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Background: The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series.Objectives: We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series.Methods: A procedure for the identification of a MVAR model combining instantaneous and lagged effects is introduced. The coefficients of the extended model are used to estimate an extended PDC (EPDC). EPDC is compared to the traditional PDC on a simulated MVAR process and on real cardiovascular variability series.Results: Simulation results evidence that the presence of zero-lag correlations may produce misleading PDC profiles, while the correct causality patterns can be recovered using EPDC. Application on real data leads to spectral causality estimates which are better interpretable in terms of the known cardiovascular physiology using EPDC than PDC.Conclusions: This study emphasizes the necessity of including instantaneous effects in the MVAR model used for the computation of PDC in the presence of significant zero-lag correlations in multivariate time series. [ABSTRACT FROM AUTHOR]

Objectives: This study aims to characterize EEG complexity, measured as the prediction error resulting from nonlinear prediction, in healthy humans during photic stimulation.Methods: EEGs were recorded from 15 subjects with eyes closed (EC) and eyes open (EO), during the baseline condition and during stroboscopic photic stimulation (PS) at 5, 10, and 15 Hz. The mean squared prediction error (MSPE) resulting from nearest neighbor local linear prediction was taken as complexity index. Complexity maps were generated interpolating the MSPE index over a schematic scalp representation.Results: Statistical analysis revealed that: i) EEG shows good predictability in all conditions and seems to be well explained by a linear stochastic process; ii) the complexity is lower with EC than with EO and increases significantly during PS, to a lesser extent during 10 Hz stimulation; iii) significant differences of EEG complexity are detectable between anterior-central and posterior scalp regions.Conclusions: Changes in EEG complexity during PS can be successfully assessed using nonlinear prediction. The observed modifications in the patterns of complexity seem to reflect neurophysiological behaviors and suggest future applicability of the method in clinical settings. [ABSTRACT FROM AUTHOR]