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Principles of Transcranial Direct Current Stimulation (tDCS): Introduction to the Biophysics of tDCS

  • Davide ReatoEmail author
  • Ricardo Salvador
  • Marom Bikson
  • Alexander Opitz
  • Jacek Dmochowski
  • Pedro C. Miranda
Chapter

Abstract

This chapter summarizes the current knowledge about the biophysics of transcranial direct current stimulation (tDCS). It begins by illustrating the basic physical principles by which weak electric currents applied transcranially induce an electric field inside the brain. This knowledge, mainly derived from computational models, is essential to estimating the intensity and distribution of the electric fields that neurons and non-neuronal elements experience during transcranial stimulation. This knowledge alone, however, is not sufficient to predict the effects of tDCS on brain function. The second part of the chapter provides a review of basic concepts, mainly derived from animal models, to explain how electrical stimulation may affect neurons. At the single neuron level, membrane polarization, firing rate and timing changes are described. The effects of weak electric currents on single neuron function are then extended to neuronal populations and modulation of synapses, both during and after the application of the stimulation. Finally, recent results describing how these changes may ultimately affect behavior are reviewed.

Keywords

tDCS Polarization Animal models Firing rate Spike timing Oscillations Network effects Plasticity Neuron models 

References

  1. Akhtari, M., Bryant, H. C., Mamelak, A. N., Flynn, E. R., Heller, L., Shih, J. J., … Sutherling, W. W. (2002). Conductivities of three-layer live human skull. Brain Topography, 14(3), 151–167.PubMedCrossRefGoogle Scholar
  2. Alagapan, S., Schmidt, S. L., Lefebvre, J., Hadar, E., Shin, H. W., & Frhlich, F. (2016). Modulation of cortical oscillations by low-frequency direct cortical stimulation is state-dependent. PLoS Biology, 14(3), e1002424.PubMedPubMedCentralCrossRefGoogle Scholar
  3. Ali, M. M., Sellers, K. K., & Frohlich, F. (2013). Transcranial alternating current stimulation modulates large-scale cortical network activity by network resonance. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 33(27), 11262–11275.CrossRefGoogle Scholar
  4. Araque, A., Parpura, V., Sanzgiri, R. P., & Haydon, P. G. (1999). Tripartite synapses: Glia, the unacknowledged partner. Trends in Neurosciences, 22(5), 208–215.PubMedCrossRefGoogle Scholar
  5. Atallah, B. V., & Scanziani, M. (2009). Instantaneous modulation of gamma oscillation frequency by balancing excitation with inhibition. Neuron, 62(4), 566–577.PubMedPubMedCentralCrossRefGoogle Scholar
  6. Barker, A. T., & Jalinous, R. (1985). Non-invasive magnetic stimulation of human motor cortex. Lancet, 1(8437), 1106–1107.PubMedPubMedCentralCrossRefGoogle Scholar
  7. Basser, P. J., Mattiello, J., & Lebihan, D. (1994). MR diffusion tensor spectroscopy and imaging. Biophysical Journal, 66(1), 259–267.PubMedPubMedCentralCrossRefGoogle Scholar
  8. Basser, P. J., & Roth, B. J. (2000). New currents in electrical stimulation of excitable tissues. Annual Review of Biomedical Engineering, 2, 377–397.PubMedCrossRefGoogle Scholar
  9. Baumann, S. B., Wozny, D. R., Kelly, S. K., & Meno, F. M. (1997). The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Transactions on Bio-medical Engineering, 44(3), 220–223.PubMedCrossRefGoogle Scholar
  10. Berenyi, A., Belluscio, M., Mao, D., & Buzsaki, G. (2012). Closed-loop control of epilepsy by transcranial electrical stimulation. Science, 337(6095), 735–737.PubMedPubMedCentralCrossRefGoogle Scholar
  11. 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(3), 369–389.PubMedCrossRefGoogle Scholar
  12. Bestmann, S., de Berker, A. O., & Bonaiuto, J. (2015). Understanding the behavioural consequences of noninvasive brain stimulation. Trends in Cognitive Sciences, 19(1), 13–20.PubMedCrossRefGoogle Scholar
  13. 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. The Journal of Physiology, 557. (Pt 1, 175–190.PubMedPubMedCentralCrossRefGoogle Scholar
  14. Bikson, M., Reato, D., & Rahman, A. (2012). Cellular and network effects of transcranial direct current stimulation. In P. M. Rossini (Ed.), Transcranial brain stimulation. CRC Press (pp. 55–91).CrossRefGoogle Scholar
  15. Bindman, L. J., Lippold, O. C., & Redfearn, J. W. (1964). The action of brief polarizing currents on the cerebral cortex of the rat (1) during current flow and (2) in the production of long-lasting after-effects. The Journal of Physiology, 172, 369–382.PubMedPubMedCentralCrossRefGoogle Scholar
  16. Bonaiuto, J. J., & Bestmann, S. (2015). Understanding the nonlinear physiological and behavioral effects of tDCS through computational neurostimulation. Progress in Brain Research, 222, 75–103.PubMedCrossRefGoogle Scholar
  17. Brette, R., & Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology, 94(5), 3637–3642.PubMedCrossRefGoogle Scholar
  18. Cambiaghi, M., Teneud, L., Velikova, S., Gonzalez-Rosa, J. J., Cursi, M., Comi, G., & Leocani, L. (2011). Flash visual evoked potentials in mice can be modulated by transcranial direct current stimulation. Neuroscience, 185, 161–165.PubMedCrossRefGoogle Scholar
  19. Cambiaghi, M., Velikova, S., Gonzalez-Rosa, J. J., Cursi, M., Comi, G., & Leocani, L. (2010). Brain transcranial direct current stimulation modulates motor excitability in mice. The European Journal of Neuroscience, 31(4), 704–709.PubMedCrossRefGoogle Scholar
  20. Carandini, M., & Ferster, D. (2000). Membrane potential and firing rate in cat primary visual cortex. The Journal of neuroscience : the official journal of the Society for Neuroscience, 20(1), 470–484.CrossRefGoogle Scholar
  21. Chan, C. Y., Hounsgaard, J., & Nicholson, C. (1988). Effects of electric fields on transmembrane potential and excitability of turtle cerebellar Purkinje cells in vitro. The Journal of Physiology, 402, 751–771.PubMedPubMedCentralCrossRefGoogle Scholar
  22. Chan, C. Y., & Nicholson, C. (1986). Modulation by applied electric fields of Purkinje and stellate cell activity in the isolated turtle cerebellum. The Journal of Physiology, 371, 89–114.PubMedPubMedCentralCrossRefGoogle Scholar
  23. Cooper, L. N., & Bear, M. F. (2012). The BCM theory of synapse modification at 30: Interaction of theory with experiment. Nature Reviews Neuroscience, 13(11), 798–810.PubMedCrossRefGoogle Scholar
  24. Creutzfeldt, O. D., Fromm, G. H., & Kapp, H. (1962). Influence of transcortical d-c currents on cortical neuronal activity. Experimental Neurology, 5, 436–452.PubMedCrossRefGoogle Scholar
  25. Datta, A., Bansal, V., Diaz, J., Patel, J., Reato, D., & Bikson, M. (2009). Gyri-precise head model of transcranial direct current stimulation: Improved spatial focality using a ring electrode versus conventional rectangular pad. Brain Stimulation, 2(4), 201–207.PubMedPubMedCentralCrossRefGoogle Scholar
  26. Datta, A., Elwassif, M., Battaglia, F., & Bikson, M. (2008). Transcranial current stimulation focality using disc and ring electrode configurations: FEM analysis. Journal of Neural Engineering, 5(2), 163–174.CrossRefGoogle Scholar
  27. Deans, J. K., Powell, A. D., & Jefferys, J. G. (2007). Sensitivity of coherent oscillations in rat hippocampus to AC electric fields. The Journal of Physiology, 583(Pt 2), 555–565.PubMedPubMedCentralCrossRefGoogle Scholar
  28. Destexhe, A., Rudolph, M., & Pare, D. (2003). The high-conductance state of neocortical neurons in vivo. Nature Reviews Neuroscience, 4(9), 739–751.PubMedCrossRefGoogle Scholar
  29. Di Castro, M. A., Chuquet, J., Liaudet, N., Bhaukaurally, K., Santello, M., Bouvier, D., … Volterra, A. (2011). Local Ca2+ detection and modulation of synaptic release by astrocytes. Nature Neuroscience, 14(10), 1276–1284.PubMedCrossRefGoogle Scholar
  30. Di Lazzaro, V., Oliviero, A., Profice, P., Saturno, E., Pilato, F., Insola, A., … Rothwell, J. C. (1998). Comparison of descending volleys evoked by transcranial magnetic and electric stimulation in conscious humans. Electromyography and Motor Control-Electroencephalography and Clinical Neurophysiology, 109(5), 397–401.CrossRefGoogle Scholar
  31. Dmochowski, J. P., Fau, B. M., Parra, L. C., & Parra, L. C. (2012). The point spread function of the human head and its implications for transcranial current stimulation. (1361-6560 (electronic)). D – NLM: NIHMS409753. Physics in Medicine and Biology, 57(20), 6459.PubMedPubMedCentralCrossRefGoogle Scholar
  32. Eaton, H. (1992). Electric field induced in a spherical volume conductor from arbitrary coils: Application to magnetic stimulation and MEG. Medical & Biological Engineering & Computing, 30(4), 433–440.CrossRefGoogle Scholar
  33. Francis, J. T., Gluckman, B. J., & Schiff, S. J. (2003). Sensitivity of neurons to weak electric fields. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 23(19), 7255–7261.CrossRefGoogle Scholar
  34. Fregni, F., Gimenes, R., Valle, A. C., Ferreira, M. J. L., Rocha, R. R., Natalle, L., … Boggio, P. S. (2006). A randomized, sham-controlled, proof of principle study of transcranial direct current stimulation for the treatment of pain in fibromyalgia. Arthritis and Rheumatism, 54(12), 3988–3998.PubMedPubMedCentralCrossRefGoogle Scholar
  35. Fritsch, B., Reis, J., Martinowich, K., Schambra, H. M., Ji, Y., Cohen, L. G., & Lu, B. (2010). Direct current stimulation promotes BDNF-dependent synaptic plasticity: Potential implications for motor learning. Neuron, 66(2), 198–204.PubMedPubMedCentralCrossRefGoogle Scholar
  36. Fritsch, G., & Hitzig, E. (1870). Über die elektrische Erregbarkeit des Grosshirns. Archives Anatomy Physiololy Wissen, 37, 300–332.Google Scholar
  37. Frohlich, F., & Mccormick, D. A. (2010). Endogenous electric fields may guide neocortical network activity. Neuron, 67(1), 129–143.PubMedPubMedCentralCrossRefGoogle Scholar
  38. Gabriel, C., Gabriel, S., & Corthout, E. (1996a). The dielectric properties of biological tissues: I. Literature survey. Physics in Medicine and Biology, 41(11), 2231–2249.CrossRefGoogle Scholar
  39. Gabriel, S., Lau, R. W., & Gabriel, C. (1996b). The dielectric properties of biological tissues. 2. Measurements in the frequency range 10 Hz to 20 GHz. Physics in Medicine and Biology, 41(11), 2251–2269.PubMedCrossRefGoogle Scholar
  40. Galea, J. M., Jayaram, G., Ajagbe, L., & Celnik, P. (2009). Modulation of cerebellar excitability by polarity-specific noninvasive direct current stimulation. The Journal of Neuroscience, 29(28), 9115–9122.PubMedPubMedCentralCrossRefGoogle Scholar
  41. Gardner-Medwin, A. R., & Nicholson, C. (1983). Changes of extracellular potassium activity induced by electric current through brain tissue in the rat. The Journal of Physiology, 335, 375–392.PubMedPubMedCentralCrossRefGoogle Scholar
  42. Gartside, I. B. (1968). Mechanisms of sustained increases of firing rate of neurons in the rat cerebral cortex after polarization: Reverberating circuits or modification of synaptic conductance? Nature, 220(5165), 382–383.PubMedCrossRefGoogle Scholar
  43. Geddes, L. A., & Baker, L. E. (1967). The specific resistance of biological material--a compendium of data for the biomedical engineer and physiologist. Medical & Biological Engineering, 5(3), 271–293.CrossRefGoogle Scholar
  44. 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.PubMedCrossRefGoogle Scholar
  45. Gomez-Gonzalo, M., Losi, G., Chiavegato, A., Zonta, M., Cammarota, M., Brondi, M., … Carmignoto, G. (2010). An excitatory loop with astrocytes contributes to drive neurons to seizure threshold. PLoS Biology, 8(4), e1000352.PubMedPubMedCentralCrossRefGoogle Scholar
  46. Grimaldi, G., Argyropoulos, G. P., Bastian, A., Cortes, M., Davis, N. J., Edwards, D. J., … Celnik, P. (2016). Cerebellar Transcranial direct current stimulation (ctDCS): A novel approach to understanding cerebellar function in health and disease. The Neuroscientist, 22(1), 83–97.PubMedPubMedCentralCrossRefGoogle Scholar
  47. Hallett, M. (2007). Transcranial magnetic stimulation: a primer. Neuron, 55(2), 187–199.PubMedCrossRefGoogle Scholar
  48. Hammerer, D., Bonaiuto, J., Klein-Flugge, M., Bikson, M., & Bestmann, S. (2016). Selective alteration of human value decisions with medial frontal tDCS is predicted by changes in attractor dynamics. Scientific Reports, 6, 25160.PubMedPubMedCentralCrossRefGoogle Scholar
  49. Hause, L. (1975). A mathematical model for transmembrane potentials secondary to extracellular fields. In Electroanaesthesia: Biomedical and biophysical studies (pp. 176–200). New York: Academic.Google Scholar
  50. Haydon, P. G., & Carmignoto, G. (2006). Astrocyte control of synaptic transmission and neurovascular coupling. Physiological Reviews, 86(3), 1009–1031.PubMedCrossRefGoogle Scholar
  51. Herrmann, C. S., Rach, S., Neuling, T., & Struber, D. (2013). Transcranial alternating current stimulation: A review of the underlying mechanisms and modulation of cognitive processes. Frontiers in Human Neuroscience, 7, 279.PubMedPubMedCentralCrossRefGoogle Scholar
  52. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500–544.PubMedPubMedCentralCrossRefGoogle Scholar
  53. Huisman, T. A. (2010). Diffusion-weighted and diffusion tensor imaging of the brain, made easy. Cancer Imag, 10 Spec no A, S163–S171.CrossRefGoogle Scholar
  54. Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks/a Publication of the IEEE Neural Networks Council, 14(6), 1569–1572.CrossRefGoogle Scholar
  55. Izhikevich, E. M. (2007). Dynamical systems in neuroscience. MIT Press.Google Scholar
  56. Jackson, M. P., Rahman, A., Lafon, B., Kronberg, G., Ling, D., Parra, L. C., & Bikson, M. (2016). Animal models of transcranial direct current stimulation: Methods and mechanisms. Clinical Neurophysiology, 127(11), 3425–3454.PubMedPubMedCentralCrossRefGoogle Scholar
  57. Jayaram, G., Tang, B., Pallegadda, R., Vasudevan, E. V. L., Celnik, P., & Bastian, A. (2012). Modulating locomotor adaptation with cerebellar stimulation. Journal of Neurophysiology, 107(11), 2950–2957.PubMedPubMedCentralCrossRefGoogle Scholar
  58. Jefferys, J. G. (1981). Influence of electric fields on the excitability of granule cells in Guinea-pig hippocampal slices. The Journal of Physiology, 319, 143–152.PubMedPubMedCentralCrossRefGoogle Scholar
  59. Joucla, S., & Yvert, B. (2009). The “mirror” estimate: An intuitive predictor of membrane polarization during extracellular stimulation. Biophysical Journal, 96(9), 3495–3508.PubMedPubMedCentralCrossRefGoogle Scholar
  60. Kabakov, A. Y., Muller, P. A., Pascual-Leone, A., Jensen, F. E., & Rotenberg, A. (2012). Contribution of axonal orientation to pathway-dependent modulation of excitatory transmission by direct current stimulation in isolated rat hippocampus. Journal of Neurophysiology, 107(7), 1881–1889.PubMedPubMedCentralCrossRefGoogle Scholar
  61. Kanai, R., Chaieb, L., Antal, A., Walsh, V., & Paulus, W. (2008). Frequency-dependent electrical stimulation of the visual cortex. Current Biology, 18(23), 1839–1843.PubMedCrossRefGoogle Scholar
  62. Koessler, L., Colnat-Coulbois, S., Cecchin, T., Hofmanis, J., Dmochowski, J. P., Norcia, A. M., & Maillard, L. G. (2016). In-vivo measurements of human brain tissue conductivity using focal electrical current injection through intracerebral multicontact electrodes. LID. (1097-0193 (Electronic)). Human Brain Mapping, 38, 974–986.PubMedCrossRefGoogle Scholar
  63. Krause, B., Marquez-Ruiz, J., & Cohen Kadosh, R. (2013). The effect of transcranial direct current stimulation: A role for cortical excitation/inhibition balance? Frontiers in Human Neuroscience, 7, 602.PubMedPubMedCentralCrossRefGoogle Scholar
  64. Kronberg, G., Bridi, M., Abel, T., Bikson, M., & Parra, L. C. (2016). Direct current stimulation modulates LTP and LTD: Activity dependence and dendritic effects. Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation.Google Scholar
  65. Laakso, I., Tanaka, S., Koyama, S., De Santis, V., & Hirata, A. (2015). Inter-subject variability in electric fields of motor cortical tDCS. Brain Stimulation, 8(5), 8.CrossRefGoogle Scholar
  66. Lafon, B., Rahman, A., Bikson, M., & Parra, L. C. (2016). Direct current stimulation alters neuronal input/output function. Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation, 10, 36–45.PubMedCrossRefGoogle Scholar
  67. Liebetanz, D., Fregni, F., Monte-Silva, K. K., Oliveira, M. B., Amancio-Dos-Santos, A., Nitsche, M. A., & Guedes, R. C. (2006a). After-effects of transcranial direct current stimulation (tDCS) on cortical spreading depression. Neuroscience Letters, 398(1–2), 85–90.PubMedCrossRefGoogle Scholar
  68. Liebetanz, D., Klinker, F., Hering, D., Koch, R., Nitsche, M. A., Potschka, H., … Tergau, F. (2006b). Anticonvulsant effects of transcranial direct-current stimulation (tDCS) in the rat cortical ramp model of focal epilepsy. Epilepsia, 47(7), 1216–1224.PubMedCrossRefGoogle Scholar
  69. Logothetis, N. K., Kayser, C., & Oeltermann, A. (2007). In vivo measurement of cortical impedance spectrum in monkeys: Implications for signal propagation. Neuron, 55(5), 809–823.PubMedCrossRefGoogle Scholar
  70. Marquez-Ruiz, J., Leal-Campanario, R., Sanchez-Campusano, R., Molaee-Ardekani, B., Wendling, F., Miranda, P. C., … Delgado-Garcia, J. M. (2012). Transcranial direct-current stimulation modulates synaptic mechanisms involved in associative learning in behaving rabbits. Proceedings of the National Academy of Sciences of the United States of America, 109(17), 6710–6715.PubMedPubMedCentralCrossRefGoogle Scholar
  71. Márquez-Ruiz, J., Leal-Campanario, R., Wendling, F., Ruffini, G., Gruart, A., & Delgado-García, J. M. (2014). Transcranial electrical stimulation in animals. In R. Cohen Kadosh (Ed.), The stimulated brain (pp. 117–144). Academic.Google Scholar
  72. Mcintyre, C. C., & Grill, W. M. (1999). Excitation of central nervous system neurons by nonuniform electric fields. Biophysical Journal, 76(2), 878–888.PubMedPubMedCentralCrossRefGoogle Scholar
  73. Minhas, P., Bansal, V., Patel, J., Ho, J. S., Diaz, J., Datta, A., & Bikson, M. (2010). Electrodes for high-definition transcutaneous DC stimulation for applications in drug delivery and electrotherapy, including tDCS. Journal of Neuroscience Methods, 190(2), 188–197.PubMedPubMedCentralCrossRefGoogle Scholar
  74. Miranda, P. C., Correia, L., Salvador, R., & Basser, P. J. (2007). The role of tissue heterogeneity in neural stimulation by applied electric fields. Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Annual Conference, 2007, 1715–1718.Google Scholar
  75. Miranda, P. C., Faria, P., & Hallett, M. (2009). What does the ratio of injected current to electrode area tell us about current density in the brain during tDCS? Clinical Neurophysiology, 120(6), 1183–1187.PubMedPubMedCentralCrossRefGoogle Scholar
  76. Miranda, P. C., Hallett, M., & Basser, P. J. (2003). The electric field induced in the brain by magnetic stimulation: A 3-D finite-element analysis of the effect of tissue heterogeneity and anisotropy. IEEE Transactions on Bio-medical Engineering, 50(9), 1074–1085.PubMedCrossRefGoogle Scholar
  77. Miranda, P. C., Lomarev, M., & Hallett, M. (2006). Modeling the current distribution during transcranial direct current stimulation. Clinical Neurophysiology, 117(7), 1623–1629.CrossRefGoogle Scholar
  78. Miranda, P. C., Mekonnen, A., Salvador, R., & Ruffini, G. (2013). The electric field in the cortex during transcranial current stimulation. NeuroImage, 70, 48–58.CrossRefGoogle Scholar
  79. Moliadze, V., Antal, A., & Paulus, W. (2010). Electrode-distance dependent after-effects of transcranial direct and random noise stimulation with extracephalic reference electrodes. Clinical Neurophysiology, 121(12), 2165–2171.CrossRefGoogle Scholar
  80. Monai, H., Ohkura, M., Tanaka, M., Oe, Y., Konno, A., Hirai, H., … Hirase, H. (2016). Calcium imaging reveals glial involvement in transcranial direct current stimulation-induced plasticity in mouse brain. Nature Communications, 7, 11100.PubMedPubMedCentralCrossRefGoogle Scholar
  81. Nitsche, M. A., Boggio, P. S., Fregni, F., & Pascual-Leone, A. (2009). Treatment of depression with transcranial direct current stimulation (tDCS): A review. Experimental Neurology, 219(1), 14–19.PubMedPubMedCentralCrossRefGoogle Scholar
  82. Nitsche, M. A., Cohen, L. G., Wassermann, E. M., Priori, A., Lang, N., Antal, A., … Pascual-Leone, A. (2008). Transcranial direct current stimulation: State of the art 2008. Brain Stimulation, 1(3), 206–223.PubMedPubMedCentralCrossRefGoogle Scholar
  83. Nitsche, M. A., & Paulus, W. (2000). Excitability changes induced in the human motor cortex by weak transcranial direct current stimulation. The Journal of Physiology, 527(Pt 3), 633–639.PubMedPubMedCentralCrossRefGoogle Scholar
  84. Nitsche, M. A., & Paulus, W. (2001). Sustained excitability elevations induced by transcranial DC motor cortex stimulation in humans. (0028–3878 (Print)). Neurology, 57, 1899.PubMedPubMedCentralCrossRefGoogle Scholar
  85. Nitsche, M. A., & Paulus, W. (2009). Noninvasive brain stimulation protocols in the treatment of epilepsy: Current state and perspectives. Neurotherapeutics: The Journal of the American Society for Experimental NeuroTherapeutics, 6(2), 244–250.CrossRefGoogle Scholar
  86. Oostendorp, T. F., Delbeke, J., & Stegeman, D. F. (2000). The conductivity of the human skull: Results of in vivo and in vitro measurements. IEEE Transactions on Bio-medical Engineering, 47(11), 1487–1492.PubMedCrossRefGoogle Scholar
  87. Opitz, A., Falchier, A., Yan, C. G., Yeagle, E. M., Linn, G. S., Megevand, P., … Schroeder, C. E. (2016). Spatiotemporal structure of intracranial electric fields induced by transcranial electric stimulation in humans and nonhuman primates. (2045-2322 (electronic)). Scientific Reports, 6, 31236. PST – epublish.Google Scholar
  88. Opitz, A., Paulus, W., Will, S., Antunes, A., & Thielscher, A. (2015). Determinants of the electric field during transcranial direct current stimulation. (1095–9572 (Electronic)). Neuroimage, 109, 140.PubMedCrossRefGoogle Scholar
  89. Opitz, A., Windhoff, M., Heidemann, R. M., Turner, R., & Thielscher, A. (2011). How the brain tissue shapes the electric field induced by transcranial magnetic stimulation. NeuroImage, 58(3), 849–859.PubMedCrossRefGoogle Scholar
  90. Ozen, S., Sirota, A., Belluscio, M. A., Anastassiou, C. A., Stark, E., Koch, C., & Buzsaki, G. (2010). Transcranial electric stimulation entrains cortical neuronal populations in rats. The Journal of neuroscience : the official journal of the Society for Neuroscience, 30(34), 11476–11485.CrossRefGoogle Scholar
  91. Panatier, A., Vallee, J., Haber, M., Murai, K. K., Lacaille, J. C., & Robitaille, R. (2011). Astrocytes are endogenous regulators of basal transmission at central synapses. Cell, 146(5), 785–798.PubMedCrossRefGoogle Scholar
  92. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  93. Parra, L. C., & Bikson, M. (2004). Model of the effect of extracellular fields on spike time coherence. Conference Proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Annual Conference, 6, 4584–4587.Google Scholar
  94. Paulus, W., & Rothwell, J. C. (2016). Membrane resistance and shunting inhibition: Where biophysics meets state-dependent human neurophysiology. The Journal of Physiology, 594, 2719–2728. PubMedPubMedCentralCrossRefGoogle Scholar
  95. 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, 18(2).PubMedCrossRefGoogle Scholar
  96. Peterchev, A. V., Jalinous, R., & Lisanby, S. H. (2008). A transcranial magnetic stimulator inducing near-rectangular pulses with controllable pulse width (cTMS). IEEE Transactions on Bio-medical Engineering, 55(1), 257–266.PubMedPubMedCentralCrossRefGoogle Scholar
  97. Peterchev, A. V., Wagner, T. A., Miranda, P. C., Nitsche, M. A., Paulus, W., Lisanby, S. H., … Bikson, M. (2012). Fundamentals of transcranial electric and magnetic stimulation dose: Definition, selection, and reporting practices. Brain Stimulation, 5(4), 435–453.CrossRefGoogle Scholar
  98. Pethig, R., & Kell, D. B. (1987). The passive electrical properties of biological systems: Their significance in physiology, biophysics and biotechnology. Physics in Medicine and Biology, 32(8), 933–970.PubMedCrossRefGoogle Scholar
  99. Plonsey, R., & Barr, R. C. (1998). Electric field stimulation of excitable tissue. IEEE Engineering in Medicine and Biology Magazine: The Quarterly Magazine of the Engineering in Medicine & Biology Society, 17(5), 130–137.CrossRefGoogle Scholar
  100. Plonsey, R., & Heppner, D. B. (1967). Considerations of quasi-Stationarity in electrophysiological systems. B Math Biophys, 29(4), 657–664.CrossRefGoogle Scholar
  101. Podda, M. V., Cocco, S., Mastrodonato, A., Fusco, S., Leone, L., Barbati, S. A., … Grassi, C. (2016). Anodal transcranial direct current stimulation boosts synaptic plasticity and memory in mice via epigenetic regulation of Bdnf expression. Scientific Reports, 6, 22180.PubMedPubMedCentralCrossRefGoogle Scholar
  102. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  103. Priori, A., Berardelli, A., Rona, S., Accornero, N., & Manfredi, M. (1998). Polarization of the human motor cortex through the scalp. Neuroreport, 9(10), 2257–2260.PubMedPubMedCentralCrossRefGoogle Scholar
  104. Purpura, D. P., & Mcmurtry, J. G. (1965). Intracellular activities and evoked potential changes during polarization of motor cortex. Journal of Neurophysiology, 28, 166–185.PubMedCrossRefGoogle Scholar
  105. 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), 215–228.PubMedPubMedCentralCrossRefGoogle Scholar
  106. Radman, T., Su, Y., An, J. H., 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 : the official journal of the Society for Neuroscience, 27(11), 3030–3036.CrossRefGoogle Scholar
  107. Rahman, A., Lafon, B., & Bikson, M. (2015). Multilevel computational models for predicting the cellular effects of noninvasive brain stimulation. Progress in Brain Research, 222, 25–40.PubMedCrossRefGoogle Scholar
  108. Rahman, A., Lafon, B., Parra, L. C., & Bikson, M. (2017). Direct current stimulation boosts synaptic gain and cooperativity in vitro. The Journal of Physiology, 595, 3535–3547. PubMedPubMedCentralCrossRefGoogle Scholar
  109. 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(10), 2563–2578.PubMedPubMedCentralCrossRefGoogle Scholar
  110. Rahman, A., Lafon, B., Parra, L. C., & Bikson, M. (2017). Direct current stimulation boosts synaptic gain and cooperativity in vitro. The Journal of Physiology, 595, 3535–3547. PubMedPubMedCentralCrossRefGoogle Scholar
  111. Rampersad, S., Fau, S. D., Oostendorp, T., & Oostendorp, T. (2011). On handling the layered structure of the skull in transcranial direct current stimulation models. (1557-170X (Print)). Conference Proceedings IEEE Engineering in Medicine and Biology Society, 2011, 1989.Google Scholar
  112. Ranck, J. B., Jr. (1975). Which elements are excited in electrical stimulation of mammalian central nervous system: A review. Brain Research, 98(3), 417–440.PubMedCrossRefGoogle Scholar
  113. Ranieri, F., Podda, M. V., Riccardi, E., Frisullo, G., Dileone, M., Profice, P., … Grassi, C. (2012). Modulation of LTP at rat hippocampal CA3-CA1 synapses by direct current stimulation. Journal of Neurophysiology, 107(7), 1868–1880.PubMedCrossRefGoogle Scholar
  114. Reato, D., Bikson, M., & Parra, L. C. (2015). Lasting modulation of in vitro oscillatory activity with weak direct current stimulation. Journal of Neurophysiology, 113(5), 1334–1341.PubMedCrossRefGoogle Scholar
  115. Reato, D., Cammarota, M., Parra, L. C., & Carmignoto, G. (2012). Computational model of neuron-astrocyte interactions during focal seizure generation. Frontiers in Computational Neuroscience, 6, 81.PubMedPubMedCentralCrossRefGoogle Scholar
  116. Reato, D., Gasca, F., Datta, A., Bikson, M., Marshall, L., & Parra, L. C. (2013a). Transcranial electrical stimulation accelerates human sleep homeostasis. PLoS Computational Biology, 9(2), e1002898.PubMedPubMedCentralCrossRefGoogle Scholar
  117. 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 : the official journal of the Society for Neuroscience, 30(45), 15067–15079.CrossRefGoogle Scholar
  118. Reato, D., Rahman, A., Bikson, M., & Parra, L. C. (2013b). Effects of weak transcranial alternating current stimulation on brain activity-a review of known mechanisms from animal studies. Frontiers in Human Neuroscience, 7, 687.PubMedPubMedCentralCrossRefGoogle Scholar
  119. Renart, A., de la Rocha, J., Bartho, P., Hollender, L., Parga, N., Reyes, A., & Harris, K. D. (2010). The asynchronous state in cortical circuits. Science, 327(5965), 587–590.PubMedPubMedCentralCrossRefGoogle Scholar
  120. Rohan, J. G., Carhuatanta, K. A., Mcinturf, S. M., Miklasevich, M. K., & Jankord, R. (2015). Modulating hippocampal plasticity with in vivo brain stimulation. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 35(37), 12824–12832.CrossRefGoogle Scholar
  121. Roth, B. J., Cohen, L. G., & Hallett, M. (1991). The electric field induced during magnetic stimulation. Electroencephalography and Clinical Neurophysiology, 43, 268–278.Google Scholar
  122. Ruffini, G., Fox, M. D., Ripolles, O., Miranda, P. C., & Pascual-Leone, A. (2014). Optimization of multifocal transcranial current stimulation for weighted cortical pattern targeting from realistic modeling of electric fields. NeuroImage, 89, 216–225.CrossRefGoogle Scholar
  123. Ruffini, G., Wendling, F., Merlet, I., Molaee-Ardekani, B., Mekkonen, A., Salvador, R., … Miranda, P. (2013). Transcranial current brain stimulation (tCS):Models and technologies. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 21(3), 333–345.PubMedCrossRefGoogle Scholar
  124. Rush, S., & Driscoll, D. A. (1968). Current distribution in the brain from surface electrodes. Anesthesia and Analgesia, 47(6), 717-723.CrossRefGoogle Scholar
  125. Rush, S., & Driscoll, D. A. (1969). Eeg electrode sensitivity – an application of reciprocity. IEEE Transactions on Bio-medical Engineering, 16(1), 15.PubMedCrossRefGoogle Scholar
  126. Sadleir, R. J., Vannorsdall, T. D., Schretlen, D. J., & Gordon, B. (2010). Transcranial direct current stimulation (tDCS) in a realistic head model. NeuroImage, 51(4), 1310–1318.CrossRefGoogle Scholar
  127. Salvador, R., Ramirez, F., V’Yacheslavovna, M., & Miranda, P. C. (2012). Effects of tissue dielectric properties on the electric field induced in tDCS: A sensitivity analysis. 34th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), San Diego, 787–790.Google Scholar
  128. Salvador, R., Wenger, C., & Miranda, P. C. (2015). Investigating the cortical regions involved in MEP modulation in tDCS. Frontiers in Cellular Neuroscience, 9.Google Scholar
  129. Saturnino, G. B., Antunes, A., & Thielscher, A. (2015). On the importance of electrode parameters for shaping electric field patterns generated by tDCS. (1095–9572 (Electronic)). Neuroimage, 120, 25.PubMedCrossRefGoogle Scholar
  130. Schlaug, G., Renga, V., & Nair, D. (2008). Transcranial direct current stimulation in stroke recovery. Archives of Neurology, 65(12), 1571–1576.PubMedPubMedCentralCrossRefGoogle Scholar
  131. Schwan, H. P. (1966). Alternating current electrode polarization. Biophysik, 3(2), 181–201.PubMedCrossRefGoogle Scholar
  132. Sehm, B., Hoff, M., Gundlach, C., Taubert, M., Conde, V., Villringer, A., & Ragert, P. (2013). A novel ring electrode setup for the recording of somatosensory evoked potentials during transcranial direct current stimulation (tDCS). Journal of Neuroscience Methods, 212(2), 234–236.PubMedCrossRefGoogle Scholar
  133. Stagg, C. J., & Nitsche, M. A. (2011). Physiological basis of transcranial direct current stimulation. The Neuroscientist: A Review Journal Bringing Neurobiology, Neurology and Psychiatry, 17(1), 37–53.CrossRefGoogle Scholar
  134. 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.PubMedPubMedCentralCrossRefGoogle Scholar
  135. Terney, D., Chaieb, L., Moliadze, V., Antal, A., & Paulus, W. (2008). Increasing human brain excitability by transcranial high-frequency random noise stimulation. The Journal of Neuroscience, 28(52), 14147–14155.PubMedCrossRefGoogle Scholar
  136. Terzuolo, C. A., & Bullock, T. H. (1956). Measurement of imposed voltage gradient adequate to modulate neuronal firing. Proceedings of the National Academy of Sciences of the United States of America, 42(9), 687–694.PubMedPubMedCentralCrossRefGoogle Scholar
  137. Tofts, P. S. (1990). The distribution of induced currents in magnetic stimulation of the nervous-system. Physics in Medicine and Biology, 35(8), 1119–1128.CrossRefGoogle Scholar
  138. Tranchina, D., & Nicholson, C. (1986). A model for the polarization of neurons by extrinsically applied electric fields. Biophysical Journal, 50(6), 1139–1156.PubMedPubMedCentralCrossRefGoogle Scholar
  139. Tuch, D. S., Wedeen, V. J., Dale, A. M., George, J. S., & Belliveau, J. W. (2001). Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proceedings of the National Academy of Sciences of the United States of America, 98(20), 11697–11701.PubMedPubMedCentralCrossRefGoogle Scholar
  140. Vogels, T. P., Rajan, K., & Abbott, L. F. (2005). Neural network dynamics. Annual Review of Neuroscience, 28, 357–376.PubMedCrossRefGoogle Scholar
  141. Wagner, S., Fau, R. S., Aydin, U., Fau, A. U., Vorwerk, J., Fau, V. J., … Wolters, C. H. (2014a). Investigation of tDCS volume conduction effects in a highly realistic head model. (1741–2552 (Electronic)). Journal of Neural Engineering, 11, 016002.PubMedCrossRefGoogle Scholar
  142. Wagner, T., Eden, U., Rushmore, J., Russo, C. J., Dipietro, L., Fregni, F., … Valero-Cabre, A. (2014b). Impact of brain tissue filtering on neurostimulation fields: A modeling study. NeuroImage, 85(Pt 3), 1048–1057.CrossRefGoogle Scholar
  143. Woods, A. J., Antal, A., Bikson, M., Boggio, P. S., Brunoni, A. R., Celnik, P., … Nitsche, M. A. (2016). A technical guide to tDCS, and related non-invasive brain stimulation tools. Clinical Neurophysiology: Official Journal of the International Federation of Clinical Neurophysiology, 127(2), 1031–1048.CrossRefGoogle Scholar
  144. Xu, W., Wolff, B. S., & Wu, J. Y. (2014). Low-intensity electric fields induce two distinct response components in neocortical neuronal populations. Journal of Neurophysiology, 112(10), 2446–2456.PubMedPubMedCentralCrossRefGoogle Scholar
  145. 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), 383–399.PubMedCrossRefGoogle Scholar
  146. Zaehle, T., Rach, S., & Herrmann, C. S. (2010). Transcranial alternating current stimulation enhances individual alpha activity in human EEG. PLoS One, 5(11), e13766.PubMedPubMedCentralCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Davide Reato
    • 1
    Email author
  • Ricardo Salvador
    • 2
  • Marom Bikson
    • 3
  • Alexander Opitz
    • 4
  • Jacek Dmochowski
    • 5
  • Pedro C. Miranda
    • 6
  1. 1.Champalimaud Centre for the Unknown, Neuroscience ProgrammeLisbonPortugal
  2. 2.NeuroelectricsBarcelonaSpain
  3. 3.Department of Biomedical EngineeringThe City College of New YorkNew YorkUSA
  4. 4.Department of Biomedical EngineeringUniversity of MinnesotaMinneapolisUSA
  5. 5.Neural Engineering Laboratory, Department of Biomedical Engineering, Grove School of EngineeringThe City College of the City University of New YorkNew YorkUSA
  6. 6.Instituto de Biofísica e Engenharia Biomédica, Faculdade de Ciências, Universidade de LisboaLisbonPortugal

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