Spatio-temporal “global” neurodynamics of the human brain in continuous and discrete picture: Simple statistics meet on-manifold microstates as multi-level cortical attractors

Abstract

The neural manifold in state space represents the mass neural dynamics of a biological system. A challenging modern approach treats the brain as a whole in terms of the interaction between the agent and the world. Therefore, we need to develop a method for this global neural workspace. The current study aimed to visualize spontaneous neural trajectories regardless of their measuring modalities (electroencephalography [EEG], functional magnetic resonance imaging [fMRI], and magnetoencephalography [MEG]). First, we examined the possible visualization of EEG manifolds. These results suggest that a spherical surface can be clearly observed within the spatial similarity space. Once valid (e.g., differentiable) and useful (e.g., low-dimensional) manifolds are obtained, the nature of the sphere, such as shape and size, becomes a possible target of interest. Because these should be practically useful, we suggest advantages of the EEG manifold (essentially continuous) or the state transition matrix (coarse-grained discrete). Finally, because our basic procedure is modality-independent, MEG and fMRI manifolds were also compared. These results strongly suggest the need to update our understanding of neural mass representations to include robust "global" dynamics.

Topographical polarity reveals continuous EEG microstate transitions and electric field direction in healthy aging

“…Furthermore, the positional relationship of each template map was identified based on the distance between maps. Specifically, the positional relationship between maps was determined by compressing the distances defined by the spatial correlation coefficients between topographies (Figure 1d; i.e., dissimilarity matrix between topographies) in three dimensions using the classical multidimensional scaling (MDS) method (Asai et al, 2023; Koenig et al, 2024). We confirmed that when the topographical polarity was considered, the EEG topographies containing EEG microstate templates, which were centroids of states in specific categories, were arranged to cover the surface of the sphere (Figures 2a and 2b).…”

“…(a) Distribution of topography over neural state space. The method for creating neural manifolds was based on that described by Asai, et al (2023). Each dot represented one state of the GFP peak data (49,980 topographies collected from all 190 participants for template clustering).…”

“…First, the positional relationships among the ten templates were clarified in 3D state space through classical MDS based on spatial correlations among template maps (Asai et al, 2023; Koenig et al, 2024). The positions of five template maps of respective positive or negative polarity were consistent with the results of the five templates without polarity (in section 2-2-2; see Figure 3).…”

“…Moreover, we attempted to extend Zanesco et al (2020) and other previous studies by considering topographical polarity. By describing microstate sequences considering topographical polarity, we could quantify the transitions between EEG discrete categories while preserving the continuous spatiotemporal dynamics, as expressed as trajectories on neural manifolds (Asai et al, 2023). Previous studies have suggested that the temporal dynamics of EEG are slower and more unitary in older people (e.g., lower peak frequency of oscillation [Ishii et al, 2017; Merkin et al, 2023; Scally et al, 2018] and lower signal variability, i.e., higher regularity in a fundamental dynamic system [Deery et al, 2023; Lau et al, 2022; Ma et al, 2021]).…”

“…Therefore, microstate label sequences can be an effective continuative discretization method for characterizing the originally continuous spatiotemporal EEG dynamics. Asai et al (2023) have shown that the dynamics of continuous EEG topographies can be visualized as continuous trajectories on spherical neural manifolds defined based on dissimilarities between topographies (see Figure S1).. In their methods, neural states are distributed on a closed spherical surface based on the dissimilarity between states, and EEG microstates are represented as attractors in the EEG state space (Férat et al, 2022; Milz et al, 2017).…”