Functional Harmonics
Functional Harmonics: Brain’s Harmonic Communication Patterns
If connectome harmonics reveal the brain’s structural foundations—the natural wave patterns that can emerge from its physical wiring—then functional harmonics illuminate the brain’s actual conversation in motion.
Building on the idea that harmonic waves can serve as the elementary building blocks of brain activity, in a 2021 study with Katharina Glomb, Gustavo Deco, Morten Kringelbach, and others (Cell Reports), we extended this framework to describe the brain’s functional connectivity. Rather than using the anatomical connectome, functional harmonics are derived from how brain regions dynamically communicate—their co-activation patterns during rest or task.
Using the same mathematical approach as connectome harmonics (the Laplace eigen decomposition), we applied it to functional connectivity matrices. The result: a new set of spatial harmonic patterns that describe how information flows across the cortex. These functional harmonics offer a frequency-specific, compact, and interpretable representation of brain dynamics—one that adapts not just to structure, but to moment-by-moment communication.
What makes functional harmonics so compelling is how they naturally capture both well-known functional networks and gradients in the brain. For example, the first few harmonics reveal major distinctions such as visual vs. somatomotor regions, or unimodal vs. multimodal areas—closely mirroring principal gradients reported in earlier research. Higher-frequency harmonics, meanwhile, offer more localized and fine-grained separations, such as distinct representations of right hand, left hand, foot, and face areas.
We found that combining just a small number of functional harmonics could recreate detailed cortical mappings, such as somatotopic and retinotopic maps. This suggests that functional harmonics form a low-dimensional but powerful vocabulary for describing complex brain functions—much like a few musical notes giving rise to an entire symphony.
Functional harmonics build a bridge between data-driven neuroscience and theory-informed models. They offer an elegant, frequency-based lens to explore how the brain organizes itself across space and time—not just through anatomy, but through patterns of interaction. This harmonic perspective opens new possibilities for studying cognition, development, and mental health using a language rooted in both mathematics and the music of the mind.
This work was made possible by the inspiring collaboration with Katharina Glomb, Gustavo Deco, Morten Kringelbach, and many others who helped bring this vision to life.
If you want to dive deeper, see the related publications below and watch the selected talks:
• Glomb, K., Kringelbach, M. L., Deco, G., Hagmann, P., Pearson, J., & Atasoy, S. (2021). Functional harmonics reveal multi-dimensional basis functions underlying cortical organization. Cell Reports, 36(8), 109554, doi.org/10.1016/j.celrep.2021.109554
• Atasoy, S., Donnelly, I., & Pearson, J. (2016). Human brain networks function in connectome-specific harmonic waves. Nature communications, 7(1), 1-10. doi:10.1038/ncomms10340.
• Atasoy, S., Roseman, L., Kaelen, M., Kringelbach, M. L., Deco, G., & Carhart-Harris, R. L. (2017). Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD. Scientific reports, 7(1), 1-18.
• Atasoy, S., Deco, G., Kringelbach, M. L., & Pearson, J. (2018). Harmonic brain modes: a unifying framework for linking space and time in brain dynamics. The Neuroscientist, 24(3), 277-293.
