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

D. Nuzzi, S. Stramaglia, M. Javorka, Daniele Marinazzo (UGent) , A. Porta and Luca Faes
(2021) PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 379(2212).
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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.
Keywords
information theory, granger causality, cardiorespiratory system, time series analysis

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Citation

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MLA
Nuzzi, D., et al. “Extending the Spectral Decomposition of Granger Causality to Include Instantaneous Influences : Application to the Control Mechanisms of Heart Rate Variability.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 379, no. 2212, 2021, doi:10.1098/rsta.2020.0263.
APA
Nuzzi, D., Stramaglia, S., Javorka, M., Marinazzo, D., Porta, A., & Faes, L. (2021). Extending the spectral decomposition of Granger causality to include instantaneous influences : application to the control mechanisms of heart rate variability. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 379(2212). https://doi.org/10.1098/rsta.2020.0263
Chicago author-date
Nuzzi, D., S. Stramaglia, M. Javorka, Daniele Marinazzo, A. Porta, and Luca Faes. 2021. “Extending the Spectral Decomposition of Granger Causality to Include Instantaneous Influences : Application to the Control Mechanisms of Heart Rate Variability.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 379 (2212). https://doi.org/10.1098/rsta.2020.0263.
Chicago author-date (all authors)
Nuzzi, D., S. Stramaglia, M. Javorka, Daniele Marinazzo, A. Porta, and Luca Faes. 2021. “Extending the Spectral Decomposition of Granger Causality to Include Instantaneous Influences : Application to the Control Mechanisms of Heart Rate Variability.” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 379 (2212). doi:10.1098/rsta.2020.0263.
Vancouver
1.
Nuzzi D, Stramaglia S, Javorka M, Marinazzo D, Porta A, Faes L. Extending the spectral decomposition of Granger causality to include instantaneous influences : application to the control mechanisms of heart rate variability. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 2021;379(2212).
IEEE
[1]
D. Nuzzi, S. Stramaglia, M. Javorka, D. Marinazzo, A. Porta, and L. Faes, “Extending the spectral decomposition of Granger causality to include instantaneous influences : application to the control mechanisms of heart rate variability,” PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, vol. 379, no. 2212, 2021.
@article{8725041,
  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.}},
  articleno    = {{20200263}},
  author       = {{Nuzzi, D. and Stramaglia, S. and Javorka, M. and Marinazzo, Daniele and Porta, A. and Faes, Luca}},
  issn         = {{1364-503X}},
  journal      = {{PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}},
  keywords     = {{information theory,granger causality,cardiorespiratory system,time series analysis}},
  language     = {{eng}},
  number       = {{2212}},
  title        = {{Extending the spectral decomposition of Granger causality to include instantaneous influences : application to the control mechanisms of heart rate variability}},
  url          = {{http://doi.org/10.1098/rsta.2020.0263}},
  volume       = {{379}},
  year         = {{2021}},
}
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