Fig 1.
Generative linear model of electrophysiological data.
Sources S in the gray matter mix according to the forward model A with the corresponding propagation of currents through tissue to the electrodes. The resulting signals X are recorded with electrodes placed on the cortical surface. The objective is to estimate the source time series from the electrode signals X with a backward model W. Three different backward models are illustrated with one specific example of their respective corresponding spatial filters and patterns. While the spatial filters can look quite different from each other, the spatial patterns point to a similar spatial origin of the extracted signal. Image source for coronal cut: public domain Gray’s anatomy plate 718 [28].
Fig 2.
Example: Spatial mixing of sensorimotor rhythms for one participant.
A) Power spectral densities for three channels along the sensorimotor strip. The gray bar indicates the frequency band defined as the signal contribution for estimating the SSD spatial filters. The power spectrum shows a peak frequency in the alpha-band, with additional harmonic peaks. The channels were selected a according to highest SNR in the chosen frequency range. B) The corresponding signal in the time domain showing oscillatory bursts in the alpha-band, amplitudes are normalized for comparison of time courses. The red box marks a time period in which less pronounced oscillations can be seen in the electrode signals, but the oscillatory power of the constituent SSD components is not decreased. C) Coefficients in the spatial patterns for the selected electrodes, i.e., electrode 2 can be approximated as a linear combination of: e2 = 0.34 component1 + 1.05 component2 + 0.59 component3. D) Power spectral densities for the first three components as estimated by SSD, showing a higher alpha-SNR, with less spectral peaks in flanking frequency bands. E) Time domain signal for the corresponding three components, showing pronounced sensorimotor bursts, normalized amplitudes for comparison of time courses. F) SNR per component, for all 25 components. The SNR drops off fast, only a number of components need to be inspected. For the components last in the sequence, the SNR increases as rhythms in flanking bands increase spectral power also in the band of interest. G) Approximate location of the ECoG-grid in head coordinates. The black markers highlight the electrodes shown in A) and B). H) Spatial filter coefficients showing similarity to bipolar and Laplacian-type filters. I) Spatial pattern coefficients showing focal contributions from sources along the sensorimotor strip.
Fig 3.
Illustration: Increase of relative SNR for sEEG.
A) Three sEEG leads (blue, green, purple color respectively) plotted on cortical surface, ventral view. The electrodes highlighted with a larger circle size correspond to the colored traces. B) Time domain signals for common average referenced (CAR) signals, bipolar referenced signals and strongest SSD components for two selected peak frequencies, with bandwidth highlighted with colored boxes in spectral plots. C) Power spectral densities for common average referenced signals, showing multiple peak frequencies in the spectrum. D) Power spectral densities for bipolar-referenced signals. E) Power spectral densities for SSD components, showing an increased SNR over standard referencing.
Fig 4.
Identifying independent sources.
A) Spatial patterns for two components with electrodes highlighted in green. B) Time domain activity for two neighboring electrodes (black) and the top SNR components for alpha range (gray span in the spectrum in C), showing that the oscillatory activity is largely captured by the first component, with a smaller alpha component in the second component that is otherwise masked in the electrode activity. C) Power spectral densities for electrode and component signals. D) Spatial spread for components with different peak frequency showing large variation. Each circle corresponds to one component. E) Example spatial pattern coefficients visualized on electrode grids, for high spatial spread (top row), where a component contributes to activity of many electrodes and low spatial spread (bottom row) with a single maximum. In contrast to A), the absolute value is plotted here to better illustrate the spread, regardless of polarity. The electrode with the largest coefficient is marked with a green circle.
Fig 5.
Variability of resting rhythms across the cortex.
A) Each subplot shows the location of electrodes (white squares) on a template brain for one individual participant. Each sphere indicates an oscillatory component, with the size indicating 1/f-corrected SNR and the color indicating peak frequency of that component. If there is no sphere of a respective color in the vicinity of an electrode, no rhythm above the SNR-threshold could be detected in that frequency band. There is large variability between participants. For improved comparison across participants, all electrodes and rhythm locations were mapped onto the right hemisphere. Participants are ordered according to the mean z-coordinate across the electrode grid, to ease comparison. B) Each component is represented as a circle, with y-position reflecting peak frequency and x-position reflecting participant ID. Color represents position along the posterior-anterior axis, with negative values reflecting most-posterior position. C) Histogram across all participants and components showing a relative lack of detectable 10 Hz rhythms.
Fig 6.
Waveform shape of intracranial neuronal rhythms.
A) Neighboring rhythms with different waveform shape for two electrodes and two components estimated based on alpha band activity. B) Power spectral density for electrodes and components. The presence of harmonic spectral peaks at exact multiples of the alpha peak frequency indicates a non-sinusoidal waveform shape. The gray marked area corresponds to the frequency range defined as a signal for estimation of spatial filters. While both electrode signals show a peak in the beta-band, in component space the sharp beta-harmonic is largely captured by the second component, showing a spike-wave waveform shape, with the first component being a triangular waveform. C) Topographies for the first and second components showing a radial and tangential source distribution (respectively); the electrodes shown as traces in B are marked with green circles. D) Group-level assessment of waveform asymmetry, with intracranial recordings showing considerable peak-trough asymmetry in the waveform (where a peak-trough asymmetry value of 0 is indicating perfect symmetry). E) Peak-trough asymmetry values, plotted across the cortex, larger circles indicate larger SNR. Rhythms with high asymmetry can be found through-out the cortex.
Fig 7.
Illustration: Removal of noise with spatial filters for ECoG data.
A) Time series of six electrodes and power spectra for raw ECoG recording for 87 electrodes, color code corresponds to electrode position, with neighboring electrodes having a similar color. B) Time series and power spectra after removal of components maximizing SNR for 60 Hz and 200 Hz spectral peaks. Note that there are no band-stop type artefacts in the spectrum since no temporal filtering was performed. C) Time series and power spectra after common average referencing. While the 200 Hz noise is largely attenuated, 60 Hz line noise still persists. D) Time series and power spectra after common average referencing and then band-stop filtering. The band-stop filters introduce artefacts in the spectral domain.