Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

This document is the Accepted Manuscript version of the following article: Reinoud Maex, ‘An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials’, Neural Computation, March 2018. Under embargo until 22 June 2018. The final, definitive version of this paper is available online at doi: https://doi.org/10.1162/NECO_a_01068. © 2018 Massachusetts Institute of Technology. Content in the UH Research Archive is made available for personal research, educational, and non-commercial purposes only. Unless otherwise stated, all content is protected by copyright, and in the absence of an open license, permissions for further re-use should be sought from the publisher, the author, or other copyright holder.Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the present computational study, we show that a model circuit of interneurons, coupled via both GABA(A) receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/f power scaling at low frequency (< 10 Hz) , power accumulation in the γ-frequency band (30–100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplifica- tion of single-neuron spectral properties, owing to the refractory period, by parameters that favour neuronal synchrony, such as delayed inhibition. The present study also confirms that both synaptic and voltage-gated membrane currents substantially contribute to the LFP, and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.Peer reviewe

Extended Recurrence Plot Analysis and its Application to ERP Data

We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.Comment: 21 pages, 8 figures; article for the workshop ''Analyzing and Modelling Event-Related Brain Potentials: Cognitive and Neural Approaches`` at November 29 - December 01, 2001 in Potsdam, German

Effective t-J Hamiltonian for the Copper Oxides

Starting from the Emery model, which is assumed to describe the copper oxygen planes, and including direct oxygen hopping matrix elements, we have been able to derive the effective t-J Hamiltonian for the copper orbitals using the Linked Cluster Expansion Method up to fourth order in the hybridization matrix element.Comment: (ps version of the dvi file, resubmitted because previous uucompressed version was corrupted), 9 page

Wavelet analysis of epileptic spikes

Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm.Comment: 4 pages, 3 figure