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Cortical neuron activation induced by electromagnetic stimulation: a quantitative analysis via modelling and simulation

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Abstract

Previous simulation works concerned with the mechanism of non-invasive neuromodulation has isolated many of the factors that can influence stimulation potency, but an inclusive account of the interplay between these factors on realistic neurons is still lacking. To give a comprehensive investigation on the stimulation-evoked neuronal activation, we developed a simulation scheme which incorporates highly detailed physiological and morphological properties of pyramidal cells. The model was implemented on a multitude of neurons; their thresholds and corresponding activation points with respect to various field directions and pulse waveforms were recorded. The results showed that the simulated thresholds had a minor anisotropy and reached minimum when the field direction was parallel to the dendritic-somatic axis; the layer 5 pyramidal cells always had lower thresholds but substantial variances were also observed within layers; reducing pulse length could magnify the threshold values as well as the variance; tortuosity and arborization of axonal segments could obstruct action potential initiation. The dependence of the initiation sites on both the orientation and the duration of the stimulus implies that the cellular excitability might represent the result of the competition between various firing-capable axonal components, each with a unique susceptibility determined by the local geometry. Moreover, the measurements obtained in simulation intimately resemble recordings in physiological and clinical studies, which seems to suggest that, with minimum simplification of the neuron model, the cable theory-based simulation approach can have sufficient verisimilitude to give quantitatively accurate evaluation of cell activities in response to the externally applied field.

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References

  • Amassian, V.E., Cracco, R.Q., & Maccabee, P.J. (1989). Focal stimulation of human cerebral cortex with the magnetic coil: a comparison with electrical stimulation. Electroencephalography and Clinical Neurophysiology, 74 (6), 401–416.

    Article  CAS  PubMed  Google Scholar 

  • Andres, A.-T., & Andreas, N. (2013). Computationally efficient simulation of electrical activity at cell membranes interacting with self-generated and externally imposed electric fields. Journal of Neural Engineering, 10(2), 026019.

    Article  Google Scholar 

  • Anwar, H., Riachi, I., Hill, S., Schurmann, F., & Markram, H. (2009). An approach to capturing neuron morphological diversity. In De Schutter, E. (Ed.), Computational Modeling Methods for Neuroscientists. Cambridge: The MIT Press.

    Google Scholar 

  • Arlotti, M., Rahman, A., Minhas, P., & Bikson, M. (2012). Axon terminal polarization induced by weak uniform dc electric fields: a modeling study. Conference proceedings :... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2012, 4575–8.

    Google Scholar 

  • Ascoli, G.A., Donohue, D.E., & Halavi, M. (2007). Neuromorpho.org: a central resource for neuronal morphologies. The Journal of Neuroscience, 27(35), 9247–51.

    Article  CAS  PubMed  Google Scholar 

  • Balslev, D., Braet, W., McAllister, C., & Miall, R.C. (2007). Inter-individual variability in optimal current direction for transcranial magnetic stimulation of the motor cortex. Journal of Neuroscience Methods, 162 (1–2), 309–313.

    Article  PubMed  Google Scholar 

  • Barker, A.T., Jalinous, R., & Freeston, I.L. (1985). Non-invasive magnetic stimulation of human motor cortex. The Lancet, 325(8437), 1106–1107.

    Article  Google Scholar 

  • Berardelli, A., Inghilleri, M., Cruccu, G., & Manfredi, M. (1990). Descending volley after electrical and magnetic transcranial stimulation in man. Neuroscience Letters, 112(1), 54–8.

    Article  CAS  PubMed  Google Scholar 

  • Bestmann, S., Baudewig, J., Siebner, H.R., Rothwell, J.C., & Frahm, J. (2003). Subthreshold high-frequency tms of human primary motor cortex modulates interconnected frontal motor areas as detected by interleaved fmri-tms. NeuroImage, 20(3), 1685–96.

    Article  PubMed  Google Scholar 

  • Bikson, M., Inoue, M., Akiyama, H., Deans, J.K., Fox, J.E., Miyakawa, H., & Jefferys, J.G. (2004). Effects of uniform extracellular dc electric fields on excitability in rat hippocampal slices in vitro. Journal of Physiology, 557(Pt 1), 175– 90.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Chen, W., Zhang, J.J., Hu, G.Y., & Wu, C.P. (1996). Electrophysiological and morphological properties of pyramidal and nonpyramidal neurons in the cat motor cortex in vitro. Neuroscience, 73(1), 39–55.

    Article  CAS  PubMed  Google Scholar 

  • Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences, 43, 50–67.

    Article  Google Scholar 

  • Debanne, D., Campanac, E., Bialowas, A., Carlier, E., & Alcaraz, G. (2011). Axon physiology. Physiological Reviews, 91(2), 555– 602.

    Article  CAS  PubMed  Google Scholar 

  • Ding, L., Shou, G., Yuan, H., Urbano, D., & Cha, Y.H. (2014). Lasting modulation effects of rtms on neural activity and connectivity as revealed by resting-state eeg. IEEE Transactions on Biomedical Engineering, 61 (7), 2070–80.

    Article  PubMed  Google Scholar 

  • Esser, S.K., Hill, S.L., & Tononi, G. (2005). Modeling the effects of transcranial magnetic stimulation on cortical circuits. Journal of Neurophysiology, 94(1), 622–639.

    Article  CAS  PubMed  Google Scholar 

  • George, M.S., Padberg, F., Schlaepfer, T.E., O’Reardon, J.P., Fitzgerald, P.B., Nahas, Z.H., & Marcolin, M.A. (2009). Controversy: Repetitive transcranial magnetic stimulation or transcranial direct current stimulation shows efficacy in treating psychiatric diseases (depression, mania, schizophrenia, obsessive-complusive disorder, panic, posttraumatic stress disorder). Brain Stimulation, 2(1), 14–21.

    Article  PubMed  Google Scholar 

  • Grill, W.M., Cantrell, M.B., & Robertson, M.S. (2008). Antidromic propagation of action potentials in branched axons: implications for the mechanisms of action of deep brain stimulation. Journal of Computational Neuroscience, 24(1), 81–93.

    Article  PubMed  Google Scholar 

  • Hines, M., & Carnevale, N. (2001). Neuron: a tool for neuroscientists. Neuroscientist, 7, 123–135.

    Article  CAS  PubMed  Google Scholar 

  • Inghilleri, M., Berardelli, A., Cruccu, G., & Manfredi, M. (1993). Silent period evoked by transcranial stimulation of the human cortex and cervicomedullary junction. Journal of Physiology, 466, 521–534.

    PubMed Central  CAS  PubMed  Google Scholar 

  • Irnich, W. (1980). The chronaxie time and its practical importance. Pacing and Clinical Electrophysiology : PACE, 3(3), 292–301.

    Article  CAS  PubMed  Google Scholar 

  • Jalinous, R. (1991). Technical and practical aspects of magnetic nerve stimulation. Journal of Clinical Neurophysiology, 8(1), 10–25.

    Article  CAS  PubMed  Google Scholar 

  • Kamitani, Y., Bhalodia, V.M., Kubota, Y., & Shimojo, S. (2001). A model of magnetic stimulation of neocortical neurons. Neurocomputing, 38-40, 697–703.

    Article  Google Scholar 

  • Kammer, T., Beck, S., Thielscher, A., Laubis-Herrmann, U., & Topka, H. (2001). Motor thresholds in humans: a transcranial magnetic stimulation study comparing different pulse waveforms, current directions and stimulator types. Clinical Neurophysiology, 112(2), 250–8.

    Article  CAS  PubMed  Google Scholar 

  • Lazzaro, V.D., Ziemann, U., & Lemon, R.N. (2008). State of the art: Physiology of transcranial motor cortex stimulation. Brain Stimulation, 1(4), 345–362.

    Article  PubMed  Google Scholar 

  • Mainen, Z., & Sejnowski, T. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature, 382, 363–366.

    Article  CAS  PubMed  Google Scholar 

  • McNeal, D. (1976). Analysis of a model for excitation of myelinated nerve. IEEE Transactions on Biomedical Engineering, 23(4), 329–337.

    Article  CAS  PubMed  Google Scholar 

  • Merton, P.A., & Morton, H.B. (1980). Stimulation of the cerebral cortex in the intact human subject. Nature, 285(5762), 227–227.

    Article  CAS  PubMed  Google Scholar 

  • Molnár, Z., & Cheung, A.F.P. (2006). Towards the classification of subpopulations of layer v pyramidal projection neurons. Neuroscience Research, 55(2), 105–115.

    Article  PubMed  Google Scholar 

  • Moreines, J.L., McClintock, S.M., & Holtzheimer, P.E. (2011). Neuropsychologic effects of neuromodulation techniques for treatment-resistant depression: a review. Brain Stimulation, 4(1), 17–27.

    Article  PubMed Central  PubMed  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), 1175–88.

    Article  CAS  PubMed  Google Scholar 

  • Nakamura, H., Kitagawa, H., Kawaguchi, Y., & Tsuji, H. (1996). Direct and indirect activation of human corticospinal neurons by transcranial magnetic and electrical stimulation. Neuroscience Letters, 210(1), 45–48.

    Article  CAS  PubMed  Google Scholar 

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

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Pelletier, S.J., & Cicchetti, F. (2015). Cellular and molecular mechanisms of action of transcranial direct current stimulation: evidence from in vitro and in vivo models. The international journal of neuropsychopharmacology / official scientific journal of the Collegium Internationale Neuropsychopharmacologicum (CINP), 18(2).

  • Radman, T., Ramos, R.L., Brumberg, J.C., & Bikson, M. (2009). Role of cortical cell type and morphology in subthreshold and suprathreshold uniform electric field stimulation in vitro. Brain Stimulation, 2(4), 215–28, 228 e1–3.

    Article  PubMed Central  PubMed  Google Scholar 

  • Rahman, A., Reato, D., Arlotti, M., Gasca, F., Datta, A., Parra, L.C., & Bikson, M. (2013). Cellular effects of acute direct current stimulation: somatic and synaptic terminal effects. The Journal of physiology, 591(Pt 10), 2563–78.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Rattay, F. (1999). The basic mechanism for the electrical stimulation of the nervous system. Neuroscience, 89 (2), 335–46.

    Article  CAS  PubMed  Google Scholar 

  • Ridding, M.C., & Rothwell, J.C. (2007). Is there a future for therapeutic use of transcranial magnetic stimulation Nature Reviews Neuroscience, 8(7), 559–67.

    Article  CAS  PubMed  Google Scholar 

  • Roth, B.J., & Basser, P.J. (1990). A model of the stimulation of a nerve fiber by electromagnetic induction. IEEE Transactions on Biomedical Engineering, 37(6), 588–97.

    Article  CAS  PubMed  Google Scholar 

  • Rothwell, J.C. (1997). Techniques and mechanisms of action of transcranial stimulation of the human motor cortex. Journal of Neuroscience Methods, 74(2), 113–122.

    Article  CAS  PubMed  Google Scholar 

  • Rusu, C.V., Murakami, M., Ziemann, U., & Triesch, J. (2014). A model of tms-induced i-waves in motor cortex. Brain Stimulation, 7(3), 401–14.

    Article  PubMed  Google Scholar 

  • Salvador, R., Silva, S., Basser, P.J., & Miranda, P.C. (2011). Determining which mechanisms lead to activation in the motor cortex: a modeling study of transcranial magnetic stimulation using realistic stimulus waveforms and sulcal geometry. Clinical Neurophysiology, 122(4), 748–58.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Schulz, R., Gerloff, C., & Hummel, F.C. (2013). Non-invasive brain stimulation in neurological diseases. Neuropharmacology, 64, 579–87.

    Article  CAS  PubMed  Google Scholar 

  • Strafella, A.P., Paus, T., Barrett, J., & Dagher, A. (2001). Repetitive transcranial magnetic stimulation of the human prefrontal cortex induces dopamine release in the caudate nucleus. The Journal of Neuroscience, 21(15), RC157.

    CAS  PubMed  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), 3004–15.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Terao, Y., & Ugawa, Y. (2002). Basic mechanisms of tms. Journal of Clinical Neurophysiology, 19(4), 322–43.

    Article  PubMed  Google Scholar 

  • Thielscher, A., & Kammer, T. (2002). Linking physics with physiology in tms: a sphere field model to determine the cortical stimulation site in tms. NeuroImage, 17(3), 1117–30.

    Article  PubMed  Google Scholar 

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

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Wang, Y., Gupta, A., Toledo-Rodriguez, M., Wu, C., & Markram, H. (2002). Anatomical, physiological, molecular and circuit properties of nest basket cells in the developing somatosensory cortex. Cerebral Cortex, 12, 395–410.

    Article  PubMed  Google Scholar 

  • Werhahn, K.J., Fong, J.K.Y., Meyer, B.U., Priori, A., Rothwell, J.C., Day, B.L., & Thompson, P.D. (1994). The effect of magnetic coil orientation on the latency of surface emg and single motor unit responses in the first dorsal interosseous muscle. Electroencephalography and Clinical Neurophysiology, 93(2), 138–146.

    Article  CAS  PubMed  Google Scholar 

  • Yi, G.S., Wang, J., Wei, X.L., Tsang, K.M., Chan, W.L., Deng, B., & Han, C.X. (2014). Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model. Journal of Computational Neuroscience, 36(3), 383–99.

    Article  PubMed  Google Scholar 

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Acknowledgments

The authors would like to thank Mandy Hang, Ng Khoon Siong, Li Zhe, and Rohit Tyagi for revision of the manuscript. We also appreciate constructive technical discussion offered by the staff of Neuroengineering lab.

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  1. Jie Fan

    Present address: Newrocare Pte Ltd, 6 Eu Tong Sen Street, #12-03, SohoCentral Singapore, 059817, Singapore

Authors and Affiliations

  1. Neuroengineering Laboratory, National University of Singapore, Block EA #04-25, 9 Engineering Drive 1, Singapore, 117576, Singapore

    Tiecheng Wu, Jie Fan & Xiaoping Li

  2. Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore

    Kim Seng Lee

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Wu, T., Fan, J., Lee, K.S. et al. Cortical neuron activation induced by electromagnetic stimulation: a quantitative analysis via modelling and simulation. J Comput Neurosci 40, 51–64 (2016). https://doi.org/10.1007/s10827-015-0585-1

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