Journal Club: Recreating non-linearity of the cochlea - use of coupling and feedback.

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Today's journal article

Ved K, Rolf HFJ, Ivanov T, Meurer T, Ziegler M, Lenk C. Coupling-induced tunability of characteristic frequency, bandwidth and gain of artificial hair cells. 

Why I picked this article

Human hearing is astonishing: ~0.1–0.4% frequency resolution, extraordinary sensitivity over a dynamic range, and a very broad frequency range of 20 Hz–20 kHz. All of this is accomplished with only ~3,000 inner hair cells as transducers in each cochlea that serve as the primary detector of sounds. Cellular machineries surrounding the cochlea, like outer hair cells for sound amplification and nerves regulating their sensitivities, as well as the tonotopic arrangements within the cochlea, enable such sensitive system. 

Re-creating this biological masterpiece by technology is a very exciting idea, but is significant challenge. One of the key biological feature that will have to be replicated is the way the cochlea tease out information about different frequencies from the sounds that are mixed frequencies, and to the nonlinear amplification of sounds driven by the outer hair cells.

This research used "multiple micro-electro-mechanical system (MEMS)"-based resonators as acoustic sensor. MEMS sensors that behave like “critical oscillators” near a Hopf bifurcation. Researchers have used the novel way to coupe them with feedback loop to acquire non-linear amplification more closely aligned with the way cochlea works. 

Some of the research findings

MEMS-based sensor system: 
  • Resonators: high-Q MEMS elements; resonance set by geometry. A silicon beam with piezoresistive deflection sensing (750 μm – 1350 μm long, 200 μm wide, thickness 1-10 μm) and integrated thermomechanical actuation. 
  • Q-factor 40-60
  • Deflection of each resonator is converted into voltage signals. 
  • This is filtered to yield the sensing signal.
  • Feedback signal is amplified sensed signal + a bial voltage. 
  • Non-linear response is achieved by Andronov–Hopf bifurcation (critical oscillator regime) dictated by a specific combination of the feedback strength and feedback. 
Bifurcation point:
  • To test the system, a sine wave sound signal was sent to a loudspeaker with a frequency of 3000−5500 Hz and an amplitude of 15 mV. The sensing signal is recorded with a sample rate of 125 kHz and a Fourier analysis is performed. 
  • The critical coupling bifurcation point for this pair of oscillators was 0.5078
  • Tunable frequency: response peak can be shifted by adjusting the bifurcation control parameter, extending bandwidth coverage with one sensor pair while retaining high Q.
Coupling & parameters: 
  • Two resonators with natural frequencies were coupled (𝑓1 = 3790 Hz and 𝑓2 = 3630 Hz)
  • Output-signal coupling between resonators creates three distinct bifurcation points in the joint system.
  • The bifurcation parameters 𝐶f were tested over the range 0-0.5078, and each of the frequencies  𝑓1 = 3790 Hz and 𝑓2 = 3630 Hz
  • Gain/bandwidth control: coupling and feedback strengths set each sensor’s gain and bandwidth; acts as an adaptive filter bank.
Figure 5A, Ved et al. 2025. Each line represents a different bifurcation parameter value. The graph show the amplitude change over a range of sound pressure. 

Haruna's takeaway

I hope I understood this publication right.... It's a very different type of manuscript, or perhaps a journal style, when the publication is to develop something and go through the development sequentially. Adding complexity of coupling and feedback seemed the critical requirement for achieving the non-linear process. Mathematically, multiplication and at least two coefficients are required to have a non-linear model; and feedback provides some analogy to the efferent system in the cochlea? Sounds like the approach to use coupling and feedback to achieve non-linearity is a concept very applicable not just for sensing sounds, but also for other detection systems to achieve a really good signal-to-noise ratio... maybe could be used for other sensors, like light?  

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This is Haruna's 60/100 of the 100-day challenge to post a science blog article every day! I love inner ear biology & cochlear physiology.