Comparison of EFD reconstructed fMRI activity (top) with SPECTRE EEG reconstruction in the frequency band 0 − 1hz at both 2mm (middle) and 1mm (bottom) spatial resolution (axial view) from a single representative subject from an open-source study with simultaneous fMRI and EEG [40].

In both cases, the weighted sum of the power over all modes is shown. The task was a simple 8Hz flashing checkerboard with 4 on/off cycles. The nonlinear registration of the fMRI to the anatomical template in the fMRI data (top) is imperfect because of significant field-induced non-linear geometric distortions in the fMRI data. The colors are the weighted sum over all estimated amplitudes of the activation modes. Intensities are scaled between 0 and 1, and thresheld at .6.

A detailed visualization of three orthogonal views of data in Fig.1) demonstrating the fine spatial resolution produced by SPECTRE, and the ability to reconstruct activations in regions prone to severe distortions in fMRI, such as the frontal lobes and cerebellum.

The colors are the weighted sum over all estimated amplitudes of the activation modes. Intensities are scaled between 0 and 1, and thresheld at .6.

Correlation coefficient in each axial slice (from inferior to superior) between the activation patterns estimated by SPECTRE EEG and the fMRI for the data in Fig.1).

Regions of high correlation indicate the similarity in activation patterns detect between the two completely different neuroimaging methods (SPECTRE and FMRI). Reduction of the correlations in the superior regions of the brain, possible due to the increased distortions in that region in this fMRI dataset.

A. Baseline-corrected EEG activity from a single subject elicited by unattended (top) and attended (bottom) visual stimuli averaged across the cluster of 3 occipital electrode sites (PO7, PO3, O1) denoted in B. by white circles.

Over the broad alpha frequency band (7-16Hz) there was a reduction in total power (from the pre- to post-stimulus latency interval) which was greater for attended, compared to unattended, visual stimuli. B. Scalp-topography of the mean difference in oscillatory (8-12Hz) activity for unattended minus attended visual stimuli across the 0-2000ms latency interval. As expected, attention modulated (reduced) the power of these oscillations over the visual cortex. C. As in A. for three frontal electrode sites (F6, F8, AF6) denoted in D. by black circles. In contrast to visual cortex, in bilateral frontal regions, unattended visual stimuli elicited a greater reduction of oscillatory activity between 5-10Hz (theta-alpha frequency). D. Frontal view of the unattended minus attended difference topography between 0-2000ms in the 8-12Hz frequency band. E. SPECTRE power estimates derived from mean (baseline-corrected) oscillatory power between 0-2000ms and across 8-12Hz for the same subject shown in panels A-D, superimposed on the MNI template brain. Hot colors (yellow to red) indicate greater attention-related modulation (reduction) of activity and the inverse for warm colors (light to dark blue). F. BOLD signal (beta parameter estimate) contrasting activation to visual stimuli when attended versus activation to the same stimulus when unattended. Attention-related enhancement of the BOLD signal in visual cortex mirrors the reduction in alpha power obtained in the same subject using EEG.

Estimated localization of neural activity for 8-12Hz oscillatory activity (unattended minus attended; 02000ms) for five participants (S1-S5).

Colors are as in 1E. A prominent bilateral occipital source associated with increased attentional modulation is observable in all participants. A bilateral source localized in middle frontal cortex and indicating less modulation is also consistently observed across participants. Note that these are difference maps from the weighted sum over all estimated amplitudes of the activation modes, so that the intensities are scaled between −1 and 1, and thresheld at absolute value .6.

Direct comparison of activation maps from two participants (Subject A, left; Subject B, right) in the bimodal (auditory + visual) stimulation paradigm described for Figures 3 and 4.

In each subject, two brain regions - the cerebellum and the occipital pole (top and bottom rows, respectively), were delineated based on the MNI atlas and EFD activation maps were correlated across these entire regions. Correlation coefficients were as follows: for Subject A, cerebellum=0.74, occipital pole=0.70; for Subject B, cerebellum=0.70, occipital pole=0.84. Correlations were computed only for regions exhibiting activation levels above 0.1. In contrast to fMRI, the SPECTRE technique identified robust activations in bilateral middle and inferior frontal cortex (indicated by yellow arrows) and middle temporal cortex (red arrows). It also discerned activations along the superior temporal cortex, including areas encompassing the primary auditory cortex (green arrows).

Orthogonal slices from whole brain electric field activation maps from a 2mm SPECTRE reconstruction of EEG data from a single subject in the attention study.

The colors are the weighted sum over all estimated amplitudes of the activation modes.

(Top row) Full array of intra-cranial EEG contacts from a recording in a medically refractory epilepsy patient (yellow dots).

Red dots indicate subset of surface-only electrodes to mimic a standard non-invasive (i.e., extra-cranial) EEG study. SPECTRE α band reconstruction from (A) full array of intra-cranial EEG sensors from an epilepsy study (yellow dots) in top row and (B) from subset of surface electrodes (red dots) in top figure. (C) Overlay of (A) and (B) validating that the surface based is correctly reconstructing the local electric field potential detected by the intra-cranial electrodes.

Statistical comparison of full vs surface intra-cranial EEG estimates.

The horizontal axis are the correlation coefficients between the estimates obtain the full set of electrodes and the deep electrodes (adjacent to the source). The vertical axis are the correlation coefficients between the full set of electrodes and just the surface electrodes, as would be collected in a standard (extra-cranial) EEG experiment. The results are highly correlated and thus support the claim that the SPECTRE recontruction of the spatial distribution of deep electrical activity from the surface measurements accurately reflects the true spatial localization of the deep electric fields.

Validation of WETCOW model with intra-cranial measurements and SPECTRE reconstruction.

(Top) Examples of wave trajectories obtained in simulation of wave propagation in real data cortical fold tissue model. Panels (a)-(c) show the complete trajectories and panels (d)-(e) show the emergent stable wave loops. The colors encode wave propagation: red - left/right, green - anterior/posterior and blue - dorsal/ventral. (Bottom) (left) EEG contacts and (right) detected WETCOW cortical loops from iEEG recordings of epileptic seizure onset in insular posterior opercular area

© 2020 Massachusetts Institute of Technology. All rights reserved. The spherical cortex shell model of is used for panels (a) and (d) and the cortical fold model is used for panels (b),(c),(e), and (f) (reprinted from [9] with permission). It is not covered by the CC-BY 4.0 licence and further reproduction of this panel would need permission from the copyright holder.

Gambling task EEG from 500 subject cohort.

Alpha power of the weighted summed over the first n = 10 SPECTRE modes. Activation in key regions of the reward circuit, including the frontal lobes, paracingulate gyrus, accumbens, and amygdala are clearly evident. Negative activation (i.e., deactivation) is evident in the supplementary motor cortex and the left temporal-parietal regions.

SPECTRE power per brain region in the Harvard-Oxford 2mm cortical (top) and subcortical (bottom) atlases.

Colormap is from hot/yellow (activated) to blue (de-activated). Activation in key regions of the reward circuit, including the frontal lobes, paracingulate gyrus, subcallosal cortex/nucleus accumbens, and amygdala are clearly evident. Negative activation (i.e., deactivation) is evident in the supplementary motor area, posterior cingulate, and thalamus. Activation of the important reward element accumbens is evident in the bottom plot. Also of note is the relatively similar activation in the bilateral subcortical elements.

Statistical significance. t-statistic between the SPECTRE power modes pre- and post-stimulus reward experiment.

Calculations were performed using the standard AFNI 3dttest++ algorithm. Yellow/red color reflects positive changes, blue color reflects negative changes. Significance threshold was p = 10−8, indicating strong statistical significance.

The significance of a detected spatiotemporal pattern.

Idealized numerical simulation in which there are two areas of activity in Gaussian random noise: a point oscillating with very high signal-to-noise (SNR) (centered on the red dot) but also a larger circular region with very low SNR (centered at the blue dot). Traditional estimation methods tend to favor high SNR signals (red dot) but have difficulty with low SNR activity with very high spatial correlations (blue dot). The EFD takes both spatial and temporal correlations into account and therefore detects both regions.

(Top left) Original lattice; (Top right) ESP probability. (Middle) Principal Components Analysis (PCA) results on same original lattice. The ESP probability locates the structure in a single calculation. The PCA decomposition even for 6 components shows significant errors. Several more components would be required to accurately fit the data. (Bottom row) Space-time ESP. (Top left) Space-time trajectory of 2D data; (Top right) ESP probability.

Schematic for the construction of space-time EFD modes from the data.

Validation of SPECTRE with iEEG data for subject 2 (see Fig.8 for details.)

Validation of SPECTRE with iEEG data for subject 3 (see Fig.8 for details.)

Validation of SPECTRE with iEEG data for subject 4 (see Fig.8 for details.)