A nonlinear causality measure in the frequency domain: nonlinear partial directed coherence with applications to EEG.
BACKGROUND
Frequency domain Granger causality measures have been proposed and widely applied in analyzing rhythmic neurophysiological and biomedical signals. Almost all these measures are based on linear time domain regression models, and therefore can only detect linear causal effects in the frequency domain.


METHODS
A frequency domain causality measure, the partial directed coherence, is explicitly linked with the frequency response function concept of linear systems. By modeling the nonlinear relationships between time series using nonlinear models and employing corresponding frequency-domain analysis techniques (i.e., generalized frequency response functions), a new nonlinear partial directed coherence method is derived.


RESULTS
The advantages of the new method are illustrated via a numerical example of a nonlinear physical system and an application to electroencephalogram signals from a patient with childhood absence epilepsy.


METHODS
The new method detects both linear and nonlinear casual effects between bivariate signals in the frequency domain, while the existing measures can only detect linear effects.


CONCLUSIONS
The proposed new method has important advantages over the classical linear measures, because detecting nonlinear dependencies has become more and more important in characterizing functional couplings in neuronal and biological systems.
Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, UK.
Fei
F
He
Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, UK. Electronic address: s.billings@sheffield.ac.uk.
Stephen A
SA
Billings
Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, UK.
Hua-Liang
HL
Wei
Department of Clinical Neurophysiology, Sheffield Teaching Hospitals NHS Foundation Trust, Royal Hallamshire Hospital, UK.
Ptolemaios G
PG
Sarrigiannis
D000465:Algorithms; D004569:Electroencephalography / Q000379:methods*; D004832:Epilepsy, Absence / Q000503:physiopathology*; D006801:Humans; D008959:Models, Neurological; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted
Coherence; Epilepsy; Granger causality; Nonlinear systems; Spectral analysis