title: Detecting causality between different frequencies.
abstract: Biological systems are usually non-linear and, as a result, the driving signal frequency (say, MHz) is in general not identical with the output frequency (say, N Hz). Coherence and causality analysis have been well-developed to measure the (directional) correlation between input and output signals with identical frequencies (N=M), but they are not applicable to the cases with different frequencies (N not equal M). In this paper, we propose a novel method called frequency-modified causality (coherence) analysis to resolve the issue. The input or output signal is first modulated by up-sampling or down-sampling, coherence and causality analysis are then applied to the frequency modulated and filtered signals. An optimal coherence and causality is found, revealing the true input-output relationship between signals. The method is successfully tested on data generated from a toy model, the van der Pol oscillator and then employed to analyze data recorded from Parkinson's disease (PD) patients.
authors.affiliation: Department of Computer Science and Mathematics, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Wu
authors.forename: Xuguang
authors.initials: X
authors.lastname: Liu
authors.forename: Jianfeng
authors.initials: J
authors.lastname: Feng
mesh_terms: D000465:Algorithms; D044962:Data Compression; D006801:Humans; D008959:Models, Neurological; D017711:Nonlinear Dynamics; D009991:Oscillometry; D010300:Parkinson Disease / Q000175:diagnosis / Q000503:physiopathology; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014947:Wounds and Injuries / Q000175:diagnosis* / Q000503:physiopathology