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The silicon cochlea: 20 years on
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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).
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.
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 Gx and Gy represent the cochlea fluid while the series connection of the Gi, Ci and Si 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.
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) .
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
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