Skip to main content
SpringerLink
Log in

Mathematical Modeling of the Information Process in the Angular Acceleration Biosensor

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

A mathematical model of the formation of output information in a biosensor of angular acceleration is presented. The functional and numerical parameters of the model have been determined by results of experiments made in 2001–2008. A comparison with the mathematical model of J. M. Goldberg and C. Fernandez (1971) describing the change in spike frequency of the primary afferent neuron spikes in response to an angular acceleration of the head as it turns around a vertical axis is carried out.

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

Similar content being viewed by others

References

  1. V. V. Aleksandrov, T. B. Aleksandrova, A. Angeles Vaskes, R. Vega, M. Reies Romero, E. Soto, K. V. Tikhonova, and N. E. Shulenina, “An output signal correction algorithm for vestibular mechanoreceptors to simulate passive turns,” Moscow Univ. Mech. Bull., 70, No. 5, 130–134 (2015).

    Article  Google Scholar 

  2. V. V. Aleksandrov, T. B. Aleksandrova, I. S. Konovalenko, and K. V. Tikhonova, “Perturbed stable systems on a plane. Pt. 2,” Moscow Univ. Mech. Bull., 72, No. 1, 19-22 (2017).

    Article  Google Scholar 

  3. V. V. Alexandrov, T. B. Alexandrova, and S. S. Migunov, “The mathematical model of the gravity-inertial mechanoreceptor,” Moscow Univ. Mech. Bull., No. 2, 59–64 (2006).

    Google Scholar 

  4. V. V. Alexandrov, T. B. Alexandrova, R. Vega, G. Castillo Quiroz, A. Angeles Vazquez, M. Reyes Romero, and E. Soto, “Information process in vestibular system,” WSEAS Trans. Biol. Biomed., 4, 193–203 (2007).

    Google Scholar 

  5. V. V. Alexandrov, A. Almanza, N. V. Kulikovskaya, R. Vega, T. B. Alexandrova, N. E. Shulenina, A. Limón, and E. Soto, “A mathematical model of the total current dynamics in hair cells,” in: Mathematical Modeling of Complex Information Processing Systems, Moscow State Univ. (2001), pp. 26–41.

  6. V. V. Alexandrov, E. Yu. Mikhaleva, E. Soto, and R. Garc´ıa Tamayo, “Modification of Hodgkin–Huxley mathematical model for the primary neuron of vestibular apparatus,” Moscow Univ. Mech. Bull., No. 5, 65–68 (2006).

    MATH  Google Scholar 

  7. T. G. Astakhova, The Mathematical Models of Semicircular Canals of Vestibular System, Candidate Thesis, Moscow State Univ. (1990).

  8. M. J. Correia, A. A. Perachio, J. D. Dickman, et al., “Changes in monkey horizontal semicircular canal afferent responses after space flight,” J. Appl. Physiol., 73, 112–120 (1992).

    Article  Google Scholar 

  9. C. Fernandez and J. M. Goldberg, “Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. I. Resting discharge and response to constant angular accelerations,” J. Neurophysiol., 34, 635–660 (1971).

    Article  Google Scholar 

  10. C. Fernandez and J. M. Goldberg, “Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. II. Response to sinusoidal stimulation and dynamics of peripheral vestibular system,” J. Neurophysiol., 34, 661–675 (1971).

    Article  Google Scholar 

  11. C. Fernandez and J. M. Goldberg, “Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. III. Variations among units in their discharge properties,” J. Neurophysiol., 34, 676–683 (1971).

    Article  Google Scholar 

  12. A. Haque, D. E. Angelaki, and J. D. Dickman, “Spatial tuning and dynamics of vestibular semicircular canal afferents in rhesus monkeys,” Exp. Brain Res., 155, No. 1, 81–90 (2004).

    Article  Google Scholar 

  13. A. J. Hudspeth and D. P. Corey, “Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli,” Proc. Natl. Acad. Sci. USA, 74, 2407–2411 (1977).

    Article  Google Scholar 

  14. E. C. Keen and A. J. Hudspeth, “Transfer characteristic of the hair cell’s afferent synapse,” Proc. Natl. Acad. Sci. USA, 103, 5537–5542 (2006).

    Article  Google Scholar 

  15. Jiayin Liu, A. M. Shkel, K. Niel, and Fan-Gang Zeng, “System design and experimental evaluation of a MEMS-based semicircular canal prosthesis,” in: First Int. IEEE EMBS Conf. on Neural Engineering, 2003. Conf. Proc. (2003), pp. 177–180.

    Chapter  Google Scholar 

  16. A. Momani and F. Cordullo, “A review of the recent literature on the mathematical modeling of the vestibular system,” in: 2018 AIAA Modeling and Simulation Technologies Conf., AIAA SciTech Forum, 09–12 January 2018, Kissimmee, Florida, USA.

  17. I. V. Orlov, The Vestibular Function [in Russian], Nauka, St. Petersburg (1998).

    Google Scholar 

  18. V. A. Sadovnichii, V. V. Aleksandrov, T. B. Aleksandrova, A. A. Konik, B. V. Pakhomov, G. Y. Sidorenko, E. Soto, K. V. Tikhonova, and N. E. Shulenina, “Mathematical simulation of correction of output signals from the gravitoinertial mechanoreceptor of a vestibular apparatus,” Moscow Univ. Mech. Bull., 68, No. 5, 111–116 (2013).

    Article  Google Scholar 

  19. V. A. Sadovnichii, V. V. Alexandrov, T. B. Alexandrova, R. Vega, G. Castillo Quiroz, M. Reyes Romero, E. Soto, and N. E. Shulenina, “A mathematical model for the generation of output information in a gravitoinertial mechanoreceptor when moving in a sagittal plane,” Moscow Univ. Mech. Bull., 63, No. 6, 53–60 (2008).

    Article  Google Scholar 

  20. V. A. Sadovnichii, V. V. Alexandrov, T. B. Alexandrova, R. Vega, and E. Soto, “Information process in the lateral semicircular canals,” Dokl. Biol. Sci., 436, No. 1, 1–5 (2011).

    Article  Google Scholar 

  21. V. A. Sadovnichii, V. V. Alexandrov, E. Soto, T. B. Alexandrova, T. G. Astakhova, R. Vega, N. V. Kulikovskaya, V. I. Kurilov, S. S. Migunov, and N. E. Shulenina, “A mathematical model of the response of the semicircular canal and otolith to vestibular system rotation under gravity,” J. Gravit. Math. Sci., 146, No. 3, 5938–5947 (2007).

    Article  Google Scholar 

  22. V. A. Sadovnichy, V. V. Alexandrov, T. B. Alexandrova, G. Y. Sidorenko, and N. E. Shulenina, “Generation of output information in the vertical semicircular canals,” Dokl. Biol. Sci., 441, No. 1, 350–353 (2011).

    Article  Google Scholar 

  23. B. N. Segal and J. S. Outerbrige, “A nonlinear model of semicircular canal primary afferents in bullfrog,” J. Neurophysiol., 47, No. 4, 563–578 (1982).

    Article  Google Scholar 

  24. B. N. Segal and J. S. Outerbrige, “Vestibular (semicircular canal) primary neurons in bullfrog: nonlinearity of individual and population response to rotation,” J. Neurophysiol., 47, No. 4, 545–562 (1982).

    Article  Google Scholar 

  25. N. E. Shulenina, Mathematical Modeling of the Canal-Otolith Response to the Vestibular Apparatus Turn under Gravity, Candidate Thesis, Moscow State Univ. (2005).

  26. W. Steinhausen, “Über die Eigenbewegung der Cupula in den Bogengangsampullen des Labyrinths,” Pflüger’s Arch. Gesamte Physiol. Menschen Tiere, 229, No. 1, 439–440 (1932).

    Article  Google Scholar 

  27. R. Vega, V. V. Alexandrov, T. B. Alexandrova, and E. Soto, “Mathematical model of the cupula-endolymph system with morphological parameters for the axolol (Ambystoma tigrinum) semicircular canals,” Open Med. Inform. J., 2, 138–148 (2008).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. V. Aleksandrov, T. B. Alexandrova, V. A. Sadovnichii, G. Yu. Sidorenko, E. Soto, K. V. Tikhonova & N. E. Shulenina

  2. Meritorious Autonomous University of Puebla, Puebla, Mexico

    R. Vega

Authors
  1. V. V. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. B. Alexandrova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Vega
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. A. Sadovnichii
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Yu. Sidorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. E. Soto
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. K. V. Tikhonova
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. N. E. Shulenina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Aleksandrov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 2, pp. 3–18, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aleksandrov, V.V., Alexandrova, T.B., Vega, R. et al. Mathematical Modeling of the Information Process in the Angular Acceleration Biosensor. J Math Sci 253, 756–767 (2021). https://doi.org/10.1007/s10958-021-05267-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-021-05267-9

Search

Navigation