Journal Club: How travelling waves emerge - insight from physical and simulation artificial models of the basilar membrane

on

Today's journal article

Shan J, Yamazaki H, Li J, Kawano S. Theoretical and experimental study on traveling wave propagation characteristics of artificial basilar membrane. 

Why I picked this article

The cochlea, our hearing organ, is a fluid-filled tube that spirals like a snail, encapsulated in the bone of the skull. The basilar membrane is a long membrane that runs along the spiral of the cochlea. The vibration of the basilar membrane or the "travelling wave", causes the activation of auditory sensory cells and perception of hearing. The thickness, width and stiffness of the basilar membrane change along the cochlea in such a way that higher frequency sounds resonate to vibrate the basilar membrane near the bottom of the spiral, while the lower frequency sounds resonate at the top of the spiral. This enables the cochlea to detect a broad range of sound frequencies. 

Understanding the factors influencing basilar membrane vibration and the travelling wave may help us develop alternative therapies for sensorineural hearing loss. This research investigated the details of how the travelling wave behaves on the artificial basilar membrane. In particular, researchers focused on the in-plane trapezoidal artificial basilar membrane, a mathematical model of the basilar membrane. 

I am increasingly interested in the modelling of cochlear function, so I have chosen this publication to add more modelling papers to the journal club mix. 

Some of the research findings

Artificial basilar membrane model (physical):

  • a trapezoidal shape membrane; 42 mm, oscillation area length 30 mm, width 2 mm - 4mm, thickness is 80μm.
  • made of PBDV membrane (KF piezoelectric film, Kureha, Japan) 
  • a whole and fixation device at either end of the membrane, and the membrane was sandwiched between three acrylic layers so that it hangs in the air/fluid-filled chamber. 
  • use of silicon oil as the model flid "we utilized silicone oil (KF-96L-2cs, Shin-Etsu Chemical, Tokyo, Japan) with a density of 8.73×102kgm−3 and a viscosity of 1.75×10−3Pas as the working fluid. These values closely resemble the properties of cochlear lymph (density: 1.01×103kgm−3, viscosity: 1.0×10−3 to 1.97×10−3Pas)"
  • the laser Doppler optical scanning vibration measurement system was used to measure the oscillation of the artificial basilar membrane. 
  • The piezoelectric actuator (AE0505D16F, Thorlabs, Newton, NJ, USA) was attached to the bottom, to induce oscillation - input frequency was 1 - 16kHz, 

Artificial basilar membrane model (simulation):

  • A 3D finite element model was developed to have the same shape and dimensions as the physical model. 
  • Assumptions were: 
    • the basilar membrane is surrounded by incompressible Newtonian fluid
    • the Navier–Stokes equation is rewritten as the unsteady Stokes equation
    • The viscosity is ignored for the flow outside the boundary layer.
  • COMSOL Multiphysics 6.0 (COMSOL, Inc., Stockholm, Sweden)
  • PVDF membrane was chosen as the material with a Young's modulus set to 3.1
  • Silicon oil was selected as the fluid surrounding the basilar membrane

Findings:

  • Numerical simulation showed displacement such that the amplitude and the area of vibration were larger in liquid than in air. The difference becomes more prominent with higher frequencies. 
  • Comparison between the simulation and experiment showed agreement in terms of displacement characteristics, but the discrepancy increased with higher frequencies (14kHz +) in the air-filled model. 
  • Comparison between the simulation and experiment showed agreement in terms of the positions of vibration across frequency ranges in the liquid-filled model. However, the amplitudes were a lot lower in the experimental model than in the simulation. 
  • The analysis of where resonance showed that the theoretical resonance matched the simulation, but the experimental data differed slightly in terms of displacement amplitude. 
  • Using models, propagation of the travelling wave from the very initial wave hitting the basilar membrane to how it creates motion after repeated oscillations could be described for both air and liquid environments. 
  • Overall, as the resonance frequency increases, the travelling wave velocity also increases along the basilar membrane. 
Figure 8d, 13.2 kHz travelling wave and how it changes from the start (red). 
Shan et al. (2025)

Haruna's takeaway

This research and publication are very descriptive, with many mathematical equations. Descriptive data from both the simulation and the physical model are very useful as they provide some numerical references for subsequent mathematical modelling studies, I would imagine. 

Many equations = ! very hard for me! which was the hardest part about reading it. I will have to come back to this publication to fully appreciate the findings and perhaps even learn if we can recreate some simulations. The concept was very simple: to compare a very simple basilar membrane model between the physical model and the simulation. Personally, this is a very good educational publication for me in learning mathematics of vibration, and I am going to need more than just a few hours allocated for this journal club challenge. It's challenging for biologists but exciting at the same time, for it's like learning mathematics in application to our favourite topic, the cochlea. 

 ------- 

This is Haruna's 31/100 of the 100-day challenge to post a science blog article every day! I love inner ear biology & cochlear physiology.