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Modeling the Functional Network for Spatial Navigation in the Human Brain
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Spatially extended balanced networks without translationally invariant connectivity.

Christopher Ebsch1, Robert Rosenbaum2,3

  • 1Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA.

Journal of Mathematical Neuroscience
|May 15, 2020
PubMed
Summary

Brain networks maintain excitation-inhibition balance for stable function. This study extends balanced network theory to include complex spatial structures, improving models of cortical dynamics.

Keywords:
Balanced networksExcitatory-inhibitory balanceMean-field theorySpiking neural network models

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Area of Science:

  • Computational neuroscience
  • Neural network dynamics
  • Theoretical neurobiology

Background:

  • Cortical neural networks require a balance between excitation and inhibition for stable function.
  • Balanced network theory models this using randomly connected neurons, reproducing asynchronous-irregular spiking.
  • Previous models assumed simplified, translationally invariant connectivity, not reflecting complex cortical topology.

Purpose of the Study:

  • To extend balanced network theory to incorporate more general spatial connectivity structures.
  • To develop a mathematical framework for analyzing excitatory-inhibitory balance in networks with non-uniform spatial topology.
  • To validate theoretical predictions against simulations of large-scale spiking neural networks.

Main Methods:

  • Utilizing the mathematical theory of integral equations to extend mean-field analysis.
  • Developing a generalized mean-field theory for balanced networks with arbitrary spatial dependence.
  • Comparing theoretical derivations with large-scale simulations of recurrently connected spiking neuron models.

Main Results:

  • The extended theory accurately describes network dynamics beyond translationally invariant connectivity.
  • Mathematical derivations align well with simulation results for complex spatial structures.
  • The study provides a more realistic framework for understanding cortical network function.

Conclusions:

  • Balanced network theory can be generalized to account for realistic spatial connectivity in cortical networks.
  • This extended framework offers improved predictions of neural activity patterns.
  • The findings advance our understanding of the principles governing brain network organization and dynamics.