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Echo state network models for nonlinear Granger causality.

Andrea Duggento1, Maria Guerrisi1, Nicola Toschi1,2

  • 1Department of Biomedicine and Prevention, University of Rome Tor Vergata, Rome, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 25, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces echo state network-based Granger causality (ES-GC) to uncover nonlinear causal links in complex biological networks. ES-GC reveals novel directed brain interactions and causal links in the central autonomic network.

Keywords:
Granger causalitybrain connectivitybrain-heart interactionecho state network

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Area of Science:

  • Neuroscience
  • Computational Biology
  • Systems Physiology

Background:

  • Traditional Granger causality (GC) relies on linear models, limiting its application to complex biological systems with nonlinear dynamics.
  • Existing nonlinear GC methods have limitations, including handling only additive nonlinearities or requiring complex neural network training.

Purpose of the Study:

  • To reformulate the Granger causality framework using echo state networks (ESNs) to capture complex nonlinear causal relationships.
  • To validate the efficacy of echo state network-based Granger causality (ES-GC) in detecting nonlinear causal links.
  • To investigate directed interactions within the human brain and between brain and cardiac systems.

Main Methods:

  • Developed an echo state network-based Granger causality (ES-GC) framework for arbitrarily complex networks.
  • Validated ES-GC using a network of noisy Duffing oscillators to assess its ability to detect nonlinear causal links.
  • Applied ES-GC to functional MRI data from the Human Connectome Project (1003 subjects) to explore human brain connectomics.
  • Analyzed joint brain-heart signals (15 subjects) to investigate causal interactions within the central autonomic network.

Main Results:

  • ES-GC demonstrated a significant advantage over traditional methods in detecting nonlinear, causal links in simulated systems.
  • Analysis of human brain fMRI data revealed previously unidentified directed within-brain interactions.
  • Directed interactions between brain networks and central vagal cardiac control were identified, offering causal insights into the central autonomic network.

Conclusions:

  • Echo state network-based Granger causality (ES-GC) provides a powerful tool for uncovering complex nonlinear causal relationships in biological networks.
  • ES-GC has successfully identified novel directed interactions in the human brain and shed light on brain-heart interactions.
  • This approach advances the study of network neuroscience and cardiovascular physiology by enabling more sophisticated causal inference.