Annals of Biomedical Engineering

, Volume 24, Issue 4, pp A241–A249 | Cite as

A model for cochlear outer hair cell deformations in micropipette aspiration experiments: An analytical solution

  • Alexander A. Spector
  • William E. Brownell
  • Aleksander S. Popel
Reprised Papers from Volume 24, Number 2
Received:
Revised:
Accepted:
  • 75 Downloads

Abstract

We propose a mathematical model, to describe the deformations of the cochlear outer hair cell (OHC) in the micropipette aspiration experiments. The bending effect is considered, and the OHC is treated as a cylindrical shell. The pipette effect is modeled by two-dimensional normal loading. Considering the OHC wall as an infinitely long cylinder, we obtain solution in terms of Fourier series with respect to the circumferential coordinate where coefficients are expressed by closed formulae. We keep leading terms in Fourier useries and derive a closed formula for the length of tongue of the aspirated cell surface in terms of pipette pressure, cell geometry, and elastic moduli. To demonstrate application of the theory, we use data recently reported from the micropipette aspiration experiments and obtain an estimate of the elastic shear modulus for the OHC lateral wall.

Keywords

Outer hair cell Cell mechanics Elastic shell model Micropipette aspiration 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Brownell, W. E. Outer hair cell electromotility and otoacoustic emissions.Ear Hear. 11:82–92, 1990.PubMedCrossRefGoogle Scholar
  2. 2.
    Calladine, C. R.Theory of Shell Structures. Cambridge, UK: Cambridge University Press, 1983, 763 pp.Google Scholar
  3. 3.
    Cheng, L. Y. Deformation analyses in cell and developmental biology, part 1: Formal methodology; part 2: Mechanical experiments on cells.J. Biomech. Eng. 109:10–17, 18–24, 1987.PubMedGoogle Scholar
  4. 4.
    Dym, C. L.Introduction to the Theory of Shells. New York: Hemisphere Publishing Corp., 1990, 165 pp.Google Scholar
  5. 5.
    Evans, E. A. New membrane concept applied to the analysis of fluid shear- and micropipette deformed red blood cell.Biophys. J. 13:941–954, 1973.PubMedGoogle Scholar
  6. 6.
    Evans, E. A. Minimum energy analysis of membrane deformations applied to pipet aspiration and surface adhesion of red blood cells.Biophys. J. 30:265–284, 1980.PubMedGoogle Scholar
  7. 7.
    Evans, E. A., and R. Skalak.Mechanics and Thermodynamics of Biomembranes. Boca Raton, FL: CRC Press, 1980, 254 pp.Google Scholar
  8. 8.
    Evans, E. A., and A. Yeung. Apparent viscosity and cortical tension of blood granulocytes determined by micropipette experiment.Biophys. J. 56:151–160, 1989.PubMedGoogle Scholar
  9. 9.
    Flügge, W.Stresses in Shells. Berlin: Springer-Verlag, 1960, 499 pp.Google Scholar
  10. 10.
    Hochmuth, R. M. Measuring the mechanical properties of individual human blood cells.J. Biomech. Eng. 115:515–519, 1993.PubMedGoogle Scholar
  11. 11.
    Holley, M. C., and J. F. Ashmore. A, cytoskeletal spring in cochlear outer hair cell.Nature 335:635–637, 1988.PubMedCrossRefGoogle Scholar
  12. 12.
    Iwasa, K. H., and R. S. Chadwick. Elasticity and active force generation of cochlea outer hair cells.J. Acoust. Soc. Am. 92:3169–3173, 1992.PubMedCrossRefGoogle Scholar
  13. 13.
    Lukasiewicz, S.Local Loads in Plates and Shells. Dordrecht: Kluwer Academic Publishers, 1979, 569 pp.Google Scholar
  14. 14.
    Mohandas, N., and E. Evans. Mechanical properties of the red blood cell membrane in relation to molecular structure and genetic effects.Annu. Rev. Biophys. Biomol. Struct. 23:787–818, 1994.PubMedCrossRefGoogle Scholar
  15. 15.
    Needham, D., and R. M. Hochmuth. Rapid flow of passive neutrophils into a 4 μm pipet and measurement of cytoplasmic viscosity.J. Biomech. Eng. 112:269–276, 1990.PubMedGoogle Scholar
  16. 16.
    Needham, D., and R. M. Hochmuth. A sensitive measure of surface stress in the resting neutrophil.Biophys. J. 61:1664–1670, 1992.PubMedGoogle Scholar
  17. 17.
    Niordsen, F. I.Shell Theory. Amsterdam: Elsevier, 1985, 408 pp.Google Scholar
  18. 18.
    Novozhilov, V. V.The Theory of Thin Shells. Groningen, The Netherlands: Noordhoff, 1959, 376 pp.Google Scholar
  19. 19.
    Popel, A. S., J. T. Ratnanather, A. A. Spector, P. S. Sit, R. A. Jerry, and W. E. Brownell. Mechanics of the cochlear outer hair cell. In:Proceedings of the Fourth China-Japan-USA-Singapore Conference on Biomechanics, edited by G. Yang, K. Hayashi, S. L.-Y. Woo, and J. C. H. Goh. Taiyuan, Shanxi, China; Beijing International Academic Publishing, 1995, pp. 433–436.Google Scholar
  20. 20.
    Ratnanather, J.-T., W. E. Brownell, and A. S. Popel. Mechanical properties of the outer hair cell. In:Biophysics of Hair Cell Sensory Systems, edited by H. Duifhuis, J. W. Horst, P. van Dijk, and S. M. van Netten. River Edge, NJ: World Scientific, 1993, pp. 199–206.Google Scholar
  21. 21.
    Ratnanather, J. T., M. Zhi, W. E. Brownell, and A. S. Popel. The ratio of elastic moduli of cochlear outer hair cells derived from osmotic experiments.J. Acoust. Soc. Am. 99: 1025–1028, 1996.PubMedCrossRefGoogle Scholar
  22. 22.
    Sato, M., M. J. Levesque, and R. M. Nerem. Application of the micropipette technique to the measurement of the mechanical properties of cultured bovine aortic endothelial cells.J. Biomech. Eng. 109:27–34, 1987.PubMedCrossRefGoogle Scholar
  23. 23.
    Sit, P. S., J. T. Ratnanather, A. S. Popel, and W. E. Brownell. Micromechanical properties of outer hair cell of the inner ear. In:Biomedical Engineering: Recent Developments, edited by J. Vossoughi. Washington, DC: University of District of Columbia, 1994, pp. 107–110.Google Scholar
  24. 24.
    Steele, C. R. Elastic behavior of the outer hair cell wall. In:The Mechanics and Biophysics of Hearing, edited by P. Dallos, C. D. Geisler, J. W. Matthews, M. A. Ruggero, and C. R. Steele. Berlin: Springer-Verlag, 1990, pp. 120–131.Google Scholar
  25. 25.
    Steele, C. R., G. Baker, J. Tolomeo, and D. Zetes. Electro-Mechanical models of the outer hair cell sensory systems. In:Biophysics, of Hair Cell Sensory Systems, edited by H. Duifhuis, J. W. Horst, P. van Dijk, and S. M. van Netten. River Edge, NJ: World, Scientific, 1993, pp. 207–214.Google Scholar
  26. 26.
    Theret, D. P., M. J. Levesque, M. Sato, R. M. Nerem, and L. T. Wheeler. The application of a homogeneous half-space model in the analysis of endothelial cell micripipette measurements.J. Biomech. Eng. 110:190–199, 1988.PubMedGoogle Scholar
  27. 27.
    Tolomeo, J. A., and Steele, C. R. Orthotropic piezoelectric properties of the cochlear outer hair cell wall.J. Acoust. Soc. Am. 97:3006–3011, 1995.PubMedCrossRefGoogle Scholar
  28. 28.
    Waugh, R. E. Reticulocyte rigidity and passage through endothelial-like pores.Blood 78:3037–3042, 1991.PubMedGoogle Scholar
  29. 29.
    Waugh, R. E., and E. A. Evans. Thermoelasticity of red blood cell membrane.Biophys. J. 26:115–132, 1979.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 1996

Authors and Affiliations

  • Alexander A. Spector
    • 1
  • William E. Brownell
    • 2
  • Aleksander S. Popel
    • 1
  1. 1.Department of Biomedical EngineeringThe Johns Hopkins UniversityBaltimoreU.S.A.
  2. 2.Department of Otorhinolaryngology and Communicative SciencesBaylor College of MedicineHouston

Personalised recommendations