Use of the fractal dimension for the analysis of electroencephalographic time series

Abstract

Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out.

Sensorimotor cortical response during motion reflecting audiovisual stimulation: evidence from fractal EEG analysis

“…b Motor-related areas of the human brain that are involved in music perception [premotor cortex and supplementary motor area (SMA)] along with regions where MNS activity has been observed (premotor cortex and inferior parietal lobule) Their anonymity was verified and they had the right to leave the recording session at any time. No statistical difference was detected in age between the two groups by the one-way ANOVA test [F (1,19) …”

“…The more the signal line fluctuates, the more the plane appears covered and thus the greater fragmentations of the waveform that are present; then provided each fragment has self similarity, the more the FD increases. Fluctuations of the FD of electrophysiological signals allow the detection of different physio-pathological conditions [1]. For this study, three FD estimation algorithms directly in the time domain were designed, i.e., Higuchi's [20], Katz's [21], and Petrosian's [34] method, following the paradigm of Esteller et al [12] for the FD-based EEG analysis.…”

“…Due to the non-linear and nonstationary characteristics of the EEG signals, the study of the electrophysiological data with linear methods, i.e., Fourier Transform, yields results that are inaccurate in a physical or physiological sense [9,24]. Fractal analysis offers immediate interpretation of the results through FD estimation and allows the investigation of transient phenomena in electrophysiological data that are undetectable by conventional methods [1]. Finally, in an effort to examine the effect of structural features to the subjects' sensorimotor response, as reflected through the FD analysis, a waveform based on rhythmic fluctuations of the ''Promenade'' theme was constructed and correlated to the estimated EEG-based FD signal.…”

Fractal dimension analysis for robust ultrasonic non-destructive evaluation (NDE) of coarse grained materials

“…The concept of fractal dimension is a generalization of the Euclidean dimension that reflects the complexity of the self-similar structure of an object or time series. The fractal dimension has been used for analysis and quantification of complicated biomedical signals such as ECG and EEG [18][19][20], and more recently in the field of tissue characterization in medical ultrasound diagnosis [21]. To estimate the fractal dimension of a time series, the signal is decomposed into different scales and then the signal complexity is evaluated.…”

Nonlinear dynamics methods for tachogram series analysis based on detrended fluctuation analysis and Higuchi’s fractal dimension

“…The fractal dimension can be used to quantify the complexity and self-similarity of a signal. This method has been used to analyze the complexity of brain signals [6] and other biological signals [7].…”