1,392 research outputs found

    Internetwork and intranetwork communications during bursting dynamics: Applications to seizure prediction

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    We use a simple dynamical model of two interacting networks of integrate-and-fire neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony declines below normal levels during the state preceding seizures (preictal state). We model the transition from the seizure free interval (interictal state) to the seizure (ictal state) as a slow increase in the mean depolarization of neurons in a network corresponding to the epileptic focus. We show that the transition from the interictal to preictal and then to the ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity due to resonance between the two interacting networks observed during the interictal period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the epileptic focus. Based on this result, we hypothesize that the beginning of the preictal period marks the beginning of the transition of the epileptic network from normal activity toward seizing

    Markers of criticality in phase synchronization

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    The concept of the brain as a critical dynamical system is very attractive because systems close to criticality are thought to maximize their dynamic range of information processing and communication. To date, there have been two key experimental observations in support of this hypothesis: (i) neuronal avalanches with power law distribution of size and (ii) long-range temporal correlations (LRTCs) in the amplitude of neural oscillations. The case for how these maximize dynamic range of information processing and communication is still being made and because a significant substrate for information coding and transmission is neural synchrony it is of interest to link synchronization measures with those of criticality. We propose a framework for characterizing criticality in synchronization based on an analysis of the moment-to-moment fluctuations of phase synchrony in terms of the presence of LRTCs. This framework relies on an estimation of the rate of change of phase difference and a set of methods we have developed to detect LRTCs. We test this framework against two classical models of criticality (Ising and Kuramoto) and recently described variants of these models aimed to more closely represent human brain dynamics. From these simulations we determine the parameters at which these systems show evidence of LRTCs in phase synchronization. We demonstrate proof of principle by analysing pairs of human simultaneous EEG and EMG time series, suggesting that LRTCs of corticomuscular phase synchronization can be detected in the resting state and experimentally manipulated. The existence of LRTCs in fluctuations of phase synchronization suggests that these fluctuations are governed by non-local behavior, with all scales contributing to system behavior. This has important implications regarding the conditions under which one should expect to see LRTCs in phase synchronization. Specifically, brain resting states may exhibit LRTCs reflecting a state of readiness facilitating rapid task-dependent shifts toward and away from synchronous states that abolish LRTCs

    Plasma Brain Dynamics (PBD): A Mechanism for EEG Waves Under Human Consciousness

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    EEG signals are records of nonlinear solitary waves in human brains. The waves have several types (e.g., α, β, γ, θ, δ) in response to different levels of consciousness. They are classified into two groups: Group-1 consists of complex storm-like waves (α, β, and γ); Group-2 is composed of simple quasilinear waves (θ and δ). In order to elucidate the mechanism of EEG wave formation and propagation, this paper extends the Vlasov-Maxwell equations of Plasma Brain Dynamics (PBD) to a set of two-fluid, self-similar, nonlinear solitary wave equations. Numerical simulations are performed for different EEG signals. Main results include: (1) The excitation and propagation of the EEG wave packets are dependent of electric and magnetic fields, brain aqua-ions, electron and ion temperatures, masses, and their initial fluid speeds; (2) Group-1 complex waves contain three ingredients: the high-frequency ion-acoustic (IA) mode, the intermediate-frequency lower-hybrid (LH) mode, and, the low-frequency ion-cyclotron (IC) mode; (3) Group-2 simple waves fall within the IA band, featured by one or a combination of the three envelopes: sinusoidal, sawtooth, and spiky/bipolar. The study proposes an alternative model to Quantum Brain Dynamics (QBD) by suggesting that the formation and propagation of the nonlinear solitary EEG waves in the brain have the same mechanism as that of the waves in space plasmas

    Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

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    This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

    Quantum calcium-ion interactions with EEG

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    Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options. \textbf{Objective}: In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach. \textbf{Method}: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. \textbf{Results}: The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models. \textbf{Conclusion}: This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.Comment: published in Sc

    Brain Dynamics across levels of Organization

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    After presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the Dynamic Core (DC) and the Global Neuronal Workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene-Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical-subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of Self-Organized Criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical Physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG

    Controlling chaos in a chaotic neural network

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    The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be controlled with this method and the states of the network can converge in one of its stored patterns if the control strength and the pinning density are chosen suitable. It is found that in general the threshold of the control strength of a controlled network is smaller at higher pinned density and the chaos of the chaotic neural network can be controlled more easily if the pinning control is added to the variant neurons between the initial pattern and the target pattern

    States and sequences of paired subspace ideals and their relationship to patterned brain function

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    It is found here that the state of a network of coupled ordinary differential equations is partially localizable through a pair of contractive ideal subspaces, chosen from dual complete lattices related to the synchrony and synchronization of cells within the network. The first lattice is comprised of polydiagonal subspaces, corresponding to synchronous activity patterns that arise from functional equivalences of cell receptive fields. This lattice is dual to a transdiagonal subspace lattice ordering subspaces transverse to these network-compatible synchronies. Combinatorial consideration of contracting polydiagonal and transdiagonal subspace pairs yields a rich array of dynamical possibilities for structured networks. After proving that contraction commutes with the lattice ordering, it is shown that subpopulations of cells are left at fixed potentials when pairs of contracting subspaces span the cells' local coordinates - a phenomenon named glyph formation here. Treatment of mappings between paired states then leads to a theory of network-compatible sequence generation. The theory's utility is illustrated with examples ranging from the construction of a minimal circuit for encoding a simple phoneme to a model of the primary visual cortex including high-dimensional environmental inputs, laminar speficicity, spiking discontinuities, and time delays. In this model, glyph formation and dissolution provide one account for an unexplained anomaly in electroencephalographic recordings under periodic flicker, where stimulus frequencies differing by as little as 1 Hz generate responses varying by an order of magnitude in alpha-band spectral power. Further links between coupled-cell systems and neural dynamics are drawn through a review of synchronization in the brain and its relationship to aggregate observables, focusing again on electroencephalography. Given previous theoretical work relating the geometry of visual hallucinations to symmetries in visual cortex, periodic perturbation of the visual system along a putative symmetry axis is hypothesized to lead to a greater concentration of harmonic spectral energy than asymmetric perturbations; preliminary experimental evidence affirms this hypothesis. To conclude, connections drawn between dynamics, sensation, and behavior are distilled to seven hypotheses, and the potential medical uses of the theory are illustrated with a lattice depiction of ketamine xylazine anaesthesia and a reinterpretation of hemifield neglect
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