An investigation into the relationship between input–output nonlinearities and rate-induced nonlinearities of click-evoked otoacoustic emissions recorded using maximum length sequences

Abstract

The maximum length sequence (MLS) technique allows otoacoustic emissions (OAEs) to be recorded using clicks presented at very high presentation rates. It has previously been found that increasing the click presentation rate leads to increasing suppression (termed “rate-suppression”) of the MLS evoked OAE (Hine, J.E., Thornton, A.R.D., 1997. Transient evoked otoacoustic emissions recorded using maximum length sequences as a function of stimulus rate and level. Ear Hear. 18, 121–128). It has been suggested that the source of rate-suppression arises from the same nonlinear processes that give rise to the well-known nonlinear growth of OAEs. Based on this assumption, a simple model of rate-suppression (Kapadia, S., Lutman, M.E., 2001. Static input–output nonlinearity as the source of nonlinear effects in maximum length sequence click-evoked OAEs. Br. J. Audiol. 35, 103–112) predicts that both input–output (I/O) nonlinearity and rate-suppression can be unified by characterising the stimulus in terms of its acoustic power which, at high rates, is proportional to the click presentation rate. The objective of this study was to test this simple model by recording MLS OAEs from a group of normally hearing adults over a range of stimulus rates from 40 to 5000 clicks/s, and of stimulus levels from 45 to 70 dB peSPL. The results are broadly in agreement with the predictions from the model, though there appears to be some tendency for the model to slightly overestimate the degree of rate-suppression for a given degree of I/O nonlinearity. It is also suggested that the model may break down more significantly in the presence of spontaneous OAEs.

Introduction

Two nonlinear phenomena exhibited by otoacoustic emissions (OAEs) are the nonlinear growth of the rms amplitude of click-evoked OAEs (CEOAEs) with the increase in amplitude of the stimulus (e.g., Kemp, 1978), and the phenomenon termed here “rate-suppression” that is seen in OAEs obtained using the maximum length sequence (MLS) technique (e.g., Thornton, 1993a, Thornton, 1993b). Rate-suppression is the reduction in the amplitude of the OAE obtained by the MLS technique that occurs with an increase in the click presentation rate. In this paper, a simple theory connecting these two phenomena is presented and its predictions compared with measurements.

Kemp and Chum (1980) reported that the CEOAE rms amplitude, measured over the 5–20 ms window post-stimulus, grew approximately linearly for very low click levels (below about 10 dB SL). Above 10 dB SL, the CEOAE showed nonlinear growth, where the degree of nonlinearity can be quantified by the gradient in dB/dB of the plot of the CEOAE rms amplitude versus stimulus amplitude. This measure of nonlinearity will be termed here the input/output (I/O) slope, where a slope of 1 dB/dB represents linear growth, and 0 dB/dB complete saturation.

Kemp (1978) reported a typical value of the I/O slope of 0.33 dB/dB for the CEOAE over the 10–12.5-ms post-stimulus window. Since then, several authors have investigated the dependence of the I/O slope on stimulus level, and on the choice of time window over which the CEOAE amplitude is calculated.

Kemp and Chum (1980) reported an I/O slope of approximately 0.43 dB/dB, which remained roughly constant from 15 to 60 dB SL. In contrast, some authors have noted that I/O slope shows some tendency to reduce with increasing stimulus levels (e.g., Hine and Thornton, 1997), though this tendency varies depending on the individual ear and the range of stimulus levels.

Using tone-burst stimuli rather than clicks, Rutten (1980) found that the I/O slope reduced with an increase in the latency of the time window over which the rms amplitude of the OAE was evaluated. Rutten (1980) reported a typical variation in I/O slope from around 0.7 dB/dB at 10 ms latency to 0.33 dB/dB at 20 ms latency. A similar trend can be seen in CEOAE data presented by several authors (e.g., Tavartkiladze et al., 1997, Hine and Thornton, 1997, Hine et al., 2001).

The MLS technique has been used to record OAEs using click trains with interstimulus intervals that are much lower than the typical duration of CEOAEs (Thornton, 1993a, Picton et al., 1993). Rather than a direct recording of the OAE response, the MLS technique only yields an OAE waveform after deconvolution. Deconvolution derives a response on the assumption that each click in the click train evokes an identical response, and that these responses sum linearly to give the actual measured response. This deconvolved response is termed here the MLS OAE. Several authors have reported that MLS OAEs recorded at high click presentation rates are reduced in amplitude relative to CEOAEs recorded conventionally, and that this reduction becomes more pronounced as the click-presentation rate is increased (Thornton, 1993a, Thornton, 1994, Picton et al., 1993, Thornton and Slaven, 1994, Hine and Thornton, 1997, Lina-Granade et al., 1997, Johannesen et al., 1998, Rassmussen et al., 1998). It is this reduction in amplitude (or “suppression”) with increasing rate that is termed “rate-suppression” (Kapadia and Lutman, 2001). It should be noted that the term “rate-suppression” is simply used here to describe the nonlinear phenomenon seen in MLS OAE recordings, and should not be taken to imply that the cochlea is sensitive to MLS rate per se. Hine and Thornton (1997) found an average reduction in MLS OAE amplitude of around 9 dB at a mean click rate of 2500 clicks/s, relative to CEOAEs recorded conventionally at 40 clicks/s.

An initial suggestion that rate-suppression may arise from an ipsilateral efferent mechanism (Thornton, 1994) was contradicted by measurements of MLS OAEs from patients who had undergone unilateral vestibular nerve section (Hine et al., 1997). Picton et al. (1993) suggested that both rate-suppression and I/O nonlinearity may arise primarily from a superposition of the ringing responses on the basilar membrane due to the rapid rate of click presentation, combined with the compressive nonlinearities in the transduction mechanisms of the outer hair cells. Similar suggestions have been made regarding the nonlinear temporal interactions of pairs of clicks (Kemp and Chum, 1980, Tavartkiladze et al., 1994, Kapadia and Lutman, 2000a, Kapadia and Lutman, 2000b). To qualitatively explain these two-click nonlinear interactions, Kemp and Chum (1980) proposed a simple model comprising a bank of parallel frequency channels. Each channel comprised a linear bandpass filter followed by an instantaneous compressive nonlinearity. This model clearly gives a greatly simplified representation of the OAE generation mechanism. However, it captures some features of current theories of the OAE generation mechanism which may explain the phenomenon of rate-suppression: elements with prolonged impulse response functions (such as bandpass filters) followed by fast-acting nonlinear elements.

Kapadia and Lutman (2001) used such a two-element model to simulate MLS rate-suppression in a single channel, and achieved qualitatively realistic rate-suppression curves in which the degree of rate-suppression depends on the degree of I/O nonlinearity. Thus, such a model predicts that rate-suppression and I/O nonlinearity arise from a common nonlinear element. This model will be termed here the Kapadia–Lutman (K–L) model. In this model, the MLS OAE shows a nonlinear dependence on rate simply because increases in MLS rate lead to increases in the rms amplitude of the stimulus. This can be interpreted physiologically by noting that the rms amplitude of the vibration of a point on the basilar membrane will increase when either the MLS rate or the MLS click amplitude is increased.

Ryan and Kemp (1996) explored the relationship between rate-suppression and I/O nonlinearity by recording high-rate OAEs over a range of click amplitudes and presentation rates using click trains apparently similar to MLSs. In an attempt to unify I/O nonlinearity and rate-suppression, they presented the resulting OAE amplitudes as a function of input power level (IPL), defined as the rms power of the stimulus over the duration of the recording epoch. The rationale for this approach can be explained with reference to the K–L model. First it is assumed that the degree of nonlinearity observed depends on the rms amplitude of the basilar membrane vibration, which is given by a bandpass filtered version of the input. This vibration amplitude can most easily be increased by an increase in the click amplitude, thereby revealing I/O nonlinearity. However, it can also be increased by reducing the interstimulus intervals, provided the interval is less than the ring-down time of the linear filter element in the model (representing the tuned basilar membrane response). In fact, the rms amplitude of filter output is proportional to the rms amplitude of the acoustic input stimulus, assuming a constant shape of input signal power spectrum.

We can formally state these arguments as a hypothesis, termed here the input power hypothesis, which runs as follows. If the IPL is increased from some baseline level, then the degree of nonlinearity observed in the OAE (relative to this baseline condition) will depend on the increase in IPL, regardless of whether this is achieved by an increase in click amplitude (for conventional CEOAEs or MLS OAEs) or in click presentation rate (for MLS OAEs). On this hypothesis, rate-suppression is simply a manifestation of the underlying compressively nonlinear amplitude dependence of the cochlear amplifier.

As will be demonstrated in Section 3 below, one consequence of the input power hypothesis is that the rate-suppression of an MLS OAE in dB is proportional to the logarithm of the mean click presentation rate, and also proportional to 1 − m, where m is the I/O slope in dB/dB. That the input level hypothesis holds true for the K–L model with an MLS input signal is confirmed by the simulations of rate-suppression given by Kapadia and Lutman (2001) in which the instantaneous compressive nonlinearity was implemented as a power law with a constant I/O slope of m dB/dB. Re-analyzing the results presented in their Fig. 6 reveals that the simulated rate-suppression in dB is in agreement with above predictions: it is approximately proportional to the logarithm of the mean click presentation rate, and to 1 − m.

An anomalous point in their data at a rate of 250 clicks/s (their Fig. 6) illustrates a limitation of the hypothesis. It only holds when the shape of the power spectrum in the region of the passband of the linear filter is unchanged by changes in rate, as otherwise the input power to the nonlinearity element (which is the output power of the filter element) is no longer proportional to the input power to the linear filter. The spectrum of the MLS signal is not perfectly white, but rather contains additional spectral lines whose location is rate dependent, which thus complicates the interpretation at low rates.

Ryan and Kemp (1996) appear to present data that might be used to test the input power hypothesis. However, it appears that they used click trains that were either MLSs of very low order (orders 2 and 3) or that were not true MLSs (such as a train of 6 clicks). Furthermore they used a limited range of mean click presentation rates (50–300 clicks/s) which produce only small degrees of rate-suppression. Thus, a direct test of the input power hypothesis is not possible. The only relevant result they report is that the I/O slope was approximately 0.25 dB/dB, while at a constant click amplitude, rate-suppression increased with IPL at 0.5 dB/dB. This result is not consistent with the input power hypothesis which, given m = 0.25 dB/dB, would predict that the rate-suppression would increase with IPL at 0.75 dB/dB.

Hine et al. (2001) compared I/O functions for conventional CEOAE data at 40 clicks/s with those for MLS OAEs at a mean rate of 2500 clicks/s. Rather than using the click amplitude, these I/O functions were constructed on an abscissa of the sensation level of the click train, which more closely corresponds its input power level. However, the form of normalisation used does not allow the input power hypothesis to be tested directly.

The primary aim of the present study is to directly compare measured results with the input power hypothesis. MLS OAEs have been measured over a wide range of click amplitudes and mean click presentation rates (40–2000 clicks/s). Also, the effect of varying the I/O slope, m, is examined by considering portions of the response at two different latencies.

The input power hypothesis stated above can be extended to cover not just the rms amplitude of the OAE defined over a portion of the waveform, but also to each instantaneous point in waveform. The rationale for this arises from the finding that the general morphology of the OAE waveform is similar for MLS OAEs and CEOAEs from a given ear (Hine and Thornton, 1997), and that this morphology shows only a small variation with changes either in stimulus level or stimulus rate. Typically, the small changes in morphology that are observed with changes in stimulus IPL arise from the differences in the degree of suppression seen at short and long latencies, rather than from any shift in the location of the peaks or troughs in the waveform. This result is also consistent with predictions from the K–L model, where the OAE waveform shows suppression without any phase shift in the carrier wave (Kapadia and Lutman, 2001). Thus, a secondary aim of this study is to compare the entire waveforms of CEOAEs and MLS OAEs at equal IPLs, which, under this extended hypothesis, should appear similar.