Construction of a Computational Model of the Cochlea

*   Edward Givelberg (PI, Johns Hopkins University) - Web page

*   Julian Bunn (Center for Advanced Computing Research, Caltech, Pasadena)

Project Introduction

This project studies a component of the inner ear, the cochlea, and its remarkable properties in hearing. More up to date information can be found at "Fluid Systems Research".

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cochlea.gif (48941 bytes)

(The source of this image is unknown - it was found on the Web sometime in the early 2000s - if you are the author/artist, please let me know.)

In the picture above, the cochlea is the coiled, snail-like object that contains the vestibular, tympanic and median canals. The following picture shows a different view, and includes the round and oval windows.

ear_anatomy2.gif (8152 bytes)

Vibrations of the eardrum are transmitted to the cochlea via a delicate set of bones which attach to the oval window.

The project is studying the main open problems in auditory signal processing: the fine tuning of the cochlea (its ability to differentiate nearby input sound frequencies), the nature of non-linear effects in auditory signal processing and the significance of curvature in cochlear geometry.

Cochlea Model

The model incorporates a new shell theory developed by Givelberg that applies techniques of differential geometry. The shell theory was derived working solely from the Kirchhoff-Love hypothesis, without the use of approximations or extraneous assumptions, such as the moderate bending assumption, used in all previous shell theories.

The partial differential equations of this shell model simulate the elastic response of the basilar membrane and together with the Navier-Stokes equations provide a realistic description of the macro-mechanics of the cochlea. This shell model has been incorporated into the framework of the immersed boundary method resulting in a practical algorithm. 

This animated gif shows the Cochlea model components, as they are built into the complete model, and short sequence of simulated time steps.

Simulation Results (2003)

Disclaimer: All results presented on this page are preliminary, and subject to revision as we tune and correct the applicatio

We have made a special run of a 256x256x256 model, with a driving force at 8kHz, with 30ns time steps and 70000 time steps in total. This model uses a correct placement of the BM in relation to the shelf (the BM was previously positioned on the inner side, incorrectly) and a "tall" cochlea (previous experiments used a squashed cochlea so that the a fluid grid size of 128 could be used in the vertical dimension.

NEW MPEG showing the propagation of a wave along the Basilar Membrane caused by an 8kHz driving force at the Oval Window (40MBytes) NEW

NEW An identical movie, but reduced image size (6MBytes) NEW

[This movie produced by Santiago Lombeyda]


Simulation Results (2002)

Disclaimer: All results presented on this page are preliminary, and subject to revision as we tune and correct the application.

Presently, an implementation of the cochlea model is running on the HP Exemplar X and V class and SuperDome machines at CACR. Simulations typically run for several days and comprise calculations of tens of thousands of time steps. Each time step takes several seconds to compute on the X and V class machines. On the SuperDome, using 32 processors, only about 1 second is required per time step.

Initially, the model was calculated at a resolution of 128x128x128 grid points, but now is being run at the desired resolution of 256x256x128 grid points.

We are currently using the SuperDome in a dedicated partition of 16 CPUs for our experiments.

This page shows plots of the displacement of the middle line on the Basilar Membrane

The following MPEG movies show the latest (Novermber 2001) result using improved Oval window and other model parameters

Movies of the displacement of the centre of the Basilar Membrane, as a function of time

Excitation (Link to MPEG)


Step Size (nanoSecs)

Equivalent duration of input (milliSecs)

Sine period (in Steps)


File Size (MBytes)


15kHz Movie





Yes (@>15,000)


10kHz Movie





Yes (@>10,000)


5kHz Movie





Yes (@>20,000)


2kHz Movie








2kHz Movie








2kHz Movie








2kHz Movie







Movies of the full 3D geometry of the Basilar Membrane, Oval and Circular Windows, as a function of time

  5kHz for 27000 40ns time steps  (12 MBytes)

Miscellaneous Movies

Response of the Oval Window to an impulse force (23 MBytes)

Behaviour of the Oval and Round Windows where the Round Window is forced at a frequency of 10kHz. This movie is an animated GIF. The length of the movie corresponds to 8000 steps at 80 nanoseconds, i.e. about 6 cycles of the sinusoidal force. The Windows lie in a fluid grid of 256x256x128 points.In the movie, the Oval Window is on the right. (7 MBytes)


Earlier Simulation Results (2001)

In the following older MPEG movies we show the motion of the centre line of the Basilar membrane as a function of time, for input excitation sinusoidal forces of 10kHz and 20kHz:

10 kHz (21 MBytes)

10 kHz 20,000 time steps (9.5 MBytes)

20 kHz time steps 20,000 to 23,000 (1.4 MBytes)

The following MPEG movies show a 3D model of the Basilar membrane and semi-circular window displacements as a function of time.

10kHz input, Unit Force, 37,000 time steps, one frame every 100 steps (2.5 MBytes)

Straight (unwrapped) Cochlea with impulse input, 2000 time steps, one frame per time step, 40 ns time step (27 MBytes)

Earlier Simulation Results (2000)

Results from 2000

Screen Shot of Application GUI

A Java3D-based tool has been developed which allows the results from the cochlea simulation to be viewed.


*      "A Comprehensive Three-Dimensional Model of the Cochlea" (PDF) [submitted]

*      "Detailed Simulation of the Cochlea: Recent Progress Using Large Shared Memory Parallel Computers: (PDF) presented at the 2001 ASME International Mechanical Engineering Congress and Exposition, and published in the proceedings of that conference.

*      "Modelling Elastic Shells Immersed in Fluid" [submitted]

Collaboration Information

Please contact Ed Givelberg or Julian Bunn (see below) if you have detailed questions on the research programme.

Edward Givelberg, Department of Mathematics, University of Michigan  email:

Julian Bunn, Center for Advanced Computing Research, California Institute of Technology: email: 

Related Information

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