Theoretical considerations and supporting evidence for the primary role of source geometry on field potential amplitude and spatial extent

Correlation dimension of high-dimensional and high-definition experimental time series

The correlation dimension (CD) is a nonlinear measure of the complexity of invariant sets. First introduced for describing low-dimensional chaotic attractors, it has been later extended to the analysis of experimental electroencephalographic (EEG), magnetoencephalographic (MEG), and local field potential (LFP) recordings. However, its direct application to high-dimensional (dozens of signals) and high-definition (kHz sampling rate) 2HD data revealed a controversy in the results. We show that the need for an exponentially long data sample is the main difficulty in dealing with 2HD data. Then, we provide a novel method for estimating CD that enables orders of magnitude reduction of the required sample size. The approach decomposes raw data into statistically independent components and estimates the CD for each of them separately. In addition, the method allows ongoing insights into the interplay between the complexity of the contributing components, which can be related to different anatomical pathways and brain regions. The latter opens new approaches to a deeper interpretation of experimental data. Finally, we illustrate the method with synthetic data and LFPs recorded in the hippocampus of a rat.

Diversity of cortical activity changes beyond depression during Spreading Depolarizations

Spreading depolarizations (SDs) are classically thought to be associated with spreading depression of cortical activity. Here, we found that SDs in patients with subarachnoid hemorrhage produce variable, ranging from depression to booming, changes in electrocorticographic activity, especially in the delta frequency band. In rats, depression of activity was characteristic of high-potassium-induced full SDs, whereas partial superficial SDs caused either little change or a boom of activity at the cortical vertex, supported by volume conduction of signals from spared delta generators in the deep cortical layers. Partial SDs also caused moderate neuronal depolarization and sustained excitation, organized in gamma oscillations in a narrow sub-SD zone. Thus, our study challenges the concept of homology between spreading depolarization and spreading depression by showing that SDs produce variable, from depression to booming, changes in activity at the cortical surface and in different cortical layers depending on the depth of SD penetration.

Uncorrelated bilateral cortical input becomes timed across hippocampal subfields for long waves whereas gamma waves are largely ipsilateral

The role of interhemispheric connections along successive segments of cortico-hippocampal circuits is poorly understood. We aimed to obtain a global picture of spontaneous transfer of activity during non-theta states across several nodes of the bilateral circuit in anesthetized rats. Spatial discrimination techniques applied to bilateral laminar field potentials (FP) across the CA1/Dentate Gyrus provided simultaneous left and right readouts in five FP generators that reflect activity in specific hippocampal afferents and associative pathways. We used a battery of correlation and coherence analyses to extract complementary aspects at different time scales and frequency bands. FP generators exhibited varying bilateral correlation that was high in CA1 and low in the Dentate Gyrus. The submillisecond delays indicate coordination but not support for synaptic dependence of one side on another. The time and frequency characteristics of bilateral coupling were specific to each generator. The Schaffer generator was strongly bilaterally coherent for both sharp waves and gamma waves, although the latter maintained poor amplitude co-variation. The lacunosum-moleculare generator was composed of up to three spatially overlapping activities, and globally maintained high bilateral coherence for long but not short (gamma) waves. These two CA1 generators showed no ipsilateral relationship in any frequency band. In the Dentate Gyrus, strong bilateral coherence was observed only for input from the medial entorhinal areas, while those from the lateral entorhinal areas were largely asymmetric, for both alpha and gamma waves. Granger causality testing showed strong bidirectional relationships between all homonymous bilateral generators except the lateral entorhinal input and a local generator in the Dentate Gyrus. It also revealed few significant relationships between ipsilateral generators, most notably the anticipation of lateral entorhinal cortex toward all others. Thus, with the notable exception of the lateral entorhinal areas, there is a marked interhemispheric coherence primarily for slow envelopes of activity, but not for pulse-like gamma waves, except in the Schafer segment. The results are consistent with essentially different streams of activity entering from and returning to the cortex on each side, with slow waves reflecting times of increased activity exchange between hemispheres and fast waves generally reflecting ipsilateral processing.