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A Non-linear Viscoelastic Model of the Incudostapedial Joint

  • Majid Soleimani
  • W. Robert J. FunnellEmail author
  • Willem F. Decraemer
Research Article

Abstract

The ossicular joints of the middle ear can significantly affect middle-ear function, particularly under conditions such as high-intensity sound pressures or high quasi-static pressures. Experimental investigations of the mechanical behaviour of the human incudostapedial joint have shown strong non-linearity and asymmetry in tension and compression tests, but some previous finite-element models of the joint have had difficulty replicating such behaviour. In this paper, we present a finite-element model of the joint that can match the asymmetry and non-linearity well without using different model structures or parameters in tension and compression. The model includes some of the detailed structures of the joint seen in histological sections. The material properties are found from the literature when available, but some parameters are calculated by fitting the model to experimental data from tension, compression and relaxation tests. The model can predict the hysteresis loops of loading and unloading curves. A sensitivity analysis for various parameters shows that the geometrical parameters have substantial effects on the joint mechanical behaviour. While the joint capsule affects the tension curve more, the cartilage layers affect the compression curve more.

Keywords

middle ear ossicular chain incudostapedial joint finite-element mechanical behaviour 

Notes

Acknowledgements

The authors thank Calcul Québec and Compute Canada for providing high performance computation facilities for this research. The authors also thank Clarinda C. Northrop for providing us with valuable histological images.

Funding Information

This work was supported by the Canadian Institutes of Health Research and the Natural Sciences and Engineering Research Council of Canada.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

References

  1. Ateshian GA, Shim JJ, Maas SA, Weiss JA (2018) Finite element framework for computational fluid dynamics in FEBio. J Biomech Eng 140:021001–021001-17.  https://doi.org/10.1115/1.4038716 CrossRefGoogle Scholar
  2. Bader D, Lee D (2000) Structure – properties of soft tissues articular cartilage. In: Pergamon Materials Series. Elsevier, pp 75–103Google Scholar
  3. Bonifasi-Lista C, Lake SP, Small MS, Weiss JA (2005) Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse and shear loading. J Orthop Res Off Publ Orthop Res Soc 23:67–76.  https://doi.org/10.1016/j.orthres.2004.06.002 CrossRefGoogle Scholar
  4. Browe DP, Voycheck CA, McMahon PJ, Debski RE (2014) Changes to the mechanical properties of the glenohumeral capsule during anterior dislocation. J Biomech 47:464–469.  https://doi.org/10.1016/j.jbiomech.2013.10.040 CrossRefPubMedGoogle Scholar
  5. Chelliah V, Juty N, Ajmera I, Ali R, Dumousseau M, Glont M, Hucka M, Jalowicki G, Keating S, Knight-Schrijver V, Lloret-Villas A, Natarajan KN, Pettit JB, Rodriguez N, Schubert M, Wimalaratne SM, Zhao Y, Hermjakob H, le Novère N, Laibe C (2015) BioModels: ten-year anniversary. Nucleic Acids Res 43:D542–D548.  https://doi.org/10.1093/nar/gku1181 CrossRefPubMedGoogle Scholar
  6. Cheng JT, Remenschneider A, Kozin E, Furlong C, Rosowski JJ (2017) Nonlinear response of human middle ear to high level sound. J Acoust Soc Am 141(5):3897–3898.  https://doi.org/10.1121/1.4988760 CrossRefGoogle Scholar
  7. Criscenti G, De Maria C, Sebastiani E et al (2015) Quasi-linear viscoelastic properties of the human medial patello-femoral ligament. J Biomech 48:4297–4302.  https://doi.org/10.1016/j.jbiomech.2015.10.042 CrossRefPubMedGoogle Scholar
  8. Davis FM (2013) Nonlinear viscoelastic behaviour of ligaments and tendons: models and experiments. Ph.D. thesis, Virginia Polytechnic Institute and State UniversityGoogle Scholar
  9. Decraemer WF, Maas SA, Funnell WRJ (2015) Finite-element modelling of the synovial fluid and contact in the incudostapedial joint. In: 7th international symposium on middle-ear mechanics in research and otology. Aalborg, DenmarkGoogle Scholar
  10. Fam H, Bryant JT, Kontopoulou M (2007) Rheological properties of synovial fluids. Biorheology 44:59–74PubMedGoogle Scholar
  11. Feizollah S, Soleimani M, Funnell WRJ (2019) Imaging of the gerbil incudostapedial joint. In: association for research in otolaryngology (ARO) 42nd annual winter meeting. Baltimore, MD, USAGoogle Scholar
  12. Funk JR, Hall GW, Crandall JR, Pilkey WD (1999) Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng 122:15–22.  https://doi.org/10.1115/1.429623 CrossRefGoogle Scholar
  13. Funnell WR, Laszlo CA (1982) A critical review of experimental observations on ear-drum structure and function. ORL J Otorhinolaryngol Relat Spec 44:181–205.  https://doi.org/10.1159/000275593 CrossRefPubMedGoogle Scholar
  14. Funnell WRJ, Heng Siah T, McKee MD et al (2005) On the coupling between the incus and the stapes in the cat. J Assoc Res Otolaryngol 6:9–18.  https://doi.org/10.1007/s10162-004-5016-3 CrossRefPubMedPubMedCentralGoogle Scholar
  15. Funnell WRJ, Daniel SJ, Alsabah B, Liu H (2006) On the coupling between the incus and the stapes. In: Auditory mechanisms: processes and models. World Scientific, pp 115–116Google Scholar
  16. Gan RZ, Wang X (2015) Modeling microstructure of incudostapedial joint and the effect on cochlear input. AIP Conf Proc 1703:060011.  https://doi.org/10.1063/1.4939366 CrossRefGoogle Scholar
  17. Gea S (2010) The application of microtomography in research of middle ear mechanics of gerbil and human at static pressure changes. Ph.D. thesis, University of AntwerpGoogle Scholar
  18. Ghosh SS, Funnell WRJ (1995) On the effects of incudostapedial joint flexibility in a finite-element model of the cat middle ear. In: IEEE EMBS 17th annual conferenceGoogle Scholar
  19. Gottlieb PK, Vaisbuch Y, Puria S (2018) Human ossicular-joint flexibility transforms the peak amplitude and width of impulsive acoustic stimuli. J Acoust Soc Am 143:3418–3433.  https://doi.org/10.1121/1.5039845 CrossRefPubMedPubMedCentralGoogle Scholar
  20. Hayes WC, Mockros LF (1971) Viscoelastic properties of human articular cartilage. J Appl Physiol 31:562–568.  https://doi.org/10.1152/jappl.1971.31.4.562 CrossRefPubMedGoogle Scholar
  21. Hewitt JD, Glisson RR, Guilak F, Vail TP (2002) The mechanical properties of the human hip capsule ligaments. J Arthroplast 17:82–89CrossRefGoogle Scholar
  22. Hüttenbrink KB (1988) The mechanics of the middle-ear at static air pressures: the role of the ossicular joints, the function of the middle-ear muscles and the behaviour of stapedial prostheses. Acta Oto-Laryngologica 105(451):1–35.  https://doi.org/10.3109/00016488809099007 CrossRefGoogle Scholar
  23. Jiang S, Gan RZ (2018) Dynamic properties of human incudostapedial joint—experimental measurement and finite element modeling. Med Eng Phys 54:14–21.  https://doi.org/10.1016/j.medengphy.2018.02.006 CrossRefPubMedGoogle Scholar
  24. June RK, Barone JR, Fyhrie DP (2006) Cartilage stress-relaxation described by polymer dynamics. In: Annual Meeting of the Orthopaedic Research SocietyGoogle Scholar
  25. Kaltsas DS (1983) Comparative study of the properties of the shoulder joint capsule with those of other joint capsules. Clin Orthop:20–26Google Scholar
  26. Karmody CS, Northrop CC, Levine SR (2009) The incudostapedial articulation: new concepts. Otol Neurotol 30:990–997.  https://doi.org/10.1097/MAO.0b013e3181b0fff7 CrossRefPubMedGoogle Scholar
  27. Kumar R, Pierce DM, Isaksen V, Davies C, Drogset J, Lilledahl M (2018) Comparison of compressive stress-relaxation behavior in osteoarthritic (ICRS graded) human articular cartilage. Int J Mol Sci 19:413.  https://doi.org/10.3390/ijms19020413 CrossRefPubMedCentralGoogle Scholar
  28. Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite elements for biomechanics. J Biomech Eng 134:011005.  https://doi.org/10.1115/1.4005694 CrossRefPubMedGoogle Scholar
  29. Maas SA, Rawlins D, Weiss JA, Ateshian GA (2018) FEBio user’s manual version 2.8Google Scholar
  30. Maftoon N, Funnell WRJ, Daniel SJ, Decraemer WF (2015) Finite-element modelling of the response of the gerbil middle ear to sound. JARO J Assoc Res Otolaryngol 16:547–567.  https://doi.org/10.1007/s10162-015-0531-y CrossRefPubMedGoogle Scholar
  31. Malda J, Benders KEM, Klein TJ, de Grauw JC, Kik MJL, Hutmacher DW, Saris DBF, van Weeren PR, Dhert WJA (2012) Comparative study of depth-dependent characteristics of equine and human osteochondral tissue from the medial and lateral femoral condyles. Osteoarthr Cartil 20:1147–1151.  https://doi.org/10.1016/j.joca.2012.06.005 CrossRefPubMedGoogle Scholar
  32. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592.  https://doi.org/10.1063/1.1712836 CrossRefGoogle Scholar
  33. O’Connor KN, Cai H, Puria S (2017) The effects of varying tympanic-membrane material properties on human middle-ear sound transmission in a three-dimensional finite-element model. J Acoust Soc Am 142:2836–2853.  https://doi.org/10.1121/1.5008741 CrossRefPubMedPubMedCentralGoogle Scholar
  34. Price GR, Kalb JT (1991) Insights into hazard from intense impulses from a mathematical model of the ear. J Acoust Soc Am 90(1):219–227.  https://doi.org/10.1121/1.401291 CrossRefGoogle Scholar
  35. Qi L, Funnell WRJ, Daniel SJ (2008) A nonlinear finite-element model of the newborn middle ear. J Acoust Soc Am 124:337–347.  https://doi.org/10.1121/1.2920956 CrossRefPubMedGoogle Scholar
  36. Qian D, Funnell WRJ (2019) Finite-element modelling of middle-ear vibrations under pressurization. In: Association for Research in Otolaryngology (ARO) 42nd annual winter meeting. Baltimore, MD, USAGoogle Scholar
  37. Rainis EJ, Maas SA, Henninger HB, McMahon PJ, Weiss JA, Debski RE (2009) Material properties of the axillary pouch of the glenohumeral capsule: is isotropic material symmetry appropriate? J Biomech Eng 131:031007.  https://doi.org/10.1115/1.3005169 CrossRefPubMedGoogle Scholar
  38. Smyth PA (2013) Viscoelastic behavior of articular cartilage in unconfined compression. Thesis, Georgia Institute of TechnologyGoogle Scholar
  39. Smyth PA, Green I (2015) Fractional calculus model of articular cartilage based on experimental stress-relaxation. Mech Time-Depend Mater 19:209–228.  https://doi.org/10.1007/s11043-015-9260-1 CrossRefGoogle Scholar
  40. Soleimani M, Funnell WRJ (2016) Deformation and stability of short cylindrical membranes. Int J Mech Sci 119:266–272.  https://doi.org/10.1016/j.ijmecsci.2016.10.017 CrossRefGoogle Scholar
  41. Soleimani M, Funnell WRJ (2018) Mechanical behaviour of short membranous liquid-filled cylinders under axial loadings. Int J Mech Sci 145:138–144.  https://doi.org/10.1016/j.ijmecsci.2018.06.034 CrossRefGoogle Scholar
  42. Soleimani M, Funnell WRJ, Decraemer WF (2018) A new finite-element model of the incudostapedial joint. AIP Conf Proc 1965:110003.  https://doi.org/10.1063/1.5038503 CrossRefGoogle Scholar
  43. Soons JAM, Aernouts J, Dirckx Joris JJ (2010) Elasticity modulus of rabbit middle ear ossicles determined by a novel micro-indentation technique. Hear Res 263(1–2):33–37.  https://doi.org/10.1016/j.heares.2009.10.001 CrossRefGoogle Scholar
  44. van Dommelen JAW, Jolandan MM, Ivarsson BJ, Millington SA, Raut M, Kerrigan JR, Crandall JR, Diduch DR (2005) Pedestrian injuries: viscoelastic properties of human knee ligaments at high loading rates. Traffic Inj Prev 6:278–287.  https://doi.org/10.1080/15389580590969436 CrossRefPubMedGoogle Scholar
  45. van Dommelen JAW, Jolandan MM, Ivarsson BJ, Millington SA, Raut M, Kerrigan JR, Crandall JR, Diduch DR (2006) Nonlinear viscoelastic behavior of human knee ligaments subjected to complex loading histories. Ann Biomed Eng 34:1008–1018.  https://doi.org/10.1007/s10439-006-9100-1 CrossRefPubMedGoogle Scholar
  46. Veronda DR, Westmann RA (1970) Mechanical characterization of skin—finite deformations. J Biomech 3:111–124.  https://doi.org/10.1016/0021-9290(70)90055-2 CrossRefPubMedGoogle Scholar
  47. Zhang X, Gan RZ (2011) Experimental measurement and modeling analysis on mechanical properties of incudostapedial joint. Biomech Model Mechanobiol 10:713–726.  https://doi.org/10.1007/s10237-010-0268-9 CrossRefPubMedPubMedCentralGoogle Scholar
  48. Zwislocki J (1957) Some impedance measurements on normal and pathological ears. J Acoust Soc Am 29(12):1312–1317.  https://doi.org/10.1121/1.1908776 CrossRefGoogle Scholar

Copyright information

© Association for Research in Otolaryngology 2019

Authors and Affiliations

  1. 1.Department of BioMedical EngineeringMcGill UniversityMontréalCanada
  2. 2.Department of Otolaryngology–Head and Neck SurgeryMcGill UniversityMontrealCanada
  3. 3.Department of Biomedical PhysicsUniversity of AntwerpAntwerpenBelgium

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