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Updated: Oct 23, 2025

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Functional harmonics reveal multi-dimensional basis functions underlying cortical organization.

Katharina Glomb1, Morten L Kringelbach2, Gustavo Deco3

  • 1Department of Radiology, Lausanne University Hospital and University of Lausanne (CHUV-UNIL), Rue du Bugnon 46, 1011 Lausanne, Switzerland.

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|August 25, 2021
PubMed
Summary
This summary is machine-generated.

Human brain organization is explained by functional harmonics, a mathematical framework revealing how specialized areas and continuous variations form networks. This principle of harmonicity underlies brain function across scales.

Keywords:
brain networksfMRIfunctional connectivityharmonic modeshuman cortex

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Mathematical Modeling

Background:

  • The human brain exhibits both modular organization in specialized areas and continuous functional variation across the cortex.
  • Existing models struggle to reconcile these two perspectives on brain organization.

Purpose of the Study:

  • To introduce a mathematical framework, "functional harmonics," that integrates modular and continuous views of brain organization.
  • To demonstrate how functional harmonics capture various organizational features across spatial scales.

Main Methods:

  • Calculation of harmonic modes from the brain's functional connectivity graph.
  • Analysis of functional harmonics to identify links with cortical organization and functional networks.
  • Reconstruction of task-evoked brain activity patterns using functional harmonics.

Main Results:

  • Functional harmonics reveal a multi-dimensional, frequency-ordered set of basis functions for brain activity.
  • These harmonics link intra-areal features (retinotopy, somatotopy), delineate brain areas, and explain macroscopic networks and global gradients.
  • Task-evoked activity patterns can be accurately reconstructed from a small subset of functional harmonics.

Conclusions:

  • The principle of harmonicity provides a unified framework for understanding human brain functional organization.
  • Functional harmonics offer a powerful tool for analyzing brain structure-function relationships across multiple scales.
  • This approach suggests a fundamental natural principle underlying cortical organization.