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Seeking help in designing three types of deformable membrane boundary.

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Old   September 30, 2013, 18:14
Default Seeking help in designing three types of deformable membrane boundary.
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Tom Li
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Hello everyone.

I am Tom, currently a PhD student struggling to finish his research. In my project, I need to simulate the human cochlea, specifically, the movements of membranes and fluids inside the human cochlea. However, the massive amount of source codes are baffling to a newcomer like me. Even though I write a decent amount in C/C++, I am not sure whether I am reading the right part of the package.

I'll describe my problem below. Any help will be appreciated!

The following two graphs illustrates the 2D cochlea fluid chamber that I want to model. Take graph (a) for example, the cochlea is modelled as a closed chamber filled with incompressible fluids. On the left is the driving membrane (oval window), coloured in blue, which exerts an oscillating force to the fluid inside the chamber. On the right is the passive membrane, coloured in green, which is driven into movement by the fluid pressure, which in turn weakly pushes the fluid back. At the bottom is the basilar membrane, which has progressive impedance along its length -- similar to an array of springs sorted in descending natural frequencies. When the cochlear fluid is driven into motion, the basilar membrane react to the change of pressure, and as a result, a specific part will be driven into motion because of resonance. The black lines represents impenetrable walls.

Graph (b) is a modified version of graph (a), where the chamber is divided into two halves, connected at the end. The basilar membrane is driven by the difference of pressure between the two chambers.


https://www.dropbox.com/s/ibcz0l1yjy...20membrane.png

So let me sum up the three types of membranes.
  1. Driving membrane that oscillate at a certain frequency.
  2. Elastic, passive membrane that simply reacts to surface pressure, serving as a pressure releaser.
  3. Elastic membrane of progressive impedance that reacts to surface pressure (or the difference between surface pressures on both sides).

Membrane 3 is the key to my research.

I am typically confused about:
  1. How to read surface pressure from nearby fluid cells.
  2. How to set up a progressive impedance along a membrane? If I am to model the movements of different points of the membrane, how should I record their states?


Any help will be appreciated!


Regards,
Tom
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Old   October 1, 2013, 04:43
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Bernhard
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What are the actual equations for the boundary conditions that you want to implement? I would assume the impedance to relate pressure and flowrate through an outlet, but as far as I understand you are applying this at the wall. What do you expect in your case?

Is the impedance frequency dependent or just a constant?

Are you actually expecting the boundary to actually move, or is it just a boundary condition for the pressure equation?
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Old   October 1, 2013, 17:23
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Tom Li
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Quote:
Originally Posted by Bernhard View Post
What are the actual equations for the boundary conditions that you want to implement? I would assume the impedance to relate pressure and flowrate through an outlet, but as far as I understand you are applying this at the wall. What do you expect in your case?

Is the impedance frequency dependent or just a constant?

Are you actually expecting the boundary to actually move, or is it just a boundary condition for the pressure equation?
Hi Bernhard,

I'll try my best to explain my thoughts. Sorry I am still new to the CFD language.

1. All three membranes will move and deform.

2. The cochlea is like a fully closed fluid chamber. Membrane 1 (blue color, bottom in (a)) vibrates to drive the incompressible fluid to movement, which changes the pressure distribution inside the fluid, which in turn makes membrane 3 (red color, bottom in (a))to react. So there is no inlet/output in the entire system, only membranes.

3. The model can be further simplified so that membrane 1 and 2 is removed. An inlet with oscillating pressure replaces membrane 1, while a compliant (grad(p) = 0, or maybe p=0) outlet replaces membrane 2. But I don't want to fall back to the simplified model yet.

4. The property of membrane 3 (basilar membrane) is a key to my research. The simplest model for it is to treat it as an array of spring systems.

https://www.dropbox.com/s/k4mf4adnke...%20springs.png

Each point (or segment) on the basilar membrane is treated as an independent spring system with its own mass (m), stiffness (k) and damping factor (c). I believe I need to store the speed(dx/dt) and displacement(x) on the point as well. Combined with the pressure value obtained from the nearby cells, I can then update the speed and displacement of the point based on Newton's second law.

Regards,
Tom
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