Dynamics of cortical activity eigenmodes including standing, traveling, and rotating waves

The eigenfrequencies of natural eigenmodes of cortical activity are calculated from corticothalamic neural field theory. These correspond to poles of a transcendental transfer function, which is accurately approximated here as a rational function. In this approximation, the least damped frequencies of the lowest order spatial eigenmodes dominate the dynamics and correspond to slow-wave ($\ensuremath{\lesssim}1$ Hz) and alpha ($\ensuremath{\sim}10$ Hz) resonances. The eigenmodes exhibit standing and rotating wave patterns in which eigenmode beating can give the appearance of sudden changes in dynamics. This provides a physical explanation of sudden transitions that have been argued to occur between artificially discretized brain activity patterns, sometimes termed microstates, and allows the dynamics to be analyzed by replacing these phenomenologically constructed activity patterns with well-defined eigenmodes. An eigenmode interpretation of large-scale brain activity can thus potentially supplant phenomenological approaches and place analysis on a systematic physical footing.