Field Theory of Electromagnetic Brain Activity

Jirsa, Viktor K.; Haken, Hermann

doi:10.1103/physrevlett.77.960

Cited by 436 publications

(383 citation statements)

References 11 publications

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“…Such unified mean-field potentials are the site of the sources of brain activity and in sum denoted by the so-called neural field (EEG) (Fig. 5) which is characterized by the location on the two-dimension folded cortical surface (space) and the dynamics (time) [188,196,197]. Because the unified mean-field potentials of neuronal assemblies are wave-mechanical phenomena, the magnitude of their modulations will be proportional only to the number of those neurons that synchronize their operations (postsynaptic potentials) [23].…”

Section: Macroscopic Level Of Brain Organizationmentioning

confidence: 99%

Natural world physical, brain operational, and mind phenomenal space–time

Fingelkurts

Neves

2010

Physics of Life Reviews

166

233

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Concepts of space and time are widely developed in physics. However, there is a considerable lack of biologically plausible theoretical frameworks that can demonstrate how space and time dimensions are implemented in the activity of the most complex life-system -the brain with a mind. Brain activity is organized both temporally and spatially, thus representing space-time in the brain. Critical analysis of recent research on the space-time organization of the brain's activity pointed to the existence of so-called operational space-time in the brain. This space-time is limited to the execution of brain operations of differing complexity. During each such brain operation a particular short-term spatio-temporal pattern of integrated activity of different brain areas emerges within related operational space-time. At the same time, to have a fully functional human brain one needs to have a subjective mental experience. Current research on the subjective mental experience offers detailed analysis of space-time organization of the mind. According to this research, subjective mental experience (subjective virtual world) has definitive spatial and temporal properties similar to many physical phenomena. Based on systematic review of the propositions and tenets of brain and mind space-time descriptions, our aim in this review essay is to explore the relations between the two. To be precise, we would like to discuss the hypothesis that via the brain operational space-time the mind subjective space-time is connected to otherwise distant physical space-time reality.Key words: spatial, temporal, consciousness, cognition, operation, architectonics, EEG, field, metastability, physics, coordinative dynamics, self-organization, cortex.

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Section: Macroscopic Level Of Brain Organizationmentioning

confidence: 99%

Natural world physical, brain operational, and mind phenomenal space–time

Fingelkurts

Neves

2010

Physics of Life Reviews

166

233

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“…To formalize the crude, qualitative interpretation of the neural underpinnings of bimanual coordination forwarded in the preceding discussion, we build on earlier theoretical studies of spatiotemporal patterning in the brain (e.g., Winfree 1967;Wilson and Cowan 1972;Freeman 1975;Ermentrout and Cowan 1979;Nunez 1995;Jirsa and Haken 1996;Liley et al 1999;Frank et al 2000;Wright et al 2001). Emanating from large ensembles of mutually interacting neurons, averaging methods like mean-field approaches result in weakly nonlinear mappings from action potentials to dendritic currents.…”

Section: Modeling Rhythmic Movementmentioning

confidence: 99%

Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account

2005

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Abstract. Based on recent brain-imaging data and congruent theoretical insights, a dynamical model is derived to account for the patterns of brain activity observed during stable performance of bimanual multifrequency patterns, as well as during behavioral instabilities in the form of phase transitions between such patterns. The model incorporates four dynamical processes, defined over both motor and premotor cortices, which are coupled through inhibitory and excitatory inter-and intrahemispheric connections. In particular, the model underscores the crucial role of interhemispheric inhibition in reducing the interference between disparate frequencies during stable performance, as well as the failure of this reduction during behavioral transitions. As an aside, the model also accounts for in-and antiphase preferences during isofrequency movements. The viability of the proposed model is illustrated by magnetoencephalographic signals that were recorded from an experienced subject performing a polyrhythmic tapping task that was designed to induce transitions between multifrequency patterns. Consistent with the model's dynamics, contra-and ipsilateral cortical areas of activation were frequency-and phase-locked, while their activation strength changed markedly in the vicinity of transitions in coordination.

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“…Solutions of (9) which are homoclinic to the origin correspond to spatially-localised steady states of (1). This technique of using Fourier transforms to convert integral equations to differential equations has been used several times before [6,17,[23][24][25][26]. Equation (9) has a number of important properties which we now discuss.…”

Section: Derivation Of Odementioning

confidence: 99%

Exploiting the Hamiltonian structure of a neural field model

Elvin

Laing

McLachlan

et al. 2010

Physica D: Nonlinear Phenomena

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We study the unexpected disappearance of stable homoclinic orbits in regions of parameter space in a neural field model with one spatial dimension. The usual approach of using numerical continuation techniques and local bifurcation theory is insufficient to explain the qualitative change in the model's behaviour. The lack of robustness of the model to small perturbations in parameters is surprising and the phenomenon may be of broader significance than just our model. By exploiting the Hamiltonian structure of the timeindependent system, we develop a numerical technique with which we discover that a small, separate solution curve exists for a range of parameter values. As the firing rate function steepens, the small curve causes the main curve to break and stable homoclinic orbits are destroyed in a region of parameter space. Numerically, we use level set analysis to find that a codimension-one heteroclinic bifurcation occurs at the terminating ends of the solution curves.By replacing the firing rate function with a step function, we show analytically that the bifurcation is related to the value of the firing threshold. We also show the existence of heteroclinic orbits at the breakpoints using a travelling front analysis in the time-dependent system.

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Field Theory of Electromagnetic Brain Activity

Cited by 436 publications

References 11 publications

Natural world physical, brain operational, and mind phenomenal space–time

Natural world physical, brain operational, and mind phenomenal space–time

Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account

Exploiting the Hamiltonian structure of a neural field model

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