Multifractality of decomposed EEG during imaginary and real visual-motor tracking.

We test the possible multifractal properties of dominant EEG frequency components, when a subject tracks a path on a map, either only by eyes (imaginary movement - IM) or by visual-motor tracking of discretely moving spot in regular (RM) and Brownian time-step (BM) (real tracking of moving spot). We check the hypotheses that the fractal properties of filtered EEG (1) change with respect to the law of spot movement; (2) differ among filtered EEG components and scalp sites; (3) differ among real and imaginary tracking. Sixteen right-handed subjects begin to perform IM, next--real spot tracking (RM and BM) following a moving spot on streets of a citymap displayed on a computer screen, by push forward/backward a joystick. Multichannel long-lasting EEG is band-pass filtered for theta, alpha, beta and gamma oscillations. The Wavelet-Transform-Modulus-Maxima-Method is applied to reveal multifractality [local fractal dimensions Dmax(h)] among task conditions, frequency bands and sites. Non-parametric statistical estimation of the fractal measures h (Dmax) is finally applied. Multifractality is established for all experimental conditions, EEG components and sites as follows among filtered components - anticorrelation (h(Dmax) < 0.5) in beta and gamma, and long-range correlation (h(Dmax) > 0.5) for theta and alpha oscillations; among tasks--for RM and BM, h (Dmax) differ significantly whereas IM resembles mostly RM; among sites--no significant difference for local fractal properties is established. The results suggest that for both imaginary and real visual-motor tracking a line, multifractal scaling, specific for lower and higher EEG oscillations, is a very stable intrinsic one for the activity of large brain areas. The external events (task conditions) insert weak effect on the scaling.

Slow brain potentials associated with motor preparation and stimulus anticipation.

The study was undertaken to analyze the cognitive determinants of event-related potentials (ERPs) under two stimulus paradigm discrimination conditions. We were interested in how the processes of anticipation and preparation for motor action are associated with the ERPs and what is the interrelation between them. Subjects were presented in randomized order three pairs of tones: warning (S1) and imperative (S2) one with different information content. Two ERPs types were studied: (1) The acoustic evoked potentials elicited by warning and imperative stimulus. (2) The early-initial (iCNV) and late-terminal (tCNV) contingent negative variation. Our data suggested that the processing of S2 depends not only on its physical characteristics and information content but also on the prestimulus brain activity reflecting expectancy or motor preparation. The higher iCNV amplitude contralaterally to the movement side under the condition requiring motor action compared to the paradigms without movement preparation could be associated also with the response related processes.

EEG frequency dynamics during movements imagery.

The study is an attempt to reveal the EEG frequency dynamic changes over sites covering areas reflecting the cognitive processes during movement imagery. Subjects were instructed to imagine a self-paced movement after listening to randomized sentences differing in lack of object or instrument of action. EEG was recorded over frontal, sensorimotor and temporo-parietal areas in both hemispheres. Frequency dynamics was estimated using power spectra (PS), band-pass filtering and bispectra. Two types of frequency dynamics were established: (A) a linear one, up to 24 Hz, with most pronounced oscillations in 12-14 Hz and in 16-22 Hz, synchronized first in frontal and precentral areas; (B) a nonlinear one between 24 and 63 Hz, with fractal structure and self-similarity, characterized by fractal dimension of 1.7-1.9. The narrow band of 23-26 Hz in the boundary between linear and nonlinear regimes expressed obvious synchronization and time re-distribution of oscillations among sites and sentence-types.

Event-related potentials elicited after sentences inducing movement imagery.

Some late components of event-related potentials (ERP) have been interpreted as psychophysiological correlates of words and sentences comprehension and imagery. This study was aimed at revealing the ERP components changes after listening to sentences inducing movement imagination. Right-handed subjects were instructed to imagine self-paced movements after listening to sentences, differing in presence/absence of object and/or instrument of action. ERP were recorded over frontal, sensorimotor and temporo-parietal areas in both hemispheres. The effects of the movement type (T) and between-site factors (E) were estimated using 2-way ANOVA. Six dominant ERP components were detected up to 1.5 s. E-factor had significant independent effect on all ERP components, while T-factor was significant for the components up to 0.8 s in frontal (left and right) and in ipsilateral sensori-motor areas. The results suggest that the larger ERP latencies and the increased amplitudes at frontal and sensorimotor areas are due to motor imagery combined with the comprehension of sentences with different structure.

Nonlinear EEG dynamics during imagined self-paced movements.

The majority of studies devoted to reveal electrophysiological correlates of words and sentences comprehension, imageability and remembering are based on the event-related potentials and frequency synchronization in different narrow frequency bands. These linear methods reveal some patterns of EEG activity in time and frequency domain. Having in mind that the activation of many cortical structures is a result of mass of nonlinearly interconnected neurons, the linear methods seem to be insufficient to discover the complexity of the information transfer. We revealed recently nonlinear dynamic transients in EEG, long before real performance of goal-directed voluntary movements with different temporal and spatial distributions over frontal, sensorimotor and parietal cortical areas (Popivanov and Dushanova, 1999). The aim of this study was to establish whether similar behavior of the nonlinear characteristics exists when the subject imagines movements of a given type. The Kolmogorov entropy computed over time after the sentence end proved to be an useful characteristic that complement the linear methods.

Nonlinear dynamics of human postural sway during upright stance.

We present a procedure for characterizing the postural sway during quiet upright stance using methods of nonlinear dynamics. The displacements of the centre of foot pressure in anterior-posterior and lateral directions were measured using a force platform. We examined the changes of the postural control mechanisms when visual or proprioceptive information are reduced. We applied four analytic procedures to test the nature of posturographic time series: Kolmogorov-Smirnov test for amplitude distribution; shapes of autocorelation functions; structure functions and log-log plots of power spectra. Nongaussian distribution and nonlinear dynamics were established by all tests. The power spectra (PS) exhibited an exponential decreasing shape, which is commonly referred to as "1/f noise". The fractal structure of the process was characterised by fractal dimension (Df) and shape of structure functions. Our results show that the maintenance of postural stability in upright stance and reduced sensory inputs is nonlinear dynamic process with fractal structure.

Assessment of EEG frequency dynamics using complex demodulation.

The complex demodulation (CD) approach was applied to human EEG recorded during a cognitive task performance, including voluntary goal-directed movements. The standard CD algorithm was extended by a simple procedure using frequency histograms and power spectra to select the characteristic frequencies of EEG segments around the task performance. In the majority of records, amplitude modulation was found, which decreased or disappeared in the period prior to and at the very beginning of the task performance. It was found that the decrease of modulation in fast beta and gamma components begins approximately one second before that of the alpha components. Frequency modulation appeared in some records at the end of the task in beta and gamma components. The results showed that a cognitive task performance is accompanied by non-linear processes in the frequency components of EEG. These dynamic changes could extend the findings of event-related desynchronization obtained by linear methods.

Dynamic characteristics of laser-Doppler flux in normal individuals and patients with Raynaud's phenomenon before and after treatment with nifedipine under different thermal conditions.

The study was aimed at choosing an appropriate characteristic of laser-Doppler flux (LDF) data for (1) distinguishing patients with Raynaud's disease from normal controls and (2) evaluating the effect of nifedipine under different thermal conditions. We checked the reliability of three characteristics of nonlinear dynamics as statistical dimension Ds, correlation dimension D2 and power-law index PLI. Their values depended heavily on the thermal condition. The most reliable characteristics that enabled us to distinguish the patients from normal controls and the effect of nifedipine under definite thermal condition proved to be Ds and PLI. The latter is simple for computation and is thus recommendable for clinical practice. Ds and PLI were higher in patients with Raynaud's compared to normal controls and diminished during the transitions from low to high temperature. However, the characteristics used were unable to distinguish significantly Raynaud's I from Raynaud's II patients.

Dynamic characteristics of laser-Doppler flux data.

Methods for tracking the dynamics of the blood flow microcirculation obtained by laser-Doppler flowmetry (LDF) technique are described. It was shown that LDF signals have complex dynamics. It was mainly characterized by fractal structures and chaos, though multiperiodic, trend-like and stochastic components were also established. Procedures for (i) describing the dynamic structure and (ii) tracking the dynamic changes in time of LDF data are proposed. Examples illustrating the efficiency of these procedures are given using both simulated and LDF data collected in experiments with reactive hyperemia. Irrespective of the universality of the methods, the procedures should be specified according to the problem-oriented clinical and experimental studies.

EEG patterns in theta and gamma frequency range and their probable relation to human voluntary movement organization.

In experiments with EEG accompanying continuous slow goal-directed voluntary movements we found abrupt short-term transients (STs) of the coefficients of EEG time-varying autoregressive (TVAR) model. The onset of STs indicated (i) a positive EEG wave related to an increase of 3-7 Hz oscillations in time period before the movement start, (ii) synchronization of 35-40 Hz prior to movement start and during the movement when the target is nearly reached. Both these phenomena are expressed predominantly over supplementary motor area, premotor and parietal cortices. These patterns were detected after averaging of EEG segments synchronized to the abrupt changes of the TVAR coefficients computed in the time course of EEG single records. The results are discussed regarding the cognitive aspect of organization of goal-directed movements.

Non-linear EEG dynamic changes and their probable relation to voluntary movement organization.

This study was undertaken to analyze systematically the non-linear dynamic changes of EEG activity accompanying slow goal-directed voluntary movements, using three non-linear characteristics (NC): point-wise correlation dimension, Kolmogorov entropy and largest Lyapunov exponents as functions of time. NC indicated transitions with non-linear properties (NT). A significant difference between times of appearance of the NT with respect to the electrode position was established: before the movement onset, NT appeared first in contralateral and midline areas including frontal, sensorimotor and parietal cortices. Before target reaching, NT appeared first in the contralateral sensorimotor area, and evolved ipsilaterally. The results suggest that the NT could be regarded as precursors of higher functional coupling between cortical areas involved in voluntary movement organization.

Testing procedures for non-stationarity and non-linearity in physiological signals.

Most of the physiological signals (EEG, ECG, blood flow, human gait, etc.) characterize by complex dynamics including both non-stationarities and non-linearities. These time series resemble red noise with long-range correlation and 1/(f beta) power spectrum. A question arises as to how to distinguish the characteristics of the process underlying the signal dynamics from the properties of the observed time series. The classical methods to determine possible non-linear (chaotic) dynamics (e.g. correlation dimension) often fail in such signals because of relatively short data records containing stochastic components and non-stationarities. We report an application of several approaches, aimed at (1) determining of the non-stationarities in the signals and (2) testing whether non-linear dynamics exists. Assessment of the intrinsic correlation properties of the dynamic process and distinguishing the same from external trends was performed using singular spectra and detrended fluctuation analysis. The existence of non-linear dynamics was tested by correlation dimension (modified algorithm of re-embedding) and by correlation integrals of real and surrogate data. The correlation integrals of real signal and surrogate data sets were statistically compared using Kolmogorov-Smirnov (K-S) test. The procedures were tested on EEG and laser-Doppler (LD) blood flow. Our suggestion is that no one approach taken alone is the best for our aims. Instead, a battery of methods should be used.

Experimental setup and instrumentation for measurement and preprocessing of EEG during voluntary goal-directed movements.

The widely used practice in the study of human complex voluntary movement organization is to record, measure and analyze EEG activity covering the period of both motor preparation and performance. The main strategy is to reveal EEG characteristics related to both cognitive and motor aspects of the action. To this end a special-purpose experimental set-ups are required providing precise enough measure of timing and characteristics of the movement in order to synchronize EEG changes time-locked to the phases of task performance. We describe an experimental set-up including a special-purpose device, which was designed for study of slow, continuous goal-directed movements. The implementation was aimed to provide (i) performance of complicated enough task in order to force the subject to concentrate his mental activity predominantly on the task; (ii) to control the successive stages of task performance. The advantages of the presented instrumentation was demonstrated by comparing power spectra of EEG segments long before and immediately prior to the movement performance. The instrumentation is flexible enough to be used in a large scale psychophysiological experiments.

Nonlinear prediction as a tool for tracking the dynamics of single-trial readiness potentials.

The performance of a voluntary act is preceded by an intrinsic process of intention and preparation accompanied by specific patterns of scalp-recorded EEG. The baseline shift to negativity and the decrease of alpha and beta oscillations prior to movement performance are considered to reflect the motor preparation and are observable even in single-trial EEG records during repetitive voluntary movements. The single-trial features of these patterns are of importance since they would reflect the dynamics of EEG activity during movement performance throughout the experimental session. Since this process is very complex and its dynamics is unclear, we applied a more general approach, i.e. the method of nonlinear prediction (NP) recommended for detection of chaos in the behavior of nonlinear dynamical systems. The NP is based on a library of past patterns of the time series used to compute the prediction of future pattern. If the time series is chaotic, the correlation coefficient between predicted and actual values would decrease as a function of the prediction step. The NP was applied to EEG records containing readiness potentials (RPs) at Fz, Cz, Pz, C3 and C4 during repetitive voluntary finger flexion. Because of nonstationarity, the prediction and the library spanned the same time period. As a result (1) chaotic segments in EEG records were detected; and (2) the sharp jumps of the absolute error between predicted and actual values indicated instances of poor prediction, which were interpreted as indicating new stages of EEG activity related to the preparatory process of motor activity.

Method for single-trial readiness potential identification, based on singular spectrum analysis.

This paper presents a brief description and the advantages of the singular spectrum analysis (SSA). SSA has recently been recommended for analysis of short, noisy time series. The method was applied to single trials of EEG activity at Cz, Fz, C4, Pz and C3, recorded 3.6 s prior to and 1.2 s after the onset of a voluntary motor act. This specific activity is known in its averaged form as readiness potential (RP) and is considered to reflect the preparation of the voluntary movement. However, some physiological investigations require identification of the parameters of single-trial RPs-their onset and successive phases. SSA is based on analysis of the principal components in vector space of delay coordinates of time series. As a result, SSA algorithm decomposes real data records to components reflecting the trend, alpha and beta frequency bands, respectively, whose oscillations appear or disappear in different time instants. The latter were interpreted to distinguish different dynamical stages of the movement preparatory process.

Brain macropotentials associated with distinct phases of voluntary sustained isometric contraction in man.

Brain potentials recorded from the scalp during voluntary sustained isometric contraction have been consistently found to accompany both the beginning and the termination of the contraction. This study attempts to evaluate the dependence of the potentials related to the voluntary termination of a sustained effort on the physical parameters of the motor task and also to further investigate the relationship between potentials related to the initiation and to the termination of action. Brain potentials from healthy male volunteers performing hand-grip squeeze were time-locked to (1) beginning of contraction; (2) execution of an additional effort; and (3) the moment of voluntary relaxation, and then averaged. The waveshape and amplitude of the entire potential curve preceding and following the decision to act were evaluated with best-fit mathematical approximation procedures. Few correlations between the various descriptive parameters of the three types of potentials were found. The brain potentials accompanying beginning of the contraction from state of rest differed significantly from those accompanying execution of an additional effort and both potentials preceding initiation of voluntary effort differed from potentials preceding decision to terminate the action. It is hypothesised that brain macropotentials are linked to separate underlying commands for initiation and termination of voluntary action.

Single-trial readiness potentials and fatigue.

The authors propose that the cognitive processes related to internal motivation and volition (e.g., intention and preparation of a voluntary action), influenced by central fatigue, could be identified and characterized by cerebral readiness potentials (RP) using methods of chaotic dynamics. The boundaries of single-trial RP and its successive phases can be detected by tracking the data dynamics, and are represented by chaotically behaved short EEG transitions.

Time series analysis of brain potentials preceding voluntary movements.

Brain potentials preceding voluntary movements, obtained after averaging single-trial EEG records synchronised with the start of movement, consist of slow potentials shifts SPS in the negative direction mixed with faster components like ongoing EEG activity. Two hypotheses were tested: SPS could be presented by a sum of smooth function (trends) and weakly stationary processes (residuals); the residuals and the ongoing EEG activity preceding SPS could be described by the same class of autoregressive (AR) or autoregressive moving average (ARMA) models. The trend was estimated by comparing several approximating functions in the sense of least mean square error. The SPS residuals, after subtracting the trend and background EEG activity, were estimated using AR and ARMA models of different orders. These procedures were performed on brain potentials recorded from vertex to linked ear lobes of five subjects instructed to voluntarily press a button. As a result, the hypotheses were not rejected. The trend was best approximated by a hyperbolic function or Chebyshev's second order polynomial. AR models fitted both the SPS residuals and ongoing EEG activity well enough. In conclusion, SPS were characterised by three parameters of the smooth function plus a time parameter defined by the potential boundaries.

Somatosensory evoked potentials during standing posture on different support surface.

Somatosensory evoked potentials in response to stimulation of the posterior tibial nerve at the ankle were recorded during standing on stable ground or on unstable support surface (seesaw) or on support surface short in relation to foot length. During standing on the seesaw and on the short support surface a decrease in the amplitude of the early component (N32-P39) was observed. The amplitude of N49-P58 decreased during standing on the short support surface. The amplitude of the later components (N49-P58; P58-N76; N76-P117) decreased during standing on the seesaw in comparison to that during standing on the stable ground and on the short support surface. Thus, the attenuation of the cerebral potential during standing depend on the conditions for maintenance of posture.