Critical fluctuations in cortical models near instability

Frontiers in Physiology

Volumn 3 AUG, Issue , 2012, Pages

  Aburn, Matthew J ^a,b   Holmes, C A ^a   Roberts, James A ^b   Boonstra, Tjeerd W ^c,d   Breakspear, Michael ^b,c,e  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b QIMR BERGHOFER MEDICAL RESEARCH INSTITUTE   (Australia)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

^d VU UNIVERSITY AMSTERDAM   (Netherlands)

^e ROYAL BRISBANE AND WOMEN'S HOSPITAL   (Australia)

Author keywords

Autocorrelation; Critical fluctuations; Hopf bifurcation; Neural mass model

Indexed keywords

EID: 84866505236     PISSN: None     EISSN: 1664042X     Source Type: Journal    
DOI: 10.3389/fphys.2012.00331     Document Type: Article

References (54)

1. Anteneodo, C., and Riera, R. (2005). Additive-multiplicative stochastic models of financial mean-reverting processes. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72, 026106.
2. Bedard, C., Kroeger, H., and Destexhe, A. (2006). Does the 1/f frequency scaling of brain signals reflect self-organized critical states? Phys. Rev. Lett. 97, 118102.
3. Braun, J., and Mattia, M. (2010). Attrac-tors and noise: twin drivers of decisions and multistability. Neuroimage 52, 740-751.
4. Breakspear, M., Roberts, J. A., Terry, J. R., Rodrigues, S., Mahant, N., and Robinson, P. A. (2006). A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb. Cortex 16, 1296.
5. Breakspear, M., and Terry, J. R. (2002). Detection and description of nonlinear interdependence in normal multichannel human EEG data. Clin. Neurophysiol. 113, 735-753.
6. Clauset, A., Shalizi, C. R., and Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Rev. Soc. Ind. Appl. Math. 51, 661-703.
7. David, O., and Friston, K. J. (2003). A neural mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage 20, 1743-1755.
8. David, O., Harrison, L., and Friston, K. J. (2005). Modelling event-related responses in the brain. Neuroimage 25, 756-770.
9. Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M., and Fris-ton, K. (2008). The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput. Biol. 4, e1000092. doi:10.1371/journal.pcbi.1000092
10. Dhooge, A., Govaerts, W., and Kuznetsov, Y. A. (2003). MAT-CONT: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29, 141-164.
11. Freeman, W. (1992). "Predictions on neocortical dynamics derived from studies in paleocortex," in Induced Rhythms in the Brain, Brain Dynamics Series, Chap. 9, eds E. Basar and T. H. Bullock (Boston: Birkhäuser), 183-199.
12. Freyer, F., Aquino, K., Robinson, P. A., Ritter, P., and Breakspear, M. (2009). Bistabilityand non-Gaussian fluctuations in spontaneous cortical activity. J. Neurosci. 29, 8512.
13. Freyer, F., Roberts, J. A., Becker, R., Robinson, P. A., Ritter, P., and Breakspear, M. (2011). Biophysical mechanisms of multistability in resting-state cortical rhythms. J. Neurosci. 31, 6353.
14. Freyer, F., Roberts, J. A., Ritter, P., and Breakspear, M. (2012). A canonical model of multistability and scale-invariance in biological systems. PLoS Comput. Biol. doi: 10.1371/journal.pcbi.1002634
15. Friston, K. J., and Dolan, R. J. (2010). Computational and dynamic models in neuroimaging. Neuroimage 52, 752-765.
16. Friston,K.J., Harrison, L., and Penny, W. (2003). Dynamic causal modeling. Neuroimage 19, 1273-1302.
17. Gardiner, C. (2010). Stochastic Methods: A Handbook for the Natural and Social Sciences, SpringerSeries in Synergetics Series. New York: Springer.
18. Grimbert, F., and Faugeras, O. (2006). Bifurcation analysis of Jansen's neural mass model. Neural Comput. 18, 3052-3068.
19. Haken, H., Kelso, J. A. S., and Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biol. Cybern. 51, 347-356.
20. He, B. J., Zempel, J. M., Snyder, A. Z., and Raichle, M. E. (2010). The temporal structures and functional significance of scale-free brain activity. Neuron 66, 353-369.
21. Jansen, B. H., and Rit, V. G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol. Cybern. 73, 357-366.
22. Jansen, B. H., Zouridakis, G., and Brandt, M. E. (1993). A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol. Cybern. 68, 275-283.
23. Jirsa, V. K., and Haken, H. (1996). Field theory of electromagnetic brain activity. Phys. Rev. Lett. 77, 960-963.
24. Kelso, J. A. S. (2010). Instabilities and phase transitions in human brain and behavior. Front. Hum. Neurosci. 4:23. doi:10.3389/fnhum.2010.00023
25. Kelso, J. A. S., Scholz, J. P., and Schöner, G. (1986). Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations. Phys. Lett. A 118, 279-284.
26. Kuehn, C. (2011). A mathematical framework for critical transitions: bifurcations, fast-slow systems and stochastic dynamics. Physica D 240, 1020-1035.
27. Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., and Ilmoniemi, R. J. (2001). Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neu-rosci. 21, 1370.
28. Linkenkaer-Hansen, K., Nikulin, V. V., Palva, J. M., Kaila, K., and Ilmoniemi, R. J. (2004). Stimulus-induced change in long-range temporal correlations and scaling behaviour of sensorimotor oscillations. Eur. J. Neurosci. 19, 203-218.
29. Lopes da Silva, F. H., Hoeks, A., Smits, H., and Zetterberg, L. H. (1974). Model of brain rhythmic activity. Biol. Cybern. 15, 27-37.
30. Marreiros, A. C., Daunizeau, J., Kiebel, S. J., and Friston, K. J. (2008). Population dynamics: variance and the sigmoid activation function. Neu-roimage 42, 147-157.
31. Miller, K. J., Sorensen, L. B., Oje-mann, J. G., and den Nijs, M. (2009). Power-law scaling in the brain surface electric potential. PLoS Comput. Biol. 5, e1000609. doi:10.1371/journal.pcbi.1000609
32. Moran, R. J., Kiebel, S. J., Stephan, K. E., Reilly, R. B., Daunizeau, J., and Friston, K. J. (2007). A neural mass model of spectral responses inelectrophysiology. Neuroimage 37, 706-720.
33. Orfanidis, S. J. (1996). Optimum Signal Processing, 2nd Edn. New York: McGraw-Hill.
34. Roberts, A. J. (2008). Normal form transforms separate slow and fast modes in stochastic dynamical systems. Physica A 387, 12-38.
35. Roberts, J. A., and Robinson, P. A. (2012). Corticothalamic dynamics: structure of parameter space, spectra, instabilities, and reduced model. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 011910.
36. Robinson, P. A., Rennie, C. J., Phillips, A. J. K., Kim, J. W., and Roberts, J. A. (2010). Phase Transitions in Physiologically-Based Multiscale Mean-Field Brain Models, Modeling Phase Transitions in the Brain. New York: Springer, 179-201.
37. Robinson,P.A., Rennie, C. J., and Rowe, D. L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 041924.
38. 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 Stat. Phys. Plasmas. Fluids Relat. Interdiscip. Topics 56, 826.
39. Rowat, P. F., and Greenwood, P. E. (2011). Identification and continuity of the distributions of burst-length and interspike intervals in the stochastic Morris-Lecar neuron. Neural Comput. 23, 1-31.
40. Rümelin, W. (1982). Numerical treatment of stochastic differential equations. SIAM J. Numer. Anal. 19, 604-613.
41. Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V., Held, H., van Nes, E. H., Rietkerk, M., and Sugihara, G. (2009). Early-warning signals for critical transitions. Nature 461, 53-59.
42. Scholz, J. P., Kelso, J. A. S., and Schöner, G. (1987). Nonequilibrium phase transitions in coordinated biological motion: critical slowing down and switching time. Phys. Lett. A 123, 390-394.
43. Sokolov, I. M., and Klafter, J. (2005). From diffusion to anomalous diffusion: a century after Einstein's Brownian motion. Chaos 15, 026103-026103.
44. Sotero, R. C., Trujillo-Barreto, N. J., Iturria-Medina,Y., Carbonell,F., and Jimenez, J. C. (2007). Realistically coupled neural mass models can generate EEG rhythms. Neural Com-put. 19, 478-512.
45. Spiegler, A., Kiebel, S. J., Atay, F. M., and Knösche, T. R. (2010). Bifurcation analysis of neural mass models: Impact of extrinsic inputs and dendritic time constants. Neuroimage 52, 1041-1058.
46. Stam, C. J., and de Bruin, E. A. (2004). Scale-free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22, 97-109.
47. Stam, C. J., Pijn, J. P. M., Suffczynski, P., anddaSilva,F.H.L. (1999). Dynamics of the human alpha rhythm: evidence for non-linearity? Clin. Neu-rophysiol. 110, 1801-1813.
48. Steyn-Ross, D. A., Steyn-Ross, M. L., Wilson, M. T., and Sleigh, J. W. (2006). White-noise susceptibility and critical slowing in neurons near spiking threshold. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 051920.
49. van Albada, S. J., Kerr, C. C., Chiang, A. K. I., Rennie, C. J., and Robinson, P. A. (2010). Neurophysiolog-ical changes with age probed by inverse modeling of EEG spectra. Clin. Neurophysiol. 121, 21-38.
50. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and nonnested hypotheses. Econometrica 57, 307-333.
51. Wendling, F., Bartolomei, F., Bellanger, J. J., and Chauvel, P. (2002). Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci. 15, 1499-1508.
52. Wendling, F., Bellanger, J. J., Bar-tolomei, F., and Chauvel, P. (2000). Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol. Cybern. 83, 367-378.
53. Wilson, H. R., and Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1-24.
54. Zavaglia, M., Astolfi, L., Babiloni, F., and Ursino, M. (2006). A neural mass model for the simulation of cortical activity estimated from high resolution EEG during cognitive or motor tasks. J. Neurosci. Methods 157, 317-329.