Fig 1.
Critical points in vector fields.
Schematic of critical point types in velocity vector fields. Dots and triangles show critical points, arrows show typical surrounding vector fields for all 2D critical point classes. Unstable and stable nodes correspond to source and sink patterns respectively, unstable and stable foci correspond to spirals-out and spirals-in respectively. Saddle pattern has stable (solid line) and unstable (dashed line) axes indicated, these axes can occur at any orientation in general.
Fig 2.
Effect of optical flow parameters on computed velocity fields.
A, Consecutive snapshots separated by arbitrary time step δt of artificial noisy phase data, containing an expanding source and contracting sink pattern, both drifting slowly across the array. B, Velocity fields between images in A calculated using optical flow with varying smoothness parameter α and non-linear penalty parameter β. Filled red circles indicate detected critical points, open blue circles indicate true critical point locations.
Fig 3.
Critical point pattern detection performance in simulated data.
A, Mean displacement (in grid spaces) between detected and true critical point location across n = 50 sequences of simulated random critical point patterns for different values of optical flow parameters α and β. Error bars indicate SEM. Outlined points indicate α parameter value used for plots D-F. B, Mean percentage of true patterns missed or misclassified by pattern detection algorithm. C, Mean number of extra, spurious patterns detected per time step. D, Mean false patterns detected per time step (false positive rate) against the percentage of patterns correctly identified (true positive rate) for different parameter values. E-G, Same as A-C, but showing performance under different levels of noise with a fixed value of α. Noise levels are given as the common logarithm of the standard deviation of added white noise relative to average signal amplitude. Outlined points indicate noise level used for plots A-C.
Fig 4.
Complex wave patterns in marmoset area MT and mouse cortex.
A, B, C, Complex wave patterns in phase maps of 4 Hz LFP oscillations during ongoing activity recorded from marmoset area MT. Velocity vector fields (black arrows) were calculated between consecutive phase maps separated by 1 ms; we use larger time gaps between snapshots here to show wave propagation more clearly. Critical points are indicated by symbols corresponding to the classes in Fig 1. D, E, Complex wave patterns in phase maps of 4 Hz optical voltage imaging oscillations in awake mouse cortex. Velocity vector fields are calculated from phase maps separated by 20 ms. F, Localized propagating activity in amplitude maps of 10 Hz optical voltage imaging oscillations in awake mouse cortex.
Fig 5.
Wave pattern properties in real data compared to noise-driven surrogate data.
A, Mean number of 6 Hz phase patterns detected per second per trial in real data (white bars, marmoset LFPs during dot-field stimulus) and surrogate data (shaded bars, white noise with equal mean and variance per recording channel to real data). Error bars indicate SEM across 100 trials for both datasets. PW, plane wave; SY, synchrony; SI, sink; SO, source; SP-I, spiral-in, SP-O, spiral-out, SA, saddle. B, Same as A, but showing percentage of recording time active. C, Same as A, but showing mean pattern duration.
Fig 6.
Distributions of plane wave propagation direction and complex pattern center location in ongoing and stimulus-evoked PVFs.
A, Histogram of plane wave propagation direction in 6 Hz phase of ongoing activity. Also shown is the percentage of time across the recording in which plane wave activity occurred. B, Spatial distribution within the recording array of critical points across all occurrences of node and saddle patterns. Note that foci have been combined with nodes for this analysis. C, D, Same as A, B, but for a recording visually evoked by moving dot fields.
Fig 7.
Tracking pattern evolution dynamics.
A, Snapshots of 6 Hz phase and phase velocity fields from marmoset area MT LFPs during dot field stimulus, showing evolution from a plane wave pattern to a sink pattern. Black dot marks stable node location. B, Mean percentage difference between number of observed and expected pattern transitions (within 50 ms) for recording shown in A. Rows give initial pattern, columns give following pattern. Bold values indicate significant differences between observed and expected counts across all trials (p<0.05, paired t-test with Bonferroni correction). PW, plane wave; SY, synchrony; SI, sink; SO, source; SA, saddle. Node and focus critical points are combined.
Fig 8.
Oscillatory filtering and velocity vector field calculation in LFPs from marmoset visual area MT during dot field stimulus.
A, Left: LFP waveforms from two nearby recording sites. Black lines indicate times at which snapshots are shown. Stimulus onset was at 0 s. Centre: Snapshots of LFPs across all recording channels at the indicated times. Right: Velocity vector field estimating the motion between the two snapshots. B, Same as A, but with waveforms filtered with Morlet wavelets to extract 8 Hz oscillations. C, Same as B, but only the amplitude of the 8 Hz oscillations. D, Same as B, but only the phase of the 8 Hz oscillations. All velocity fields have normalized average magnitude.
Fig 9.
Dominant principal component analysis and vector singular value decomposition modes in 10Hz marmoset LFP oscillations during dot-field stimuli.
A, Top spatial PCA modes of filtered LFPs, with percentage variance explained. B, Top spatial SVD modes of phase velocity fields, showing coherent spatiotemporal activity patterns. C, Temporal evolution of PCA modes, averaged across all trials. Stimulus onset at 0 s. Non-causal effects are due to time smoothing of signal filtering. D, Same as C, but for SVD modes.
Fig 10.
Real and complex vector singular value decomposition modes in 10 Hz phase velocity fields.
LFPs were taken from the same recording as in Fig 9, but during ongoing activity. A, Top spatial SVD modes in velocity fields, with percentage variance explained. Modes correspond to spatiotemporal patterns, which are scaled but not rotated as they evolve over time. B, Top spatial cSVD modes, with percentage variance explained. These modes are both scaled and rotated over time, effectively combining multiple SVD modes as indicated by colors: cSVD mode 1 contains SVD modes 1 and 2; cSVD mode 2 contains SVD modes 3 and 6; and cSVD mode 3 contains SVD modes 4 and 5.
Fig 11.
Schematic of data flow in the methodological framework and NeuroPatt toolbox.
Neural recordings can either contain oscillatory (e.g. EEG, LFP) or intensity (e.g. VSD) data, and these inputs are processed to find the spatiotemporal patterns present. White boxes indicate data entities; shaded boxes represent analysis methods.