One of the most popular approaches to the evaluation of brain connectivity is based on describing a set of multiple neurological time series by means of a multivariate (MV) autoregressive (MVAR) model, and then computing connectivity measures from the frequency domain representation of the model coefficients. Within this framework, the directed coherence (DC) and partial DC (PDC) are well-known connectivity measures quantifying lagged causality from one series to another in the MV representation. An open issue in MVAR-based connectivity analysis is that, although zero-lag interactions are very common in experimental time series, the model traditionally used to compute DC and PDC forsakes instantaneous effects, i.e. effects occurring within the same time lag. This study aims at investigating the impact of instantaneous causality on the evaluation of MVAR-based connectivity measures. To this end, we introduce an extended MVAR representation in which instantaneous effects are explicitly described in terms of model coefficients. The extended model allows evaluation of a generalized form of causality including instantaneous effects in addition to the lagged ones, but can be adopted also to infer lagged causality through exclusive consideration of time-delayed influences. Using theoretical examples we show that, in the presence of significant instantaneous causality, the interpretation of lagged causality may change considerably if instantaneous effects are not described. In such a case, the DC and PDC computed from the traditional MVAR model yields misleading connectivity patterns, while the correct interpretation is obtained defining the two functions from the coefficients of the extended model. Moreover, we show that extended causality may be tested in the frequency domain by incorporating both lagged and instantaneous effects into the definitions of DC and PDC. Finally, we discuss the practical application of the extended MVAR model, providing an algorithm for its full identification and showing the PDC patterns related to the propagation of alpha EEG activity assessed in normal subjects in the eyes-closed condition.
Investigating the impact of instantaneous causality on frequency domain connectivity measures
Faes, Luca;Nollo, Giandomenico
2011-01-01
Abstract
One of the most popular approaches to the evaluation of brain connectivity is based on describing a set of multiple neurological time series by means of a multivariate (MV) autoregressive (MVAR) model, and then computing connectivity measures from the frequency domain representation of the model coefficients. Within this framework, the directed coherence (DC) and partial DC (PDC) are well-known connectivity measures quantifying lagged causality from one series to another in the MV representation. An open issue in MVAR-based connectivity analysis is that, although zero-lag interactions are very common in experimental time series, the model traditionally used to compute DC and PDC forsakes instantaneous effects, i.e. effects occurring within the same time lag. This study aims at investigating the impact of instantaneous causality on the evaluation of MVAR-based connectivity measures. To this end, we introduce an extended MVAR representation in which instantaneous effects are explicitly described in terms of model coefficients. The extended model allows evaluation of a generalized form of causality including instantaneous effects in addition to the lagged ones, but can be adopted also to infer lagged causality through exclusive consideration of time-delayed influences. Using theoretical examples we show that, in the presence of significant instantaneous causality, the interpretation of lagged causality may change considerably if instantaneous effects are not described. In such a case, the DC and PDC computed from the traditional MVAR model yields misleading connectivity patterns, while the correct interpretation is obtained defining the two functions from the coefficients of the extended model. Moreover, we show that extended causality may be tested in the frequency domain by incorporating both lagged and instantaneous effects into the definitions of DC and PDC. Finally, we discuss the practical application of the extended MVAR model, providing an algorithm for its full identification and showing the PDC patterns related to the propagation of alpha EEG activity assessed in normal subjects in the eyes-closed condition.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
