Multivariate Frequency Domain Analysis of Causal Interactions in Physiological Time Series

A common way of obtaining information about a physiological system is to measure one or more signals from the system, consider their temporal evolution in the form of numerical time series, and obtain quantitative indexes through the application of time series analysis techniques. While historical approaches to time series analysis were addressed to the study of single signals, recent advances have made it possible to study collectively the behavior of several signals measured simultaneously from the considered system. In fact, multivariate (MV) time series analysis is nowadays extensively used to characterize interdependencies among multiple signals collected from dynamical physiological systems. Applications of this approach are ubiquitous, for instance, in neurophysiology and cardiovascular physiology (see, e.g., (Pereda et al., 2005) and (Porta et al., 2009) and references therein). In neurophysiology, the time series to be analyzed are obtained, for example, sampling electroencephalographic (EEG) or magnetoencephalographic (MEG) signals which measure the temporal dynamics of the electro-magnetic fields of the brain as reflected at different locations of the scalp. In cardiovascular physiology, the time series are commonly constructed measuring at each cardiac beat cardiovascular and cardiorespiratory variables such as the heart period, the systolic/diastolic arterial pressure, and the respiratory flow. It is well recognized that the application of MV analysis to these physiological time series may provide unique information about the coupling mechanisms underlying brain dynamics and cardiovascular control, and may also lead to the definition of quantitative indexes useful in medical settings to assess the degree of mechanism impairment in pathological conditions. MV time series analysis is not only important to detect coupling, i.e., the presence or absence of interactions, between the considered time series, but also to identify driver-response relationships between them. This problem is a special case of the general question of assessing causality, or cause-effect relations, between (sub)systems, processes or phenomena. The assessment of coupling and causality in MV processes is often performed by linear time series analysis approaches, i.e. approaches in which a linear model is supposed to underlie the generation of temporal dynamics and interactions of the considered signals (Kay, 1988; Gourevitch et al., 2006). While non-linear methods are continuously under development