Resting state EEG microstates: is a new FORM all you need?

Abstract

Introduction: Before asking which microstate an EEG sample belongs to, there is a simpler question: can it look like a microstate at all? Yet a winning correlation mixes three different properties: how microstate-like the scalp field is, where it lies within that geometry, and how well the available templates represent that direction. We asked whether a fixed geometry, independent of any microstate solution, could explain common structure of microstate maps, constrain how strongly EEG patterns can match them, and describe that structure in interpretable terms. Methods: We introduce First-Order spherical haRMonic (FORM), projecting normalized scalp topographies onto a fixed three-dimensional subspace defined only by sensor geometry. Direction describes field geometry; projection norm, {rho}, measures FORM conformity and the maximum correlation attainable by any FORM topography. We tested simulations, literature templates, and 374 recordings from 187 LEMON participants. Results: FORM captured canonical microstate geometry despite being defined a priori of a microstate solution: FORM explained energy, {rho} squared, was 0.990-0.998 for five meta-microstates and 0.966-0.986 for pooled LEMON maps. Across 313 literature templates, FORM angular distances preserved their independently derived organization (Spearman {rho}=0.987). In continuous EEG, FORM conformity explained a median 74.4% of within-subject variance in winning-template correlation, versus 21.7% for GFP. As independently estimated dictionaries increased from k=1 to k=12, the median fitted fraction of the FORM ceiling rose from 0.613 to 0.970. Discussion: FORM places an a priori continuous geometry beneath discrete microstate labels. It separates properties intrinsic to the scalp field - whether it is microstate-like and where it lies within that geometry - from how well the chosen template dictionary represents it. FORM therefore provides an interpretable, clustering-independent reference for assignment strength, template comparison and continuous microstate dynamics.