CHAOS IN THE BRAIN

// PAPERS //

Vortices in brain activity: Their mechanism and significance for perception. Walter J. Freeman (2009). Neural Networks 22(5-6): 491-501.

Abstract:
Brains interface with the world through perception. The process extracts information from microscopic sensory inputs and incorporates it into the mesoscopic memory store for retrieval in recognition. The process requires creation of spatiotemporal patterns of neural activity. The construction is done through phase transitions in cortical populations that condense the background activity through spontaneous symmetry breaking. Large-scale interactions create fields of synaptically driven activity that is observed by measuring brain waves (electrocorticogram, ECoG) and evaluated by constructing a mesoscopic vectorial order parameter as follows. The negative feedback among excitatory and inhibitory neurons creates spatially and spectrally distributed gamma oscillations (20-80 Hz) in the background activity. Band pass filtering reveals beats in ECoG log analytic power. In some beats that recur at theta rates (3-7 Hz), the order parameter transiently approaches zero, giving a null spike in which the microscopic activity is uniformly disordered (symmetric). A phase transition that is manifested in an analytic phase discontinuity breaks the symmetry. As the null spike terminates, the resurgent order parameter imposes mesoscopic order seen in spatial patterns of ECoG amplitude modulation (AM) that actualize and update the memory of a stimulus. Read-out is through a divergent/convergent projection that performs on cortical output an irreversible spatiotemporal integral transformation. The ECoG reveals a conic phase gradient that accompanies an AM pattern. The phase cone manifests a vortex, which is initiated by the null spike, and which is inferred to help stabilize and prolong its accompanying AM pattern that might otherwise be rapidly degraded by the turbulent neural noise from which it emerges.

Broadband Criticality of Human Brain Network Synchronization. Kitzbichler et al. (2009). PLoS Computational Biology, 5(3):e1000314+.

Abstract :
Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.

Emotion is From Preparatory Brain Chaos; Irrational Action is From Premature Closure. Walter J. Freeman (2005). Behavioral and Brain Sciences 28 (2):204-205.

Abstract:
EEG evidence supports the view that each cerebral hemisphere maintains a scale-free network that generates and maintains a global state of chaos. By its own evolution, and under environmental impacts, this hemispheric chaos can rise to heights that may either escape containment and engender incontinent action or be constrained by predictive control and yield creative action of great power and beauty.

// BOOKS //

CHAOS IN BRAIN ? Proceedings of the Workshop
University of Bonn, Germany, 10 – 12 March 1999
edited by K Lehnertz (University of Bonn, Germany) , C E Elger (University of Bonn, Germany) , J Arnhold (NIC, Forschungszentrum Jülich, Germany) , & P Grassberger (NIC, Forschungszentrum Jülich, Germany)

Abstract :
There has been a heated debate about whether chaos theory can be applied to the dynamics of the human brain. While it is obvious that nonlinear mechanisms are crucial in neural systems, there has been strong criticism of attempts to identify at strange attractors in brain signals and to measure their fractal dimensions, Lyapunov exponents, etc. Conventional methods analyzing brain dynamics are largely based on linear models and on Fourier spectra. Regardless of the existence of strange attractors in brain activity, the neurosciences should benefit greatly from alternative methods that have been developed in recent years for the analysis of nonlinear and chaotic behavior.

Contents:
· Cortical Dynamics — Experiments and Models (S Rotter & A Aertsen)
· Is Nonlinearity Evident in Time Series of Brain Electrical Activity? (T Schreiber)
· Finding and Characterizing Unstable Fixed Points by Controlling System Dynamics (D T Kaplan)
· Detection of Phase Locking from Noisy Data: Application to Magnetoencephalography (M Rosenblum et al.)
· Dynamical Analysis in Clinical Practice (P E Rapp & T I Schmah)
· Rhythms of the Brain: Between Randomness and Determinism (F H Lopes da Silva et al.)
· Pre-ictal Changes of the EEG Dynamics in Epileptic Patients: Clinical and Neurobiological Implications (M Baulac et al.)
· Spatio-Temporal Dynamics of Epileptogenic Networks (M Le van Quyen et al.)
· Pre-ictal Changes and EEG Analyses Within the Framework of Lyapunov Theory (H R Moser et al.)
· Epilepsy — When Chaos Fails (J C Sackellares et al.)
· Possible Clinical and Research Applications of Nonlinear EEG Analysis in Humans (K Lehnertz et al.)
· Dynamics of EEG Signals During Petit-Mal Epileptic Seizures (R Friedrich)
· Detection of Epileptic Dynamics in Neuromagnetic Signals: Spectral Analyses Versus Characteristics of Correlation Function (E Bohl et al.)
· Nonlinear Methods for Evoked Potential Analyses and Modeling (B H Jansen)
· From Slow Potentials to Chaos: Processing in the Brain and Controlling the Brain (H Preiβl & W Lutzenberger)
· and other papers

// LINKS //

Introduction to Chaos and Nonlinear Dynamics by Takashi Kanamaru, J. Michael & T. Thompson
http://brain.cc.kogakuin.ac.jp/~kanamaru/Chaos/e/

Brain and Chaos from indian Lab. by Atin Das:
http://www.cerebromente.org.br/n14/mente/chaos.html

Chaos in the brain by Lewis Dartnell
http://plus.maths.org/issue35/features/dartnell/

Walter J. Freeman Neurobiology Full Manuscript Archives
http://sulcus.berkeley.edu/FreemanWWW/manuscripts/wjfmanuscripts.html

VIDEO - Entheological Paradigm, Part 6: Infinity Loops
http://www.encyclopedia.com/video/iQM-FaJ96os-entheological-paradigm-part-6-infinity.aspx