Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T01:01:18.415Z Has data issue: false hasContentIssue false
  • English
  • Français

A hydroelastic model of macromechanics in the endolymphatic vestibular canal

Published online by Cambridge University Press:  26 April 2006

R. D. Rabbitt  and
E. R. Damiano
R. D. Rabbitt
Affiliation:
Department of Mechanical Engineering, Washington University, St. Louis, MO 63130, USA
E. R. Damiano
Affiliation:
Department of Mechanical Engineering, Washington University, St. Louis, MO 63130, USA Current address: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A hydroelastic model describing the mechanics of the human semicircular canal is presented that extends previous work to address the influence of the shape of the labyrinth and the interaction between the endolymph and the cupula. The analysis is based extensively on the three-dimensional geometry and structure of the system and exploits the slender toroidal geometry to obtain an asymptotic solution describing the velocity distribution of the endolymph, the pressure distribution and the deflection of the cupula. All parameters appearing in the model are explicitly defined in terms of physical properties and the geometry. Results for the structure of an infant human endolymphatic canal agree well with experimental measurements of the end-organ velocity gain and phase over the entire physiological range of angular head frequencies. From 0.09 to 1.5 Hz the mechanical response relative to head velocity is essentially constant and the end-organ acts as an angular velocity transducer. Below 0.09 Hz the velocity gain is diminished and above 1.5 Hz the velocity gain is enhanced. For a 1 rad sinusoidal rotation of the head, the analysis predicts an average cupula displacement for the infant canal of approximately 8 × 10−5 cm at 0.09 Hz and 2 × 10−3 cm at 2.0 Hz.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 337 - 369
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bell, J. & Holmes, M. H. 1986 A nonlinear model for transduction in hair cells. Hearing Res. 21, 97–108.Google Scholar
Corey, D. P. & Hudspeth, A. J. 1977 Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc. Natl Acad. Sci. USA 74, 2407–2411.Google Scholar
Corey, D. P. & Hudspeth, A. J. 1979 Ionic basis of the receptor potential in a vertebrate hair cell. Nature 281, 675–677.Google Scholar
Curthoys, I. S. & Oman, C. M. 1987 Dimensions of the horizontal semicircular duct, ampulla and utricle in the human. Acta. Otolaryngol (Stockholm) 103, 254–261.Google Scholar
Damiano, E. R. 1989 A hydroelastic model of the dynamics in a circular duct and its description of the macromechanics in the vestibular canal. Master's thesis, Washington University.
Ewald, J. R. 1892 Physiologische Untersuchingen uber das Endorgan des Nervus Octavus. Wiesbaden: Bergmann.
Fernandez, C. & Goldberg, J. M. 1971 Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. II Response to sinusoidal stimulation and dynamics of peripheral vestibular system. J. Neurophysiol. 34, 661–675.Google Scholar
Grant, J. W. & Van Buskirk, W. C. 1976 Experimental measurement of the stiffness of the cupula. Biophys. J. 16, 669–677.Google Scholar
Groen, J. J. 1949 Medische Physica; de Evenwichtszintuigen pp. 510–561. Amsterdam: NH Uitgeversmij.
Groen, J. J. 1957 The mechanics of the semicircular canals. J. Physiol. Lond. 110, 1–17.Google Scholar
Hamakiotes, C. C. & Berger, S. A. 1988 Fully developed pulsatile flow in a curved pipe. J. Fluid Mech. 195, 23–55.Google Scholar
Hamakiotes, C. C. & Berger, S. A. 1990 Periodic flows through curved tubes: the effect of the frequency parameter. J. Fluid Mech. 210, 353–370.Google Scholar
Hudspeth, A. J. 1983 Mechanoelectrical transduction by hair cells in the acouticolateralis sensory system. Ann. Rev. Neurosci. 6, 187–215.Google Scholar
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.
Lowenstein, O. E. 1974 Comparative morphology and physiology. In Handbook of Sensory Physiology. VI/1: Vestibular System (ed. H. H. Kornhuber), pp. 75–115. Springer.
McLaren, J. W. 1977 The configuration of movement of the semicircular canal cupula. Ph.D. thesis, University of Iowa.
McLaren, J. W. & Hillman, D. E. 1976 Configuration of the cupula during endolymph pressure changes. Neurosci. Abstr. 3, 544, Abstr. 1730.Google Scholar
Monkey, K. E., Bonen, L., Beatty, J. D., Kuehn, L. A., Sokoloff, M. & Weaver, R. S. 1971 Physical properties of fluids and structures of vestibular apparatus of the pigeon. Am. J. Physiol. 110, 140–147.Google Scholar
Moon, P. & Spencer, D. E. 1961 Field Theory for Engineers. D. Van Nostrand.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, Part I. McGraw-Hill.
Ohmori, H. 1985 Mechano-electrical transduction currents in isolated vestibular hair cells of the chick. J. Physiol. Lond. 359, 189–217.Google Scholar
Oman, C. M., Marcus, E. N. & Curthoys, I. S. 1987 The influence of semicircular canal morphology on endolymph flow dynamics. Acta Otolaryngol (Stockholm) 103, 1–13.Google Scholar
Potter, M. C. & Foss, J. F. 1975 Fluid Mechanics. Wiley.
Rabbitt, R. D. & Friedrich, M. T. 1991 Ear canal cross-sectional pressure distributions: Mathematical analysis and computation. J. Acoust. Soc. Am. 89, 2379–2390.Google Scholar
Reddy, J. N. 1984 Energy and Variational Methods in Applied Mechanics. Wiley Interscience.
Steer, R. 1967 The influence of angular and linear acceleration and thermal stimulation on the human semicircular canal. Sc.D. thesis, MIT.
Steinhausen, W. 1933 Uber die beobachtungen der cupula in den bognegangsampullen des labyrinthes des libenden hecths. Pflugers Arch. 232, 500–512.Google Scholar
Stinson, M. R. 1982 A general acoustic network representation of the middle ear. Can. Acoust. Assoc. Symp. on Acoustics, Toronto, Canada.
Van Buskirk, W. C. 1977 The effect of the utricle on fluid flow in the semicircular canals. Ann. Biomed. Engng 5, 1–11.Google Scholar
Van Buskirk, W. C. 1987 Vestibular mechanics. In Handbook of Bioengineering (ed. R. Skalak & S. Chien), pp. 31.1–31.17. McGraw Hill.
Van Buskirk, W. C. & Grant, J. W. 1973 Biomechanics of the semicircular canals. Biomechanics Symp. pp. 53–54. ASME.
Van Buskirk, W. C., Watts, R. G. & Liu, Y. K. 1976 The fluid mechanics of the semicircular canals. J. Fluid Mech. 78, 87–98.Google Scholar
Wilson, V. J. & Jones, G. M. 1979 Mammalian Vestibular Physiology. Plenum.
Womersley, J. R. 1955 Method for the calculation of velocity, rate of flow, and viscous drag in arteries when the pressure gradient is known. J. Physiol. Lond. 127, 553–563.Google Scholar
Womersley, J. R. 1958 Oscillatory flow in arteries I. The constrained elastic tube as a model of arterial flow and pulse transmission. Phys. Med. Biol. 2, 177–187.Google Scholar
Young, L. R. & Oman, C. R. 1969 Model of vestibular adaptation to horizontal rotation. Aerospace Med. 40, 1076–1080.Google Scholar