Skip to main content
SpringerLink
Log in

Dynamics of the middle ear with an implantable hearing device: an improved electromechanical model

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

An implantable middle ear hearing device is a promising and novel apparatus that can help improve hearing for patients with both sensorineural and conductive hearing loss. Therefore, it is of key importance to have an adequate mathematical and numerical model for testing. In this paper, a multi-degree-of-freedom lumped parameter model with electromechanical coupling is proposed. The model has been significantly improved compared with the previous one reported in the literature. Periodic vibrations of the stapes are calculated by means of the harmonic balance method and verified numerically. Irregular and chaotic behaviour patterns are found as well as numerical simulations are performed. As a result, the maps of possible regular and irregular solutions are developed, indicating that bistable periodic solutions and subharmonic stapes motion can be observed even for stimulation necessary for normal hearing.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

The datasets generated and analysed during the current study are not publicly available due to the University data protection policy but are available from the corresponding author on reasonable request.

References

  1. Chen, T., Ren, L.J., Yin, D.M., Li, J., Yang, L., Dai, P.D., Zhang, T.Y.: A comparative study of MED-EL FMT attachment to the long process of the incus in intact middle ears and its attachment to disarticulated stapes head. Hear. Res. 353, 97–103 (2017). https://doi.org/10.1016/j.heares.2017.06.006

    Article  Google Scholar 

  2. Feng, B., Gan, R.Z.: A lumped-parameter mechanical model of human ear for sound transmission. Second Joint Embs-Bmes Conference 2002, vol. 1–3, Conference Proceedings, pp. 267–268 (2002)

  3. Gamm, U.A., Grossöhmichen, M., Salcher, R.B., Prenzler, N.K., Lenarz, T., Maier, H.: Optimum coupling of an active middle ear actuator: effect of loading forces on actuator output and conductive losses. Otol. Neurotol. 40(6), 789–796 (2019). https://doi.org/10.1097/MAO.0000000000002253

    Article  Google Scholar 

  4. Grossöhmichen, M., Waldmann, B., Salcher, R., Prenzler, N., Lenarz, T., Maier, H.: Validation of methods for prediction of clinical output levels of active middle ear implants from measurements in human cadaveric ears. Sci. Rep. 7(1), 54 (2017). https://doi.org/10.1038/s41598-017-16107-9

    Article  Google Scholar 

  5. He, M., Macdonald, J.H.: An analytical solution for the galloping stability of a 3 degree-of-freedom system based on quasi-steady theory. J. Fluids Struct. 60, 23–36 (2016). https://doi.org/10.1016/j.jfluidstructs.2015.10.004

    Article  Google Scholar 

  6. Liu, H., Ge, S., Cheng, G., Yang, J., Rao, Z., Huang, X.: Transducer type and design influence on the hearing loss compensation behaviour of the electromagnetic middle ear implant in a finite element analysis. Adv. Mech. Eng. 6(3), 867108 (2014). https://doi.org/10.1155/2014/867108

    Article  Google Scholar 

  7. Liu, H., Xu, D., Yang, J., Yang, S., Cheng, G., Huang, X.: Analysis of the influence of the transducer and its coupling layer on round window stimulation. Acta Bioeng. Biomech. 19(2), 103–111 (2017). https://doi.org/10.5277/ABB-00783-2016-03

    Article  Google Scholar 

  8. Maier, H., Salcher, R., Schwab, B., Lenarz, T.: The effect of static force on round window stimulation with the direct acoustic cochlea stimulator. Hear. Res. 301, 115–124 (2013). https://doi.org/10.1016/j.heares.2012.12.010

    Article  Google Scholar 

  9. Nakajima, H.H., Dong, W., Olson, E.S., Rosowski, J.J., Ravicz, M.E., Merchant, S.N.: Evaluation of round window stimulation using the floating mass transducer by intracochlear sound pressure measurements in human temporal bones. Otol. Neurotol. 31(3), 506–511 (2010). https://doi.org/10.1097/MAO.0b013e3181c0ea9f

    Article  Google Scholar 

  10. Nakajima, H.H., Ravicz, M.E., Merchant, S.N., Peake, W.T., Rosowski, J.J.: Experimental ossicular fixations and the middle ears response to sound: evidence for a flexible ossicular chain. Hear. Res. 204, 60–77 (2005)

    Article  Google Scholar 

  11. Needham, A.J., Jiang, D., Bibas, A., Jeronimidis, G., O’Connor, A.F.: The effects of mass loading the ossicles with a floating mass transducer on middle ear transfer function. Otol. Neurotol. 26(2), 218–224 (2005). https://doi.org/10.1097/00129492-200503000-00015

    Article  Google Scholar 

  12. Park, Y.A., Kong, T.H., Chang, J.S., Seo, Y.J.: Importance of adhesiolysis in revision surgery for vibrant soundbridge device failures at the short incus process. Eur. Arch. Otorhinolaryngol. 274(11), 3867–3873 (2017). https://doi.org/10.1007/s00405-017-4715-4

    Article  Google Scholar 

  13. Ravicz, M.E., Peake, W.T., Nakajima, H.H., Merchant, S.N., Rosowski, J.J.: Modeling flexibility in the human ossicular chain: comparision to ossicular fixation data. In: Gyo, K., Wada, H. (eds.) Middle Ear Mechanics in Research and Otology. Word Scientific, Singapore (2004)

    Google Scholar 

  14. Rosowski, J.J., Chien, W., Ravicz, M.E., Merchant, S.N.: Testing a method for quantifying the output of implantable middle ear hearing devices. Audiol. Neurootol. 12(4), 265–276 (2007). https://doi.org/10.1159/000101474

    Article  Google Scholar 

  15. Rusinek, R.: Sound transmission in the first nonlinear model of middle ear with an active implant. Math. Probl. Eng. 2020(2), 1–23 (2020). https://doi.org/10.1155/2020/4580467

    Article  MathSciNet  Google Scholar 

  16. Rusinek, R.: Effect of transducer fixation in the human middle ear on sound transfer. Eur. J. Mech. A. Solids 85, 104068 (2021). https://doi.org/10.1016/j.euromechsol.2020.104068

    Article  Google Scholar 

  17. Rusinek, R., Kecik, K.: Effect of linear electromechanical coupling in nonlinear implanted human middle ear. Mech. Syst. Signal Process. 151(1–2), 107391 (2021). https://doi.org/10.1016/j.ymssp.2020.107391

    Article  Google Scholar 

  18. Rusinek, R., Weremczuk, A.: Recent advances in periodic vibrations of the middle ear with a floating mass transducer. Meccanica 55(12), 2609–2621 (2020). https://doi.org/10.1007/s11012-020-01226-x

    Article  MathSciNet  Google Scholar 

  19. Salcher, R., Schwab, B., Lenarz, T., Maier, H.: Round window stimulation with the floating mass transducer at constant pretension. Hear. Res. 314, 1–9 (2014). https://doi.org/10.1016/j.heares.2014.04.001

    Article  Google Scholar 

  20. Schraven, S.P., Mlynski, R., Dalhoff, E., Heyd, A., Wildenstein, D., Rak, K., Radeloff, A., Hagen, R., Gummer, A.W.: Coupling of an active middle-ear implant to the long process of the incus using an elastic clip attachment. Hear. Res. 340, 179–184 (2016). https://doi.org/10.1016/j.heares.2016.03.012

    Article  Google Scholar 

  21. Seong, K.W., Jung, E.S., Lim, H.G., Lee, J.W., Kim, M.W., Woo, S.H., Lee, J.H., Park, I.Y., Cho, J.H.: Vibration analysis of human middle ear with differential floating mass transducer using electrical model. IEICE Trans. Inf. Syst. E92–D(10), 2156–2158 (2009). https://doi.org/10.1587/transinf.E92.D.2156

  22. Stieger, C., Bernhard, H., Waeckerlin, D., Kompis, M., Burger, J., Haeusler, R.: Human temporal bones versus mechanical model to evaluate three middle ear transducers. J. Rehabil. Res. Dev. 44(3), 407 (2007). https://doi.org/10.1682/JRRD.2006.09.0114

    Article  Google Scholar 

  23. Tian, J., Huang, X., Rao, Z., Ta, N.A., Xu, L.: Finite element analysis of the effect of actuator coupling conditions on round window stimulation. J. Mech. Med. Biol. 15(4), 1550048 (2015). https://doi.org/10.1142/S0219519415500487

    Article  Google Scholar 

  24. Tringali, S., Koka, K., Deveze, A., Holland, N.J., Jenkins, H.A., Tollin, D.J.: Round window membrane implantation with an active middle ear implant: a study of the effects on the performance of round window exposure and transducer tip diameter in human cadaveric temporal bones. Audiol. Neurotol. 15(5), 291–302 (2010). https://doi.org/10.1159/000283006

    Article  Google Scholar 

  25. Wang, X., Hu, Y., Wang, Z., Shi, H.: Finite element analysis of the coupling between ossicular chain and mass loading for evaluation of implantable hearing device. Hear. Res. 280(1–2), 48–57 (2011). https://doi.org/10.1016/j.heares.2011.04.012

    Article  Google Scholar 

  26. Zhang, Xiangming, Gan, R.Z.: A comprehensive model of human ear for analysis of implantable hearing devices. IEEE Trans. Biomed. Eng. 58(10), 3024–3027 (2011). https://doi.org/10.1109/TBME.2011.2159714

    Article  Google Scholar 

  27. Yang, S., Xu, D., Liu, X.: Evaluation of round window stimulation performance in otosclerosis using finite element modeling. Comput. Math. Methods Med. 2016(7), 1–10 (2016). https://doi.org/10.1155/2016/3603207

  28. Zhou, K., Liu, H., Yang, J., Zhao, Y., Rao, Z., Yang, S.: Influence of middle ear disorder in round-window stimulation using a finite element human ear model. Acta Bioeng. Biomech. 21(1), 3–12 (2019)

Download references

Funding

This research was funded by the Lublin University of Technology under research grant no. FD-20/IM-5/131 (AW) and FD-20/IM-5/094 (RR).

Author information

Author notes

  1. Andrzej Weremczuk and Rafal Rusinek have contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618, Lublin, Poland

    Andrzej Weremczuk & Rafal Rusinek

Authors
  1. Andrzej Weremczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafal Rusinek
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

RR contributed to study conception and design, data collection and numerical simulations; AW contributed to analytical method analysis and interpretation of analytical results; and RR and AW contributed to draft manuscript preparation and graphical design. All authors discussed and reviewed the results and approved the final version of the manuscript.

Corresponding author

Correspondence to Rafal Rusinek.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weremczuk, A., Rusinek, R. Dynamics of the middle ear with an implantable hearing device: an improved electromechanical model. Nonlinear Dyn 112, 2219–2235 (2024). https://doi.org/10.1007/s11071-023-09141-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-09141-y

Keywords

Search

Navigation