A Comprehensive Three-Dimensional Model of the Cochlea

TL;DR

The paper presents a comprehensive three-dimensional computational model of the cochlea capturing fluid-structure interactions via the immersed boundary method, integrating curved anatomy, non-linear Navier–Stokes dynamics, and elastic shell components such as the basilar membrane. It demonstrates large-scale parallel simulations on a 32-processor HP Superdome, reproducing traveling-wave behavior and frequency-place characteristics consistent with passive cochlear mechanics. While the results are preliminary, they validate the feasibility of high-fidelity 3D cochlear modeling and establish a foundation for incorporating active amplification and finer meshes as computational resources improve. The work highlights the potential of large-scale computational modeling to address fundamental questions in cochlear mechanics and transduction.

Abstract

The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry, intricate construction and small physical size. We have developed, and are continuing to refine, a detailed three-dimensional computational model based on an accurate cochlear geometry obtained from physical measurements. In the model, the immersed boundary method is used to calculate the fluid-structure interactions produced in response to incoming sound waves. The model includes a detailed and realistic description of the various elastic structures present. In this paper, we describe the computational model and its performance on the latest generation of shared memory servers from Hewlett Packard. Using compiler generated threads and OpenMP directives, we have achieved a high degree of parallelism in the executable, which has made possible several large scale numerical simulation experiments that study the interesting features of the cochlear system. We show several results from these simulations, reproducing some of the basic known characteristics of cochlear mechanics.

Figures (5)

• Figure 1: Execution wall-clock time per time step vs. number of processors.
• Figure 2: A rendering of the geometric model of the cochlea with several parts of the outer shell removed in order to expose the cochlear partition consisting of the narrow basilar membrane and the bony shelf. The round window is located directly below the oval window and in this picture it is partially obscured by the cochlear partition.
• Figure 3: A close-up snapshot of the traveling wave propagating along the basilar membrane. The magnitude of the basilar membrane displacement has been amplified in the normal direction.
• Figure 4: A snapshot of the center line of the basilar membrane response and wave envelope. The top plot shows the response to the 15 kHz input sound. The wave snapshot is taken after 55000 time steps (1.65 msec). The wave envelope was computed over time steps 45,000 - 55,000. The bottom plot shows a 10 kHz experiment. The wave is shown after 30,000 time steps and the envelope was computed over time steps 20,000 - 30,000. The unit of vertical scale is 10$^{-5}$cm.
• Figure 5: A snapshot of the center line of the basilar membrane response and wave envelope. The top plot shows the response to the 5 kHz input sound. The wave snapshot is taken after 70000 time steps. The wave envelope was computed over time steps 60,000 - 70,000. The bottom plot shows a 2 kHz experiment. The wave is shown after 100,000 time steps and the envelope was computed over time steps 100,000 - 130,000. The unit of vertical scale is 10$^{-6}$cm and 10$^{-7}$cm in the top and in the bottom plots, respectively.