Solving the brain synchrony eigenvalue problem: conservation of temporal dynamics (fMRI) over subjects doing the same task

Brain measures often show highly structured temporal dynamics that synchronize when observers are doing the same task. The standard method for analysis of brain imaging signals (e.g. fMRI) uses the GLM for each voxel indexed against a specified experimental design but does not explicitly involve temporal dynamics. Consequently, the design variables that determine the functional brain areas are those correlated with the design variation rather than the common or conserved brain areas across subjects with the same temporal dynamics given the same stimulus conditions. This raises an important theoretical question: Are temporal dynamics conserved across individuals experiencing the same stimulus task? This general question can be framed in a dynamical systems context and further be posed as an eigenvalue problem about the conservation of synchrony across all brains simultaneously. We show that solving the problem results in a non-arbitrary measure of temporal dynamics across brains that scales over any number of subjects, stabilizes with increasing sample size, and varies systematically across tasks and stimulus conditions.