Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability

Abstract

Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of ‘instantaneous’ effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index of undirected instantaneous causality and (ii) a novel measure of GC including instantaneous effects. An effective procedure to speed up the optimization of parameters in this frame is also presented. After illustrating the proposed formalism in a theoretical example, we apply it to two datasets of cardiovascular and respiratory time series and compare the values obtained within the frequency bands of physiological interest by the proposed total measure of causality with those derived from the standard GC analysis. We find that the inclusion of instantaneous causality allows us to correctly disentangle the baroreflex mechanism from the effects related to cardiorespiratory interactions. Moreover, studying how controlling the respiratory rhythm acts on cardiovascular interactions, we document an increase of the direct (non-baroreflex mediated) influence of respiration on the heart rate in the respiratory frequency band when switching from spontaneous to paced breathing. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

“…Negative correlation was found between the phase-lag and instantaneous causality, implying that the stronger the common input, the closer to zero the phase lag. The study suggests that instantaneous causality should be accounted for when dealing with highly interconnected neural data, since disregarding it may have a great impact on the computation of GC indexes [ 152 ].…”

Spectral decomposition of cerebrovascular and cardiovascular interactions in patients prone to postural syncope and healthy controls

“…Here, instantaneous interactions were assigned to a specific causal direction based on physiological knowledge in the cardiovascular analysis, and were left unassigned in the absence of such knowledge in the cerebrovascular analysis. Alternative approaches have been explored, including the use of non-Gaussian modelling and independent component analysis to set the direction of instantaneous effects without prior knowledge (Faes et al, 2013c;Schiatti et al, 2015), and the use of disconnected AR models studied in the frequency domain to provide undirected measures of instantaneous causality and extended measures of Granger causality (Nuzzi et al, 2021). Since our work confirms that instantaneous effects play a fundamental role in cardiovascular and cerebrovascular variability analysis, future studies are envisaged to compare our framework with existing approaches, to assess the agreement of these methods in the evaluation of frequency-domain interaction and shed more light on this delicate issue.…”

“…While the presence of these effects is accounted in the decomposition of the total time-domain dependence between processes (Geweke, 1982), their spectral interpretation is far less intuitive (Chicharro, 2011). Several approaches have been proposed to account for instantaneous correlations in frequency domain measures, either using extended AR models that incorporate zerolag effects after determining their direction (Faes et al, 2013a) or keeping them as undirected but including them in "extended" spectral causality measures (Baccalá and Sameshima, 2021;Nuzzi et al, 2021).…”

Advanced computation in cardiovascular physiology: new challenges and opportunities

“…Through the analysis of HRV, systolic and diastolic arterial pressure, and respiration variability series gathered during postural changes, the framework allows us to retrieve information on cardiovascular and cardio-respiratory oscillations within specific frequency bands, which are otherwise not detectable by standard timedomain information measures. By exploiting a recently proposed method for the estimation of causal influences in the spectral domain, Nuzzi et al [10] show how to estimate instantaneous interactions between cardiovascular and cardio-respiratory oscillations, thus obtaining a novel index of undirected instantaneous causality and a novel measure of Granger causality including instantaneous effects. This study shows that the inclusion of instantaneous causality allows the baroreflex mechanism to be correctly disentangled from the effects related to cardiorespiratory interactions.…”