that recent tests of the slowwave model [6] provide no convincing evidence against slow-wave OAEs. Furthermore, slow-wave OAEs appear necessary to account for varied aspects of OAE phenomenology well established in the literature. Although our counterarguments support the slow-wave model, they must not be construed to suggest that fast-wave OAEs do not exist; absence of evidence is not evidence of absence. Indeed, we take the totalitarian view of physical law that everything not forbidden is mandatory, and we therefore fully expect that both slow- and fastwave OAEs occur in the normal cochlea. The problem, then, becomes one of establishing the relative contributions of the two (or more?) emission modes and understanding their physical and physiological determinants. In principle, there need be no universal answer to these questions: The dominant OAE mode may vary with species and order (e.g., from amphibians to mammals), with cochlear location (e.g., from base to apex), and with stimulus or other experimental parameters. We have provided examples illustrating the importance of slow-wave contributions to the generation of mammalian OAEs; the role played by fast waves remains to be elucidated. 454

7 Acknowledgments Supported by grants from the NIDCD, National Institutes of Health. We thank Nigel Cooper, Paul Fahey, and Tianying Ren for helpful discussions. References 1. Allen, J.B. and Fahey, P.F., Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane. J. Acoust. Soc. Am. 92, de Boer, E., Nuttall, A.L., Hu, N., Zou, Y., and Zheng, J., The Allen Fahey experiment extended. J. Acoust. Soc. Am. 107, Dong, W. and Olson, E.S., Two-tone distortion in intracochlear pressure. J. Acoust. Soc. Am. 117, Knight, R.D. and Kemp, D.T., Wave and place fixed DPOAE maps of the human ear. J. Acoust. Soc. Am. 109, Meenderink, S.W.F., Narins, P.M., and van Dijk, P., Detailed f 1,f 2 area study of distortion product otoacoustic emissions in the frog. J. Assoc. Res. Otolaryngol. 6, Ren, T., Reverse propagation of sound in the gerbil cochlea. Nat. Neurosci. 7, Rhode, W.S., Some observations on cochlear mechanics. J. Acoust. Soc. Am. 64, Ruggero, M.A., Comparison of group delays of 2f 1 f 2 distortion product otoacoustic emissions and cochlear travel times. Acoust. Res. Lett. Online 5, Shera, C.A. and Guinan, J.J., Measuring cochlear amplification and nonlinearity using distortion-product otoacoustic emissions as a calibrated intracochlear sound source. Assoc. Res. Otolaryngol. Abs. 20, Shera, C.A. and Guinan, J.J., Evoked otoacoustic emissions arise by two fundamentally different mechanisms: A taxonomy for mammalian OAEs. J. Acoust. Soc. Am. 105, Shera, C.A., Wave interference in the generation of reflection- and distortion-source emissions. In: Gummer, A.W. (Eds.), Biophysics of the Cochlea: From Molecules to Models, World Scientific, Singapore, pp Talmadge, C.L., Tubis, A., Long, G.R., and Piskorski, P., Modeling otoacoustic emission and hearing threshold fine structures. J. Acoust. Soc. Am. 104, Wilson, J.P., Model for cochlear echoes and tinnitus based on an observed electrical correlate. Hear. Res. 2,

8 Comments and Discussion Tianying Ren: The purpose of the following comments is not to defend the cochlear compression wave theory. Instead, they try to clarify a few points for helping our thinking of the DPOAE. Counter-Argument #1 reads, in brief: The group-delay argument against slow waves fails when the DPs are generated near the point of the measurement rather than remotely. The longitudinal pattern of basilar membrane vibration measured at the same location as for the emission measurement in the gerbil shows a normal forward travel delay (Ren, 2002, PNAS, 99: ). If the backward traveling wave is symmetrical to the forward wave it should show the same delay, which was not shown by the data. Counter-Argument #2 reads: The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather than remotely. Since the measured region of the basilar membrane responses to tones goes from 8 to 24 khz (Ren, 2002, PNAS, 99: ), the phase curve near the basal end should have revealed the backward traveling wave, if it exists. In Fig. 1d (Ren, 2004, Nat. Neurosci., 7:333 4) the observed location is clearly out of the DP generation site because the basilar membrane response to a 12 khz tone is linear at the 17 khz BM location. Most importantly, the 2f 1 f 2 phase calculated based on the f 1 and f 2 phases of BM vibration is different from the measured 2f 1 f 2 phase, which demonstrates that the measured phase data are not dominated by the locally generated DP. Counter-Argument #3 reads: The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and uppersideband DPOAEs. The reverse propagation of the upper-sideband DPOAEs is different from that of lower-sideband emissions. Although the slow-wave model can explain the fast phase change of the upper-sideband emission, the alternative interpretation based on the fast-wave model remains plausible, since the observed emission delay can be caused by the cochlear filter rather than by a backward traveling wave (Avan et al., 1998, Eur. J. Neurosci., 10: ; Ruggero, 2004, ARLO, 5:143 7). Reply: Thank you for your thoughtful comments. 1. Model calculations indicate that relationships between the spatial patterns of BM phase produced by single tones (e.g., those reported in your PNAS paper) and the slopes of 2f 1 f 2 phase-vs-frequency functions (i.e., DP phase-gradient delays) measured on the BM, at the stapes, or in the ear canal are neither always straightforward nor intuitive. We therefore suggest caution when interpreting both experimental and numerical results, espe- 456

9 cially when the effective DP generation site is distributed over a relatively broad region of the cochlea and/or reflection from the stapes occurs. 2. Measurements of distortion in single-tone responses are not the most sensitive indicators of the intermodulation distortion produced by two tones, especially when the total distortion is small compared to the primaries (the BM DPs in Fig. 1d are 20 db or more below the primary tones). When local distortion dominates the measured response slow-wave theory indicates that the 2f 1 f 2 DP phase is only approximately equal to 2φ 1 (x) φ 2 (x); even though local distortion makes the controlling contribution, it is not the only component of the response. The main point of our first two counter-arguments is that the slow-wave model can account for the salient features of the data that have been used to argue against slow-wave mechanisms. 3. As pointed out elsewhere (e.g., Koshigoe and Tubis, 1982, JASA, 71: ; de Boer, 1997, JASA, 102: ; Shera et al., 2000, JASA, 108: ), most of the so-called filter build-up cannot be separated from the travel time because the amplitude of the wave builds up while it is traveling. Tubis et al. (2000, JASA, 108: ) demonstrated that the cochlear filter defined as the contribution to the BM mechanical transfer function arising from the resonant denominator in the WKB expression gives only small contributions to the DPOAE phase derivatives in an active model. Even if it were possible to separate travel time from filter buildup time in some other meaningful way, it s not clear to what alternative interpretation you refer. Although slow-wave theory indicates that the reverse propagation of the upper-sideband DPOAEs is different from that of lower-sideband emissions, the same is not true in simple fast-wave models, in which fast-wave DPs propagate as compressional waves unaffected by the filtering (or other) properties of the BM (e.g., Wilson, 1980, Hear. Res., 2:527 32; Shera et al., 2005, ARO Abs., 28:657). 457