Relationship between correlation dimension and indices of linear analysis in both respiratory movement and electroencephalogram

Objective: We investigate the relationships between signals from the electroencephalogram (EEG) and those from respiratory movement using the correlation dimension (D₂). Methods: Respiratory movement and EEG were recorded for 7.5 h from 7 clinically healthy men. D₂ was calculated by applying an algorithm slightly modified from that proposed by Grassberger and Procaccia (Phys Rev Lett 50 (1983) 346). Non-linearity in respiratory movement and EEG was tested by comparing D₂ for the original data with that for surrogate data. Results: A statistically significant positive correlation between D₂ of the EEG and D₂ of the respiratory movement was observed for the original data, but not for the surrogate data. Conclusions: A reduced D₂ of the EEG may be associated with an increased regularity of breathing in deep sleep (stage IV). Likewise, the increased D₂ of respiratory movement during rapid eye movement may be associated with increased complexity of the signals. Whether there is a direct coordination between brain and lungs or whether brainstem systems, including that of the cholinergic system, affect both respiration and cortex requires further investigation.