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TECHNICAL PAPERS

A Finite Element Method for Mechanical Response of Hair Cell Ciliary Bundles

[+] Author and Article Information
John R. Cotton, J. Wallace Grant

Biomechanics Program, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060

J Biomech Eng 122(1), 44-50 (Jul 28, 1999) (7 pages) doi:10.1115/1.429626 History: Received August 20, 1998; Revised July 28, 1999
Copyright © 2000 by ASME
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References

Tilney,  L. G., Egelman,  E. H., DeRosier,  D. J., and Saunders,  J. C., 1983, “Actin Filaments, Stereocilia, and Hair Cells of the Bird Cochlea II: Packing of the Actin Filaments in the Stereocilia and in the Cuticular Plate and What Happens to the Organizations When the Stereocilia Are Bent,” J. Cell Biol., 96, pp. 822–834.
Howard,  J., Roberts,  W. M., and Hudspeth,  A. J., 1988, “Mechanoelectrical Transduction by Hair Cells,” Annu. Rev. Biophys. Biophysic Chem., 17, pp. 99–124.
Lewis, E. R., Leverenz, E. L., and Bialek, W. S., 1985, The Vertebrate Inner Ear, CRC Press, Boca Raton, FL, p. 19.
Szymko,  Y., Dimitri,  P., and Saunders,  J., 1992, “Stiffness of Hair Bundles in the Chick Cochlea,” Hear. Res., 59, pp. 241–249.
Pickles,  J. O., 1993, “A Model for the Mechanics of the Stereociliar Bundle on Acousticolateral Hair Cells,” Hear. Res., 68, pp. 159–172.
Duncan, R. K., 1993, “Finite Element Analysis of Inner Ear Hair Bundles: A Parameter Study of Bundle Mechanics,” Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
Duncan,  R. K., and Grant,  J. W., 1997, “A Finite Element Model of Inner Ear Hair Bundle Micromechanics,” Hear. Res., 104, pp. 15–26.
Reddy, J. N., 1993, An Introduction to the Finite Element Method, McGraw-Hill, New York.
Crisfield, M. A., 1991, Nonlinear Finite Element Analysis of Solids and Structures, 1 , Wiley, New York.
Gittes,  F., Mickey,  B., Nettleton,  J., and Howard,  J., 1993, “Flexural Rigidity of Microtubules and Actin Filaments Measured From Thermal Fluctuation in Shape,” J. Cell Biol., 120, pp. 923–924.
Peterson,  E. H., Cotton,  J. R., and Grant,  J. W., 1996, “Structural Variation in Ciliary Bundles of the Posterior Semicircular Canal. Quantitative Anatomy and Computational Analysis,” Ann. NY Acad. Sci., 781, pp. 85–102.
Cotton,  J. R., Grant,  J. W., and Peterson,  E. H., 1996, “Finite Element Model of Utricular Ciliary Bundles in a Turtle,” Soc. Neurosciences Ab., 22, p. 1064.
Cotton, J. R., Peterson, E. H., and Grant, J. W., 1998, “Mechanical Nonlinearities in Deformation of Hair Cell Ciliary Bundles,” Abstracts of the ARO, p. 144.
Cotton, J. R., 1998, “Mechanical Models of Vestibular Hair Cell Bundles,” Ph.D. Dissertation, Virginia Polytechnic Institute and State University.
Cotton, J. R., and Grant, J. W., 1997, “Analytic and Finite Element Analysis of Stereocilia-Link Systems: Using Deformation Profiles to Infer Hair Cell Bundle Properties,” Abstracts of the ARO, p. 40.

Figures

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(a) Hair cell showing the bundle extending out of the apical surface (AS). The dark mass is the cuticular plate (CP). (b) A close up of the bundle shows drop-off in cilia height and three-dimensional arrangement. (c) Single stereocilia usually taper at their base. (d) Side view of two neighboring cilia depicts geometry of tip link (dark) and side links (light). (e) Top view of bundles shows in the distribution of tip links towards the tallest neighbor. (f ) Side links extend in the direction of every neighbor.
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Section of stereocilia before (dark) and after (light) deformation showing transverse deflection, w, and rotation, φ
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(a) Nodal degrees of freedom showing the deflections and rotations, and (b) loads for each stereocilia element
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Link representation as a rod with end points i and j, showing global (x,y,z) and element local (x*,y*,z*) coordinates. Such a member resists deformation and carries forces only along its long axis, here x*.
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Top view of two stereocilia connected by links: (a) undeformed configuration; (b) deformed geometry without the consideration of link extension. Such a treatment would result in underestimation of link displacement. (c) Method used to compute the geometry with link extension.
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Flow chart of the bundle modeler program algorithm
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Deformed geometry of structure showing: (a) skew, (b) side, and (c) top view of representative bundle
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Plot of stiffness versus tip deflection

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