Fig 1.
Topographical mapping of temporal and spatial correlations in cortex over extended periods of time.
Left: Projection of invasive EEG electrodes from an exemplary subject with brain surfaces along the cortical hierarchy colour coded. Middle: γ-power timeseries for original and time-shuffled data. Right: Autocorrelation functions (top two panels) and cross-correlation functions (bottom two panels) are used to calculate temporal and spatial correlations, respectively.
Fig 2.
Spatial and temporal correlations (SC, TC) are tightly linked, decline under AED action and break down during slow-wave sleep (SWS).
A, B Timeseries of TC and SC over one day for high and low AED dosages for one exemplary patient. SWS is marked with green squares and seizures (grey bars) are excluded from the analysis. C Co-variation of SC and TC shown for one patient. The black line indicates a logarithmic fit. D Surrogate data of SC and TC are overall smaller and exhibit no co-dependence. E, F Autocorrelation and cross-correlation functions averaged over all patients exhibit a faster decline during high AED load days. The grey shaded area in F was used for the SC calculation. G, H Reduction of TC and SC during SWS and high AED load (Wilcoxon signed rank test). Single patient values are indicated as thin lines, the median is given as dashed line and whiskers extend to the 95% confidence interval calculated via bootstrapping. Surrogate data (grey bars) exhibit no difference.
Fig 3.
Temporal correlations increase with functional hierarchy.
A, B Lateral and medial view of the left-hemisphere of a reference brain with electrodes of all patients projected onto the surface with coloured areas similar to [6]. C, D Number of electrodes and TC for each region. Thin lines indicate data from individual patients, coloured bars averages and dashed lines median values across patients. Whiskers denote the 95% confidence interval.
Fig 4.
STC in a neural network model.
Model simulations are shown for N = 1600 neurons on a 2-dimensional grid with periodic boundary conditions and distance-dependent connectivity strength. Other parameters are finh = fexc = λ = 1, if not stated otherwise. One neuron was activated randomly every maxt = 2000 time steps. Coloured bars give the ensemble average with whiskers extending to the 95% confidence interval. Results for surrogate data (shuffled time series) are given as grey bars. A, B The state of high AED can be mimicked in the model by decreasing the excitability of excitatory neurons, i.e., fexc = 1→0.95, leading to decreased SC, TC. C Co-variation between TC and SC for different model realizations with λ∈{0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0} (104 runs each, 7·104 runs in total, Spearman ρ = 0.79, p<m.p. (machine precision)). The black line shows a logarithmic fit. D No correlations are found in time-shuffled data. E, F SC and TC increase with the absolute value of the largest eigenvalue λ approaching its critical value of λ = 1 similar to the hierarchical increase of TC in iEEG data (Fig 3).