Scale-similar activity in the brain

The spectral analysis of multichannel magnetoencephalographic data is presented. This analysis revealed a local similarity regime in brain activity ~in more than two decades of frequencies! and provided new parameters for noninvasive experimental studies of the brain. @S1063-651X~97! 50509-5# PACS number~s! : 87.10.1e, 87.22. Jb The study of systems with strong interactions of many degrees of freedom is one of the most important subjects in physics. Examples of these systems are turbulent flows of ordinary fluid and plasma, the global structure of the universe, and the unified theory of fields~superstrings! Turbulence is more accessible ~analytically, experimental, and numerically! and its study can provide guidelines for the analysis of other systems. The nature of these systems and the mechanism of interaction can be quite different. However, in many of these systems we may expect characteristic cascade processes and a regime of scale similarity ~see @1# and references therein! The present Rapid Communication is a test of scalesimilar activity in the brain. The human brain consists of about hundred billion neurons. Each neuron has up to ten thousand connections ~for a description of the brain from a point of view of physics see recent works @2‐5# and references therein! Neurons are assembled in a hierarchical structure, from a small group of neurons to larger groups, etc. A flux of activity in this hierarchy can produce a similarity regime. Data for this study were obtained from the Scripps Research Institute ~La Jolla, CA! , using a dual probe 37channel superconducting quantum interference device ~SQUID; see @6# for details! magnetoencephalograph. We did an analysis of the measurements of the normal component of the magnetic field on the brain surface from 70 channels in the range from 0.1 to 115 Hz. A sketch of the relative positions of channels is presented in Fig. 1. The distance of each sensor from the skull is between 2 and 2.5 cm. The magnetometer was in a magnetically shielded room and the power of the environmental noise was, at least, one order of magnitude lower than that of the neural signals. Power-line interference ~highly correlated and spectrally localized! was eliminated from the data. The data presented here are from a healthy female ~age 39! and a healthy male ~age 38! , both lying on their right side, while resting with their eyes closed. The data were recorded over 30 min with a sampling frequency of 231.5 Hz. The power spectra were calculated by the FFT method, averaging 50 intervals with 8192 points each. The power spectrum of individual channels has peaks corresponding to typical brain rhythms @Figs. 2~a! and ~b! and 3~a! and ~b! #. However, when we took the spectrum of the difference between the signals of two channels, the peaks practically disappear in many cases and we obtained a similarity regime ~power law! for, at least, two decades of frequencies @Figs. 2~c! and 3~c! #. The similarity parameters (a,b) and the error « were determined by minimizing the mean square deviation Q5^@logF~v! 2a2b logv# 2 &, ~1! «5 Q 1/2 ^ulogF~v! u& , ~2! where F(v) is the power spectrum and brackets ^& indicate averaging over the range of frequencies v. The range in this presentation was from 0.4 to 40 Hz, but analogous results also hold for the ranges 0.2‐20 and 0.5‐50 Hz. The parameters ( a,b,«) were calculated for the spectra of 70 channels and for the spectra of signal differences for all 2415 pairs of channels. Let us denote $% for averaging over all pairs of channels. The averaged parameters and rms deviations for the range 0.4‐40 Hz are $a 1%523.11,s~a 1! 50.856,$a 2%524.02,s~a 2! 50.913, ~3!