Skip to main content

Advertisement

SpringerLink
Log in

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

  • Research Article
  • Published:
Journal of the Association for Research in Otolaryngology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7

Similar content being viewed by others

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

References

  • Asai M, Huber A, Goode R (1999) Analysis of the best site on the stapes footplate for ossicular chain reconstruction. Acta Otolaryngol (Stockh) 119(5):356–361

    CAS  Google Scholar 

  • Binnig G, Quate CF, Gerber C (1986) Atomic force microscope. Phys Rev Lett 56:930–933

    Article  PubMed  Google Scholar 

  • Bolz EA, Lim DJ (1972) Morphology of the stapediovestibular joint. Acta Otolaryngol 73:10–17

    Article  CAS  PubMed  Google Scholar 

  • Brunner H (1954) Attachment of the stapes to the oval window in man. AMA Arch Otolaryngol 59:18–29

    Article  CAS  PubMed  Google Scholar 

  • Chien W, Rosowski JJ, Ravicz ME, Rauch SD, Smullen J, Merchant SN (2009) Measurement of stapes velocity in live human ears. Hear Res 249:54–61

    Article  PubMed Central  PubMed  Google Scholar 

  • Cancura W (1979) On the elasticity of the ligamentum annulare. Arch Otorhinolaryngol 107:27–32

    Article  Google Scholar 

  • Cumpson PJ, Hedley J, Zhdan P (2003) Accurate force measurement in the atomic force microscope: a microfabricated array of reference springs for easy cantilever calibration. Nanotechnology 14:918–924

    Article  CAS  Google Scholar 

  • Dai C, Cheng T, Wood MW, Gan RZ (2007) Fixation and detachment of superior and anterior malleolar ligaments in human middle ear: experiment and modeling. Hear Res 230(1–2):24–30

    Article  PubMed Central  PubMed  Google Scholar 

  • Darling EM, Zauscher S, Guilak F (2006) Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy. Osteoarthritis Cartilage 14(6):571–579

    Article  CAS  PubMed  Google Scholar 

  • Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1(4):601–609

    Article  Google Scholar 

  • Eiber A, Huber AM, Lauxmann M, Chatzimichalis M, Sequeira D, Sim JH (2012) Contribution of complex stapes motion to cochlea activation. Hear Res 284(1):82–92

    Article  PubMed  Google Scholar 

  • Ekwińska M, Rymuza Z (2009) Normal force calibration method used for calibration of atomic force microscope. Acta Phys Pol A 116:S78–S81

    Google Scholar 

  • Ferris P, Prendergast PJ (2000) Middle ear dynamics before and after ossicular replacement. J Biomech 33:581–590

    Article  CAS  PubMed  Google Scholar 

  • Gan RZ, Cheng T, Dai C, Yang F, Wood MW (2009) Finite element modeling of sound transmission with perforations of tympanic membrane. J Acoust Soc Am 126(1):243–253

    Article  PubMed Central  PubMed  Google Scholar 

  • Gan RZ, Reeves BP, Wang X (2007) Modeling of sound transmission from the ear canal to cochlea. Ann Biomed Eng 35(12):2180–2195

    Article  PubMed  Google Scholar 

  • Gan RZ, Sun Q, Feng B, Wood MW (2006) Acoustic-structural coupled finite element analysis for sound transmission in human ear—pressure distributions. Med Eng Phys 28:395–404

    Article  PubMed  Google Scholar 

  • Gan RZ, Wang X (2007) Multifield coupled finite element analysis for sound transmission in otitis media with effusion. J Acoust Soc Am 122(6):3527–3538

    Article  PubMed  Google Scholar 

  • Gan RZ, Yang F, Zhang X, Nakmali D (2011) Mechanical properties of stapedial annular ligament. Med Eng Phys 33:330–339

    Article  PubMed Central  PubMed  Google Scholar 

  • Gentil F, Parente M, Martins P, Garbe C, Jorge RN, Ferreira A, Tavares JM (2011) The influence of the mechanical behavior of the middle ear ligaments: a finite element analysis. Proc Inst Mech Eng H 225(1):68–76

    Article  CAS  PubMed  Google Scholar 

  • Goode RL, Kilion M, Nakamura K, Nishihara S (1994) New knowledge about the function of the human middle ear: development of an improved analog model. Am J Otol 15(2):145–154

    Article  CAS  PubMed  Google Scholar 

  • Guinan JJ Jr, Peake WT (1967) Middle-ear characteristics of anesthetized cats. J Acoust Soc Am 41(5):1237–1261

    Article  PubMed  Google Scholar 

  • Hagr AA, Funnell WRJ, Zeitouni AG, Rappaport JM (2004) High-resolution X-ray computed tomographic scanning of the human stapes footplate. J Otolaryngol 33(4):217–221

    Article  PubMed  Google Scholar 

  • Hato N, Welsh JT, Goode RL, Stenfelt S (2001) Acoustic role of the buttress and posterior incudal ligament in human temporal bones. Otolaryngol Head Neck Surg 124:274–278

    Article  CAS  PubMed  Google Scholar 

  • Heiland K, Goode R, Asai M, Huber A (1999) A human temporal bone study of stapes footplate movement. Am J Otol 20:81–86

    CAS  PubMed  Google Scholar 

  • Huber A, Koike T, Wada H, Nandapalan V, Fish U (2003) Fixation of the anterior mallear ligament: diagnosis and consequences for hearing results in stapes surgery. Ann Otol Rhinol Laryngol 112:348–355

    Article  PubMed  Google Scholar 

  • Huber A, Linder T, Ferrazzini M, Schmid S, Dillier N, Stoeckli S, Fisch U (2001) Intraoperative assessment of stapes movement. Ann Otol Rhinol Laryngol 110(1):31–35

    Article  CAS  PubMed  Google Scholar 

  • Huber AM, Sequeira D, Breuninger C, Eiber A (2008) The effects of complex stapes motion on the response of the cochlea. Otol Neurotol 29(8):1187–1192

    Article  PubMed  Google Scholar 

  • Ikai A, Afrin R, Sekiguchi H, Okajima T, Alam MT, Nishida S (2003) Nano-mechanical methods in biochemistry using atomic force microscopy. Curr Protein Pept Sci 4(3):181–193

    Article  CAS  PubMed  Google Scholar 

  • Kelly DJ, Prendergast PJ, Blayney AW (2003) The effect of prosthesis design on vibration of the reconstructed ossicular chain: a comparative finite element analysis of four prostheses. Otol Neurotol 24:11–19

    Article  CAS  PubMed  Google Scholar 

  • Koike T, Wada H, Kobayashi T (2000) Analysis of the finite-element method of transfer function of reconstructed middle ears and their postoperative changes. In: Rosowski JJ, Merchant SN (eds) The function and mechanics of normal, diseased and reconstructed middle ears. Kugler, The Hague, pp 309–320

    Google Scholar 

  • Kwacz M, Wysocki J, Krakowian P (2012) Reconstruction of the 3D geometry of the ossicular chain based on micro-CT imaging. Biocybernetics Biomed Eng 32(1):27–40

    Article  Google Scholar 

  • Kwacz M (2013) A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery. Biomech Model Mechanobiol 12:1243–1261

    Article  PubMed Central  PubMed  Google Scholar 

  • Kwacz M, Marek P, Borkowski P, Gambin W (2014) Effect of different stapes prostheses on the passive vibration of the basilar membrane. Hear Res 310:13–26

    Article  PubMed  Google Scholar 

  • Ladak HM, Funnell WR (1996) Finite element modeling of the normal and surgically repaired cat middle ear. J Acoust Soc Am 100:933–944

    Article  CAS  PubMed  Google Scholar 

  • Lauxmann M, Eiber A, Haag F, Ihrle S (2014) Nonlinear stiffness characteristics of the annular ligament. J Acoust Soc Am 136:1756–1767

    Article  CAS  PubMed  Google Scholar 

  • Lynch TJ, Nedzelnitsky V, Peake WT (1982) Input impedance of the cochlea in cat. J Acoust Soc Am 72:108–130

    Article  PubMed  Google Scholar 

  • Merchant SN, Ravicz ME, Rosowski JJ (1996) Acoustic input impedance of the stapes and cochlea in human temporal bones. Hear Res 97:30–45

    Article  CAS  PubMed  Google Scholar 

  • Murakoshi M, Yoshida N, Iida K, Kumano S, Kobayashi T, Wada H (2006) Local mechanical properties of mouse outer hair cells: atomic force microscopy study. Auris Nasus Larynx 33(2):149–157

    Article  PubMed  Google Scholar 

  • Myhra S (1998) in: JC Riviere, S Myhra (eds.) Handbook of surface and interface analysis methods for problem solving, Marcel Dekker, New York, 1998, pp. 52

  • Ohashi M, Ide S, Kimitsuki T, Komune S, Suganuma T (2006) Three-dimensional regular arrangement of the annular ligament of the rat stapediovestibular joint. Hear Res 213:11–16

    Article  PubMed  Google Scholar 

  • Ohashi M, Ide S, Kimitsuki T, Sawaguchi A, Kimitsuki T, Komune S, Suganuma T (2008) Histochemical localization of the extracellular matrix components in the annular ligament of rat stapediovestibular joint with special reference to fi brillin, 36-kDa microfi bril-associated glycoprotein (MAGP-36), and hyaluronic acid. Med Mol Morphol 41:28–33

    Article  CAS  PubMed  Google Scholar 

  • Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation measurements. J Mater Res 7(6):1564–1583

    Article  CAS  Google Scholar 

  • Prendergast PJ, Ferris P, Rice HJ, Blayney AW (1999) Vibro-acoustic modeling of the outer and middle ear using the finite-element method. Audiol Neuro Otol 4:185–191

    Article  CAS  Google Scholar 

  • Radmacher M (1997) Measuring the elastic properties of biological samples with the AFM. IEEE Eng Med Biol Mag 16(2):47–57

    Article  CAS  PubMed  Google Scholar 

  • Reddy JN (2007) Theory and analysis of elastic plates and shells. CRC Press, Taylor & Francis

  • Rosowski JJ, Davis PJ, Merchant SN, Donahue KM, Coltrera MD (1990) Cadaver middle ears as models for living ears: comparisons of middle ear input immittance. Ann Otol Rhinol Laryngol 99:403–412

    Article  CAS  PubMed  Google Scholar 

  • Schuknecht H (1968) Temporal bone removal at autopsy. Preparation and uses. Arch Otolaryngol 87(2):129–137

    Article  CAS  PubMed  Google Scholar 

  • Sim JH, Chatzimichalis M, Lauxmann M, Röösli C, Eiber A, Huber AM (2010) Complex stapes motions in human ears. J Assoc Res Otolaryngol 11(3):329–341

    Article  PubMed Central  PubMed  Google Scholar 

  • Sim JH, Röösli C, Chatzimichalis M, Eiber A, Huber AM (2013) Characterization of stapes anatomy: investigation of human and guinea pig. J Assoc Res Otolaryngol 14(2):159–173

    Article  PubMed Central  PubMed  Google Scholar 

  • Stenfelt S, Hato N, Goode RL (2004) Fluid volume displacement at the oval and round windows with air and bone conduction stimulation. J Acoust Soc Am 115(2):797–812

    Article  PubMed  Google Scholar 

  • Sun Q, Gan RZ, Chang KH, Dormer KJ (2002) Computer-integrated finite element modeling of human middle ear. Biomech Model Mechanobiol 1(2):109–122

    Article  CAS  PubMed  Google Scholar 

  • Sugawara M, Ishida Y, Wada H (2002) Local mechanical properties of guinea pig outer hair cells measured by atomic force microscopy. Hear Res 174(1–2):222–229

    Article  PubMed  Google Scholar 

  • Takai E (2005) Osteoblast elastic modulus measured by atomic force microscopy is substrate dependent. Ann Biomed Eng 33(7):963–971

    Article  PubMed  Google Scholar 

  • Thurner PJ (2009) Atomic force microscopy and indentation force measurement of bone. Wiley Interdiscip Rev Nanomed Nanobioltechnol 1(6):624–649

    Article  Google Scholar 

  • Wada H, Metoki T, Kobayashi T (1992) Analysis of the dynamic behavior of the human middle ear using a finite-element method. J Acoust Soc Am 92:3157–3168

    Article  CAS  PubMed  Google Scholar 

  • Whyte JR, Gonzalez L, Cisneros AI, Yus C, Torres A, Sarrat R (2002) Fetal development of the human tympanic ossicular chain articulations. Cells Tissues Organs 171:241–249

    Article  CAS  PubMed  Google Scholar 

  • Wolff D, Bellucci R (1956) The human ossicular ligaments. Ann Otol Rhinol Laryngol 65:895–909

    Article  CAS  PubMed  Google Scholar 

  • Yao W, Li B, Huang X, Guo C, Luo X, Zhou W, Duan M (2012) Restoring hearing using total ossicular replacement prostheses—analysis of 3D finite element model. Acta Otolaryngol 132(2):152–159

    Article  PubMed  Google Scholar 

  • Young WC, Budynas RG (2002) Formulas for stress and strain, 7th edn. McGraw-Hill, New York, Table 14.1, p. 702

    Google Scholar 

  • Zahnert T, Schmidt R et al (1997) FE-simulations of vibrations of the Dresden middle ear prosthesis. In: Huttenbrink K-B (ed) Middle ear mechanics in research and otosurgery. Technical University of Dresden, Dresden, pp 200–206

    Google Scholar 

  • Zhao F, Koike T, Wang J, Sienz H, Meredith R (2009) Finite element analysis of the middle ear transfer functions and related pathologies. Med End Phys 31(8):907–916

    Article  Google Scholar 

Download references

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.

Author information

Authors and 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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zygmunt Rymuza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcin Michałowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jarosław Wysocki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Monika Kwacz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

Keywords

Search

Navigation