This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
R.F. Melendy, Resolving the biophysics of axon transmembrane polarization in a single closed-form description. Journal of Applied Physics, 118(24), (2015). https://doi.org/10.1063/1.4939278MelendyR.F.Resolving the biophysics of axon transmembrane polarization in a single closed-form description118242015https://doi.org/10.1063/1.493927810.1063/1.4939278Search in Google Scholar
R.F. Melendy, A subsequent closed-form description of propagated signaling phenomena in the membrane of an axon. AIP Advances, 6(5), (2016). https://doi.org/10.1063/1.4948985MelendyR.F.A subsequent closed-form description of propagated signaling phenomena in the membrane of an axon652016https://doi.org/10.1063/1.494898510.1063/1.4948985Search in Google Scholar
A.L. Hodgkin, Evidence for electrical transmission in nerve. Journal of Physiology, 90, 183-210 (1937). https://doi.org/10.1113/jphysiol.1937.sp003507HodgkinA.L.Evidence for electrical transmission in nerve901832101937https://doi.org/10.1113/jphysiol.1937.sp00350710.1113/jphysiol.1937.sp003507139506016994885Search in Google Scholar
J.B. Hursh, Conduction velocity and diameter of nerve fibers. American Journal of Physiology, 127, 131-139 (1939). https://doi.org/10.1152/ajplegacy.1939.127.1.131HurshJ.B.Conduction velocity and diameter of nerve fibers1271311391939https://doi.org/10.1152/ajplegacy.1939.127.1.13110.1152/ajplegacy.1939.127.1.131Search in Google Scholar
B. Frankenhaeuser, The ionic currents in the myelinated nerve fiber. Journal of General Physiology, 48, 79-81 (1965). https://doi.org/10.1085/jgp.48.5.79FrankenhaeuserB.The ionic currents in the myelinated nerve fiber4879811965https://doi.org/10.1085/jgp.48.5.7910.1085/jgp.48.5.79221377514326141Search in Google Scholar
B. Naundorf, F. Wolf, M. Volgushev, Unique features of action potential initiation in cortical neurons. Nature, 440, 1060-1063 (2006). https://doi.org/10.1038/nature04610NaundorfB.WolfF.VolgushevM.Unique features of action potential initiation in cortical neurons440106010632006https://doi.org/10.1038/nature0461010.1038/nature0461016625198Search in Google Scholar
K.S. Cole, H.J. Curtis, Electric impedance of the squid giant axon during activity. Journal of General Physiology, 22, 649-670 (1939). https://doi.org/10.1085/jgp.22.5.649ColeK.S.CurtisH.J.Electric impedance of the squid giant axon during activity226496701939https://doi.org/10.1085/jgp.22.5.64910.1085/jgp.22.5.649214200619873125Search in Google Scholar
D.E. Goldman, Potential, impedance, and rectification in membranes. Journal of General Physiology, 27, 37-60 (1943). https://doi.org/10.1085/jgp.27.1.37GoldmanD.E.Potential, impedance, and rectification in membranes2737601943https://doi.org/10.1085/jgp.27.1.3710.1085/jgp.27.1.37214258219873371Search in Google Scholar
A.L. Hodgkin, B. Katz, The effect of sodium ions on the electrical activity of the giant axon of the squid. Journal of Physiology, 108, 37-77 (1949). https://doi.org/10.1113/jphysiol.1949.sp004310HodgkinA.L.KatzB.The effect of sodium ions on the electrical activity of the giant axon of the squid10837771949https://doi.org/10.1113/jphysiol.1949.sp00431010.1113/jphysiol.1949.sp004310139233118128147Search in Google Scholar
J. Koester, S.A. Siegelbaum, in Principles of Neural Science, E.R. Kandel, J.H. Schwartz, T.M. Jessell, Eds. (McGraw-Hill, New York, 2000), pp. 140-149.KoesterJ.SiegelbaumS.A.KandelE.R.SchwartzJ.H.JessellT.M.McGraw-HillNew York2000140149Search in Google Scholar
A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500-544 (1952). https://doi.org/10.1113/jphysiol.1952.sp004764HodgkinA.L.HuxleyA.F.A quantitative description of membrane current and its application to conduction and excitation in nerve117500-5441952https://doi.org/10.1113/jphysiol.1952.sp00476410.1113/jphysiol.1952.sp004764139241312991237Search in Google Scholar
R.E. Taylor, in Physical Techniques in Biological Research, W.L. Natsiik, Ed. (Academic Press, New York, 1963), pp. 219-262.TaylorR.E.NatsiikW.L.Academic PressNew York1963219262Search in Google Scholar
R. Iansek, S.J. Redman, An analysis of the cable properties of spinal motoneurones using a brief intracellular current pulse. Journal of Physiology, 234, 613-636 (1973). https://doi.org/10.1113/jphysiol.1973.sp010364IansekR.RedmanS.J.An analysis of the cable properties of spinal motoneurones using a brief intracellular current pulse2346136361973https://doi.org/10.1113/jphysiol.1973.sp01036410.1113/jphysiol.1973.sp010364Search in Google Scholar
W. Rall, J. Segev, The Theoretical Foundation of Dendritic Function: Selected Papers of Wilfrid Rall with Commentaries (MIT Press, Boston, MA, 1995).RallW.SegevJ.MIT PressBoston, MA1995Search in Google Scholar
M. London, C. Meunier, I. Segev, Signal transfer in passive dendrites with nonuniform membrane conductance. Journal of Neuroscience, 19, 8219-8233 (1999). https://doi.org/10.1523/JNEUROSCI.19-19-08219.1999LondonM.MeunierC.SegevI.Signal transfer in passive dendrites with nonuniform membrane conductance19821982331999https://doi.org/10.1523/JNEUROSCI.19-19-08219.199910.1523/JNEUROSCI.19-19-08219.1999Search in Google Scholar
F. Nadim, J. Golowasch, Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter. Journal of Neurophysiology, 95, 3831-3843 (2006). https://doi.org/10.1152/jn.00033.2006NadimF.GolowaschJ.Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter95383138432006https://doi.org/10.1152/jn.00033.200610.1152/jn.00033.2006Search in Google Scholar
H.M. Lieberstein, On the Hodgkin-Huxley partial differential equation. Mathematical Biosciences, 1, 45-69 (1967). https://doi.org/10.1016/0025-5564(67)90026-0LiebersteinH.M.On the Hodgkin-Huxley partial differential equation145691967https://doi.org/10.1016/0025-5564(67)90026-010.1016/0025-5564(67)90026-0Search in Google Scholar
W. Rall, Core Conductor Theory and Cable Properties of Neurons: Handbook of Physiology, the Nervous System, Cellular Biology of Neurons (American Physiological Society, 1977), pp. 39-93.RallW.American Physiological Society1977399310.1002/cphy.cp010103Search in Google Scholar
R. West, E. Schutter, G. Wilcox, in The IMA Volumes in Mathematics and its Applications: Evolutionary Algorithms, L.D. Davis et al., Eds. (Springer, New York, 1999), pp. 33-64.WestR.SchutterE.WilcoxG.DavisL.D.SpringerNew York1999336410.1007/978-1-4612-1542-4_3Search in Google Scholar
C. Bédard, A. Destexhe, A modified cable formalism for modeling neuronal membranes at high frequencies. Biophysical Journal, 94, 1133-1143 (2008). https://doi.org/10.1529/biophysj.107.113571BédardC.DestexheA.A modified cable formalism for modeling neuronal membranes at high frequencies94113311432008https://doi.org/10.1529/biophysj.107.11357110.1529/biophysj.107.113571Search in Google Scholar
J.J.B. Jack, D. Noble, R.W. Tsien, Electric Current Flow in Excitable Cells (Clarendon Press, Oxford, 1975).JackJ.J.B.NobleD.TsienR.W.Clarendon Press, Oxford1975Search in Google Scholar
D. Sterratt, Principles of Computational Modelling in Neuroscience (Cambridge University Press, Cambridge, 2011). https://doi.org/10.1017/CBO9780511975899SterrattD.Cambridge University PressCambridge2011https://doi.org/10.1017/CBO978051197589910.1017/CBO9780511975899Search in Google Scholar
R. Hobbie, Intermediate Physics for Medicine and Biology (AIP Press, New York, 1997).HobbieR.AIP PressNew York1997Search in Google Scholar
R. Plonsey, R. Barr, Bioelectricity: A Quantitative Approach (Springer, Boston, 2000). https://doi.org/10.1007/978-1-4757-3152-1PlonseyR.BarrR.SpringerBoston2000https://doi.org/10.1007/978-1-4757-3152-110.1007/978-1-4757-3152-1Search in Google Scholar
N. Sperelakis, N. Sperelakis, Cell Physiology Sourcebook: Essentials of Membrane Biophysics (Academic Press, London, 2012).SperelakisN.SperelakisN.Academic PressLondon2012Search in Google Scholar
J. Malmivuo, R. Plonsey, Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields (Oxford University Press, New York, 2000).MalmivuoJ.PlonseyR.Oxford University PressNew York2000Search in Google Scholar
B. Roth, J. Wikswo, The magnetic field of a single axon: a comparison of theory and experiment. Biophysical Journal, 48, 93-109 (1985). https://doi.org/10.1016/S0006-3495(85)83763-2RothB.WikswoJ.The magnetic field of a single axon: a comparison of theory and experiment48931091985https://doi.org/10.1016/S0006-3495(85)83763-210.1016/S0006-3495(85)83763-2Search in Google Scholar
B. Roth, J. Wikswo, The electrical potential and the magnetic field of an axon in a nerve bundle. Mathematical Biosciences, 76, 37-57 (1985). https://doi.org/10.1016/0025-5564(85)90045-8RothB.WikswoJ.The electrical potential and the magnetic field of an axon in a nerve bundle7637571985https://doi.org/10.1016/0025-5564(85)90045-810.1016/0025-5564(85)90045-8Search in Google Scholar
R.S. Wijesinghe, Detection of magnetic fields created by biological tissues. Journal of Electrical and Electronic Systems, 3, 1-7 (2014). https://doi.org/10.4172/2332-0796.1000120WijesingheR.S.Detection of magnetic fields created by biological tissues3172014https://doi.org/10.4172/2332-0796.100012010.4172/2332-0796.1000120Search in Google Scholar
B. Greenebaum, F. Barnes, Bioengineering and Biophysical Aspects of Electromagnetic Fields (CRC/Taylor & Francis, Boca Raton, FL., 2007).GreenebaumB.CRC/Taylor & FrancisBoca Raton, FL2007Search in Google Scholar
B. Commoner, J. Townsend, G.E. Pake, Free radicals in biological materials. Nature, 174, 689-691 (1954). https://doi.org/10.1038/174689a0CommonerB.TownsendJ.PakeG.E.Free radicals in biological materials1746896911954https://doi.org/10.1038/174689a010.1038/174689a0Search in Google Scholar
V.N. Varfolomeev et al., Paramagnetic properties of hepatic tissues and transplantable hepatomas. Biofizika. 21, 881-886 (1976).VarfolomeevV.N.Paramagnetic properties of hepatic tissues and transplantable hepatomas218818861976Search in Google Scholar
R. Pethig, D.B. Kell, The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology. Physics in medicine and biology, 32, 933-970 (1987). https://doi.org/10.1088/0031-9155/32/8/001PethigR.KellD.B.The passive electrical properties of biological systems: their significance in physiology, biophysics and biotechnology329339701987https://doi.org/10.1088/0031-9155/32/8/00110.1088/0031-9155/32/8/001Search in Google Scholar
C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2008).KittelC.WileyNew York2008Search in Google Scholar
W.T. Coffey, Y.P. Kalmykov, J.T. Waldron, The Langevin Equation, with Applications in Physics, Chemistry, and Electrical Engineering (World Scientific, River Edge, NJ, 1996).CoffeyW.T.KalmykovY.P.WaldronJ.T.World ScientificRiver Edge, NJ199610.1142/2256Search in Google Scholar
J. Koester, S.A. Siegelbaum, in Principles of Neural Science, E.R. Kandel, J.H. Schwartz, T.M. Jessell, Eds. (McGraw-Hill, New York, 2000), pp. 150-169.KoesterJ.SiegelbaumS.A.KandelE.R.SchwartzJ.H.JessellT.M.McGraw-HillNew York2000150169Search in Google Scholar
A.F. Huxley, From overshoot to voltage clamp. Trends in Neurosciences, 25, 553-558 (2002). https://doi.org/10.1016/S0166-2236(02)02280-4HuxleyA.F.From overshoot to voltage clamp255535582002https://doi.org/10.1016/S0166-2236(02)02280-410.1016/S0166-2236(02)02280-4Search in Google Scholar
E.O. Hernández-Ochoa, M.F. Schneider, Voltage clamp methods for the study of membrane currents and SR Ca2+ release in adult skeletal muscle fibres. Progress in Biophysics and Molecular Biology, 108, 98-118 (2012). https://doi.org/10.1016/j.pbiomolbio.2012.01.001Hernández-OchoaE.O.SchneiderM.F.Voltage clamp methods for the study of membrane currents and SR Ca2+ release in adult skeletal muscle fibres108981182012https://doi.org/10.1016/j.pbiomolbio.2012.01.00110.1016/j.pbiomolbio.2012.01.001332111822306655Search in Google Scholar
S.G. Waxman, J.D. Kocsis, P.K. Stys, Eds., The Axon: Structure, Function and Pathophysiology (Oxford University Press, New York, 1995). https://doi.org/10.1093/acprof:oso/9780195082937.001.0001WaxmanS.G.KocsisJ.D.StysP.K.Oxford University PressNew York1995https://doi.org/10.1093/acprof:oso/9780195082937.001.000110.1093/acprof:oso/9780195082937.001.0001Search in Google Scholar
A.V. Holden, P.G. Haydon, W. Winlow, Multiple equilibria and exotic behavior in excitable membranes. Biological Cybernetics, 46, 167-172 (1983). https://doi.org/10.1007/BF00336798HoldenA.V.HaydonP.G.WinlowW.Multiple equilibria and exotic behavior in excitable membranes461671721983https://doi.org/10.1007/BF0033679810.1007/BF003367986850003Search in Google Scholar
R. Guttman, S. Lewis, J. Rinzel, Control of repetitive firing in squid axon membrane as a model for a nuroneoscillator. Journal of Physiology, 305, 377-395 (1980). https://doi.org/10.1113/jphysiol.1980.sp013370GuttmanR.LewisS.RinzelJ.Control of repetitive firing in squid axon membrane as a model for a nuroneoscillator3053773951980https://doi.org/10.1113/jphysiol.1980.sp01337010.1113/jphysiol.1980.sp01337012829797441560Search in Google Scholar
H.R. Leuchtag, Voltage-Sensitive Ion Channels: Biophysics of Molecular Excitability (Springer, New York, Philadelphia, 2008). https://doi.org/10.1007/978-1-4020-5525-6LeuchtagH.R.SpringerNew York, Philadelphia2008https://doi.org/10.1007/978-1-4020-5525-610.1007/978-1-4020-5525-6Search in Google Scholar
D.A. Hill, Electromagnetic Fields in Cavities: Deterministic and Statistical Theories (IEEE Press Series on Electromagnetic Wave Theory, NJ, 2009). https://doi.org/10.1002/9780470495056HillD.A.IEEE Press Series on Electromagnetic Wave TheoryNJ2009https://doi.org/10.1002/978047049505610.1002/9780470495056Search in Google Scholar
D.A. McQuarrie, Mathematical Methods for Scientists and Engineers (University Science Books, CA, 2003).McQuarrieD.A.University Science BooksCA2003Search in Google Scholar
R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1, 445-466 (1961). https://doi.org/10.1016/S0006-3495(61)86902-6FitzHughR.Impulses and physiological states in theoretical models of nerve membrane14454661961https://doi.org/10.1016/S0006-3495(61)86902-610.1016/S0006-3495(61)86902-6Search in Google Scholar
G. Zhao, Z. Hou, H. Xin, Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges. Chaos: An Interdisciplinary Journal of Nonlinear Science, 16, 043107 (2006). https://doi.org/10.1063/1.2360503ZhaoG.HouZ.XinH.Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges160431072006https://doi.org/10.1063/1.236050310.1063/1.2360503Search in Google Scholar
S.Y. Gordleeva, et al., Bi-directional astrocytic regulation of neuronal activity within a network. Frontiers in Computational Neuroscience, 6, 104-114 (2012). https://doi.org/10.3389/fncom.2012.00092GordleevaS.Y.Bi-directional astrocytic regulation of neuronal activity within a network61041142012https://doi.org/10.3389/fncom.2012.0009210.3389/fncom.2012.00092Search in Google Scholar
R.W. Aldrich, P.A. Getting, S.H. Thompson, Inactivation of delayed outward current in molluscan neurone somata. Journal of Physiology, 291, 507-530 (1979). https://doi.org/10.1113/jphysiol.1979.sp012828AldrichR.W.GettingP.A.ThompsonS.H.Inactivation of delayed outward current in molluscan neurone somata2915075301979https://doi.org/10.1113/jphysiol.1979.sp01282810.1113/jphysiol.1979.sp012828Search in Google Scholar
K. Aihara, G. Matsumoto, in Nerve Excitation and Chaos: Dynamical Systems and Nonlinear Oscillations, Gikō Ikegami, Ed. (World Scientific Publishing Co., 1986). Pp. 254-267.AiharaK.MatsumotoG.GikōIkegamiWorld Scientific Publishing Co1986254267Search in Google Scholar
J. Rinzel, G. Huguet, Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Direction. Communications on Pure and Applied Mathematics, 66(9), 1464-1494 (2013). https://doi.org/10.1002/cpa.21469RinzelJ.HuguetG.Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Direction669146414942013https://doi.org/10.1002/cpa.2146910.1002/cpa.21469Search in Google Scholar
Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35, 193-213 (1981). https://doi.org/10.1016/S0006-3495(81)84782-0MorrisHLecar, Voltage oscillations in the barnacle giant muscle fiber351932131981https://doi.org/10.1016/S0006-3495(81)84782-010.1016/S0006-3495(81)84782-0Search in Google Scholar
T. Sasaki, N. Matsuki, Y. Ikegaya, Action-potential modulation during axonal conduction. Science, 331, 599-601 (2011). https://doi.org/10.1126/science.1197598SasakiT.MatsukiN.IkegayaY.Action-potential modulation during axonal conduction3315996012011https://doi.org/10.1126/science.119759810.1126/science.1197598Search in Google Scholar
N.H. Sabah, K.N. Leibovic, The effect of membrane parameters on the properties of the nerve impulse. Biophysical Journal, 12, 1132-1144 (1972). https://doi.org/10.1016/S0006-3495(72)86150-2SabahN.H.LeibovicK.N.The effect of membrane parameters on the properties of the nerve impulse12113211441972https://doi.org/10.1016/S0006-3495(72)86150-210.1016/S0006-3495(72)86150-2Search in Google Scholar
N.F. Britton, Essential Mathematical Biology (Springer-Verlag, London, 2003). https://doi.org/10.1007/978-1-4471-0049-2BrittonN.F.Springer-VerlagLondon2003https://doi.org/10.1007/978-1-4471-0049-210.1007/978-1-4471-0049-2Search in Google Scholar
J.D. Murray, Mathematical Biology I: An Introduction (Springer-Verlag, Berlin, 2002).MurrayJ.D.Springer-VerlagBerlin200210.1007/b98868Search in Google Scholar
E.O. Voit, A First Course in Systems Biology (Garland Science, Taylor & Francis, New York, 2013).VoitE.O.Garland ScienceTaylor & Francis, New York201310.1201/9780429258510Search in Google Scholar
R.L. Armstrong, J.D. King, The Electromagnetic Interaction (Prentice Hall, Englewood Cliffs, NJ, 1973).ArmstrongR.L.KingJ.D.Prentice HallEnglewood Cliffs, NJ1973Search in Google Scholar
G.B. Arfken, H.J. Weber, F.E. Harris, Mathematical Methods for Physicist: A Comprehensive Guide (Elsevier, MA, 2013).ArfkenG.B.WeberH.J.HarrisF.E.ElsevierMA2013Search in Google Scholar
E. Weisstein, CRC Concise Encyclopedia of Mathematics (CRC Press, Boca Raton, 2003).WeissteinE.CRC PressBoca Raton200310.1201/9781420035223Search in Google Scholar
The electrical system of the body: The physics of the nervous system (Medical Physics, University of Notre Dame, n.d., http://www3.nd.edu/~nsl/Lectures/mphysics/).Medical Physics, University of Notre Dame, n.dhttp://www3.nd.edu/~nsl/Lectures/mphysics/)Search in Google Scholar
R.I. Macey, in Membrane Physiology, T.E. Andreoli, J.F. Hoffman, D.D. Fanestil, Eds. (Springer, New York, 1980), pp. 125-146. https://doi.org/10.1007/978-1-4757-1718-1_7MaceyR.I.AndreoliT.E.HoffmanJ.F.FanestilD.D.SpringerNew York1980125146https://doi.org/10.1007/978-1-4757-1718-1_710.1007/978-1-4757-1718-1_7Search in Google Scholar
T. Begenisic, Magnitude and location of surface charges on myxicola giant axons. The Journal of General Physiology, 66, 47-65 (1975). https://doi.org/10.1085/jgp.66.1.47BegenisicT.Magnitude and location of surface charges on myxicola giant axons6647651975https://doi.org/10.1085/jgp.66.1.4710.1085/jgp.66.1.4722261851159402Search in Google Scholar
J. Enderle, S. Blanchard, J. Bronzino, Introduction to Biomedical Engineering (Elsevier Academic Press, Amsterdam, Boston, London, New York, 2005).EnderleJ.BlanchardS.BronzinoJ.Elsevier Academic PressAmsterdam, Boston, London, New York2005Search in Google Scholar
P. Smejtek, in Permeability and Stability of Lipid Bilayers, E. Anibal Disalvo, S.A. Simon, Eds. (CRC Press, Boca Raton, Ann Arbor, London, 1994), pp. 197-236.SmejtekP.Anibal DisalvoE.SimonS.A.CRC PressBoca Raton, Ann Arbor, London1994197236Search in Google Scholar