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Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model

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Abstract

To investigate how extracellular electric field modulates neuron activity, a reduced two-compartment neuron model in the presence of electric field is introduced in this study. Depending on neuronal geometric and internal coupling parameters, the behaviors of the model have been studied extensively. The neuron model can exist in quiescent state or repetitive spiking state in response to electric field stimulus. Negative electric field mainly acts as inhibitory stimulus to the neuron, positive weak electric field could modulate spiking frequency and spike timing when the neuron is already active, and positive electric fields with sufficient intensity could directly trigger neuronal spiking in the absence of other stimulations. By bifurcation analysis, it is observed that there is saddle-node on invariant circle bifurcation, supercritical Hopf bifurcation and subcritical Hopf bifurcation appearing in the obtained two parameter bifurcation diagrams. The bifurcation structures and electric field thresholds for triggering neuron firing are determined by neuronal geometric and coupling parameters. The model predicts that the neurons with a nonsymmetric morphology between soma and dendrite, are more sensitive to electric field stimulus than those with the spherical structure. These findings suggest that neuronal geometric features play a crucial role in electric field effects on the polarization of neuronal compartments. Moreover, by determining the electric field threshold of our biophysical model, we could accurately distinguish between suprathreshold and subthreshold electric fields. Our study highlights the effects of extracellular electric field on neuronal activity from the biophysical modeling point of view. These insights into the dynamical mechanism of electric field may contribute to the investigation and development of electromagnetic therapies, and the model in our study could be further extended to a neuronal network in which the effects of electric fields on network activity may be investigated.

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References

  • Bawin, S. M., Sheppard, A. R., Mahoney, M. D., & Adey, W. R. (1984). Influences of sinusoidal electric fields on excitability in the rat hippocampal slice. Brain Research Reviews, 323(2), 227–237.

    Article  CAS  Google Scholar 

  • Berzhanskaya, J., Chernyy, N., Gluckman, B. J., Schiff, S. J., & Ascoli, G. A. (2013). Modulation of hippocampal rhythms by subthreshold electric fields and network topology. Journal of Computational Neuroscience, 34, 369–389.

    Article  PubMed  Google Scholar 

  • Bikson, M., Inoue, M., Akiyama, H., Deans, J. K., Fox, J. E., Miyakawa, H., et al. (2004). Effects of uniform extracellular DC electric fields on excitability in rat hippocampal slices in vitro. The Journal of Physiology, 557(Pt 1), 175–190.

    Google Scholar 

  • Chan, C. Y., & Nicholson, C. (1986). Modulation by applied electric fields of Purkinje and stellate cell activity in the isolated turtle cerebellum. Journal of Physiology, 371, 89–114.

    CAS  PubMed Central  PubMed  Google Scholar 

  • Chan, C. Y., Houndsgaard, J., & Nicholson, C. (1988). Effects of electric fields on transmembrane potential and excitability of turtle cerebellar Purkinje cells in vitro. Journal of Physiology, 402, 751–771.

    Google Scholar 

  • Duong, D. H., & Chang, T. (1998). The influence of electric fields on the epileptiform bursts induced by high potassium in CA3 region of rat hippocampal slice. Neurological Research, 20(6), 542–548.

    CAS  PubMed  Google Scholar 

  • Durand, D. M. (2003). Electric field effects in hyperexcitable neural tissue: a review. Radiation Protection Dosimetry, 106(4), 325–331.

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout, B. (2002). Simulating, analyzing, and animating dynamical systems: a guide to Xppaut for researchers and students. Philadelphia: SIAM.

    Book  Google Scholar 

  • Francis, J. T., Gluckman, B. J., & Schiff, S. J. (2003). Sensitivity of neurons to weak electric fields. The Journal of Neuroscience, 23(19), 7255–7261.

    CAS  PubMed  Google Scholar 

  • Fröhlich, F., & McCormick, D. A. (2010). Endogenous electric fields may guide neocortical network activity. Neuron, 67(1), 129–143.

    Article  PubMed Central  PubMed  Google Scholar 

  • Gluckman, B. J., Neel, E. J., Netoff, T. I., Ditto, W. L., Spano, M. L., & Schiff, S. J. (1996). Electric field suppression of epileptiform activity in hippocampal slices. Journal of Neurophysiology, 76(6), 4202–4205.

    CAS  PubMed  Google Scholar 

  • Gluckman, B. J., Nguyen, H., Weinstein, S. L., & Schiff, S. J. (2001). Adaptive electric field control of epileptic seizures. The Journal of Neuroscience, 21(2), 590–600.

    CAS  PubMed  Google Scholar 

  • Izhikevich, E. M. (2005). Dynamical systems in neuroscience: The geometry of excitability and bursting. London: The MIT Press.

    Google Scholar 

  • Jefferys, J. G. R. (1981). Influence of electric fields on the excitability of granule cells in guinea-pig hippocampal slices. Journal of Physiology, 319, 143–152.

    CAS  PubMed Central  PubMed  Google Scholar 

  • Lopez, L., Chan, C. Y., Okada, Y. C., & Nicholson, C. (1991). Multimodal characterization of population responses evoked by applied electric field in vitro: extracellular potential, magnetic evoked field, transmembrane potential, and current source density analysis. Journal of Neuroscience, 11(7), 1998–2010.

    Google Scholar 

  • Mclntyre, C. C., & Grill, W. M. (1999). Excitation of central nervous system neurons by nonuniform electric fields. Biophysical Journal, 76(2), 878–888.

    Article  Google Scholar 

  • Nagarajan, S. S., Durand, D. M., & Warman, E. N. (1993). Effects of induced electric fields on finite neuronal structures: a simulation study. IEEE Transactions on Biomedical Engineering, 40(11), 1175–1188.

    Article  CAS  PubMed  Google Scholar 

  • Park, E. H., So, P., Barreto, E., Gluckman, B. J., & Schiff, S. J. (2003). Electric field modulation of synchronization in neuronal networks. Neurocomputing, 52–54, 169–175.

    Article  Google Scholar 

  • Park, E. H., Barreto, E., Gluckman, B. J., Schiff, S. J., & So, P. (2005). A model of the effects of applied electric fields on neuronal synchronization. Journal of Computational Neuroscience, 19(1), 53–70.

    Article  PubMed Central  PubMed  Google Scholar 

  • Pashut, T., Wolfus, S., Friedman, A., Lavidor, M., Bar-Gad, I., Yeshurun, Y., et al. (2011). Mechanisms of magnetic stimulation of central nervous system neurons. PLoS Computational Biology, 7(3), e1002022.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Peterchev, A. V., Rosa, M. A., Deng, Z., Prudic, J., & Lisanby, S. H. (2010). ECT stimulus parameters: rethinking dosage. The Journal of ECT, 26(3), 159–174.

    Article  PubMed Central  PubMed  Google Scholar 

  • Peterchev, A. V., Wagner, T. A., Miranda, P. C., Nitsche, M. A., Paulus, W., Lisanby, S. H., et al. (2012). Fundamentals of transcranial electric and magnetic stimulation dose: definition, selection, and reporting practices. Brain Stimulation, 5, 435–453.

    Article  PubMed Central  PubMed  Google Scholar 

  • Prescott, S. A., De Koninck, Y., & Sejnowski, T. J. (2008). Biophysical basis for three distinct dynamical mechanisms of action potential initiation. PLOS Computational Biology, 4(10), e1000198.

    Article  PubMed Central  PubMed  Google Scholar 

  • Purpura, D. P., & McMurtry, J. G. (1965). Intracellular activities and evoked potential changes during polarization of motor cortex. Journal of Neurophysiology, 28, 166–185.

    CAS  PubMed  Google Scholar 

  • Radman, T., Su, Y., Hi An, J., Parra, L. C., & Bikson, M. (2007). Spike timing amplifies the effect of electric fields on neurons: implications for endogenous field effects. The Journal of Neuroscience, 27(11), 3030–3036.

    Article  CAS  PubMed  Google Scholar 

  • Radman, T., Ramos, R. L., Brumberg, J. C., & Bikson, M. (2009). Role of cortical cell type and morphology in sub- and suprathreshold uniform electric field stimulation. Brain Stimulation, 2(4), 215–228.

    Article  PubMed Central  PubMed  Google Scholar 

  • Reato, D., Rahman, A., Bikson, M., & Parra, L. C. (2010). Low-intensity electrical stimulation affects network dynamics by modulating population rate and spike timing. The Journal of Neuroscience, 30(45), 15067–15079.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Schiff, S. J. (2012). Neural control engineering. Cambridge: MIT Press.

    Google Scholar 

  • Svirskis, G., Baginskas, A., Hounsgaard, J., & Gutman, A. (1997). Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation. Biophysical Journal, 73(6), 3004–3015.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Tranchina, D., & Nicholson, C. (1986). A model for the polarization of neurons by extrinsically applied electric fields. Biophysical Journal, 50(6), 1139–1156.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Wagner, T., Valero-Cabre, A., & Pascual-Leone, A. (2007). Noninvasive human brain stimulation. Annual Review of Biomedical Engineering, 9, 527–565.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grants 61372010, 61072012 and 61172009, the Young Scientists Fund of the National Natural Science Foundation of China under Grants 61104032 and 60901035, and Tianjin Municipal Natural Science Foundation under Grants 12JCZDJC21100 and 13JCZDJC27900.

Conflict of interest statement

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072, People’s Republic of China

    Guo-Sheng Yi, Jiang Wang, Xi-Le Wei & Bin Deng

  2. Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China

    Kai-Ming Tsang & Wai-Lok Chan

  3. School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin, 300222, People’s Republic of China

    Chun-Xiao Han

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  1. Guo-Sheng Yi
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  2. Jiang Wang
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  5. Wai-Lok Chan
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  6. Bin Deng
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  7. Chun-Xiao Han
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Correspondence to Xi-Le Wei.

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Action Editor: Gaute T. Einevoll

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Yi, GS., Wang, J., Wei, XL. et al. Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model. J Comput Neurosci 36, 383–399 (2014). https://doi.org/10.1007/s10827-013-0479-z

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  • DOI: https://doi.org/10.1007/s10827-013-0479-z

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