Journal Club: Cochlear micromechanics - Finite element modelling of the Organ of Corti based on mouse cochlea

on

Today's journal article

Wang Y, Puria S. "Evaluation of thin-slice finite-element models for 3D cochlear organ of Corti mechanics." 

Why I picked this article

Computer modelling of biological processes is an awesome tool for us to test our current understanding of the system, predict how it may change, and to further generate additional constraints/factors we may not be aware of about the system. The cochlea may represent one of the most fun and challenging organs to model, because the cochlea is a small biological system fine-tuned for the whole purpose of propagating and detecting sounds, in the form of tiny pressure changes in the fluid inside. 

I must say computer modelling is not my expertise, but I do want to get more familiar with the mathematical modelling and work more with engineers and modellers in our collaboration. 

This publication focuses on the modelling of the organ of Corti, the part of the cochlea that acts as a biological sound sensor, and converts mechanical vibration of the fluid into an array of electrical signals. The organ of Corti is made up of multiple different types of cells, including sensory hair cells (inner hair cells and outer hair cells) and supporting cells, sitting on the basilar membrane. 

This present study focuses on the evaluation of Floquet boundary conditions in a 3-dimensional (3D) finite element modelling. 

How do you model something so complex like the cochlea? (Figure made using Biorender.com)

Some of the research findings

Definitions relative to the cochlea:

  • Transverse-radial plane - cross-section across the cochlear duct. The transverse axis is the axis through the three chambers, and the radial axis is from the centre of the cochlea to the outside of the cochlea (from the bony osseous spiral lamina towards the lateral wall). 
  • Longitudinal axis - the length along the cochlea, assuming the cochlea as a long, straight tube. 
  • Floquet boundary conditions - used in this study to define how adjacent structures are attached to each other.
  • Input data (for modelling): anatomical data and also displacement data provided from other research, as indicated in the publication. 

Methodology:

3-dimensional (3D) finite element models were built by simplifying the design, and based on anatomical measures from a number of studies as summarised in Table 1 of this publication. The model was solved using COMSOL Multiphysics 6.2

  • Full-length box model:
    • used to calculate how pressure and wave number of different frequencies travel along the cochlea, to feed into slice models. 
    • The model includes the oval window, round window and the helicotrema equivalent locations. 
    • The round window had 0 PA, the oval window had an input fluid velocity of 0.1mm/s. 
    • Bones were immobilised.
    • For fluid, linearised Navier-Stokes equations were solved. 
    • The total degree of freedom was 2,478,839. 
    • Model results were compared to data from OCT (Dewey et al. 2021). 
  • Slice model - captures the organ of Corti as: organ of Corti + off-centred fluid tunnel + basilar membrane, anchored to fixed bony structures. 
    • The model based on the location 4.6 mm
    • For stimulation, three options were investigated, where pressures came from either the bottom wall of the scala tympani, the top wall of the scala vestibuli, or both (see Figure 3a of the publication). 
    • The target pressure for different frequencies of sound was obtained from the full-length box model. 
  • Material properties (assumptions) examples:

    • Fluid in the cochlea was assumed to have the same density and viscosity as water
    • Biological materials (the Basilar membrane and the organ of Corti) were assumed to have the same density as the fluid. 
    • Elastic properties were: the basilar membrane = orthotropic elastic material, and the organ of Corti = isotropic elastic material. 

The result output from the slice model seems to agree mostly with the full-length box model. The simulation shows that the transverse, or vertical movement of the organ of Corti is the most prominent, with some movement in radial orientation, and minimal in longitudinal direction. This seems to align with what we want to model for the cochlea. Comparing three different stimulation methods (i.e. where the pressure comes from) for the slice model, there were minimal differences, with some (the most) variation in longitudinal displacement (Figure 6). Between 4kHz and 6kHz, the place of the maximum pressure shifts from the left side of the tunnel to the other side in a frequency-dependent manner. 

Visualisation of the fluid movement simulation surrounding the organ of Corti shows that in both models, the pressure changes are in close proximity to where the maximum pressure within the tissue is simulated. There seems to be a subtle difference between the slice model and the full-length model at about the fluid inside the tunnel (of Corti). Finally, by adjusting the wave number in the simulation, they show that there was an impact on the longitudinal motion. 

Haruna's takeaway

As I am very naive to any cochlear micromechanical modelling research, I wouldn't comment on the novelty or how this study compares to other models. From what I could understand, though, I do find it very interesting to note that the asymmetric design of the slice model (i.e. the tunnel is not in the centre of the slice, which represents the organ of Corti) results in an asymmetric and concentrated area of the organ of Corti with higher pressure/displacement, as you would expect for the organ of Corti. I tend to want to believe in the complexity of the biological system, but it is actually very interesting to see how a simple model can re-create some prominent features that are observed in biological systems. 

Modelling is a powerful tool, and researchers who can construct a model are end-users of the research output, which provides some input data from the biological target system, in this case, the cochlea. As our research group focus a lot on anatomical and descriptive data, modellers and engineers are very much collaborators and end-users of our raw research output. I hope I can read and familiarise myself more with this type of simulation/modelling research, so that I can appreciate their expertise and approach more, and hopefully collaborate in the future with our research in large animal models and vasculature in the cochlea. 

 ------- 

This is Haruna's 8/100 of the 100-day challenge to post a science blog article every day! I love inner ear biology & cochlear physiology.