Givelberg, Edward; Bunn, Julian A comprehensive three-dimensional model of the cochlea. (English) Zbl 1024.92005 J. Comput. Phys. 191, No. 2, 377-391 (2003). Summary: 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. 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. Cited in 11 Documents MSC: 92C30 Physiology (general) 65Y05 Parallel numerical computation 92-08 Computational methods for problems pertaining to biology 65C20 Probabilistic models, generic numerical methods in probability and statistics 92C05 Biophysics Keywords:cochlea; immersed boundary method; Navier-Stokes equations; parallel computation; shared memory PDFBibTeX XMLCite \textit{E. Givelberg} and \textit{J. Bunn}, J. Comput. Phys. 191, No. 2, 377--391 (2003; Zbl 1024.92005) Full Text: DOI arXiv References: [1] Available from <http://pcbunn.cacr.caltech.edu/cochlea/; Available from <http://pcbunn.cacr.caltech.edu/cochlea/ [2] Allaire, P.; Raynor, S.; Billone, M., J. Acoust. Soc. Am., 55, 1252-1258 (1974) [3] Allen, J. B., Two-dimensional cochlear fluid model: new results, J. Acoust. Soc. Am., 61, 110-119 (1977) [4] Allen, J. B.; Sondhi, M. M., Cochlear macromechanics: time domain solutions, J. Acoust. Soc. Am., 66, 123-132 (1979) · Zbl 0411.76056 [5] Beyer, R. P., A computational model of the cochlea using the immersed boundary method, J. Comp. Phys., 98, 145-162 (1992) · Zbl 0744.76128 [6] Bogert, B. P., Determination of the effects of dissipation in the cochlear partition by means of a network representing the basilar membrane, J. Acoust. Soc. Am., 23, 151-154 (1951) [7] Chadwick, R. F., Studies in cochlear mechanics, (Holmes, M. H.; Rubenfeld, A., Mathematical Modeling of the Hearing Process, Lecture Notes in Biomathematics, vol. 43 (1980), Springer: Springer Berlin) [8] Clark, W. W.; Kim, D. O.; Zurek, P. M.; Bohne, B. A., Spontaneous otoacoustic emissions in chinchilla ear canals: correlation with histopathology and suppression by external tones, Hear. Res., 16, 299-314 (1984) [9] de Boer, B. P., Solving cochlear mechanics problems with higher order differential equations, J. Acoust. Soc. Am., 72, 1427-1434 (1982) · Zbl 0498.73108 [10] Fletcher, H., On the dynamics of the cochlea, J. Acoust. Soc. Am., 23, 637-645 (1951) [11] Geisler, C. D., From Sound to Synapse (1998), Oxford University Press: Oxford University Press New York [12] E. Givelberg, Modeling elastic shells immersed in fluid, Ph.D. Thesis, New York University, 1997; E. Givelberg, Modeling elastic shells immersed in fluid, Ph.D. Thesis, New York University, 1997 · Zbl 1118.74014 [13] Gold, T., Hearing. ii. The physical basis of the action of the cochlea, Proc. R. Soc. Lond. [Biol.], 135, 492-498 (1948) [14] Holmes, M. H., A mathematical model of the dynamics of the inner ear, J. Fluid Mech., 116, 59-75 (1982) · Zbl 0499.76071 [15] Inselberg, A.; Chadwick, R. F., Mathematical model of the cochlea. i: formulation and solution, SIAM J. Appl. Math., 30, 149-163 (1976) · Zbl 0337.76038 [16] Johnstone, B. M.; Boyle, A. J.F., Basilar membrane vibration examined with the Mössbauer technique, Science, 158, 390-391 (1967) [17] Kemp, D. T., Stimulated acoustic emissions from within the human auditory system, J. Acoust. Soc. Am., 64, 66-81 (1978) [18] Khanna, S. M.; Leonard, D. G.B., Basilar membrane tuning in the cat cochlea, Science, 215, 305-306 (1982) [19] Kim, D. O.; Milnar, C. E.; Pfeiffer, R. R., A system of nonlinear differential equations modeling basilar membrane motion, J. Acoust. Soc. Am., 54, 1517-1529 (1973) [20] Kohllöffel, S. M., A study of basilar membrane vibrations ii. The vibratory amplitude and phase pattern along the basilar membrane (post-mortem), Acoustica, 27, 66-81 (1972) [21] Kolston, P. J., Finite element micromechanical modeling of the cochlea in three dimensions, J. Acoust. Soc. Am., 99, 1, 455-467 (1996) [22] Kolston, P. J., Comparing in vitro, in situ and in vivo experimental data in a three dimensional model of mammalian cochlear mechanics, Proc. Natl. Acad. Sci. USA, 96, 3676-3681 (1999) [23] Lesser, M. B.; Berkley, D. A., Fluid mechanics of the cochlea. Part i, J. Fluid Mech., 51, 497-512 (1972) · Zbl 0232.76098 [24] Leveque, R. J.; Peskin, C. S.; Lax, P. D., Solution of a two-dimensional cochlea model with fluid viscosity, SIAM J. Appl. Math., 48, 191-213 (1988) · Zbl 0647.92011 [25] Loh, C. H., Multiple scale analysis of the spirally coiled cochlea, J. Acoust. Soc. Am., 74, 95-103 (1983) · Zbl 0556.76069 [26] Manoussaki, D.; Chadwick, R. S., Effects of geometry on fluid loading in a coiled cochlea, SIAM J. Appl. Math., 61, 369-386 (2000) · Zbl 0993.92007 [27] Nuttall, A.; Ren, T., Extracochlear electrically evoked otoacoustic emissions: a model for in vivo assessment of outer hair cell electromotility, Hear. Res., 92, 178-183 (1995) [28] Parthasarati, A. A.; Grosh, K.; Nuttall, A. L., Three-dimensional numerical modeling for global cochlear dynamics, J. Acoust. Soc. Am., 107, 1, 474-485 (2000) [29] Peskin, C. S., J. Comp. Phys., 25, 20 (1977) [30] Peskin, C. S., The immersed boundary method, Acta Numerica, 11, 479-517 (2002) · Zbl 1123.74309 [31] C.S. Peskin, D.M. McQueen, A general method for the computer simulation of biological systems interacting with fluids, in: Proceedings of SEB Symposium on Biological Fluid Dynamics, Leeds, England, July, 1994; C.S. Peskin, D.M. McQueen, A general method for the computer simulation of biological systems interacting with fluids, in: Proceedings of SEB Symposium on Biological Fluid Dynamics, Leeds, England, July, 1994 [32] Peskin, C. S.; Printz, B. F., Improved volume conservation in the computation of flows with immersed elastic boundaries, J. Comp. Phys., 105, 33-46 (1993) · Zbl 0762.92011 [33] Peterson, L. C.; Bogert, B. P., A dynamical theory of the cochlea, J. Acoust. Soc. Am., 22, 369-381 (1950) [34] Ramamoorthy, S.; Grosh, K.; Dodson, J. M., Theoretical study of structural acoustic silencers for hydraulic systems, J. Acoust. Soc. Am., 111, 5, 2097-2108 (2002) [35] Ranke, O. F., Theory of operation of the cochlea: a contribution to the hydrodynamics of the cochlea, J. Acoust. Soc. Am., 22, 772-777 (1950) [36] Rhode, W. S., Observations of the vibrations of the squirrel monkeys using the Mössbauer technique, J. Acoust. Soc. Am., 49, 1218-1231 (1971) [37] Robles, L.; Ruggero, M.; Rich, N. C., Mössbauer measurements of basilar membrane tuning curves in the chinchilla, J. Acoust. Soc. Am., 76, S35 (1984) [38] Schroeder, M. R., J. Acoust. Soc. Am., 53, 429-434 (1973) [39] Sellick, P. M.; Patuzzi, R.; Johnston, B. M., Measurement of basilar membrane motion in the guinea pig using the Mössbauer technique, J. Acoust. Soc. Am., 72, 131-141 (1982) [40] Siebert, W. M., Ranke revisited – a simple short-wave cochlear model, J. Acoust. Soc. Am., 56, 596-600 (1974) [41] Steele, C. R., Behaviour of the basilar membrane with pure-tone excitation, J. Acoust. Soc. Am., 55, 148-162 (1974) [42] Steele, C. R.; Taber, L. A., Comparison of wkb calculations and experimental results for three-dimensional cochlear models, J. Acoust. Soc. Am., 65, 1007-1018 (1979) · Zbl 0407.76041 [43] Steele, C. R.; Zais, J. G., Effect of coiling in a cochlear model, J. Acoust. Soc. Am., 77, 5, 1849-1852 (1985) [44] Viergever, M. A., Basilar membrane motion in a spiral shaped cochlea, J. Acoust. Soc. Am., 64, 1048-1053 (1978) · Zbl 0384.76054 [45] von Békésy, G., Experiments in Hearing (1960), McGraw-Hill: McGraw-Hill New York [46] Zweig, G.; Lipes, R.; Pierce, J. R., The cochlear compromise, J. Acoust. Soc. Am., 59, 975-982 (1976) [47] Zwislocki, J. J., Analysis of some auditory characteristics, (Buck, R. R.; Luce, R. D.; Galanter, E., Handbook of Mathematical Psychology (1965), Wiley: Wiley New York) [48] Zwislocki, J. J.; Moscicki, J., Theorie der schenkenmechanik – qualitative und quantitative ananlyse, Acta Otolaryng., 72, Suppl. (1948) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.