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.
We describe a numerical method to simulate an elastic shell immersed in a viscous incompressible fluid. The method is developed as an extension of the immersed boundary method using shell equations based on the Kirchhoff-Love and the planar stress hypotheses. A detailed derivation of the shell equations used in the numerical method is presented. This derivation, as well as the numerical method, uses techniques of differential geometry. Our main motivation for developing this method is its use in constructing a comprehensive, threedimensional computational model of the cochlea (the inner ear). The central object of study within the cochlea is the basilar membrane, which is immersed in fluid and whose elastic properties rather resemble those of a shell. We apply the method to a specific example, which is a prototype of a piece of the basilar membrane, and study the convergence of the method in this case. Some typical features of cochlear mechanics are already captured in this simple model. In particular, numerical experiments have shown a traveling wave propagating from the base to the apex of the model shell in response to external excitation in the fluid.
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.1. Introduction. The immersed boundary method is a general numerical method for computational modeling of systems involving fluid-structure interactions. Complex systems where elastic (and possibly active) tissue is immersed in a viscous, incompressible fluid arise naturally in biology and engineering. The immersed boundary method was developed by Peskin and McQueen to study the patterns of the blood flow in the heart [17,15]. It has subsequently been applied to a variety of problems, such as platelet aggregation during blood clotting [6], the deformation of red blood cells in a shear flow [5], the flow in collapsible thin-walled vessels [22], the swimming of eels, sperm, and bacteria [7,4], the flow past a cylinder [14], two-dimensional [3] and three-dimensional models of the cochlea [10], valveless pumping [13], and flexible filament flapping in a flowing soap film [26]. For a recent review of the research in immersed boundary computations and further applications, see [18].Realistic immersed boundary simulations of complex systems, such as the heart and the cochlea, require very large computing resources: The heart model experiments were carried out on the Cray T90 [19,16], and the cochlea was constructed on the HP Superdome at Caltech [11]. Large computational grids are necessary to reduce the numerical error and to incorporate the finer details of the simulated system into
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.
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