Spatio-temporal "global" neurodynamics in both continuous and discrete pictures for human brains

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 where canonical microstates are on-manifold. 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.