Enrique A. Lopez-Poveda

1. A computational model for simulating basilar-membrane nonlinearity in subjects with normal and impaired hearing Enrique A. Lopez-Poveda Centro Regional de Investigación Biomédica, Facultad de Medicina, Universidad de Castilla-La Mancha, 02071 Albacete, Spain. ealopez@med-ab.uclm.es Ray Meddis Centre for the Neural Basis of Hearing, University of Essex, Colchester CO4 3SQ, United Kingdom. rmeddis@essex.ac.uk

2. Abstract 1 Psychophysical masking experiments show that hearing impairment implies not only an increase in hearing thresholds and in the width of the auditory filters, but also a loss of the nonlinearity associated with the cochlear compressive response (for a review see Moore, 1998). Loudness recruitment is a consequence of this loss that can not be overcome with linear hearing aids. The ideal hearing aid should, therefore, be able to compensate for the loss of nonlinearity as well as for the loss of sensitivity and sharpening of the auditory filters. Here, we present ongoing research towards the development of a human nonlinear digital cochlear filter bank. Our approach is based on adapting a digital dual-resonance nonlinear (DRNL) computational model of cochlear frequency selectivity (Meddis et al., in preparation) for simulating the results of masking experiments in human subjects with normal and impaired hearing. We measure the amplitude of the DRNL filter output in response to two tonal stimuli: one of them (‘the signal’) at the filter’s best frequency (BF) and a second one (‘the masker’) with a frequency 0.6 times the frequency of the signal. The criterion we have applied when fitting the masking data is that the amplitude in response to the masker must be equal to or just exceed the output amplitude in response to the signal. Preliminary results show that psychophysical masking data for subjects with normal and impaired hearing can be simulated by changing only the parameters of the compression function of the DRNL filter, at least for individual frequency channels. Our final goal is to enhance the DRNL filter so that it provides us with a good quantitative description of hearing impairment for a range of frequency channels. The system will have the ability to predict the benefit of any particular hearing aid and could be, therefore, a useful aid for designing and testing personalized nonlinear hearing aids.

3. Stapes-velocity waveform (m/s) DRNL filter Stapes ‘impedance’ z = p / v Pressure waveform (Pa) BM-velocity waveform (m/s) The model 2 The model is digital implementation of two stages: • Stage 1: Gives out stapes velocity (m/s) as a function of stimulus pressure (Pa). Thus, we call it stapes ‘impedance’ (see below). • Stage 2: The DRNL filter gives out basilar membrane (BM) velocity (m/s) as a function of stapes velocity. (See panel 3). Chinchilla The middle-ear stage: The ‘stapes impedance’ at any stimulus frequency is computed directly by linear interpolation between measured data points for chinchilla (figure on the right). Data from Ruggero et al. (1998), Rhode & Cooper (1996).

4. Cascade of 2 1st-order gammatone bandpass filters Cascade of 4 2nd-order Butterworth Low-pass filters Linear gain Basilar membrane velocity (m/s) Stapes velocity (m/s) g CFlin, BWlin LPlin CFnl, BWnl a, b, n CFnl, BWnl LPnl Cascade of 3 1st-order gammatone bandpass filters Broken-stick nonlinearity Nonlinear gain Cascade of 3 1st-order gammatone bandpass filters Cascade of 3 2nd-order Butterworth Low-pass filters The DRNL filter(Meddis et al., in preparation) 3 The input signal to the DRNL filter follows two paths: one linear and one nonlinear. The output signal is the sum of the resulting signals from both paths. Each path consists of a cascade of signal processing elements (see figure). The composite filter is computed digitally in the time domain. The filter parameters are shown in red color. For the i-th sample, the output from the broken-sticknonlinearity is as follows: yi = sign(xi)  min(a|xi|, b|xi|n).

5. Modelling direct animal BM measurements 4 The DRNL filter was originally designed to simulate direct measurements of basilar membrane (BM) activity. It is not a model of cochlear mechanics but reproduces a large number of animal BM data like input/output functions, cochlear tuning curves, two-tone suppression, local distortion products, as well as changes in phase, bandwidth, best frequency and impulse response with signal level. (Meddis et al., in preparation). Here are only two examples: Animal data (Ruggero et al., 1997) Model (Meddis et al., in preparation) The DRNL simulates animal BM I/O functions The DRNL generates the right combination tones

6. Modelling human BM nonlinearity 5 Caution: Our approach could be interpreted as if we were implying that masking occurs only as a result that the peak velocity of BM vibration in response to the signal and the masker are comparable. We are not implying that. In fact, our model is not intended to be a model of forward masking. The model was tuned to simulate human BM nonlinearity as estimated by psychoacoustical masking experiments (Plack & Oxenham, 2000). Because our model is deterministic, our paradigm is a simplified version of the paradigm used by Plack & Oxenham. Paradigm: • Two stimuli were passed through the model: a) the signal and b) the ‘masker’. The signal frequency was equal to the DRNL-filter BF. The masker frequency was 0.6 times the signal frequency (as in Plack & Oxenham, 2000). Both stimuli had the same duration and were ramped up and down with 2ms raised-cosine ramps. • We then measured the peak value of the DRNL response to the signal (OS) and the masker (OM) during the last half of the stimulus duration. • For each signal intensity (Is), the task was to find out a masker intensity (IM) such that the ratio OS/OM equals (or just exceeded) 1. The value of 1 is arbitrary.

7. Experimental. Plack & Oxenham (2000). Subject YO. Model Results for normal hearing:Masker level vs. Signal level 6 The DRNL parameters were tuned to fit to the experimental masking data for subject YO of Plack & Oxenham (2000) at different signal frequencies. The parameters are given in panel 9.

8. Results for normal hearing:Tuning curves & bandwidths 7 The figure on the right shows modelled isoresponse (tuning) curves at an output velocity of 5e5 m/s, the BM velocity associated with hearing threshold (HT). Notice the absolute HT in the model coincides with the subject’s. The numbers correspond to model BW3dB The figure on the left shows that the 3dB-down bandwidth (BW3dB) of the modelled filters agree with the human BW3dB as calculated by the Glasberg and Moore (1983) formula: BW3dB 0.89  ERB  0.89  [24.7  (4.37CF + 1)] where CF is expressed in KHz

9. Results for normal hearing:Isointensity response 8 The figures below show the isointensity response of the model. Notice that (i) the response gets wider and (ii) the BF changes slightly as the intensity of the stimulus increases. These are important properties of the DRNL filter which reflect the real behaviour (Rosen et al., 1998). Isointensity response at various CFs Normalised isointensity responses The notches in the response are likely to be caused by phase cancellation between the linear and the nonlinear paths. They disappear when the nonlinear path is switched off (i.e., when parameter a equals zero — see panel 10).

10. Model parameters 9 The table shows the DRNL parameters used through out to simulate the characteristics of subject YO’s normal hearing. In principle, this set of parameteres is ‘subject-specific’. Different subjects would require different parameters. The figure shows the dependence of DRNL parameters as a function of BF. Notice that all of the curves (except ‘a’) could be approximated by a straight line of the form: log10(parameter) = y0 + mlog10(BF)

11. Modelling human BM for impaired hearing subjects 10 Impaired hearing usually implies auditory filters less tuned and a more linear masker level-to-signal level relationship in forward masking experiments. In our model, impaired hearing can be simulated by adjusting the value of parameter ‘a’, the gain of the nonlinear path. Isoresponse curves (output = 5e5 m/s) Masking functions Isointensity curves at 0 dB SPL As ‘a’ decreases the masking function becomes more ‘linear’ as observed for impaired listeners (Oxenham & Plack, 1997). As ‘a’ decreases the absolute hearing threshold increases and the ‘tuning curve’ becomes less sharp, as observed for impaired listeners.

12. We have presented a model of human nonlinear cochlear frequency selectivity based on a dual-resonance mechanism. Notice that it does not require a feedback mechanism of gain control. The model can be fitted to reproduce direct animal BM data as well as psychoacoustic human BM data. Here, it has been fitted to reproduce the observed masker level-to-signal level data for a specific subject with normal hearing (subject YO in Plack & Oxenham, 2000). It also reproduces: the subject’s absolute hearing threshold, the expected 3dB-down bandwidths, reasonable tuning curves, an increase of filter bandwidth with stimulus level, a slight change in best-frequency with stimulus intensity. Notice that our model is not a model of forward masking. It simply tries to reproduce human nonlinear filters as characterised by masking experiments in a way similar to gammatone filters. In principle, it is possible to simulate impaired hearing by changing only parameter a. However, there are two important issues to bear in mind: We have used ‘chinchilla’ middle-ear characteristics and not subject YO’s. Parameter ‘a’ of the DRNL filter may be compensating the differences between subject YO’s and chinchilla middle-ear characteristics. The parameters provided must be considered as subject-specific. Different subjects would require different parameters. The underlying mechanism and overall behaviour, however, would be the same for all of them. These results are preliminary but promising. The plot of the model parameters as a function of best frequency shows that it is possible to develop a nonlinear human filterbank by interpolation of the DRNL filter parameters. The filterbank may be constructed as generic or subject-specific. Discussion and Conclusions 11

13. Our model will have a wide range of applications for hearing-aid development. Our plans for the near future include carrying out applied research on the following: Hearing-aid testing To design a battery of tests based on our model for objectively measuring the benefit of current hearing aids and anticipating the benefit of new ones. The advantages of this procedure are: hearing aids could be tested for a range of hearing defficiencies as characterised by the the value of parameter ‘a’, the tests could be generic but also subject-specific. Hearing-aid fitting To desing an in-the-lab procedure for the pre-fitting of hearing aids to meet generic as well as subject-specific needs. Hearing-aid design To design a novel, fast signal processing algorithm based on the DRNL filter to be implemented as part of auditory implants without the need for a feedback mechanism of gain control. To design a novel algorithm inverse to the DRNL filter that (like an auditory lens) compensates for hearing defficiencies without the need for an automatic gain control system. Practical applications of the model to hearing-aids 12

14. Acknowledgements and References 13 Acknowledgements Author EALP’s work is supported by a internal research grant of the Universidad de Castilla-La Mancha. References Meddis R, O’Mard LP, Lopez-Poveda EA (in preparation). A computational algorithm for computing nonlinear auditory frequency selectivity. Moore BCJ, Glasberg BR (1983). Suggested formulae for calculating auditory-filter bandwidths and excitation patterns. J. Acoust. Soc. Am.74: 750-753. Moore BCJ (1998). Cochlear hearing loss, (Whurr Publishers Ltd., London). Oxenham AJ, Plack CJ (1997). A behavioral measure of basilar-membrane nonlinearity in listeners with normal and impaired hearing. J. Acoust. Soc. Am. 101: 3666-3675. Plack CJ, Oxenham AJ (2000). Basilar-membrane nonlinearity estimated by pulsation threshold. J. Acoust. Soc. Am. 107: 501-507. Rosen S, Baker RJ, Darlin A (1998). Auditory filter nonlinearity at 2kHz in normal hearing listeners. J. Acoust. Soc. Am. 103: 2539-2550. Rhode WS, Cooper NP (1996). Nonlinear mechanics in the apical turn of the chinchilla cochlea in vivo. Aud. Neurosc. 3: 101-121. Ruggero MA, Rich NC, Shivapuja BG (1990). Middle-ear response in the chinchilla and its relationship to mechanics at the base of the cochlea. J. Acoust. Soc. Am. 87:1612-1629. Ruggero MA, Rich NC, Recio A, Narayan SS, Robles L (1997). Basilar-membrane responses to tones at the base of the chinchilla cochlea. J. Acoust. Soc. Am. 101: 2151-2163.