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Nonequilibrium Green's Functions for Functional Connectivity in the Brain.

Francesco Randi1, Andrew M Leifer1,2

  • 1Department of Physics, Princeton University, Jadwin Hall, Princeton, New Jersey 08544, USA.

Physical Review Letters
|April 2, 2021
PubMed
Summary

This study introduces a new theoretical framework using nonequilibrium Green's functions to model time-dependent functional connectivity in neural networks. This approach captures the brain's nonlinear dynamics, offering insights into neuronal signal propagation.

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Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Systems Neuroscience

Background:

  • Functional connectivity describes neural interactions but existing models often assume linear, time-invariant systems.
  • The brain exhibits complex nonlinear and time-dependent dynamics, which traditional models struggle to capture.
  • Dynamical functions like Green's functions are conceptually useful but limited to linear systems.

Purpose of the Study:

  • To develop a theoretical framework for time-dependent functional connectivity in neural networks.
  • To extend the utility of Green's functions to nonlinear and time-dependent systems.
  • To relate theoretical connectivity measures to experimentally measurable response functions.

Main Methods:

  • Utilized nonequilibrium Green's functions to model neuronal network dynamics.
  • Developed a framework for continuous-variable neural networks.
  • Established a connection between functional connectivity and measurable response functions.
  • Performed numerical calculations inspired by Caenorhabditis elegans.

Main Results:

  • Successfully applied nonequilibrium Green's functions to describe time-dependent functional connectivity.
  • Demonstrated the relationship between theoretical connectivity and measurable response functions.
  • Provided two numerical examples illustrating the framework's application.

Conclusions:

  • The proposed framework accurately models time-dependent functional connectivity in nonlinear neural systems.
  • Nonequilibrium Green's functions offer a powerful tool for understanding brain dynamics.
  • The study provides a basis for analyzing complex neural network behavior.