**Correlation of the Brain Compartments in the Attention Deficit and Hyperactivity Disorder Calculated by the Method of Virtual Electrodes from Magnetic Encephalography Data**
**Ustinin M.N., Rykunov S.D., Boyko A.I.**
*Keldysh Institute of Applied Mathematics RAS, Moscow, Russia*

**Abstract**. New method to study the correlation of the human brain compartments based on the magnetic encephalography data analysis was proposed. The time series for the correlation analysis are generated by the method of virtual electrodes. First, the multichannel time series of the subject with confirmed attention deficit and hyperactivity disorder are transformed into the functional tomogram - spatial distribution of the magnetic field sources structure on the discrete grid. This structure is provided by the inverse problem solution for all elementary oscillations, found by the Fourier transform. Each frequency produces the elementary current dipole located in the node of the 3D grid. The virtual electrode includes the part of space, producing the activity under study. The time series for this activity is obtained by the summation of the spectral power of all sources, covered by the virtual electrode. To test the method, in this article we selected ten basic compartments of the brain, including frontal lobe, parietal lobe, occipital lobe and others. Each compartment was included in the virtual electrode, obtained from the subjects' MRI. We studied the correlation between compartments in the frequency bands, corresponding to four brain rhythms: theta, alpha, beta, and gamma. The time series for each electrode were calculated for the period of 300 seconds. The correlation coefficient between power series was calculated on the 1 second epoch and then averaged. The results were represented as matrices. The method can be used to study correlations of the arbitrary parts of the brain in any spectral band.

**Key words**: *magnetic encephalography, spectral analysis, inverse problem solution, functional tomogram, virtual electrode, correlation, human brain rhythms. *