A synaptic input portal for a mapped clock oscillator model of neuronal electrical rhythmic activity

Journal of Neural Engineering

Volumn 1, Issue 3, 2004, Pages 158-164

  Zariffa, José ^a   Ebden, Mark ^a   Bardakjian, Berj L ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CELL CULTURE; ENZYME INHIBITION; FUNCTIONS; MATHEMATICAL MODELS; TOPOLOGY;

MAPPED CLOCK OSCILLATOR (MCO) MODEL; POWER FUNCTION; SYNAPTIC PORTAL; TRANSMEMBRANE VOLTAGE OSCILLATIONS;

OSCILLATORS (ELECTRONIC);

ARTICLE; ELECTRIC ACTIVITY; MATHEMATICAL MODEL; NERVE CELL; NERVE POTENTIAL; OSCILLATION; POSTSYNAPTIC POTENTIAL; PRESYNAPTIC NERVE; PRIORITY JOURNAL; SYNAPSE; ANIMAL; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPARATIVE STUDY; COMPUTER SIMULATION; EVALUATION; FEEDBACK SYSTEM; HIPPOCAMPUS; NERVE CELL INHIBITION; NERVE CELL NETWORK; PERIODICITY; PHYSIOLOGY; RAT; SYNAPTIC TRANSMISSION; VALIDATION STUDY;

ANIMALS; BIOLOGICAL CLOCKS; COMPUTER SIMULATION; FEEDBACK; HIPPOCAMPUS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL INHIBITION; NEURONS; PERIODICITY; RATS; SYNAPTIC TRANSMISSION;

EID: 19044364442     PISSN: 17412560     EISSN: None     Source Type: Journal    
DOI: 10.1088/1741-2560/1/3/005     Document Type: Article

References (28)

1. Liaw J and Berger T W 1999 Dynamic synapse: harnessing the computing power of synaptic dynamics Neurocomputing 26-27 199-206
2. Ermentrout B 2003 Dynamical consequences of fast-rising, slow-decaying synapses in neuronal networks Neural Comput. 15 2483-522
3. White J A, Chow C C, Ritt J, Soto-Trevino C and Kopell N 1998 Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons J. Comput. Neurosci. 5 5-16
4. Traub R D, Whittington M A, Colling S B, Buzsáki G and Jefferys J G R 1996 Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo J. Physiol. 493 471-84
5. Plant R E and Kim M 1976 Mathematical description of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations Biophys. J. 16 227-44
6. Lee Y S, Chay T R and Ree T 1983 On the mechanism of spiking and bursting in excitable cells Biophys. Chem. 18 25-34
7. Chay T R 1990 Bursting excitable cell models by a slow calcium current J. Theor. Biol. 142 305-15
8. Ermentrout G B and Kopell N 1998 Fine structure of neural spiking and synchronization in the presence of conduction delays Proc. Natl Acad. Sci. USA 95 1259-64
9. Ermentrout B, Pascal M and Gutkin B 2001 The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators Neural Comput. 13 1285-310
10. Kopell N and Ermentrout G B 1986 Subcellular oscillations and bursting Math. Biosci. 78 265-91
11. Bardakjian B L, Sarna S K and Diamant N E 1990 Composite synthesized relaxation oscillators: application to modeling of colonic electrical control and response activity J. Gastrointest. Motil. 2 109-16
12. Ermentrout G B and Kopell N 1991 Multiple pulse interactions and averaging in systems of coupled neural oscillators J. Math. Biol. 29 195-217
13. Chiu A W L and Bardakjian B L 2004 Stochastic and coherence resonance in an in-silico neural model Ann. Biomed. Eng. 32 732-43
14. Winfree A T 2001 The Geometry of Biological Time 2nd edn (New York: Springer)
15. Bardakjian B L and Diamant N E 1994 A mapped clock oscillator model for transmembrane electrical activity in excitable cells J. Theor. Biol. 166 225-35
16. Bardakjian B L and Sarna S K 1980 A computer model of human colonic electrical control activity (ECA) IEEE Trans. Biomed. Eng. 27 193-202
17. Bardakjian B L, El-Sharkawy T Y and Diamant N E 1983 On a population of labile synthesized relaxation oscillators IEEE Trans. Biomed. Eng. 30 696-701
18. Bardakjian B L, Aschenbrenner-Scheibe R, Perez-Velazquez J L and Carlen P L 1995 Transmembrane voltage oscillations in CA3 neurons Proc. 17th Int. Conf. IEEE/EMBS, Montreal, Quebec, 20-23 Sept. pp 1503-4
19. Chiu A W L and Bardakjian B L 2004 Control of state transitions in an in-silico model of epilepsy using small perturbations IEEE Trans. Biomed. Eng. 51 at press
20. Minorsky N 1962 Nonlinear Oscillations (Princeton, NJ: Van Nostrand)
21. Gear C W 1971 Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall)
22. Parker T S and Chua L O 1989 Practical Numerical Algorithms for Chaotic Systems (New York: Springer)
23. Radhakrishnan K and Hindmarsh A C 1993 Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations NASA Reference Publication 1327 Lawrence Livermore National Laboratory Report
24. Migliore M, Cook E P, Jaffe D B, Turner D A and Johnston D 1995 Computer simulations of morphologically reconstructed CA3 hippocampal neurons J. Neurophysiol. 73 1157-68
25. Bardakjian B L and Courville A 2000 Chaosmakers: Rhythm breakers Proc. 2nd Int. ICSC Symp. on Neural Computation (NC' 2000) (Berlin, Germany, 23-26 May) pp 121i-v
26. Zariffa J and Bardakjian B L 2004 Topology and complexity in coupled mapped clock oscillators representing CA3 neural networks Proc. BMES 2004 Annual Fall Meeting (Philadelphia, PA, 13-16 Oct.)
27. Draguhn A, Traub R D, Schimtz D and Jefferys J G R 1998 Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro Nature 394 189-92
28. Faber D S and Korn H 1989 Electrical field effects: their relevance in central neural networks Physiol. Rev. 69 821-63