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Elastic Properties of the Annular Ligament of the Human Stapes—AFM Measurement

Journal of the Association for Research in Otolaryngology volume 16, pages 433–446 (2015)Cite this article

Abstract

Elastic properties of the human stapes annular ligament were determined in the physiological range of the ligament deflection using atomic force microscopy and temporal bone specimens. The annular ligament stiffness was determined based on the experimental load-deflection curves. The elastic modulus (Young’s modulus) for a simplified geometry was calculated using the Kirchhoff–Love theory for thin plates. The results obtained in this study showed that the annular ligament is a linear elastic material up to deflections of about 100 nm, with a stiffness of about 120 N/m and a calculated elastic modulus of about 1.1 MPa. These parameters can be used in numerical and physical models of the middle and/or inner ear.

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Abbreviations

A, b, h :

Dimensions of the annular ligament circular plate (outer radius, inner radius, and thickness, respectively)

AFM:

Atomic force microscope

AL:

Annular ligament

defl c :

Deflection of the cantilever

E :

Elastic (Young’s) modulus of the annular ligament of the human stapes

F :

Force acting between the sample and the tip

F-d :

Force-distance curve

FE:

Finite element

K :

Deflection sensitivity factor

k c :

Real spring constant (stiffness) of the cantilever

k c_nom :

Nominal spring constant of the cantilever

k ref :

Spring constant of the reference cantilever

L OW, W OW :

Length and width of the oval window

L SF, W SF :

Length and width of the stapes footplate

ν :

The Poisson’s ratio

SF:

Stapes footplate

SPL:

Sound pressure level

SVJ:

Stapedio-vestibular joint

V :

Voltage of the photodiode

V rigid :

Voltage of the photodiode for the rigid sample

w :

Deflection of the annular ligament plate

z :

Displacement of the piezoactuator

z AL :

Displacement of the piezoactuator on the AL sample

z rigid :

Displacement of the piezoactuator on the rigid sample

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Acknowledgments

We gratefully acknowledge the valuable comments from the reviewers and the section editor.

Conflict of Interest

The authors declare that they have no competing interest.

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Affiliations

  1. Faculty of Mechatronics, Institute of Micromechanics and Photonics, Warsaw University of Technology, ul. św. A. Boboli 8, 02-525, Warsaw, Poland

    Monika Kwacz, Zygmunt Rymuza & Marcin Michałowski

  2. Department of Otolaryngology, Medical University of Warsaw, Warsaw, Poland

    Jarosław Wysocki

Authors
  1. Monika Kwacz
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  2. Zygmunt Rymuza
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  3. Marcin Michałowski
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  4. Jarosław Wysocki
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Correspondence to Monika Kwacz.

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Kwacz, M., Rymuza, Z., Michałowski, M. et al. Elastic Properties of the Annular Ligament of the Human Stapes—AFM Measurement. JARO 16, 433–446 (2015). https://doi.org/10.1007/s10162-015-0525-9

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  • DOI: https://doi.org/10.1007/s10162-015-0525-9

Keywords

  • annular ligament
  • stapes
  • elastic modulus
  • atomic force microscopy