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Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

Nature Human Behaviour volume 7, pages 1196–1215 (2023)Cite this article

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Abstract

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

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Fig. 1: Schematic illustration of spiral-like, rotational wave patterns and their interactions.
Fig. 2: Detection of brain spirals based on moment-by-moment fMRI signals.
Fig. 3: Dynamical properties of brain spirals.
Fig. 4: Interactions among brain spirals of the same spatial scale and across different spatial scales.
Fig. 5: Brain spirals are task specific during cognitive processing.
Fig. 6: Task-specific brain spiral distributions and task classifications.
Fig. 7: Brain spirals in unfiltered fMRI signals.
Fig. 8: Task-specific activity flow flexibly organized by arrays of brain spirals.

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Data availability

The fMRI source data used in this study are publicly available through the HCP database and can be downloaded at the following URL: https://db.humanconnectome.org/data/projects/HCP_1200. Source data are provided with this paper.

Code availability

The MATLAB scripts used for conducting the analysis and generating example figures are publicly available in a GitHub repository at the following URL: https://github.com/BrainDynamicsUSYD/BrainVortexToolbox. These scripts can be used to reproduce the analysis and main figures presented in this study.

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Acknowledgements

We thank P. Robinson, P. Martin and B. Fulcher for feedback on the paper. This work was supported by the Australian Research Council (grant no. DP160104316, P.G.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Author notes

  1. These authors contributed equally: Yiben Xu, Xian Long.

Authors and Affiliations

  1. School of Physics, University of Sydney, Sydney, New South Wales, Australia

    Yiben Xu, Xian Long & Pulin Gong

  2. ARC Centre of Excellence for Integrative Brain Function, University of Sydney, Sydney, New South Wales, Australia

    Yiben Xu, Xian Long & Pulin Gong

  3. Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China

    Jianfeng Feng

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  1. Yiben Xu
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Contributions

P.G., Y.X. and X.L. designed the study. Y.X., X.L. and P.G. performed all the analyses. All authors discussed the results and contributed to writing the paper.

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Correspondence to Pulin Gong.

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Nature Human Behaviour thanks Ryan Raut, Kentaroh Takagaki and Joana Cabral for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The null model preserves both the power spectrum and autocorrelations across space and time of the fMRI slow fluctuations.

a, Radially averaged 2-D power spectral density averaged across all time steps of all subjects during the resting state. Blue and red (mostly occluded) lines represent the radially averaged power spectral density of the temporal bandpass filtered original fMRI signal and the null model. Shades denote s.e.m., n = 100 subjects. To remove the impact of NaN values outside the irregular borders of the flattened cortical map, we conducted the calculation based on a maximal sized rectangular region across the cortex in both fMRI signals and the null model. b, Population and channel-averaged temporal (1-D) power spectral density of both the original temporal bandpass filtered fMRI signal (blue line) and the null model (red line), within the same maximal sized rectangular region as a. The shades represent s.e.m., n = 100 subjects. c, Population-averaged spatial autocorrelations (Moran’s I) across spatial lags of both the slow fluctuations of fMRI signal (blue line) and the null model (red line). Shades (mostly occluded) denote s.e.m., n = 100 subjects. d, Same as c, but with temporal autocorrelations.

Source data

Extended Data Fig. 2 Brain spirals across the flattened cortex are not sensitive to sulcal patterns.

a, Projection of the sulcal depth map onto 3D brain space of a sample subject. Blue/red colour scheme denote the sulcal depths from −1.8 (sulci) to 1.7 (gyri). b, The same sulcal depth map projected onto the flattened cortex, overlayed with the boundary of 22 parcellation mapping52 (black dotted lines). c, The topological regions of sulci (left), gyri (middle) and inflections (right) separated by sulcal depths based on arbitrary thresholds. d, The population-averaged spiral densities of three topological regions. The error bars represent mean ± s.e.m., n = 100 subjects. Black dots represent the mean spiral densities of individual subjects. No significant difference is observed between these topological regions. e, Seven functional networks59 marked by the colormap across the unflattened left cortex (left and middle) and the flattened left cortex (right). Dark blue: VIS, visual network. Blue: SMN, motor/tactile network. Light blue: AUD, auditory network. Green: CON, cingulo-opercular network. Yellow: DAN, dorsal attention network. Red: FPN, frontoparietal network. Dark red: DMN, default-mode network. f, Population-combined z-score maps of brain spirals in the flattened left cortex during the resting state (same as Fig. 2d top), black dashed lines separate the cortical map into seven functional networks59.

Source data

Extended Data Fig. 3 The task-specific trial-averaged curl maps are similar to spiral density maps and with substantial trial-by-trial variabilities at the boundary between 7 function networks40.

a, Top left, trial-averaged curl maps during story listening tasks; Top right, trial-by-trial variability of curl values (standard deviations) during the same task. The white dotted lines mark the boundary between seven functional networks59. Bottom left and right, same as top left and right, but in the right hemisphere. b, Same as a, but during math listening tasks. c, Same as a, but during story answering tasks. d, Same as a, but during math answering tasks.

Source data

Extended Data Fig. 4 Task-specific trial-averaged spiral density maps of the left hemisphere during different working memory tasks.

a, Trial-averaged spiral density maps of the 0-back working memory tasks where subjects responded correctly following the presentation of four distinct types of stimuli: ‘body’ (1st column), ‘face’ (2nd column), ‘place’ (3rd column) and ‘tool’ (4th column). The colour scheme denotes spiral clusters of a particular rotational direction (clockwise in blue, anticlockwise in red), across all trials and subjects. Regions with blue/red colours mark the cortical regions that are either clockwise-dominant (blue) or anticlockwise-dominant (red). b, Same as a, but during the 2-back working memory tasks. c, Same as a, but when subjects responded incorrectly. d, Same as b, but when subjects responded incorrectly.

Source data

Extended Data Fig. 5 Brain spirals in task-evoked unfiltered fMRI signals.

a, Top, Same as Fig. 7c, snapshots of task-evoked unfiltered fMRI signals surrounding a brain spiral at the boundary between superior parietal cortex (SPC) and posterior cingulate cortex (PCC) of the flattened right cortex, 2.16s–10.8 s after the onset of math listening tasks. Colour map represents task-evoked unfiltered fMRI signals, min-max normalized (Methods). Middle, same as top, but at the boundary between the primary motor cortex (M1) and dorsal premotor cortex (PMd) of the left cortex. Bottom, same as middle, but of the right cortex. b, Same as a, but after the onset of math answering tasks.

Source data

Extended Data Fig. 6 Single-trial side-by-side comparisons between phase fields under different stages of filtering and flattening procedures.

a, the simultaneous snapshots showing phase fields in the spatially filtered (left) and unfiltered fMRI slow fluctuations (middle), as well as original (demeaned) fMRI signals (right) across the inflated left cortex (lateral view). The white circles (A and B) mark the surface locations of sample spirals highlighted in panel c, d and e. The circular colormap represents the phase. b, same as a, but with a medial view. c, Same as a and b, but over the flattened cortical surface. The black squares with dashed lines mark the regions shown in d and e. The white circles mark the sample spirals highlighted in d and e. d, The zoomed-in time-lapse snapshots of the sample spirals highlighted by the white circles in c (marked by the black square on the left). Each column shows the phase field of the same region in either spatiotemporal bandpass filtered (left), temporal bandpass filtered (middle) or raw (original, demeaned, right) fMRI signals. Each row shows the temporal evolution of the corresponding phase fields. The white arrows highlight the rotational direction of the sample spirals. The black arrows mark the time step around which the full brain snapshots in a, b and c were captured. e, Same as d, but within a different cortical region highlighted in c (marked by the black square on the right).

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Extended Data Fig. 7 Correlated deactivations of PCC, IPC and LTC during math tasks are coordinated by the rotation of brain spirals.

a, Trial-averaged task-evoked fMRI responses (temporally filtered, 0.01–0.1 Hz) at the onset of math (listening) tasks over the flattened (left) and inflated (lateral view: middle; medial view: right) cortical surface. The colour map denotes the min-max normalized fMRI amplitude. Gray solid lines mark the boundaries separating seven functional networks59. Black circles highlight the centres of anticlockwise brain spirals. White circles highlight the centres of clockwise brain spirals. b, Zoomed-in snapshots of trial-averaged task-evoked fMRI responses following task onset in regions around PCC, SPC and DS over both flattened (left) and inflated (right) cortical surface. c, Same as b, but in regions around IPC. d, Same as c, but in regions around LTC and MTC.

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Extended Data Fig. 8 Correlated activations of PCC, IPC and LTC during story tasks are also coordinated by the rotation of brain spirals.

a, Trial-averaged task-evoked fMRI responses (temporally filtered, 0.01–0.1 Hz) at the onset of story (listening) tasks over the flattened (left) and inflated (lateral view: middle; medial view: right) cortical surface. The colour map denotes the min-max normalized amplitude. Gray solid lines mark the boundaries separating seven functional networks59. Black circles denote the centres of anticlockwise brain spirals. White circles denote the centres of clockwise brain spirals. b, Zoomed-in snapshots of trial-averaged task-evoked fMRI responses following task onset in regions around PCC, SPC and DS over both flattened (left) and inflated (right) cortical surface. c, Same as b, but in regions around IPC. d, Same as c, but in regions around LTC and MTC.

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Extended Data Fig. 9 Coupled phase oscillator-based phenomenological model.

a, Sample full-annihilation interaction between two spirals of opposite rotational directions. The black streamlines represent the phase flows of the simulated phase field. The red and blue circles denote the anticlockwise and clockwise rotating spirals, respectively. b, Same as a, but showcasing the repulsive interaction between two anticlockwise spirals. c, The reversal of rotational directions in selected spirals reorganizes large-scale activity flow. 1st column, the phase flows (white streamlines) immediately before the reversal of two selected spirals at the end of original simulation (t = 150), overlayed with the colourmap representing the absolute angle differences between the phase flows before and after the reversal (the region of coordination, or ROC, where phase flows are reversed is highlighted in red); 2nd column, the phase flows (white streamlines) 150 iterations (time steps) following the reversal, also overlayed with the same colourmap of angle differences as in the first column; 3rd column, the original phase flows immediately before the reversal. The red circles mark the two spirals to be reversed. 4th column, the phase flows immediately following the reversal; 5th column, the phase flows 10 iterations following the reversal; 6th column, the phase flows 150 iterations following the reversal. d, Same as c, but all spirals within the phase field have their rotational directions reversed. e, Same as d, but selected spirals to be reversed are spread across the entire phase field.

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Extended Data Fig. 10 Trial-by-trial and timing variability of task-specific activity flows.

a, The trial-averaged activity flows represented by black streamlines, overlaid with the colourmap representing the trial-by-trial variability (MSE, Methods) of single-trial task-specific activity flows, during the onset (left), mid-task (middle) and offset (right) of the math listening tasks. b, Same as a, but during the math questioning tasks. c, Same as a, but during the math answering tasks. d, The twenty-two parcellation map across the flattened left cortex52. The annotated colour map denotes the parcellation ID (1~22). Abbreviations from parcellation 22 to 1: DLPC: dorsolateral prefrontal cortex; IFC: inferior frontal cortex; OFC: orbital frontal cortex; ACC: anterior cingulate cortex; mPFC: medial prefrontal cortex; PCC: posterior cingulate cortex; IPC: inferior parietal cortex; SPC: superior parietal cortex; TPO: temporo-parieto-occipital; LTC: lateral temporal cortex; MTC: medial temporal cortex; IC: insular cortex; AAC: association auditory cortex; A1: primary auditory cortex; POC: posterior opercular cortex; PMC: premotor cortex; MCC: midcingulate cortex; PCL: paracentral lobule; SMC: sensory-motor cortex; MT+: middle temporal and medial superior temporal cortex; VS: ventral stream; DS: dorsal stream; V1: primary visual cortex; EVC: early visual cortex e, The consistency ratios (or similarity index, Methods) between single-trial and trial-averaged activity flows following the onset of each task trial of math listening (left) and answering tasks (right). The colour map represents the consistency ratio of each time step following the onset of each task trial. Similar to a histogram, the black dashed lines count the number of trials with single-trial consistency ratios peaking at individual time steps following the task onset.

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Supplementary information

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Supplementary fig. 1.

Reporting Summary

Supplementary Video 1

Supplementary Video 1. Sample illustrations of simultaneously recorded phase field, vorticity (curl) field and phase vector field. Left: sample single-trial instantaneous phase field. The colour map denotes phase values (in radians). Right: simultaneously recorded sample vorticity (curl) field overlaid with phase vector field of the same time. The colour map denotes vorticity (curl) values between −2 and 2. The grey vectors denote phase vector field.

Supplementary Video 2

Supplementary Video 2. Rotational dynamics in task-evoked unfiltered fMRI signals of both hemispheres following math task onset. Left: zoomed-in view of the rotational dynamics in task-evoked unfiltered fMRI signals covering the PCC, DS and SPC of the flattened left cortex, 0.72–14.4 s after the math task onset. Right: same as left, but over the flattened right cortex. The colour map denotes the min–max normalized unfiltered task-evoked fMRI signals averaged across trials. The white solid lines mark the boundaries separating 22 functional regions52.

Supplementary Video 3

Supplementary Video 3. Side-by-side comparisons of task-evoked fMRI signals across different stages of filtering and flattening procedures following the math task onset. Top row: task-evoked unfiltered original fMRI signals over the flattened left cortex (left) and the inflated left cortex (middle and right). Middle row: same as top row but in fMRI slow fluctuations (0.01–0.1 Hz) after temporal bandpass filtering. Bottom row: same as top row, but in spatially filtered fMRI slow fluctuations. The colour map denotes the min–max normalized task-evoked fMRI signals averaged across trials.

Supplementary Video 4

Supplementary Video 4. Side-by-side comparisons of task-evoked fMRI signals across different stages of filtering and flattening procedures following the story task onset. Top row: task-evoked unfiltered original fMRI signals over the flattened left cortex (left) and the inflated left cortex (middle and right). Middle row: same as top row but in fMRI slow fluctuations (0.01–0.1 Hz) after temporal bandpass filtering. Bottom row: same as top row, but in spatially filtered fMRI slow fluctuations. The colour map denotes the min–max normalized task-evoked fMRI signals averaged across trials.

Supplementary Video 5

Supplementary Video 5. Correlated activations and de-activations of DMN collectively coordinated by multiple brain spirals during math tasks. Top row: task-evoked fMRI slow fluctuations (0.01–0.1 Hz) over the flattened left cortex (left), as well as zoomed-in views of rotational dynamics covering PCC/DS/PC (mid-left), IPC (mid-right) and LTC/MTC (right). The colour map denotes min–max normalized task-evoked fMRI slow fluctuations. The black and white circles approximate the centres of anticlockwise and clockwise rotational dynamics, respectively. The grey solid lines mark the boundaries separating seven functional networks59. Middle and bottom row: same as top row, but over the inflated left cortex.

Supplementary Video 6

Supplementary Video 6. Correlated activations and de-activations of DMN collectively coordinated by multiple brain spirals during story tasks. Top row: task-evoked fMRI slow fluctuations (0.01–0.1 Hz) over the flattened left cortex (left), as well as zoomed-in views of rotational dynamics covering PCC/DS/PC (mid-left), IPC (mid-right) and LTC/MTC (right). The colour map denotes min–max normalized task-evoked fMRI slow fluctuations. The black and white circles approximate the centres of anticlockwise and clockwise rotational dynamics, respectively. The grey solid lines mark the boundaries separating seven functional networks59. Middle and bottom row: same as top row, but over the inflated left cortex.

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Xu, Y., Long, X., Feng, J. et al. Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing. Nat Hum Behav 7, 1196–1215 (2023). https://doi.org/10.1038/s41562-023-01626-5

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