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Fractal geometry predicts dynamic differences in structural and functional connectomes.

Anca Rădulescu1, Eva Kaslik2, Alexandru Fikl3

  • 1Department of Mathematics, SUNY New Paltz, New Paltz, New York 12561, USA.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces fractal geometry to analyze brain networks, revealing distinct properties of structural and functional connectomes. Fractal-based methods offer superior markers for brain dynamics compared to traditional graph theory.

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Network Science

Background:

  • Understanding brain network architecture is crucial for cognition and disease research.
  • Traditional graph theory has limitations in capturing emergent properties of neural dynamics.
  • Novel methods are needed to quantify complex brain network behavior.

Purpose of the Study:

  • To introduce a novel approach for quantifying brain networks using complex dynamics and fractal geometry.
  • To explore the application of Mandelbrot-like sets and quadratic iterations to brain connectomes.
  • To differentiate between structural and functional connectomes and identify superior markers for network dynamics.

Main Methods:

  • Applied concepts from complex dynamics, fractal geometry, and asymptotic analysis to brain connectomes.
  • Utilized quadratic iterations and geometric properties of Mandelbrot-like sets.
  • Analyzed structural (positive) and functional (signed) connectomes, including their positive and negative sub-networks.

Main Results:

  • Revealed fundamental distinctions between structural and functional connectomes through cusp orientation and equi-M set geometry.
  • Structural connectomes showed robust and predictable features, while functional connectomes exhibited increased variability during tasks.
  • Equi-M set invariants effectively differentiated between rest and emotional task states, outperforming traditional graph-theoretical measures.

Conclusions:

  • Fractal-based methods provide novel insights into structural and functional brain network dynamics.
  • These methods offer superior markers for emergent network dynamics compared to static connectivity measures.
  • Incorporating fractal geometry enhances network neuroscience for understanding information flow in natural systems.