![]() In this case, the obtained eigenvalue spectrum exhibits a decrease in the last eigenvalue and a compensatory increase in the lower eigenvalues compared to case (b), which consequently yields a meanλ 1:60% value between those in cases (a) and (b). ![]() (c) A set of IMFs extracted from different channels within a 1-s ictal period leads to a R N×N matrix with values between case (a) and (b), showing a partial synchronization among the oscillators. In this case, the eigenvalue decomposition of the R N×N matrix yields five for the last eigenvalue and zero for the rest of the eigenvalues. (b) Five-times copied version of an IMF leads to a R N×N matrix, in which all of its values are equal to one, showing a full phase-synchronization among the oscillators. In this case, all the eigenvalues resulted from the eigenvalue decomposition of the R N×N are close to one. Due to the nearly orthogonal nature of the IMFs extracted from one channel, all the R N×N values are near to zero, showing no phase-synchronization among the oscillators. This experiment looks at synchrony as a subjective auditory percept in the context of several auditory scenes. Often, it is interpreted as signals/systems operating at the same frequency with a consistent phase relationship. (a) Five decomposed IMFs from a 1-s, bipolar-derivate ECoG signal using the NA-MEMD process, along with their corresponding mean-phase coherence matrix, eigenvalue spectrum, and the average value of the first 60% lower-index eigenvalues, meanλ 1:60%. In a pulse radar system, coherence describes the phase relationships between the transmitted and the received pulses. In many ways, the term Phase-coherent is not strictly defined. ![]() All of the values in the mean-phase coherence matrix, R N×N, were normalized and color-coded between zero (black), to one (white). This result suggests that hyper-synchronization of the epileptic network may be an essential self-regulatory mechanism by which the brain terminates seizures.Įvaluating phase-synchrony levels among neuronal oscillators using eigenvalue decomposition of the mean-phase coherence matrix. These coherence changes exhibit properties similar to those of receptive field remapping, a phenomenon in which individual neurons change their receptive fields according to the metrics of each saccade. However, the network phase-synchrony started to increase toward seizure end and achieved its maximum level at seizure offset for both types of epilepsy. Drug-refractory patients with frontal and temporal lobe epilepsy demonstrated a reduction in phase-synchrony around seizure onset. ![]() The extracted neuronal oscillators were grouped with respect to their frequency range into wideband (1-600 Hz), ripple (80-250 Hz), and fast-ripple (250-600 Hz) bands in order to investigate the dynamics of ECoG activity in these frequency ranges as seizures evolve. The phase-synchrony dynamics were then assessed using eigenvalue decomposition. Next, the instantaneous phases of the oscillatory functions were extracted using the Hilbert transform in order to be utilized in the mean-phase coherence analysis. The amount of coherence can readily be measured by the interference visibility, which looks at the size of the interference fringes relative to the input waves (as the phase offset is varied) a precise mathematical definition of the degree of coherence is given by means of correlation functions. A set of finite neuronal oscillators was adaptively extracted from a multi-channel electrocorticographic (ECoG) dataset utilizing noise-assisted multivariate empirical mode de-composition (NA-MEMD). In this paper, a non-linear analytical methodology is proposed to quantitatively evaluate the phase-synchrony dynamics in epilepsy patients. To extend v's answer and link it to some concerns in your question:Ĭoherences are the phase relationships between sections of our system.Īs you noted, coherence is related to the superposition of states $|\psi\rangle = w_a |a\rangle + w_b e^$ a coherence, because its magnitude represents the strength of the phase relationship between the states, and the phase of one is precisely the "averaged" phase relationship of the mixtures.Spatiotemporal evolution of synchrony dynamics among neuronal populations plays an important role in decoding complicated brain function in normal cognitive processing as well as during pathological conditions such as epileptic seizures. ![]()
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