Random field-union intersection tests for EEG/MEG imaging.

Electrophysiological (EEG/MEG) imaging challenges statistics by providing two views of the same spatiotemporal data: topographic and tomographic. Until now, statistical tests for these two situations have developed separately. This work introduces statistical tests for assessing simultaneously the significance of spatiotemporal event-related potential/event-related field (ERP/ERF) components and that of their sources. The test for detecting a component at a given time instant is provided by a Hotelling's T(2) statistic. This statistic is constructed in such a manner to be invariant to any choice of reference and is based upon a generalized version of the average reference transform of the data. As a consequence, the proposed test is a generalization of the well-known Global Field Power statistic. Consideration of tests at all time instants leads to a multiple comparison problem addressed by the use of Random Field Theory (RFT). The Union-Intersection (UI) principle is the basis for testing hypotheses about the topographic and tomographic distributions of such ERP/ERF components. The performance of the method is illustrated with actual EEG recordings obtained from a visual experiment of pattern reversal stimuli.

Nonlinear EEG analysis based on a neural mass model.

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 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.

Comparison of DNA migrations in two clamped homogeneous electric field chambers of different sizes. Relation between sample thickness and electrophoresis time.

We present here a method to compare the mathematical descriptions of DNA migration per pulse as a function of pulse time. It is based on obtaining robust estimates and variances of DNA reorientation time, migration velocities during and after DNA reorientation; and on the statistical comparisons of these estimates. We demonstrated an equal description for the migration per pulse of each DNA molecule separated under identical conditions in clamped homogeneous electric field (CHEF) and miniCHEF chambers. However, miniCHEF resolved the patterns in shorter times, because it uses thinner samples. The relationship between sample thickness and CHEF run time is also presented.

Reparametrization of autoregressive models with coefficients depending on covariables: application to EEG spectrum maturation.

To describe the spectral characteristics of the EGG development through autoregressive (AR) time series models it is necessary to perform regression analysis of the AR parameters with regards to the age of the subject. A major difficulty in this approach is the very complex nature of the admissible region of the AR coefficients, which impedes the straight use of regression techniques. The present paper overcomes this difficulty by first applying the Barndoff-Nielsen and Schou reparametrization of AR models, followed by Fisher's transformation and then carrying out age regression analysis of the transformed parameters. We apply this approach to real EEG data obtained from a normative sample of subjects in the age range from 5 to 95 years.

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.

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 (AU)

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.

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.

Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach.

A new measure of dissimilarity between two EEG segments is proposed. It is derived from the application of the mathematical concept of distance between series of one-step predictions according to the estimated non-linear autoregressive functions. The non-linear autoregressive estimation is performed by non-parametric regression using kernel estimators. The possibility of applying this measure for automatic classification of EEG segments is explored. For this purpose multidimensional scaling and cluster analyses are applied on the basis of the calculated dissimilarity measures. In particular, its application to different EEG segments with delta activity and also with alpha waves reveals high agreement with visual classification by EEG specialists.

Maximum a posteriori estimation of change points in the EEG.

A new approach for EEG segmentation is introduced. This is based on a methodology for optimal segmentation of non-stationary signals derived from the maximum a posteriori estimation principle. It is a model-based, not sequential approach that allows for segmentation at different resolution levels. The features of the methodology are illustrated by its application to EEG recordings containing several types of spectral changes due to normal and pathological variations of spontaneous brain rhythmic activities, as well as physiological artifacts.

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.

A global scale factor in brain topography.

In this paper statistical resampling techniques are used to support the presence of an equiangular first principal component in EEG log spectra and therefore the existence of a global scale factor in EEG recordings. the Log transformed spectra from a normal sample (n = 211, age 5-97) were analyzed. To reach this conclusion a method for estimating the scale factor is introduced. It is also shown that this factor remains constant in each individual for all derivations and frequencies and across functional states. The contribution of this scale factor to the overall variance of the normal EEG reaches 42% of the total variance of age corrected data. Part of the variance of the scale factor exhibits age dependency. Scale factor correction of EEG spectra data improves the diagnostic accuracy for detecting pathological EEG spectra from an almost random level (Area under the ROC curve = .6) to .84.

Multivariate statistical brain electromagnetic mapping.

Brain Electromagnetic Topography (BET) has attained widespread use. The representation of EEG or MEG parameters as scalp maps (BETm) aids its clinical interpretation. However, some critical issues limit the usefulness of BETm. In particular, the conventional statistical assessment of BETm with respect to normative data is based upon marginal significance probability scales which involve multiple univariate comparisons (one at each recording site). As a consequence, the probability of false positive findings (type I error) is increased above its nominal level. The use of conservative levels avoids this phenomenon but results in a considerable increase of the probability of not detecting real abnormality (type II error). Furthermore, BETm are constructed without taking into consideration the patterns of correlations characteristic of electromagnetic data under normal states of brain functioning. This limits the capability of BETm of representing multivariate aspects of abnormality. This paper introduces some techniques to approach these difficulties. Multivariate Brain Electromagnetic Topographic maps (MBETm) are defined, which retain the attractive features of mapping but also take advantage of multivariate characteristics (in the spatial and frequency domains) to highlight aspects of neuropathology. Moreover, simultaneous significance probability (SSP) scales, valid for both BETm and MBETm, are introduced for the global control of the probability of a type I error. The use of these techniques is illustrated with data from patients with cortical tumours and with epilepsy. ROC analysis shows that in some cases there is a significant improvement in both detection and localization accuracy.

High resolution quantitative EEG analysis.

High 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.

QEEG in a public health system.

For the past decade the Cuban Neuroscience Center has organized on behalf of the Ministry of Public Health of the Republic, a nationwide Program for the introduction of quantitative EEG (qEEG). This Program has involved a) development of standardized equipment for "paperless" EEG, qEEG and brain topography; b) establishment of a network of 21 laboratories of clinical neurophysiology; c) creation of the specialty of clinical neurophysiology which trains physicians from all provinces in both traditional and quantitative electrophysiological methods; d) introduction of standardized protocols for the collection of clinical and electrophysiological information; e) organization of a national normative and neuropsychiatric database; f) establishment of normative regression equations. Among the special issues discussed are: 1) relationship between traditional and quantitative methods; 2) evaluation of the effectiveness of the technology introduced; 3) use of qEEG in the early detection of brain dysfunction.

Frequency domain models of the EEG.

The structure of the normal resting EEG crosspectrum SVV(omega) 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(omega) of 211 normal individuals (ages 5 to 97) may be decomposed into two types of processes: the xi 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 xi 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.

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.

Different functional properties of on and off components in auditory brainstem responses to tone bursts.

Auditory brainstem responses to tone bursts of constant rise and fall time and variable plateau were obtained in 7 normal hearing adults with a vertex to mastoid electrode configuration. In all records, two vertex-positive components (A, B) were present. Peak A is probably an onset response. Peak B latency increased linearly with plateau duration (r = 0.93) and seems to be an off response. White and notched acoustic noise masking had a different effect on the two components. A greater latency shift was observed for peak A than for peak B, thus reducing the interpeak interval in the masked response. When using high-pass noise, as we lowered the cut-off points from 4 to 0.5 kHz, there was also a greater latency increment for peak A than for peak B. These results suggest a more apical cochlear origin for the off response.

Different functional properties of on and off components in auditory brainstem responses to tone bursts

Auditory brainstem responses to tone bursts of constant rise and fall time and variable plateau were obtained in 7 normal hearing adults with a vertex to mastoid electrode configuration. In all records, two vertex-positive components (A, B) were present. Peak A is probably an onset response. Peak B latency increased linearly with plateau duration (r = 0.93) and seems to be an off response. White and notched acoustic noise masking had a different effect on the two components. A greater latency shift was observed for peak A than for peak B, thus reducing the interpeak interval in the masked response. When using high-pass noise, as we lowered the cut-off points from 4 to 0.5 kHz, there was also a greater latency increment for peak A than for peak B. These results suggest a more apical cochlear origin for the off response (AU)