R. Biscay

Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex

Information processing in the visual cortex depends on complex and context sensitive patterns of interactions between neuronal groups in many different cortical areas. Methods used to date for disentangling this functional connectivity presuppose either linearity or instantaneous interactions, assumptions that are not necessarily valid. In this paper a general framework that encompasses both linear and non-linear modelling of neurophysiological time series data by means of Local Linear Non-linear Autoregressive models (LLNAR) is described. Within this framework a new test for non-linearity of time series and for non-linearity of directedness of neural interactions based on LLNAR is presented. These tests assess the relative goodness of fit of linear versus non-linear models via the bootstrap technique. Additionally, a generalised definition of Granger causality is presented based on LLNAR that is valid for both linear and non-linear systems. Finally, the use of LLNAR for measuring non-linearity and directional influences is illustrated using artificial data, reference data as well as local field potentials (LFPs) from macaque area TE. LFP data is well described by the linear variant of LLNAR. Models of this sort, including lagged values of the preceding 25 to 60 ms, revealed the existence of both uni- and bi-directional influences between recording sites.

Nonlinear EEG analysis based on a neural mass model.

Abstract. The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics.

Testing topographic differences between event related brain potentials by using non-parametric combinations of permutation tests

MANOVA and repeated measures ANOVA approaches have provided evidence of a number of limitations in several event-related potential (ERP) studies due to violations of their statistical assumptions and the typically moderate size of the available sample. Alternative, computer-intensive methods based on permutation principles have recently been developed. Up to now this methodology has focused mostly on magnitude differences between scalp distributions as measured by t statistics. In this paper the scope of permutation techniques in ERP analysis was widened. A new statistic (D statistic) is introduced to compare the shapes of scalp distributions of ERPs. Additionally a general non-parametric combinatory technique is introduced to evaluate, by means of multivariate permutation tests, several time points and/or recording sites in ERP data. The methodology described here was used to test if two ERP components elicited during word-pair matching tasks to semantic or phonological incongruences had different scalp distributions.

Frequency domain models of the EEG

SummaryThe structure of the normal resting EEG crosspectrum Svv(ω) is analyzed using complex multivariate statistics. Exploratory data analysis with Principal Component Analysis (PCA) is followed by hypothesis testing and computer simulations related to possible neural generators. The Svv(ω) of 211 normal individuals (ages 5 to 97) may be decomposed into two types of processes: the ξ process with spatial isotropicity reflecting diffuse, correlated cortical generators with radial symmetry, and processes that seem to be generated by more spatially concentrated, correlated sources. The latter are reflected as spectral peaks such as the process. The eigenvectors of the ξ process are the Spherical Harmonic Functions which explains the recurring pattern of maps characteristic of the spatial PCA of qEEG data. A new method for estimating sources in the frequency domain which fits dipoles to the whole crosspectrum is applied to explain the characteristics of the localized sources.

High resolution quantitative EEG analysis

SummaryHigh resolution spectral methods are explored as an alternative to broad band spectral parameters (BBSP) in quantitative EEG analysis. In a previous paper (Valdes et al. 1990b) regression equations (“Developmental surfaces”) were introduced to characterize the age-frequency distribution of the mean and standard deviation of the log spectral EEG power in a normative sample. These normative surfaces allow the calculation of z transformed spectra for all derivations of the 10/20 system and z maps for each frequency. Clinical material is presented that illustrates how these procedures may pinpoint frequencies of abnormal brain activity and their topographic distribution, avoiding the frequency and spatial “smearing” that may occur using BBSP. The increased diagnostic accuracy of high resolution spectral methods is demonstrated by means of receiver operator characteristic (ROC) curve analysis. Procedures are introduced to avoid type I error inflation due to the use of more variables in this type of procedure.

MULTIRESOLUTION DECOMPOSITION OF NON-STATIONARY EEG SIGNALS: A PRELIMINARY STUDY

Wavelet representation is a recent development in the analysis of non-stationary signals. Its possibilities for use in the description of time-frequency characteristics of both transients in spontaneous EEG and time-varying rhythms in event related brain activity are explored here. By way of illustration, multiresolution decompositions of a wide variety of EEG transients are carried out in this work, including spike-and-waves, single spikes, sharp waves, blink artifacts, frontal intermittent rhythmic delta activity (FIRDA) and paroxysmal delta activity. Also, the application of the wavelet representation to study related spectra perturbations is illustrated with data from psychophysical experiments on the perception of image motion. The results demonstrate the capabilities of the wavelet transform, as an alternative to the Fourier transform, for the representation and analysis of non-stationary EEG signals.

Brain-stem auditory evoked potentials and brain death

BAEP records were obtained from 30 brain-dead patients. Three BAEP patterns were observed: (1) no identifiable waves (73.34%), (2) an isolated bilateral wave I (16.66%), and (3) an isolated unilateral wave I (10%). When wave I was present, it was always significantly delayed. Significant augmentation of wave I amplitude was present bilaterally in one case and unilaterally in another. On the other hand, in serial records from 3 cases wave I latency tended to increase progressively until this component disappeared. During the same period, wave I amplitude fluctuations were observed. A significant negative correlation was found for wave I latency with heart rate and body temperature in 1 case. Two facts might explain the progressive delay and disappearance of wave I in brain-dead patients: a progressive hypoxic-ischaemic dysfunction of the cochlea and the eighth nerve plus hypothermia, often present in brain-dead patients. Then the incidence of wave I preservation reported by different authors in single BAEP records from brain-dead patients might depend on the moment at which the evoked potential study was done in relation to the onset of the clinical state. It is suggested that, although BAEPs provide an objective electrophysiological assessment of brain-stem function, essential for BD diagnosis, this technique could be of no value for this purpose when used in isolation.

Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression

A spatial-temporal model for the description of electroencephalographic (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. Its spatial aspect is formulated in a general framework that covers interpolation, smoothing, and regression. Contrary to the multivariate time series models used for EEG analysis up to date, the introduced model provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of practical importance, the case in which the spatial reconstruction is based on spherical splines is developed in detail. Illustrative examples are presented that show the flexibility of the model to describe both normal and abnormal EEG data.

Projective Methods for the Magnetic Direct Problem

The prediction of magnetic fields due to prescribed current sources in realistically shaped body models is usually approached by approximating the body as a set of piecewise homogeneous conductors with arbitrary geometry, separated by surfaces S l (l = 1, ..., M). One of the regions contains the primary current sources \(\vec j\left( {\vec r} \right)\) and S 1 encloses all other surfaces; \(\vec r\) is a arbitrary position vector.

EEG predictability: adequacy of non-linear forecasting methods

The predictive properties of EEG segments were analyzed. The sample included alpha, delta as well as spike and wave EEG activity recordings. Most of these segments are better described with non-linear autoregressive models, and a non-linear forecasting algorithm is routinely required. In terms of their predictive properties, segments can be divided into unpredictable, predictable and very predictable, these three groups being similarly represented among the alpha activity EEG segments. In EEG segments with alpha activity, poor predictability is associated with poor organization of the rhythmic pattern. Concerning dynamic properties, it was found that cyclic skeletons were highly represented among the very predictable segments, which reflect a contribution of the deterministic component of the autoregressive model to the predictability of the segments. Notable contributions of the noise component may explain the properties of unpredictable segments. These results point to a great diversity of predictive patterns among EEG recordings. Other factors besides the existence of chaotic dynamics must be regarded.