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.

Does the Kolmogorov entropy give more information about the organization of the voluntary movement?

Nonlinear temporal and spatial dynamic changes of human EEG signals during voluntary finger movements were investigated with tracking Kolmogorov entropy (K2). Segments with higher values of K2 defined dynamic transients, distinguishing consecutive phases of the movement organization. The maximum of K2, determined immediately before the movement onset, was specific only for the contralateral sensorimotor area. This nonlinear characteristic, computed over time for EEG single records, indicates the local dynamic properties and detect those EEG patterns, where the underlying process changes the dynamics prior to the task performance. In addition to the present mechanisms, found by the linear methods, qualitatively new mechanisms of neuronal activity were discovered in brain functioning during the organization of voluntary movements.

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.

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.

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.

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.

Similarity in shape, timing and amplitude of H- and T-reflex potentials concurrently recorded along the broad skin area over soleus muscle.

Variations in shape, timing and amplitude of both mono- and bipolarly measured H- and T-reflex potentials can be influenced to a great extent by the muscle architecture and the peculiarities of the extracellular potential field. The "best point" for bipolar measurements, where the amplitude of the bipolar H- and T-potentials is maximal, occurred for the various subjects at a distance of 3.0 to 5.0 cm below the insertion of the gastrocnemii on the Achilles tendon. In contrast, the corresponding "best point" for monopolar H- and T-potentials is located 5.0 to 9.0 cm below the gastrocnemii insertion. The shape, total duration and timing of H- and T-potentials, concurrently measured at the various points along soleus muscle are similar. When the amplitude of the monopolar H- and T-potentials are levelled at the "best point" for monopolar measurements, the changes in the amplitude of both sets of potentials, monopolarly and bipolarly measured along soleus muscle, are identical. These results imply similar efferent outputs for both H- and T-reflexes, i.e. recruitment of motoneurons of comparable size.