Functional harmonics reveal multi-dimensional basis functions underlying cortical organization

Katharina Glomb*, Morten L. Kringelbach, Gustavo Deco, Patric Hagmann, Joel Pearson, Selen Atasoy

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


The human brain consists of specialized areas that flexibly interact to form a multitude of functional networks. Complementary to this notion of modular organization, brain function has been shown to vary along a smooth continuum across the whole cortex. We demonstrate a mathematical framework that accounts for both of these perspectives: harmonic modes. We calculate the harmonic modes of the brain's functional connectivity graph, called “functional harmonics,” revealing a multi-dimensional, frequency-ordered set of basis functions. Functional harmonics link characteristics of cortical organization across several spatial scales, capturing aspects of intra-areal organizational features (retinotopy, somatotopy), delineating brain areas, and explaining macroscopic functional networks as well as global cortical gradients. Furthermore, we show how the activity patterns elicited by seven different tasks are reconstructed from a very small subset of functional harmonics. Our results suggest that the principle of harmonicity, ubiquitous in nature, also underlies functional cortical organization in the human brain.

Original languageEnglish
Article number109554
JournalCell Reports
Number of pages21
Publication statusPublished - Aug 2021


  • brain networks
  • fMRI
  • functional connectivity
  • harmonic modes
  • human cortex


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