Metabifurcation analysis of a mean field model of the cortex

Physica D: Nonlinear Phenomena

Volumn 240, Issue 11, 2011, Pages 949-962

  Frascoli, Federico ^a   Van Veen, Lennaert ^b   Bojak, Ingo ^c   Liley, David T J ^a  

^a SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

^b UNIVERSITY OF ONTARIO INSTITUTE OF TECHNOLOGY   (Canada)

^c RADBOUD UNIVERSITY   (Netherlands)

Author keywords

Anesthesia; Bifurcation analysis; Brain dynamics; Electroencephalogram (EEG); Mean field model; Thalamus

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; ELECTROENCEPHALOGRAPHY; MEAN FIELD THEORY; PHYSIOLOGY;

ANESTHESIA; BIFURCATION ANALYSIS; BRAIN DYNAMICS; ELECTRO-ENCEPHALOGRAM (EEG); MEAN FIELD MODELING; THALAMUS;

PHYSIOLOGICAL MODELS;

EID: 79953761080     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.02.002     Document Type: Article

References (45)

1. V.K. Jirsa, and H. Haken Field theory of electromagnetic brain activity Phys. Rev. Lett. 77 1996 960 963 (Pubitemid 126625592)
2. P.A. Robinson, C.J. Rennie, and J.J. Wright Propagation and stability of waves of electrical activity in the cerebral cortex Phys. Rev. E 56 1997 826 840 (Pubitemid 127614927)
3. D.T.J. Liley, P.J. Cadusch, and M.P. Dafilis A spatially continuous mean field theory of electrocortical activity Netw.: Comput. Neural Syst. 13 2002 67 113 Corrigendum, Netw.: Comput. Neural Syst. 14 (2003) 369
4. H.R. Wilson, and J.D. Cowan Excitatory and inhibitory interactions in localized populations of model neuron Biophys. J. 12 1972 1 24
5. H.R. Wilson, and J.D. Cowan A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue Kybernetik 13 1973 55 80
6. F.H. Lopes da Silva, A. Hoeks, H. Smits, and L.H. Zetterberg Model of brain rhythmic activity: the alpha-rhythm of the thalamus Kybernetik 15 1973 27 37
7. W.J. Freeman Mass Action in the Nervous System: Examination of the Neurophysiological Basis of Adaptive Behavior Through the EEG 1st ed. 1975 Academic Press New York
8. F.H. Lopes da Silva, A. van Rotterdam, P. Barts, E. van Heusden, and W. Burr Models of neuronal populations: the basic mechanism of rhythmicity Prog. Brain Res. 45 1975 281 308
9. L.H. Zetterberg, L. Kristiansson, and K.H. Mossberg Performance of a model for a local neuron population Biol. Cybern. 31 1978 15 26 (Pubitemid 9043104)
10. D.T.J. Liley, and I. Bojak Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents J. Clin. Neurophysiol. 22 2005 300 313 (Pubitemid 43191839)
11. I. Bojak, and D.T.J. Liley Modeling the effects of anesthesia on the electroencephalogram Phys. Rev. E 71 2005 041902
12. B.H. Jansen, and V.G. Rit Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns Biol. Cybern. 73 1995 357 366
13. C.J. Rennie, P.A. Robinson, and J.J. Wright Unified neurophysical model of EEG spectra and evoked potentials Biol. Cybern. 86 2002 457 471
14. D.A. Steyn-Ross, M.L. Steyn-Ross, J.W. Sleigh, M.T. Wilson, I.P. Gillies, and J.J. Wright The sleep cycle modelled as a cortical phase transition J. Biol. Phys. 31 2005 547 569 (Pubitemid 41758706)
15. A.J.K. Phillips, and P.A. Robinson A quantitative model of sleepwake dynamics based on the physiology of the brainstem ascending arousal system J. Biol. Rhythms 22 2007 167 179 (Pubitemid 46568647)
16. J.J. Wright EEG simulation: variation of spectral envelope, pulse synchrony and ≈40Hz oscillation Biol. Cybern. 76 1997 181 194 (Pubitemid 127665178)
17. C.J. Rennie, J.J. Wright, and P.A. Robinson Mechanisms of cortical electrical activity and emergence of gamma rhythm J. Theoret. Biol. 205 2000 17 35
18. I. Bojak, and D.T.J. Liley Self-organized 40 Hz synchronization in a physiological theory of EEG Neurocomputing 70 2007 2085 2090 (Pubitemid 46671093)
19. F. Wendling, J.-J. Bellanger, F. Bartolomei, and P.Y. Chauvel Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals Biol. Cybern. 83 2000 367 378
20. P.A. Robinson, C.J. Rennie, and D.L. Rowe Dynamics of large-scale brain activity in normal arousal states and epileptic seizures Phys. Rev. E 65 2002 041924
21. F.H. Lopes da Silva, W. Blanes, S.N. Kalitzin, J. Parra, P. Suffczyski, and D.N. Velis Dynamical diseases of brain systems: different routes to epileptic seizures IEEE Trans. Biomed. Eng. 50 2003 540 548
22. M.A. Kramer, H.E. Kirsch, and A.J. Szeri Pathological pattern formation and cortical propagation of epileptic seizures J. R. Soc. Interface 2 2005 113 127
23. G.R. Deco, V.K. Jirsa, P.A. Robinson, M. Breakspear, and K.J. Friston The dynamic brain: from spiking neurons to neural masses and cortical fields PLoS Comput. Biol. 4 2008 e1000092
24. S. Coombes Large-scale neural dynamics: simple and complex NeuroImage 52 2010 731 739
25. D.T.J. Liley, D.M. Alexander, J.J. Wright, and M.D. Aldous Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons Netw.: Comput. Neural Syst. 10 1999 79 92
26. M.P. Dafilis, D.T.J. Liley, and P.J. Cadusch Robust chaos in a model of the electroencephalogram: implications for brain dynamics Chaos 11 2001 474 478
27. L. van Veen, and D.T.J. Liley Chaos via Shilnikov's saddle-node bifurcation in a theory of the electroencephalogram Phys. Rev. Lett. 97 2006 208101
28. F. Frascoli, L. van Veen, I. Bojak, M.P. Dafilis, and D.T.J. Liley Dynamical complexity in a mean-field model of human EEG Proc. SPIE 7270 2008 72700V
29. M.P. Dafilis, F. Frascoli, P.J. Cadusch, and D.T.J. Liley Chaos and generalised multistability in a mesoscopic model of the electroencephalogram Physica D 13 2009 1056 1060
30. W.J. Freeman How Brains Make Up their Minds 1st ed. 2001 Columbia University Press New York
31. S.M. Sherman, and R.W. Guillery Exploring the Thalamus and its Role in Cortical Function 2nd ed. 2006 MIT Press Cambridge, MA
32. P.L. Nunez Electric Fields of the Brain: The Neurophysics of EEG 1st ed. 1981 Oxford University Press New York
33. H.C. Tuckwell Introduction to theoretical neurobiology: linear cable theory and dendritic structure Cambridge Studies in Mathematical Biology vol. 1 1988 Cambridge University Press Cambridge
34. I. Bojak, and D.T.J. Liley Axonal velocity distributions in neural field equations PLoS Comput. Biol. 6 2010 e1000653
35. D.A. Steyn-Ross, M.L. Steyn-Ross, Modeling Phase Transitions in the Brain 2010 Springer-Verlag Berlin
36. U. Rudolph, and B. Antkowiak Molecular and neuronal substrates for general anaesthetics Nat. Rev. Neurosci. 2004 709 720 (Pubitemid 39150142)
37. E.J. Doedel Auto: a program for the automatic bifurcation analysis of autonomous systems Congr. Numer. 30 1981 265 284
38. A. Dhooge, W.J.F. Govaerts, and Y.A. Kuznetsov Matcont: a MATLAB package for numerical bifurcation analysis of ODEs ACM T. Math. Software 29 2003 141 164 (Pubitemid 40001448)
39. V. Arnold The Theory of Singularities and its Applications 1993 Cambridge University Press
40. Y.A. Kuznetsov Elements of Applied Bifurcation Theory 3rd ed. 2004 Springer-Verlag New York
41. W.W. Mapleson Effect of age on MAC in humans: a meta-analysis Br. J. Anaesth. 76 1996 179 185
42. N.P. Franks, and W.R. Lieb Temperature dependence of the potency of volatile general anesthetics: implications for in vitro experiments Anesthesiology 84 1996 716 720 (Pubitemid 26092542)
43. V. Billard, P.L. Gambus, N.G. Chamoun, D.R. Stanski, and S.L. Shafer A comparison of spectral edge, delta power, and bispectral index as EEG measures of alfentanil, propofol, and midazolam drug effect Clin. Pharmacol. Ther. 61 1997 45 58 (Pubitemid 27072883)
44. D.M. Endres, and J.E. Schindelin A new metric for probability distributions IEEE Trans. Inform. Theory 49 2003 1858 1860
45. A.E. Walker The Primate Thalamus 1938 University of Chicago Press Chicago