Mathematical Phenomenology of Neural Stimulation by Periodic Fields

Abden, M.A. & Stuchly, M.A. (1994). Modeling of magnetic field stimulation of bent neurons. IEEE Transactions on biomedical Engineering, 41, 1092–1095.

Apollonio, F., D'Inzeo, G. & Tarricone, L. (1998). Modeling of neuronal cells exposed to RF fields from mobile telecommunication equipment. Bioelectrochemistry and Bioenergetics, 47, 199–205.

Balduzzo, M., Minelli, T.A. & Turicchia, L. (1999). Signal analysis and simulation of the EEG activity. Chaos Theory and Applications, 4, 7–14.

Barnes, F.S. (1992). Some engineering models for interactions of electric and magnetic fields with biological systems. Bioelectromagnetics Supplement, 1, 67–85.

Bendat, J.J. & Piersol, A.G. (1986). Random data. New York: Wiley.

Besthorn, C., Förstl, H., Geiger-Kabisch, C., Sattel, H., Gasser, T. & Schreiter-Grasser, U. (1994). EEG Coherence in Alzheimer disease. Electroencephalography and Clinical Neurophysiology, 90, 242–24

Boccaletti, S., Grebogi, C., Lai, Y.-C. Mancini, H. & Maza, D. (2000). The control of chaos. Physics Reports, 329, 103–197.

Burke, D., Kiernan, M.C. & Bostock, H. (2001). Excitability of human axons. Clinical Neurophysiology, 112, 1575–1585.

Clark, J.W. (1991). Neural network modeling. Physics in Medicine and Biology, 36, 1259–1317.

Connors, B.W. & Amitai, Y. (1997). Making waves in the neocortex. Neuron, 18, 347–349.

Cook, M.R., Graham, C., Cohen, H.D. & Gerkovich, M.M. (1992). A replication study of human exposure to 60 Hz fields: Effects of neurobehavioral measures, Bioelectromagnetics, 13, 261–285.

Cracco, R.Q., Cracco, G.B., Maccabee, P.J., & Amassian, V.E. (1999). Cerebral function revealed by transcranial magnetic stimulation. Journal of Neuroscience Methods, 86, 209–219.

Deutsch, S. & Deutsch, A. (1993). Understanding the nervous system. New York: IEEE.

Draguhn, A., Traub, R.D., Schmitz, D. & Jefferys, J.G.R. (1998). Electrical coupling underlies high-frequency in the hippocampus in vitro. Nature, 394, 189–192.

Engelhardt, H., Gaub, H. & Sackman, E. (1984). Viscoelastic properties of erythrocyte membranes in hig-frequency electric field. Nature, 307, 378–380.

Ferro Milone, F., Minelli, T.A. & Turicchia, L. (1998). Neuron synchronization and human EEG phenomenology simulation. Nonlinear Dynamics, Psychology, and Life Sciences, 2, 21–33.

FitzHug, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysics Journal, 1, 445–466.

Glass, A., Zappulla, R.A., Nieves, J. & Diamond, S.P. (1992). EEG Coherence as a predictor of spike propagation. Electroencephalography and Clinical Neurophysiology, 82, 10–16.

Goodman, R., Basset, C.A.L. & Henderson, A.S. (1983). Pulsing Electromagnetic Fields Induces Cellular Transcription. Science, 220, 1283–1285.

Graham, C., Cook, M.R., Cohen, H.D. & Gerkovich, M.M. (1994). Dose response study of human exposure to 60 Hz magnetic and electric fields, Bioelectromagnetics, 15, 447–463.

Grill, W.M. (1999). Modeling the effects of electric fields on nerve fibers. IEEE Transactions on biomedical Engineering, 46, 918–928.

Hodgkin, A. & Huxley, A. (1939). Action potentials recorded from inside a nerve fiber. Nature 144, 710–711.

Hodgkin, A. & Huxley, A. (1952). Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Journal of Physiology 116, 449–472.

Hopfield, J.J. (1994). Neurons, dynamics and computation. Physics Today, 47, 40–46.

Izhikevich, E.M. (1999). Weakly connected quasi-periodic oscillators, FM interactions, and multiplexing in the brain. SIAM Journal of Applied Mathematics, 59, 2193–2223.

Jing, H. & Takigawa, K. (2000). Observation of EEG coherence after repetitive transcranial magnetic stimulation. Clinical Neurophysiology, 111, 1620–1631.

Kantz, H., & Schreiber, T. (1995). Dimension estimates and physiological data. Chaos, 5, 143–154.

Kantz, H. and Schreiber, T. Nonlinear time series analysis. (1997) Cambridge, MA: Cambridge University Press.

Kaplan, D. & Glass, L. (1995). Understanding the nonlinear dynamics. New York: Springer-Verlag.

King, R.W.P. (1999). Nerves in a human body exposed to low frequency electromagnetic field. IEEE Transactions on biomedical Engineering, 46, 1426–1431.

Kuramoto, Y., (1991). Collective Synchronization of Pulse Coupled Oscillators. Physica, D50, 15–30.

Lebedeva, N.N., Sulimov, A.V., Sulimova, O.P., Kotrovskaya, T.I. & Gailus, T. (2000). Cellular phone electromagnetic field effects on bio-electric activity of human brain. Critical Reviews in Biomedical Engineering, 28, 323–337.

Lopes da Silva, F.H. (1991). Neural mechanisms underlying brain waves: From neural membranes to networks. Electroencephalography and Clinical Neurophysiology 79, 81–93.

Lopes da Silva, F.H. & Pfurtscheller, G. (1999). Basic concepts on EEG synchronization and desynchronozation. In G. Pfurtscheller & F.H. Lopes da Silva (Eds.), Handbook of elecroencephalography and clinical neurophysiology VI (pp. 3–11). Amsterdam: Elsevier.

Mann, K. and Roschke, J. (1996). Effects of pulsed High-frequency electromagnetic field on human sleep. Neuropsychobiology, 33, 41–47.

Miltner, W.H.R., Braun, C., Witte, H. & Taub, E. (1999). Coherence of the gamma band activity as a basis for associative learning. Nature, 397, 434–436.

Minelli, T.A. & Turicchia, L. (1999). Progressive coherence patterns for EEG phenomenology, Nonlinear Dynamics, Psychology, and Life Sciences, 3, 129–142.

Mirollo, R.E., & S.H. Strogaz, S.H. (1990). Synchronization of pulse coupled oscillators, SIAM Journal of Applied Mathematics, 50, 1645–1662.

Munk, M.H.J., Roelfsema, P.R., Koenig, P., Engel, A.K. & Singer, W. (1996). Role of reticular activation in the modulation of intracortical synchronization. Science, 272, 271–274.

Murray, J.D. (1993). Mathematical biology. Berlin: Springer-Verlag.

Myers, J.M. (1999). Modelling the effect of an external electric field on the velocity of spike propagation in a nerve fiber. Physics Review E, 60, 5918–5925.

Nagarajan, S.S. (1996). A generalized cable equation for magnetic stimulation of axons. IEEE Transactions on Biomedical Engineering, 43, 304–312.

Nagumo, J. Aximoto, S. and Yoshizawa, S. (1962). An active pulse transmission simulating nerve axon. Proc. IRE 50, 2061–2071.

Nayfeh, A.H. & Balachandran, B. (1995). Applied nonlinear dynamics. NewYork: Wiley.

Nunez, P.L. (1995). Neocortical dynamics and human EEG rhythms. New York: Oxford University Press.

Oberfeld, G. (Ed.) (2000). Proceedings of the International Conference on Cell Tower Siting–Salzburg June 7–8 2000. Printing Office Federal State of Salzburg.

Pascual-Leone, A., Valls-Sole, J., Wassermann, E.M., Brasil Neto, J. P. & Hallett, M. (1994). Response to rapid rate transcranial magnetic stimulation of the human motor cortex. Brain, 117, 847–858.

Persinger, M.A., Richards, P.M., Koren, S.A. (1997). Differential entrainment of electroencephalographic activity by weak complex electromagnetic fields. Perception and Motor Skills 84, 527–536.

Preece, A.W., Wesnes, K.A. & Iwi, G.R. (1998). The effect of a 50 Hz magnetic field on cognitive functions in humans. International Journal of Radiation Biology, 74, 463–47.

Pyragas, K. (1998). Properties of generalized synchronization of chaos. Nonlinear Analysis: Modelling and Control, 3, 1–29.

Rattay, F. (1998). Analysis of the electrical excitation of CNS neurons. IEEE Transactions on Biomedical Engineering, 45, 766–772.

Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J. Renault, B. & Varela, F.J. (1999). Perception shadow: long-distance synchronization of human brain activity. Nature, 397, 430–433.

Ruohonen, J., Ravazzani, P. & Grandori, F. (1998). Functional magnetic stimulation: theory and coil optimization. Bioelectrochemistry and Bioenergetics, 47, 213–219.

Sabah, N.H. (2000). Aspects of nerve conduction. IEEE Engineering in Medicine and Biology. November/December, 19(6), 111–118.

Sannita, W.G. (2000). Stimulus-specific oscillatory responses of the brain. Clinical Neurophysiology, 111, 565–583.

Scott, A. & Luzader, S.D. (1979). Coupled solitary waves in neurophysics. Physica Scripta, 20, 395–401.

Schnabel, V. & Struijk, J.J. (2001), Calculation of electric field in a multiple cylindrical volume conductor induced by magnetic coils. IEEE Transactions on Biomedical Engineering, 48, 78–86.

Sebastian, J.L., Munoz, S., Rancho, M., & Miranda, J.M. (2001). Analysis of the influence of the cell geometry, orientation and cell proximity effects on the electric field distribution from direct RF exposure. Physics in Medicine and Biology, 46, 213–225.

Schurmann, K., Nikouline, V.V., Soljanlahti, S., Ollikainen, M., Basar, E., Ilmoniemi, R.J.(2001). EEG responses to combined somatosensory and transcranial magnetic stimulation. Clinical Neurophysiology, 112, 19–24.

Siebner, H.R., Willoch, F., Peller, M., Auer, C., Boecker, H., Conrad, B., and Bartenstein, P. (1998). Imaging brain activation induced by long trains of repetitive transcranial magnetic stimulation. NeuroReport, 9, 943–948.

Singer, W. (1994): The role of synchrony in neocortical networks, In E. Domany, J.L. van Hemmen and K. Shulten (Eds.). Models of neural networks II. (pp. 141–173). New York: Springer-Verlag.

Stuchly, M. & Dawson, T.W. (2000). Interaction of low-frequenchy electric and magnetic field with human body. IEEE Proceedings, 88, 643–664.

Suihko, V. (1998). Modeling direct activation of corticospinal axon using transcranial electrical stimulation. Electroencephalography and Clinical Neuriphysiology, 109, 238–244.

Thatcher, R.W., Krause, P.J. & Hrybyk, M. (1986). Cortico-cortical associations and EEG coherence: a two-compartimental model. Electroencephalography and Clinical Neurophysiology, 64, 123–143.

Traub, R.D., Jefferys, J.G.R. & Whittington, M.A. (1997). Simulation of gamma rhythms in networks of interneurons and pyramidal cells. Journal of Computational Neuroscience, 4, 141–150.

Trimmel, M., Schweiger, E. (1998). Effects of an ELF (50 Hz, 1 mT) electromagnetic field (EMF) on concentration in visual attention, perception and memory including effects on EMF sensitivity. Toxicology Letters, 96, 97, 377–382.

von Krosigk, M., Bald, T., & McCormick, D.A. (1993). Cellular mechanisms of synchronized oscillations in the thalamus. Science, 261, 361–364.

Walsh, V. & Rushwort, M. (1999). A primer of magnetic stimulation as a tool for neurophysiology. Neuropsychologia, 37, 125–135.

Warman, E.N., Grill, W.M. & Durand, D.(1992). Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds. IEEE Transactions on Biomedical Engineering, 39, 1244–1254.

Whitle, P.(1998). Neural nets and chaotic carriers. New York: Wiley.

Zierhofer, C.M. (2001). Analysis of a linear model for electrical stimulation of axons. IEEE Transactions on Biomedical Engineering, 48, 173–184.