Mapping nonlinear brain dynamics by phase space embedding with fMRI data

The human brain is a complex neurobiological system exhibiting complex nonlinear spatiotemporal dynamics. While functional magnetic resonance imaging (fMRI) has been widely used to study brain activity, whole-brain nonlinear dynamics in fMRI data have not been extensively examined. The present study applied phase space embedding on resting-state fMRI data and characterized their phase space dynamics with the sum of lengths of portrait edges (SE) in the reconstructed phase portrait. The effects of repetition time (TR), bandpass filtering and the added noise power of BOLD signals on the optimal embedding parameters (embedding time delay τ and embedding dimension m) were examined with experimental or simulated fMRI data. Our results show that τ and m vary with the three acquisition parameters. The present method was applied to the autism spectrum disorder dataset from Autism Imaging Data Exchange I to demonstrate its capability in the characterization of abnormal brain dynamics. The resultant SE maps were statistically compared between patients and controls, and the significant differences in SE were fed into a support vector machine (SVM) for classification. A significant increase in SE in the default mode network (DMN) and salience network (SN), as well as the visual network, was found in autistic patients. With the SE features of these regions, our SVM classifier achieved superior accuracy (74.55% with 10-folds cross validation) compared with prior studies, indicating that phase space embedding and SE mapping are promising in characterizing the nonlinear dynamics of the BOLD signal and might be useful for brain biomarker discovery in clinical psychiatry.