Fractal Dynamics in electrophysiological signals

Electrophysiological studies on human brain function have traditionally focused on event-related responses with a time course of up to a few hundred milliseconds, because this is the time scale of processing brief sensory input. The brain, however, generates pronounced levels of ongoing activity, which evolves in complex temporal patterns on time scales ranging from milliseconds to tens of seconds. Only in recent years have the quantitative properties of these multiple-scale fluctuations been explored. A growing body of evidence indicates that fluctuations in ongoing brain signals have a fractal organization as reflected in the power-law scaling of the power spectrum and in the long-range memory of the autocorrelation function.

In an EEG study on hypothesis testing, we have provided the first evidence that fractal dynamics is modulated by a cognitive task (Buiatti et al., 2007).

Left panel: Topography of Detrended Fluctuations Analysis (DFA) scaling exponents averaged across all subjects for positive feedback condition. Color bars indicate the correspondence between colors and scaling exponent values. Right panel: Log–log plots of DFA residuals as a function of time window length averaged over positive (black squares) and negative (gray triangles) feedback conditions (electrode POZ). The slopes of DFA residuals are markedly higher in the negative feedback condition than in the positive feedback one. From (Buiatti et al., 2007).

Parallel theoretical work investigates the nature of the non-stationary regime of fractal dynamics in electrophysiological signals (Kalashyan et al., 2009).

In (Buiatti, 2008) I have reviewed evidence on the correlated nature of the large-scale neural activity, both in space and time. I have suggested that such correlations could be used to identify the spontaneous spatiotemporal patterns of neural activity at rest and to track their evolution and dynamical interactions during cognitive processing.

In (Buiatti, 2023) I have reviewed recent work about fractal brain dynamics at multiple spatial and temporal scales and I have proposed a link between microscopic biophysical models of scale-free signal generation and large-scale self-organizing properties of brain function.

References:

Buiatti M, Papo D, Baudonniere PM, van Vreeswijk C,

Feedback modulates the temporal scale-free dynamics of brain electrical activity in a hypothesis testing task,

Neuroscience, 146 (3), 1400-1412 (2007).

Kalashyan A, Buiatti M, Grigolini P,

Ergodicity breakdown and scaling in single sequences,

Chaos, Solitons & Fractals 39(2), 895-909 (2009).

Buiatti M

The correlated nature of large scale brain activity unveiled by the resting brain, 

Biology Forum 101, 353-73 (2008).

Buiatti M, 

Fractal brain dynamics: Origins, limits and functional relevance of scale-free temporal brain fluctuations, 

in Paolo Grigolini and 50 years of Statistical Physics, Cambridge Scholars Publishing, Newcastle Upon Tyne, Uk (2023).