Abstract
What are the functional neuroimaging measurements required for more fully characterizing the events and locations of neocortical activity? A prime assumption has been that modulation of cortical activity will inevitably be reflected in changes in energy utilization (for the most part) changes of glucose and oxygen consumption. Are such a measures complete and sufficient? More direct measures of cortical electrophysiological activity show event or task-related modulation of amplitude or band-limited oscillatory power. Using magnetoencephalography (MEG), these measures have been shown to correlate well with energy utilization sensitive BOLD fMRI. In this paper, we explore the existence of state changes in electrophysiological cortical activity that can occur independently of changes in averaged amplitude, source power or indices of metabolic rates. In addition, we demonstrate that such state changes can be described by applying a new measure of complexity, rank vector entropy (RVE), to source waveform estimates from beamformer-processed MEG. RVE is a non-parametric symbolic dynamic informational entropy measure that accommodates the wide dynamic range of measured brain signals while resolving its temporal variations. By representing the measurements by their rank values, RVE overcomes the problem of defining embedding space partitions without resorting to signal compression. This renders RVE-independent of absolute signal amplitude. In addition, this approach is robust, being relatively free of tunable parameters. We present examples of task-free and task-dependent MEG demonstrating that RVE provides new information by uncovering hidden dynamical structure in the apparent turbulent (or chaotic) dynamics of spontaneous cortical activity.
Highlights
ENTROPY AND COMPLEXITY The term “entropy” is commonly defined as a measure of the order or disorder in a physical system
Our single most important finding is that the rank vector entropy (RVE) measure of complexity adds new information about brain dynamics that was previously hidden within the apparent chaos of spontaneous cortical signals
RVE, when combined with a scalar beamformer, reveals an underlying spatiotemporal complexity pattern that is modulated by stimuli and tasks
Summary
ENTROPY AND COMPLEXITY The term “entropy” is commonly defined as a measure of the order or disorder in a physical system. The spatiotemporal patterns observed with changing parameter values include transitions from laminar (linear) flow via a Hopf bifurcation to periodic oscillations, followed by two or more simultaneous irrationally related periodic flows and the aperiodic oscillations of turbulent (chaotic) dynamics (Ruelle and Takens, 1971). The latter state is characterized by positive entropy generation (Eckmann and Ruelle, 1985) similar to that observed in the MEG record (Mandell et al, 2011a,b; Robinson et al, 2012)
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