## Energetic Link Between Spike Frequencies and Brain Fractal Dimensions

**Authors:** Arturo Tozzi, James F. Peters, Mehmet Niyazi Çankaya, Jan Korbel, Marzieh Zare, David Papo

Oscillations in brain activity exhibit a power law distribution which appears as a straight line when plotted on logarithmic scales in a log power versus log frequency plot. The line’s slope is given by a single constant, the power law exponent. Since a variation in slope may occur during different functional states, the brain waves are said to be multifractal, i.e., characterized by a spectrum of multiple possible exponents. A role for such non-stationary scaling properties has scarcely been taken into account. Here we show that changes in fractal slopes and oscillation frequencies, and in particular in electric spikes, are correlated. Taking into account techniques for parameter distribution estimates, which provide a foundation for the proposed approach, we show that modifications in power law exponents are associated with variations in the Rényi entropy, a generalization of Shannon informational entropy. Changes in Rényi entropy, in turn, are able to modify brain oscillation frequencies. Therefore, results point out that multifractal systems lead to different probability outcomes of brain activity, based solely on increases or decreases of the fractal exponents. Such approach may offer new insights in the characterization of neuroimaging diagnostic techniques and the forces required for transcranial stimulation, where doubts still exist as to the parameters that best characterize waveforms.

**Comments:** 11 Pages.

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### Submission history

[v1] 2016-09-08 14:03:41

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