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| Paper IPM / Cognitive / 13434 |
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Phase coupling and synchronization have been an important concept in the study of oscillations of neural systems for the past few decades. The phase coupling of various neuronal measurements was observed within local activity of cortical and subcortical areas and even between activities in distant brain regions [1]. Nevertheless, previous methods for estimating phase couplings are limited. Both standard phase correlation and phase coherence compute static pairwise dependency of two oscillators, therefore are limited to uncover underlying couplings of multiple oscillators, and are blind to their underlying dynamics. Recently, Cadieu and Koepsell [2] provided a model-based method that allows us to directly and simultaneously estimate underlying undirected couplings of multiple oscillators using the Kuramoto model of an oscillator network. However, this and other previous methods cannot reveal causal relations between the oscillators. Here we propose a method to estimate the causality in the phase space from measurements of neural oscillations. A new probabilistic method was developed to estimate directed coupling parameters of the phase oscillators from noisy multivariate circular time-series data. In this method, we constructed a probabilistic description of the Kuramoto model, and developed an algorithm to estimate the coupling parameters under the maximum likelihood principle. We demonstrate that the proposed method recovers the underlying direction and weights of couplings between noisy dynamic oscillators while previous approaches by the phase correlations and the Granger causality were unable to recover these values correctly. We stress that the method performs well on a relatively large number of oscillators even in the presence of noise. The estimated directed graphs provide us useful tools to uncover causal relations of cortical networks, such as casual interactions of local micro-circuitries, and extract their network topology. [1] Buzsaki, G. and et al. (2013) Neuron. [2] Cadieu and Koepsell (2010) Neural Comput.
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