Computational Modelling of the Cat Auditory Periphery: Recent Developments and Future Directions

After more than twenty years of development by many different research groups, much progress has been made in capturing the fundamental properties of cochlear processing in composite computational models of the mammalian auditory periphery to explain auditory nerve responses to a range of acoustic stimuli. In this paper we review recent developments in modelling the cat auditory periphery in particular. Several important cochlear nonlinearities, such as compression and suppression, the shift in tuning with sound pressure level, and the component-1/component-2 transition at very high sound pressure levels, have been incorporated into the latest models. Examination of the latter two properties in the model provides some interesting insights into how cochlear filtering and transduction may be functioning—as well as raising many more questions. In addition, we discuss the remaining inaccuracies of these models and possible approaches to correcting these problems. INTRODUCTION Since physiological investigations of auditory-nerve (AN) response properties began more than 40 years ago, efforts quickly followed to create mathematical and computational models to explain the experimental results. While some of these models were designed to explain a specific set of data for a particular stimulus paradigm, interesting physiological data for speech and noise stimuli motivated the development in the 1980s of computational models that could be applied to arbitrary stimuli. Many of these early models utilised linear basilar membrane (BM) models, but it was soon realised that cochlear nonlinearities were important for AN responses, especially to broadband stimuli such as speech and noise stimuli [1]. A recent review of different approaches to capturing these nonlinearities is provided by Lopez-Poveda [2]. One of the first models of the complete auditory-periphery to tackle incorporating BM nonlinearity was the 1993 model of Carney [3]. A series of models of the cat auditory periphery has subsequently been developed by Laurel H. Carney, students and collaborators over the past 14 years, which has seen continued improvement in describing physiological data recorded from the cat AN. Table I provides a comparison of some of the features of the successive models. The original model of [3] is a phenomenological model that incorporates a feedback signal to control the gain and bandwidth of a gammatone BM filter, such that BM compression and broadening of the BM filter is observed with increasing presentation level of a broadband noise, consistent with the physiological data. However, because of the use of a feedback mechanism to control the filter, changes to the filter gain and bandwidth are only observed for stimulus components falling within the excitatory tuning curve of a model AN fibre. Consequently, Zhang et al. [4] replaced the feedback control path with a feed-forward control path with a wider filter than the BM signal path, such that it is able to produce wide-band suppression effects that are observed for stimuli such as multi-tone complexes and vowels. Table I.Comparison of features of some models of the cat auditory periphery. Carney (1993) Zhang et al. (2001) Bruce et al. (2003) Tan & Carney (2003) Zilany & Bruce (2006, 2007) Middle-ear filtering no no yes yes yes Signal-path filter gammatone 4-order gammatone 4-order gammatone 4-order chirp filter 20-order chirp filter 10-order Moderate-level effects: i) Compression yes yes yes yes yes ii) Suppression no yes yes yes yes High-level effects: i) Broadened tuning yes yes yes yes yes ii) BF-shift with level no no no yes yes iii) C1/C2 transition no no no no yes iv) Peak-splitting no no no no yes Bruce et al. [5] made several further improvements to this model to enable it to more accurately describe the responses of normal and impaired AN fibres to vowel stimuli. One addition is a middle-ear filter, which is important because of its effect on the relative amplitudes of the formants of a vowel. It was also necessary to modify somewhat the architecture of the control path to avoid some undesirable distortion products. This model allows for impairment of outer hair cells (OHCs) and inner hair cells (IHCs), such that it can describe data for low and moderate stimulus sound pressure levels from cats with noise-induced hearing loss. However, the gammatone BM filter used in these three models is unable to describe the frequency glide in the impulse response of the BM that has been observed in BM vibration data and AN recordings. This level-independent frequency glide or “chirp” combines with the level-dependent change in the BM impulse response envelope to produce a shift in the BM filter’s peak or “best frequency” (BF) with increasing stimulus level. Tan and Carney [6] replaced the gammatone BM filter with a chirping filter; with careful and systematic placement of the filter poles and zeros, the filter’s impulse response has a frequency glide in its instantaneous frequency and a gammashaped envelope, consistent with the physiological data. However, this model retained the control-path architecture of Zhang et al. [4]. On the other hand, the model of Bruce et al. [5] is not able to accurately describe high-level effects such as the BF-shift with level, a phase shift in responses at high levels (referred to as the C1/C2 transition) and “peak splitting” in the phaselocked response. This prompted the development of the most recent version of the model by Zilany and Bruce [7, 8]. THE MODEL OF ZILANY & BRUCE (2006, 2007) A schematic of the model of Zilany and Bruce [7, 8] is given in Fig. 1. The input of the model is the stimulus time-domain waveform and the output is the resulting spike times for an AN fibre with a particular characteristic frequency (CF). After middle-ear filtering, the stimulus passes through three parallel filter paths. The C1 filter path describes the filtering properties of the primary mode of BM vibration, which dominates at low and moderate stimulus intensities. This filter is based on the chirping filter of Tan and Carney [6] and consequently exhibits a frequency shift with stimulus level. The compressive and suppressive BM nonlinearities are generated in this filter by moving its poles and zeros according to the wide-band control path output. The control path models the effects of OHC function, and OHC impairment can be realised by varying a parameter COHC. The C2 filter describe a passive (linear) mode of BM vibration; this filter is the same as the C1 filter with complete OHC dysfunction (COHC = 0.0). The C1 and C2 filter paths each have their own separate IHC transduction function. The C1 transduction function is a rectifying Boltzmann-like nonlinearity (NL) that can be impaired via adjustment of the parameter CIHC. In contrast, the C2 transduction function is an inverting (INV), non-rectifying 19 INTERNATIONAL CONGRESS ON ACOUSTICS – ICA2007MADRID 2 function that is shallower than the C1 function for low to medium sound pressure levels, then steeper for high sound pressure levels, and eventually saturating for extremely high sound pressure levels. Consistent with physiological data, the C2 transduction function is robust to cochlear damage. The outputs of the two IHC transduction functions are summed and low-pass (LP) filtered to produce a model IHC receptor potential. This potential drives an IHC-AN synapse model, which subsequently leads to the generation of spikes according to an inhomogeneous Poisson process with refractoriness.