title: Deriving theoretical phase locking values of a coupled cortico-thalamic neural mass model using center manifold reduction.
abstract: Cognitive functions such as sensory processing and memory processes lead to phase synchronization in the electroencephalogram or local field potential between different brain regions. There are a lot of computational researches deriving phase locking values (PLVs), which are an index of phase synchronization intensity, from neural models. However, these researches derive PLVs numerically. To the best of our knowledge, there have been no reports on the derivation of a theoretical PLV. In this study, we propose an analytical method for deriving theoretical PLVs from a cortico-thalamic neural mass model described by a delay differential equation. First, the model for generating neural signals is transformed into a normal form of the Hopf bifurcation using center manifold reduction. Second, the normal form is transformed into a phase model that is suitable for analyzing synchronization phenomena. Third, the Fokker-Planck equation of the phase model is derived and the phase difference distribution is obtained. Finally, the PLVs are calculated from the stationary distribution of the phase difference. The validity of the proposed method is confirmed via numerical simulations. Furthermore, we apply the proposed method to a working memory process, and discuss the neurophysiological basis behind the phase synchronization phenomenon. The results demonstrate the importance of decreasing the intensity of independent noise during the working memory process. The proposed method will be of great use in various experimental studies and simulations relevant to phase synchronization, because it enables the effect of neurophysiological changes on PLVs to be analyzed from a mathematical perspective.
authors.affiliation: Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan. ogawa@neuron.t.u-tokyo.ac.jp.
authors.forename: Yutaro
authors.identifier: http://orcid.org/0000-0002-7848-8259
authors.initials: Y
authors.lastname: Ogawa
authors.affiliation: Graduate School of Education, The University of Tokyo, Tokyo, Japan.
authors.forename: Ikuhiro
authors.initials: I
authors.lastname: Yamaguchi
authors.affiliation: Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan.|PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Japan.
authors.forename: Kiyoshi
authors.initials: K
authors.lastname: Kotani
authors.affiliation: Graduate School of Engineering, The University of Tokyo, Tokyo, Japan.
authors.forename: Yasuhiko
authors.initials: Y
authors.lastname: Jimbo
mesh_terms: D001921:Brain; D001931:Brain Mapping; D004569:Electroencephalography; D006801:Humans; D008959:Models, Neurological; D013788:Thalamus / Q000502:physiology*
keywords: Center manifold reduction; Cortico-thalamic neural mass model; Neural mass model; Phase locking value; Phase synchronization