LORETA EEG phase reset of the default mode network.

Example of phase reset of LORETA current density time series from one subject. Top are the LORETA EEG phase differences with respect to the left Hemisphere Brodmann area (BA) 8 time series. The last four traces are the phase difference (degrees) for BA8L–BA28L, BA8–BA35L, BA8L–BA36L, and BA8L–BA37L. Bottom are the 1st derivatives of the phase differences in the top traces in degrees/centiseconds. A 1st derivative ≥5°/cs marked the onset of a phase shift and an interval of time following the phase shift where the 1st derivative ~0 defined the phase lock duration.

The locations of the six Default Mode Networks as summarized by Buckner et al. (2008) and represented by the Key Institute LORETA voxels (Lancaster et al., 2000; Pascual-Marqui, 2004).

Phase shift durations between Brodmann areas in the x, y, z LORETA time series directions and the resultant vector in the lower right where R=x2+y2+z2. The x-axis is phase shift duration in milliseconds and the y-axis is the percent of subjects that exhibited a given phase shift duration for different Brodmann area pairs. The solid line is the eyes closed condition and the dashed line is the eyes open condition. All of the subjects are represented within each curve. For example, 100% of the subjects exhibited a phase shift duration between 18 and 35 ms for Brodmann areas 8 and 9 (upper left panel x-shift) and similarly for each Brodmann area pair. The finding of discrete phase shift durations with none or little overlap of data points under each phase shift duration curve was a dominant feature of phase shift duration and demonstrates discrete “temporal quanta.”

Phase lock durations between Brodmann areas in the x, y, z LORETA time series directions and the resultant vector in the lower right where R=x2+y2+z2. The x-axis is phase lock duration in milliseconds and the y-axis is the percent of subjects that exhibited a given phase lock duration for different Brodmann area pairs. The solid line is the eyes closed condition and the dashed line is the eyes open condition. All of the subjects are represented within each curve. For example, 100% of the subjects exhibited a phase shift duration between 250 and 500 ms for Brodmann areas 8 and 10 (upper left panel x-lock) and similarly for each Brodmann area pair. The finding of discrete phase lock durations with none or little overlap of data points under each phase lock duration curve was a dominant feature of phase lock duration and demonstrates discrete “temporal quanta.”

The x-axis is the Euclidean distance between the center voxels that comprise the DMN Brodmann areas as described in Table 1. The y-axis is phase shift duration (Top) and phase lock duration (Bottom) of the Brodmann areas described in Table 1. The left row are the left hemisphere Brodmann areas and the right row are the right hemisphere Brodmann areas. The red line is the fit of an exponential equation T = b1 + eb2 + (b3/d) where T = duration time (ms), d = distance between Brodmann areas (mm) and b1, b2, and b3 are coefficients. R = regression correlation and p = statistical probability. Phase shift and phase lock are inversely related where Brodmann areas with short phase shift duration exhibit long phase lock durations while Brodmann areas with short phase lock durations exhibit long phase shift durations.

Test of volume conduction. The y-axis is the mean absolute phase differences (degrees) of the resultant vector between Brodmann areas. The x-axis is the Euclidian distance (mm) between all Brodmann area pairs. The left graph is from the left hemisphere and the right graph is from the right hemisphere.

(A) (Top) is an example of discrete durations or “temporal quanta” of phase shift duration in different Brodmann areas of the DMN. The eyes vs. eyes closed shift to longer durations are due to increased functional connectivity with increased input that is like a “shutter” whose duration is proportional to the number of recruited neurons. The discontinuities are due to different packing densities in different Brodmann areas. The bottom plot (B) is the evaluation of Equation (1) using the mean LORETA phase shift and lock duration for both eyes closed and open conditions for the 91 Brodmann area combinations: T = b1 + eb2 + (b3/d) The link between EEG phase shift and neural packing density is the physiological observation of action potential bursts when in-phase to LFPs vs. suppression of action potentials when ant-phase to LFPs Hughes and Crunelli (2007). EEG is the summation of LFPs therefore phase shifts are necessarily related to neural packing density, i.e., the higher the packing density than the longer the phase shift as a property of summation. It is hypothesized that the increased shift duration between eyes closed vs. eyes open is due to increased arousal and increased depolarization resulting in increased functional connectivity (increased neural resource). Phase lock is inversely proportional to phase shift duration based on the spatial-temporal GABA connections and delays between excitatory neurotransmitter EPSPs in local and long distance loops. The physiological differences in the genesis of phase shift vs. phase lock is related to the “Gap” of time which is a transition time between local EPSP excitation and re-enterant long distance EPSPs that produce the phase shift followed by long duration inhibitory synaptic potentials that contribute to phaselock duration. The rebound from inhibition and arrival of EPSPs starts the phase reset process. Predicted phase shift and lock durations can be evaluated by using the coefficients in Table 3. For example, the distance between Module1 and Module2 from Hagmann et al. (2008) and Thatcher et al. (2011, Table 3) is 43.4 mm which that predicts a phase shift duration = 56 ms and phase lock duration = 300 ms based on Equation (1).