Yiben Xu, Xian Long, Jianfeng Feng and Pulin Gong (2023), Nature Human Behaviour 7(7):1196–1215 — DOI-10.1038/s41562-023-01626-5
Key takeaways
- The phase map of band-passed (0.01–0.1 Hz) cortical fMRI, on a flattened cortex, organises around phase singularities: points of near-zero amplitude round which every phase occurs and the phase field rotates. Many such “brain spirals” coexist (16.33 ± 2.22 in the left hemisphere at rest), with radii of 4–31 mm, mostly spanning more than one cortical region and concentrated on the boundaries between functional regions, not on sulcal patterns.
- Their centres drift at about 2.2 mm/s, superdiffusively (mean-squared displacement exponent β ≈ 1.5, 96% of trajectories above 1), and spirals interact: opposite rotations collide and fully or partly annihilate (51% and 46% of interactions), like rotations repel (2.6%). The authors liken this to defect-mediated turbulence in fluids, active matter and the heart, and note that in turbulent fluids defects diffuse normally instead.
- Spiral locations and topological charges are task-specific. On single trials they decode four language-task conditions at 48.3% (replication cohort 50.4%; chance 25%; phase-randomised null 24.3%), above a matched decoder on raw fMRI amplitude (30.2%), and decode working-memory stimulus type, load and accuracy above chance.
- Two pairwise rules, opposite spirals as a “gate” that passes activity flow and like spirals as a “wall” that diverts it, explain the task-specific flow the authors trace from phase-vector streamlines: bottom-up from primary auditory to lateral temporal cortex while listening to math, top-down along the reverse path while answering.
Standing in the record
Filed on 2026-10-03 at the owner’s request, in a batch of four works on large-scale neural dynamics with Verzhbinsky et al. (LIT-633), Muller et al.’s traveling-wave review (LIT-647, unread) and Vishne et al. (LIT-644). No anthology topic holds a study of human cortical wave dynamics, and the paper carries no instruction for machine-learning practice.
It joins the record’s line on pattern formation outside equilibrium. The objects it finds in cortex are the ones that line already describes in chemistry. Zhabotinsky’s review of the Belousov–Zhabotinsky reaction (LIT-531, read in NOTE-414) reports that in unstirred layers colliding waves annihilate and broken fronts curl into spirals. Cross and Hohenberg’s review (LIT-527, NOTE-418) holds that phase dynamics and topological defects of broken continuous symmetry are established in non-equilibrium laboratory systems. Turing’s morphogenesis paper (LIT-535, NOTE-427) has travelling waves as one of its six onset cases, the one that needs three morphogens. Xu et al. cite none of these. They rely on Kuramoto’s phase-oscillator lattice and on Coullet, Gil and Lega’s defect-mediated turbulence. So no relation is declared; what the record gains is the first claim it holds that those structures organise brain activity.
Rival account: LIT-080. Vohryzek et al.’s review of whole-brain
modelling describes non-stationary brain dynamics as visits to a
repertoire of discrete substates, with dwell times and transition
probabilities on an attractor landscape kept metastable near criticality
(NOTE-054). Xu et al. argue the reverse for the same phenomenon: their
spiral-based coordination means transitions between functional networks
“evolve continuously across space and time, rather than discrete or sudden
changes between different metastable states as previously suggested”
(Discussion). Neither tests the other. Xu et al. cite earlier papers from
the same programme, not this review, and the review predates the spiral
result. So the relation is rivals, not corrects: deciding it would take
a dataset analysed both ways, asking whether state-switching statistics
survive once spiral motion is accounted for. Kelso’s sense of metastability
(LIT-601), relative coordination without fixed states, is closer to Xu et
al. than to discrete switching. It is not the target of their sentence.
Muller et al.’s review (LIT-647) is the natural companion: travelling waves within single areas, measured electrophysiologically, against spirals across the whole cortex in fMRI. Xu et al. cite Davis, Muller et al. (2020) on waves gating perception. The review is unread, so the two are not compared here.
No extends is declared. The spiral-detection and turbulence methods it
builds on are not in the record.