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Modeling Neuronal Dynamics: From Electrophysiology to Burst Oscillations

This work discusses various models of neuronal dynamics including the electrodiffusion and ionic pumps based on circuit theory, as well as classical models like the van der Pol and FitzHugh-Nagumo oscillators. Key contributions from Kandel, Hodgkin, Huxley, and others are reviewed to illustrate the transition from analog to computational neuron models. The research underscores the significance of these models in understanding excitability, spiking, and bursting behaviors in neurons, bridging foundational neuroscience with circuit theory.

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Modeling Neuronal Dynamics: From Electrophysiology to Burst Oscillations

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  1. Neuron Circuits & Communication Bo Deng University of Nebraska-Lincoln Sept. 2004

  2. Rinzel & Wang (1997)

  3. Gated Currents by Electrodiffission Ionic Pumps by Chemical Energy

  4. Circuit Model • Kandel, E.R., J.H. Schwartz, and T.M. Jessell • Principles of Neural Science, 3rd ed., Elsevier, 1991. • Zigmond, M.J., F.E. Bloom, S.C. Landis, J.L. Roberts, and L.R. Squire • Fundamental Neuroscience, Academic Press, 1999.

  5. Alan Lloyd Hodgkin Andrew Fielding Huxley Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(1952), pp.500--544.

  6. Kirchhoff Laws - I (t)

  7. -I (t)

  8. Mahowald, M. and Douglas, R. A silicon neuron. Nature, 354(1991), pp.515-518.

  9. Equivalent Circuit Electrophysiological Model Chua, L.O., Introduction to Nonlinear Circuit Theory, McGraw-Hill, New York, 1969.

  10. Balthazar van der Pol (1889-1959) van der Pol Oscillator (R = 0) and FitzHugh-Nagumo Oscillator van der Pol (1928), FitzHugh(1961), Nagumo(1964) Keener(1982)

  11. V IL I

  12. Deng(1991) (Non-circuit) Models for Square Burster and Other Bursters • Morris, C. and H. Lecar, • Voltage oscillations in the barnacle giant muscle fiber, • Biophysical J., 35(1981), pp.193--213. • Hindmarsh, J.L. and R.M. Rose, • A model of neuronal bursting using three coupled first order differential • equations, • Proc. R. Soc. Lond. B. 221(1984), pp.87--102. • Chay, T.R., Y.S. Fan, and Y.S. Lee • Bursting, spiking, chaos, fractals, and universality in biological • rhythms, Int. J. Bif. & Chaos, 5(1995), pp.595--635. • Izhikevich, E.M • Neural excitability, spiking, and bursting, • Int. J. Bif. & Chaos, 10(2000), pp.1171--1266. • (also see his article in SIAM Review)

  13. Disclaimer: With the exception of the square burster and SEED simulation, all artworks are found from the internet.

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