The paper presents the algorithm and the mathematical support to estimate the correlation dimensions of attractors manifested themselves in the most powerful harmonics of spectra retrieved during Doppler sonography assessment of human cerebral circulation. The objective of the present study was to estimate the correlation dimensions for power spectral densities of the most powerful harmonics. The results of real clinical data analysis are given. The estimates of the correlation dimensions were formed for the different examined body’s states: in the rest and under test for hypocapnia. The significant relation was found between those estimates of the correlation dimensions and psychoemotional state of volunteer.