The extended Granger causality analysis for Hodgkin-Huxley neuronal models

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Network Science

Background:

• Extracting information flow direction in dynamical systems from empirical data is challenging.
• Granger causality (GC) analysis is effective for linear systems but its validity in nonlinear systems is unknown.
• Hodgkin-Huxley (HH) neuronal circuits are complex nonlinear dynamical systems.

Purpose of the Study:

• To investigate the validity of the extended Granger causality (GC) analysis for nonlinear dynamical systems.
• To determine if extended GC analysis can accurately map causal connectivity to synaptic connectivity in HH neuronal networks.
• To assess the robustness of extended GC analysis in the presence of observational noise and different dynamical regimes.

Main Methods:

• Applied the nonlinear extension of Granger causality (extended GC) analysis.
• Utilized voltage time series from simulated Hodgkin-Huxley (HH) neuronal networks.
• Introduced measurement/observational noise to the time series to simulate experimental conditions.

Main Results:

• The causal connectivity derived from the extended GC analysis consistently matched the underlying synaptic connectivity of the HH neuronal network.
• This consistency was maintained across different dynamical regimes, including chaotic and non-chaotic states.
• The findings were robust despite the addition of observational noise.

Conclusions:

• The extended Granger causality (GC) analysis is a valid and robust method for determining information flow in nonlinear dynamical systems.
• Extended GC analysis accurately reflects the structural (synaptic) connectivity in Hodgkin-Huxley neuronal networks.
• This approach holds potential for application to other low-dimensional nonlinear dynamical systems.