A spatially continuous mean field theory of electrocortical activity

Network: Computation in Neural Systems

Volumn 13, Issue 1, 2002, Pages 67-113

  Liley, David T J ^a   Cadusch, Peter J ^a   Dafilis, Mathew P ^a  

^a SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

AGENTS INTERACTING WITH TRANSMITTER, HORMONE OR DRUG RECEPTORS;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BRAIN CORTEX; CELL MEMBRANE POTENTIAL; ELECTROENCEPHALOGRAPHY; ELECTROPHYSIOLOGY; KINETICS; NERVE CONDUCTION; NONLINEAR SYSTEM; PHYSIOLOGY; STATISTICAL MODEL; SYNAPTIC TRANSMISSION;

ALGORITHMS; CEREBRAL CORTEX; ELECTROENCEPHALOGRAPHY; ELECTROPHYSIOLOGY; KINETICS; LINEAR MODELS; MEMBRANE POTENTIALS; MODELS, NEUROLOGICAL; NEURAL CONDUCTION; NEUROTRANSMITTER AGENTS; NONLINEAR DYNAMICS; PHYSIOLOGY; SYNAPTIC TRANSMISSION;

EID: 0041885311     PISSN: 0954898X     EISSN: None     Source Type: Journal    
DOI: 10.1088/0954-898X/13/1/303     Document Type: Article

References (96)

1. Abeles M 1982 Local Cortical Circuits: an Electrophysiological Study (Berlin: Springer)
2. Abeles M 1991 Corticonics: Neural Circuits of the Cerebral Cortex (Cambridge: Cambridge University Press)
3. Alvarez-Maubecin V, Garcia-Hernandez F, Williams J T and van Bockstaele E J 2000 Functional coupling between neurons and glia J. Neurosci. 20 4091-8
4. Amit D J 1989 Modelling Brain Function: the World of Attractor Neural Nets (New York: Cambridge University Press)
5. Andersen P and Andersson S A 1968 Physiological Basis of the Alpha Rhythm (New York: Appleton-Century-Crofts)
6. Arbib M A, Érdi P and Szentágothai J 1998 Neural Organization: Structure, Function and Dynamics (Cambridge, MA: MIT Press)
7. A-mediated inhibition and in vitro epileptogenesis in the human neocortex J. Neurophysiol. 73 468-84
8. Babloyantz A 1985 Strange attractors in the dynamics of brain activity Complex Systems ed H Haken (Berlin: Springer) pp 116-22
9. Babloyantz A 1989 Estimation of correlation dimensions from single and multichannel recordings - a critical view Brain Dynamics: Progress and Perspectives (Springer Series in Brain Dynamics Vol. 2) ed E Başar and T H Bullock (Berlin: Springer) pp 122-30
10. Babloyantz A 1991 Evidence for slow brain waves: a dynamical approach Electroencephalogr. Clin. Neurophysiol. 78 402-5
11. Babloyantz A and Destexhe A 1986 Low-dimensional chaos in an instance of epilepsy Proc: Natl Acad. Sci. USA 83 3513-17
12. Babloyantz A, Salazar J M and Nicolis G 1985 Evidence of chaotic dynamics of brain activity during the sleep cycle Phys. Lett. A 111 152-6
13. Bal T and McCormack D A 1993 Mechanisms of oscillatory activity in guinea-pig nucleus reticularis thalami in vitro: a mammalian pacemaker J. Physiol. (Lond.) 468 669-91
14. Berger H 1929 Über das elektrenencephalogramm des menschen Arch. Psychiatr. Nervenkr. 87 527-70
15. Biella G and Sotgui M L 1995 Evidence that inhibitory mechanisms mask inappropriate somatotopic connections in the spinal cord of normal rat J. Neurophysiol. 74 495-505
16. Braitenberg V 1978 Cell assemblies in the cerebral cortex Lecture Notes in Biomathematics: Theoretical Approaches to Complex Systems vol 21, ed R Heim and G Palm (Berlin: Springer) pp 171-88
17. Braitenberg V and Schüz A 1998 Anatomy of the Cortex: Statistics and Geometry 2nd edn (Berlin: Springer)
18. Breimer L T, Hennis P J, Burm A G, Danhof M, Bovill J G, Spierdijk J and Vletter A A 1990 Quantification of the EEG effect of midazolam by aperiodic analysis in volunteers, pharmacokinetic/pharmacodynamic modelling Clin. Pharmacokinet. 18 245-53
19. Calvin W H 1975 Generation of spike trains in CNS neurons Brain Res. 84 1-22
20. Chang H J and Freeman W J 1996 Parameter optimization in an olfactory neural system Neural Netw. 1 1-14
21. Chang H J, Freeman W J and Burke B C 1998 Optimization of olfactory model in software to give 1/f power spectra reveals numerical instabilities in solutions governed by aperiodic (chaotic) attractors Neural Netw. 11 449-66
22. Christiansen F and Rugh H H 1997 Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization Nonlinearity 10 1063-72
23. Cochilla A J and Alford S 1999 NMDA receptor-mediated control of presynaptic calcium and neurotransmitter release J. Neurosci. 19 193-205
24. Cohen S D and Hindmarsh A C 1996 CVODE, a stiff/nonstiff ODE solver in C Comput. Phys. 10 138-43
25. Corless R M, Gonnet G H, Hare D E G and Jeffrey D J 1993 On Lambert's W function Technical Report 93-03 Department of Computer Science, University of Waterloo
26. Dafilis M P, Liley D T J and Cadusch P J 2001 Robust chaos in a model of the electroencephalogram: implications for brain dynamics Chaos 11 474-8
27. Destexhe A 1994 Oscillations, complex spatiotemporal behaviour and information transport in networks of excitatory and inhibitory neurons Phys. Rev. E 150 1201-30
28. Dvorak J and Siska J 1986 On some problems encountered in the estimation of the correlational dimension of the EEG Phys. Lett. A 118 63-6
29. Elul R 1972 The genesis of the EEG Int. Rev. Neurobiol. 15 227-72
30. Ermentrout G B 1998 Neural networks as spatio-temporal pattern forming systems Rep. Prog. Phys. 61 353-430
31. Franks N P and Leib W R 1994 Molecular and cellular mechanisms of general anaesthesia Nature 367 607-14
32. Freeman W J 1975 Mass Action in the Nervous System (New York: Academic)
33. Freeman W J 1979 Nonlinear gain mediating cortical stimulus-response relations Biol. Cybern. 33 237-47
34. Freeman W J 1987 Simulation of chaotic EEG patterns with a dynamic model of the olfactory system Biol. Cybern. 56 139-50
35. Freeman W J 1991 The physiology of perception Sci. Am. 264 78-85
36. Freeman W J 1991 Predictions on neocortical dynamics derived from studies in paleocortex Induced Rhythms of the Brain ed E Başar and T H Bullock (Basel: Birkhauser) pp 200-32
37. Freeman W J 1992 Tutorial on neurobiology: from single neurons to brain chaos Int. J. Bifurcation Chaos 2 451-82
38. Freeman W J, Rogers L J, Holmes M D and Silbergeld D L 2000 Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands J. Neurosci. Methods 95 111-21
39. Gebber G L, Zhong S. Lewis C and Barman S M 1999 Human brain alpha rhythm: non-linear oscillations or filtered noise Brain Res. 818 556-60
40. Granit R, Kernell D and Shortess G K 1963 Quantitative aspects of repetitive firing of mammalian motorneurons caused by injected currents J. Physiol. 168 911-31
41. Haken H 1999 What can synergetics contribute to the understanding of brain function Analysis of Neurophysiological Brain Functioning (Springer Series in Synergetics) ed C Uhl (Berlin: Springer) pp 7-40
42. Hebb D O 1949 Organization of Behaviour. A Neuropsychological Theory (New York: Wiley)
43. Hegger R, Kantz H and Schreiber T 1999 Practical implementation of non-linear time series methods: the TISEAN package Chaos 9 413-35
44. Jahnsen H and Llinás R 1984 Ionic basis for the electroresponsiveness and oscillatory properties of guinea-pig thalamic neurons in vitro J. Physiol. (Lond.) 349 227-47
45. Jirsa V and Haken H 1996 Field theory of electromagnetic brain activity Phys. Rev. Lett. 77 960-63
46. Jirsa V K and Kelso JAS 2000 Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies Phys. Rev. E 62 8462-5
47. A receptor channel function in the nervous system Prog. Neurobiol. 42 489-537
48. Kelso J A S and Fuchs A 1995 Self-organizing dynamics of the human brain: critical instabilities and Šil'nikov chaos Chaos 5 64-9
49. Layne S P, Mayer-Kress G and Holzfuss J 1986 Problems associated with dimensional analysis of electroencephalogram data Dimensions and Entropies in Chaotic Systems ed G Mayer-Kress (Berlin: Springer)
50. Liley D T J and Wright J J 1994 Intracortical connectivity of pyramidal and stellate cells: estimates of synaptic densities and coupling symmetry Network: Comput. Neural Syst. 5 175-89
51. Llinás R 1988 The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function Science 242 1654-64
52. Lopes da Silva F H, Hoeks A, Smits H and Zetterberg L H 1974 Model of brain rhythmic activity: the alpha rhythm of the thalamus Kybernetik 15 27-37
53. Lopes da Silva F H, Van Lierop T H M T, Schrijer C F and Storm van Leeuwen W 1973 Organization of thalamic and cortical alpha rhythms: spectra and coherences Electroencephalogr. Clin. Neurophysiol. 35 626-39
54. Lopes da Silva F H, Pijn J P, Velis D and Nijssen P C G 1997 Alpha rhythms: noise, dynamics and models. Int. J. Psychophysiol. 26 237-49
55. Lopes da Silva F H and Storm van Leeuwen W 1977 The cortical source of alpha rhythm Neurosci. Lett. 6 237-47
56. Lopes da Silva F H and Storm van Leeuwen W 1978 The cortical alpha rhythm of the dog: the depth and profile of phase Architectonics of the Cerebral Cortex ed M A B Brazier and H Petsche (New York: Raven) pp 150-87
57. Lopes da Silva F H, Van Lierop T H M T, Schrijer C F M and Storm van Leeuwen W 1973 Essential differences between alpha rhythms and barbiturate spindles: spectra and thalamo-cortical coherences Electroencephalogr. Clin. Neurophysiol. 38 93-6
58. A receptor channels Annu. Rev. Neurosci. 17 569-602
59. Mar A and Drapeau P 1996 Modulation of conduction blocks in leech mechanosensory neurons J. Neurosci. 16 4335-43
60. McKenna T M, McMullen T A and Shlesinger M F 1994 The brain as a dynamic physical system Neuroscience 60 587-605
61. Niedermeyer E 1997 Alpha rhythms as physiological and abnormal phenomena Int. J. Psychophysiol. 26 31-49
62. Niedermeyer E and Lopes da Silva F 1999 Electroencephalography: Basic Principles, Clinical Applications and Related Fields 4th edn (Baltimore, MD: Williams and Wilkins)
63. Nunez P L 1981 Electric Fields of the Brain: the Neurophysics of EEG (New York: Oxford University Press)
64. Nunez P L 1989 Generation of human EEG by a combination of long and short range neocortical interactions Brain Topogr. 1 199-215
65. Nunez P L 1995 Neocortical Dynamics and Human EEG Rhythms (New York: Oxford University Press)
66. Nunez P L 2000 Toward a quantitative description of large-scale neocortical dynamic function and EEG Behav. Brain Sci. 23 371-98
67. Palm G 1982 Neural Assemblies. An Alternative Approach to Artificial intelligence (Heidelberg: Springer)
68. Palm G 1993 On the internal structure of cell assemblies Spatio-Temporal Aspects of Brain Function ed A Aertson (Amsterdam: Elsevier) pp 261-70
69. Paluš M 1999 Nonlinear dynamics in the EEG analysis: disappointments and perspectives Nonlinear Dynamics and Brain Functioning ed N Pradhan, P E Rapp and R Sreenivasan (Commack, NY: Nova Science) pp 201-16
70. Pinault D, Smith Y and Deschenes M 1997 Dendrodendritic and axoaxonic synapses in the thalamic reticular nucleus of the adult rat J. Neurosci. 17 3215-33
71. Prast J W 1949 An interpretation of certain EEG patterns as transient responses of a transmission system Electroencephalogr. Clin. Neurophysiol. 1 370
72. Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992 Numerical Recipes in C: the Art of Scientific Computing 2nd edn (New York: Cambridge University Press)
73. Rall W 1962 Electrophysiology of a dendritic neuron model Biophys. J. 2 145-75
74. Rapp P E 1995 Is there evidence for chaos in the human central nervous system Chaos Theory in Psychology and the Life Sciences ed R Robertson and A Combs (Mahawah, NJ: Erlbaum) pp 89-100
75. Rapp P E, Zimmermann I D, Albano A M, de Guzman G C, Greenabaum N N and Bashore T S 1986 Experimental studies of chaotic neuronal behaviour: cellular activity and electroencephalographic signals Nonlinear Oscillations in Biology and Chemistry ed H G Othmer (Berlin: Springer) pp 175-205
76. Rennie C J, Wright J J and Robinson P A 2000 Mechanisms of cortical electrical activity and emergence of gamma rhythm J. Theor. Biol. 205 17-35
77. Richtmyer R D and Morton K W 1967 Difference Methods for Initial Value Problems 2nd edn (New York: Wiley)
78. Robinson P A, Rennie C J and Wright J J 1997 Propagation and stability of waves of electrical activity in the cerebral cortex Phys. Rev. E 56 826-40
79. Robinson P A, Rennie C J, Wright J J, Bahramali H, Gordon E and Rowe D L 2001 Prediction of electroencephalographic spectra from neurophysiology Phys. Rev. E 63 21 903-21
80. Robinson P A, Rennie C J, Wright J J and Bourke P D 1998 Steady states and global dynamics of electrical activity in the cerebral cortex Phys. Rev. E 58 3557-71
81. Rotterdam A, Lopes da Silva F H, van der Ende J, Viergever M A and Hermans A J 1982 A model of the spatio-temporal characteristics of the alpha rhythm Bull. Math. Biol. 44 283-305
82. Schuster H G and Wagner P P 1990 A model for neuronal oscillations in the visual cortex: 1. Mean-field theory and derivation of the phase equations Biol. Cybern. 64 77-82
83. Sholl D A 1956 The Organization of the Cerebral Cortex (New York: Wiley)
84. Silberstein R B 1995 Neuromodulation of neocortical dynamics Neocortical Dynamics and Human EEG Rhythms (New York: Oxford University Press) pp 591-622
85. Stam C J, Pijn J P M, Suffczynski P and Lopes da Silva F H 1999 Dynamics of the human alpha rhythm: evidence for non-linearity? Clin. Neurophysiol. 110 1801-13
86. Steriade M, Gloor P, Llinás R, Lopes da Silva F H and Mesulam M M 1990 Basic mechanisms of cerebral rhythmic activity Electroencephalogr. Clin. Neurophysiol. 76 481-508
87. Steriade M and Llinás R 1988 The functional states of the thalamus and the associated neuronal interplay Phys. Rev. 68 649-742
88. Steyn-Ross M L, Steyn-Ross D A, Sleigh J W and Liley D T J 1999 Theoretical EEG stationary spectrum for a white-noise-driven cortex: evidence for a general anesthetic-induced phase transition Phys. Rev. E 60 7299-311
89. Traub R D, Jefferys J G R and Whittington M A 1999 Fast Oscillations in Cortical Circuits (Cambridge, MA: MIT Press)
90. Wall P D 1994 Control of impulse conduction in long-range branches of afferents by increases and decreases of primary afferent depolarization in the rat Eur. J. Neurosci. 6 1136-42
91. Wang X J 1994 Multiple dynamical modes of thalamic relay neurons: rhythmic bursting and intermittent phase-locking Neuroscience 59 21-31
92. Wiener N 1961 Cybernetics: or Control and Communication in the Animal and the Machine (Cambridge, MA: MIT Press)
93. Wilson H R and Cowan J D 1972 Excitatory and inhibitory interactions in localised populations of model neurons Biophys. J. 12 1-24
94. Wilson H R and Cowan J D 1973 A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue Kybernetik 13 55-80
95. Wright J J and Liley D T J 1994 A millimetric scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density Network: Comput. Neural Syst. 5 191-202
96. Young M P, Scannell J W and Burns G 1995 The Analysis of Cortical Connectivity (Austin, TX: Landes)