Over 20 years ago Richard Lyon and Carver Mead published the world's first ‘silicon’ cochlea¹ and spawned a new field called neuromorphic engineering. In the time since this breakthrough publication there have been a number of different silicon cochlea designs: far too many to reference here!. This has kept research in this area interesting and dynamic despite the fact that we are still falling short of producing something that approximates the biological cochlea. But why is the cochlea so interesting? On the simplest level the cochlea can be thought of as a transduction organ that changes an acoustic input signal into electrical (neural) signals. However, it does so much more than this. Covering a dynamic range of 120dB SPL (sound pressure level) the cochlea allows us to hear from the softest whisper to the roar of a Boeing 747 flying overhead. The cochlea adapts itself to the changing sound scene allowing us to comfortably hear a wide range of sounds and—as I sit here in my office and listen to my Josh Grosban CD and hear noise from the hallway and adjacent offices—I can truly appreciate the wonderful engineering contained in this small, snail-shaped organ.

My research in silicon cochleae began in 2004 and follows the work of Shiraishi,² van Schaik,³ and Fragnière.⁴ Coming from a background in cochlear implants, I simply thought of the cochlea as a black box that divides sound input into frequency bands: essentially a spectrum analyser. I soon discovered its remarkable dynamics and set about trying to find a way to model its most interesting features.

In my opinion the most attractive (engineering) feature of the cochlea is its ability to adapt to a very wide input dynamic range. It seems obvious (as an engineer) that the cochlea must be selectively adding energy to low-energy input signals while dampening the response of high-energy input signals. The mechanism behind this active amplification/attenuation has been a matter of much debate in cochlea-research circles for many years. Figure 1 shows the effects of the nonlinear, active behaviour of the cochlea on the velocity of the basilar membrane (BM): one of two membranes that span the cochlea duct (the other being Reissner's). The BM deflects in response to changes in the input to the cochlea. Its velocity increases as the intensity of the input signal increases. Figure 1 shows both the response of the cochlea if it were simply a spectrum analyser (passive) and a representation of what has actually been measured in biology (active).

Shown left is a plot of frequency versus the velocity of the basilar membrane (BM) at a particular place along it's length. Here we see that if the cochlea (and hence the BM) was passive, the characteristic response at each place would be a stationary, band-pass filter (labelled ‘passive’). In reality, however, the characteristic frequency and gain at a particular place adapt to changes in the input signal intensity. If this intensity were low, for instance, the characteristic response might look like that labelled ‘active’. Shown right is a plot of input signal level versus basilar membrane velocity. A passive response would result in a linear relationship between these two. In reality, however, there is more gain for low input signals while the gain saturates for high input signals. Both plots illustrate the effects of the nonlinear, active behaviour of the cochlea on the basilar membrane velocity. (Adapted from Plack's figure.⁵)

The outer hair cells (OHCs) sit atop a structure known as the organ of Corti that sits atop the BM. They have long been thought to be responsible for the active behaviour of the cochlea. Recent research suggests that they are poised on a mathematical nonlinearity known as the Hopf bifurcation:⁶ a critical point in a nonlinear system where there is a transition between a stable equilibrium point and a limit cycle. A feature of the Hopf bifurcation is that there is a smooth transition between this stable equilibrium and the limit cycle and back again without hysteresis. This is an important feature for a biological system where there is sure to be mismatch and noise that may otherwise push it into an unstable region without the ability to re-establish its correct operating point. The differential equation that represents the Hopf bifurcation contains a cubic term that is representative of a compressive nonlinearity at resonance. This results in a damped response for large inputs and a highly tuned response for small. Hence, the Hopf equation possesses similar dynamics to those observed in the mammalian cochlea.

Recently⁷ we showed that a feedback loop that adds the weighted energy of its output signal to its input possesses the dynamical properties of a Hopf bifurcation. Hence, a generic resonant system of the form shown in Figure 2 should approximate the dynamics of the OHCs.

A generic resonant system with positive feedback. Here x represents the input signal, y represents the output signal, A is a feedback term, K is the gain of the feedforward system, and s is the Laplace operator, ξis an energy dissipation term, and ω₀is the resonant frequency of the feedforward system.

A simplified 2D model of the cochlea. Here the G terms represent conductances, C is capacitance and S represents frequency-dependent negative resistance.

In order to create an entire silicon cochlea we need to connect a number of the resonant elements described by Figure 2 together in a way that best approximates the actual structure of the biological cochlea. A simplified version of the two-dimensional (2D) cochlea model first proposed by Fragnière⁴ is used for this purpose. This model may be described as 2D since it models the wave propagation horizontally along the BM and vertically in the fluid around it. This simplified model is shown in Figure 3.

In Figure 3 the conductances G_x and G_y represent the cochlea fluid while the series connection of the G_i, C_i and S_i components represent a resonant element. These resonant elements have resonant frequencies that exponentially decrease from the base (start of the cochlea) to the apex (end of the cochlea). In this model we replace these passive elements with resonant elements that are described by Figure 2.

As part of my doctoral studies I made several versions of this model in silicon. The results showed many of the features of the biological cochlea. Figure 4 shows the gain at a particular place along the cochlea for different input levels. Data from a silicon cochlea is shown on the left with data from a chinchilla⁸ on the right. The silicon version shows a similar response to the biological cochlea for sound pressure levels between 50dB and 80dB.

A comparison in gain at a particular place along the basilar membrane between a silicon cochlea (left) and biology⁸ (right).

Physiological experiments with the live cochlea have shown that the magnitude of the output signal in response to a test tone is reduced in the presence of another tone. This phenomenon is called two-tone suppression. Figure 5 shows this phenomenon in a silicon cochlea (left) and in biology⁹ (right) .

Two-tone suppression in a silicon cochlea (left) and in biology⁹(right).

The results from my five-year cochlear odyssey suggest that we are getting closer to being able to explain the dynamics of the cochlea and reproduce these dynamics in silicon. My PhD supervisor (André van Schaik) and I are currently working on another silicon cochlea that will (hopefully!) span a frequency range and input dynamic range comparable to biology. With this silicon cochlea we'll be able to start looking at modelling higher auditory centres and use this to explain the ‘cocktail party problem’ amongst other things. This research can assist with making better hearing aid devices, building smarter robots, and solving real-world engineering problems. For further information, please see my doctoral thesis.¹⁰

2. R. F. Lyon and C. Mead, An analog electronic cochlea, IEEE Trans. on Acoustics, Speech, and Signal Processing 36, pp. 1, 1988.
   
   
3. H. Shiraishi, Design of an Analog VLSI Cochlea, PhD thesis, 2004. School of Electrical and Information Engineering The University of Sydney, Australia
   
   
4. A. van Schaik and E. Fragnière, Pseudo-voltage domain implementation of a 2-dimensional silicon cochlea, Int'l Symp. on Circuits and Systems (ISCAS), 2001.
   
   
5. E. Fragnière, Analogue VLSI Emulation of the Cochlea, PhD thesis, 1998. Département d'électricité Lausanne EPFL
   
   
6. C. J. Plack, The Sense of Hearing, Lawrence Erlbaum Associates, Inc., 2005.
   
   
7. S. Camalet, T. Duke, F. Julicher and J. Prost, Auditory Sensitivity Provided by Self-Tuned Critical Oscillations of Hair Cells, Proc. Nat. Acad. Sci. 97, pp. 3, 2000.
   
   
8. J. Tapson, T. J. Hamilton, C. Jin and A. van Schaik, Self-Tuned Regenerative Amplification and the Hopf Bifurcation, 2008.
   
   
9. M. A. Ruggero, Responses to sound of the basilar membrane of the mammalian cochlea, Current Opinion in Neurobiology 2, pp. 449-456, 1992.
   
   
10. M. A. Ruggero, L. Robles and N. C. Rich, Two-tone suppression in the basilar membrane of the cochlea: mechanical basis of auditory-nerve rate suppression, J. Neurophysiology 68, pp. 1, 1992.
    
    
11. T. J. Hamilton, Analogue VLSI Implementations of Two Dimensional, Nonlinear, Active Cochlea Models, PhD thesis, Australia, 2008. School of Electrical and Information Engineering, The University of Sydney