Abstract
A three-dimensional inner stereocilium model is established by PATRAN. According to the relevant data, the corresponding pressure is applied to one side of the inner stereocilia. The top displacement of the inner stereocilia along the cross section of the basilar membrane (the x-displacement) is similar to the available data in the literature, which verifies the correctness of the model. Based on Castigliano’s theorem, the displacement of a single stereocilium is achieved under the inverted triangle force. The results are in good agreement with the data obtained from the finite element (FE) model, which confirms the validity of the formula. With the FE model, the effects of the movement of the hair cells and fluid in the cochlear duct on the x-displacements of the inner stereocilia are studied. The results show that the movement of the hair cells affects the x-displacements of the inner stereocilia, especially for the shortest stereocilium, and the fluid in the cochlear duct affects the x-displacements of the inner stereocilia, especially for the middle stereocilium. Moreover, compared with the effects of the hair cells on the stereocilia, the effect of the cochlear duct fluid is greater.
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References
Hemmert, W., Zenner, H. P., and Gummer, A. W. Three-dimensional motion of the organ of Corti. Biophysical Journal, 78, 2285–2297 (2000)
Matsui, T., Nakajima, C., Yamamoto, Y., Andoh, M., Iida, K., Murakoshi, M., Kumano, S., and Wada, H. Analysis of the dynamic behavior of the inner hair cell stereocilia by the finite element method. JSME International Journal, 49, 828–836 (2006)
Tilney, L. G. and Tilney, M. S. Functional organization of the cytoskeleton. Hearing Research, 22, 55–77 (1986)
You, L., Cowin, S. C., Schaffler, M. B., and Weinbaum, S. A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. Journal of Biomechanics, 34, 1375–1386 (2001)
Han, Y., Cowin, S. C., Schaffler, M. B., and Weinbaum, S. Mechanotransduction and strain amplification in osteocyte cell processes. Proceedings of the National Academy of Sciences of the United States of America, 101, 16689–16694 (2004)
Lin, H. W., Schneider, M. E., and Kachar, B. When size matters: the dynamic regulation of stereocilia lengths. Current Opinion in Cell Biology, 17, 55–61 (2005)
DeRosier, D. J., Tilney, L. G., and Egelman, E. Actin in the inner ear: the remarkable structure of the stereocilium. nature, 287, 291–296 (1980)
Tilney, L. G., Egelman, E. H., Derosier, D. J., and Saunder, J. C. Actin filaments, stereocilia, and hair cells of the bird cochlea, II: packing of actin filaments in the stereocilia and in the cuticular plate and what happens to the organization when the stereocilia are bent. Journal of Cell Biology, 96, 822–834 (1983)
Pickles, J. O., Comis, S. D., and Osborne, M. P. Cross-links between stereocilia in the guinea pig organ of Corti, and their possible relation to sensory transduction. Hearing Research, 15, 103–112 (1984)
Zetes, D. E. and Steele, C. R. Fluid-structure interaction of the stereocilia bundle in relation to mechanotransduction. Journal of the Acoustical Society of America, 101, 3593–3601 (1997)
Duncan, R. K. and Grant, J. W. A finite-element model of inner ear hair bundle micromechanics. Hearing Research, 104, 15–26 (1997)
Eiichi Ishiyama, M. D. and Koichi Ishiyama, M. D. Atlas of the Inner Ear Morphology (in Japanese), Sozo Publishing, An Phu Ward, 9–10 (2002)
Hackney, C. M. and Furness, D. N. Mechanotransduction in vertebrate hair cells: structure and function of the stereociliary bundle. American Journal of Physiology, 268, 1–13 (1995)
Strelioff, D. and Flock, A. Stiffness of sensory-cell hair bundles in the isolated guinea pig cochlea. Hearing Research, 15, 19–28 (1984)
Furness, D. N., Zetes, D. E., and Hackney, C. M. Kinematic analysis of shear displacement as a means for operating mechanotransduction channels in the contact region between adjacent stereocilia of mammalian cochlear hair cells. Proceedings of the Royal Society B: Biological Sciences, 264, 45–51 (1997)
Kachar, B., Parakkal, M., Kurc, M., Zhao, Y. D., and Gillespie, P. G. High-resolution structure of hair-cell tip links. Proceedings of the National Academy of Sciences of the United States of America, 97, 13336–13341 (2000)
Tsuprun, V. and Santi, P. Structure of outer hair cell stereocilia side and attachment links in the chinchilla cochlea. Journal of Histochemistry & Cytochemistry, 50, 493–502 (2002)
Ulfendahl, M., Flock, A., and Scarfone, E. Structural relationships of the unfixed tectorial membrane. Hearing Research, 151, 41–47 (2001)
Andoh, M. and Wada, H. Prediction of the characteristics of two types of pressure waves in the cochlea: Theoretical considerations. Journal of the Acoustical Society of America, 116, 417–425 (2004)
Tomotika, S. and Aoi, T. An expansion formula for the drag on a circular cylinder moving through a viscous fluid at small reynolds numbers. Quarterly Journal of Mechanics & Applied Mathematics, 4, 401–406 (1951)
Duncan, R. K. and Grant, J. W. A finite-element model of inner ear hair bundle micromechanics. Hearing Research, 104, 15–26 (1997)
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Project supported by the National Natural Science Foundation of China (Nos. 11272200 and 11572186)
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Yao, W., Chen, Y. Numerical simulation based on three-dimensional model of inner stereocilia. Appl. Math. Mech.-Engl. Ed. 38, 997–1006 (2017). https://doi.org/10.1007/s10483-017-2211-6
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DOI: https://doi.org/10.1007/s10483-017-2211-6