https://homepages.rpi.edu/~kramep/Public/preprintStochIB.pdf

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales

The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map sounds of different frequencies onto corresponding characteristic positions on the basilar membrane (BM). Sounds enter the fluid-filled cochlea and cause deflection of the BM due to pressure differences between the cochlear fluid chambers. These deflections travel along the cochlea, increasing in amplitude, until a frequency-dependent characteristic position and then decay away rapidly. The hair cells can detect these deflections and encode them as neural signals. Modelling the mechanics of the cochlea is of help in interpreting experimental observations and also can provide predictions of the results of experiments that cannot currently be performed due to technical limitations. This paper focuses on reviewing the numerical modelling of the mechanical and electrical processes in the cochlea, which include fluid coupling, micromechanics, the cochlear amplifier, nonlinearity, and electrical coupling.

/pdf/modelling-cochlear-mechanics-2n9d5nxgjf.pdf

Modelling Cochlear Mechanics

The immersed boundary method is a general numerical method for modeling elastic boundaries immersed within a viscous, incompressible fluid. It has been applied to several biological and engineering systems, including large-scale models of the heart and cochlea. These simulations have the potential to improve our basic understanding of the biological systems they model and aid in the development of surgical treatments and prosthetic devices. Despite the popularity of the immersed boundary method and the desire to scale the problems to accurately capture the details of the physical systems, parallelization for large-scale distributed memory machines has proved challenging. The primary difficulty is in achieving a load-balanced computation, while maintaining low communication costs when modeling the interactions between the fluid and the moving immersed boundary. In this paper we describe a parallelized algorithm for the immersed boundary method that is designed for scalability on distributed memory multiprocessors and clusters of SMPs. It is implemented using the Titanium language, a Java-based language designed for high performance scientific computing. Our software package, called IB, takes advantage of the object-oriented features of Titanium to provide a framework for simulating immersed boundaries that separates the generic immersed boundary method code from the specific application features that define the immersed boundary structure and the forces that arise from those structures. Our results demonstrate the scalability of our design and the feasibility of large-scale immersed boundary computations with the IB package.

/pdf/distributed-immersed-boundary-simulation-in-titanium-1pqaj71kct.pdf

Distributed Immersed Boundary Simulation in Titanium

To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories.

https://downloads.hindawi.com/archive/2011/435135.pdf

Quantitative reappraisal of the helmholtz-guyton resonance theory of frequency tuning in the cochlea.

Purpose: A cochlea modeling approach is presented allowing for a user defined degree of geometry simplification which automatically adjusts to the patient specific anatomy. Model generation can be performed in a straightforward manner due to error estimation prior to the actual generation, thus minimizing modeling time. Therefore, the presented technique is well suited for a wide range of applications including finite element analyses where geometrical simplifications are often inevitable. Methods: The method is presented for n=5 cochleae which were segmented using a custom software for increased accuracy. The linear basilar membrane cross sections are expanded to areas while the scalae contours are reconstructed by a predefined number of arc segments. Prior to model generation, geometrical errors are evaluated locally for each cross section as well as globally for the resulting models and their basal turn profiles. The final combination of all reconditioned features to a 3D volume is performed in Autodes...

Three-dimensional modeling of the cochlea by use of an arc fitting approach.

We have developed and are refining a detailed three-dimensional computational model of the human cochlea. The model uses the immersed boundary method to calculate the fluid-structure interactions produced in response to incoming sound waves. An accurate cochlear geometry obtained from physical measurements is incorporated. The model includes a detailed and realistic description of the various elastic structures present. Initially, a macro-mechanical computational model was developed for execution on a CRAY T90 at the San Diego Supercomputing Center. This code was ported to the latest generation of shared memory high performance 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 to run several large scale numerical simulation experiments to study the interesting features of the cochlear system. In this paper, we outline the methods, algorithms and software tools that were used to implement and fine tune the code, and discuss some of the simulation results.

J. Bunn

Papers

Detailed Simulation of the Cochlea: Recent Progress Using Large Shared Memory Parallel Computers