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Functional brain networks reflect spatial and temporal autocorrelation

Nature Neuroscience volume 26, pages 867–878 (2023)Cite this article

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Abstract

High-throughput experimental methods in neuroscience have led to an explosion of techniques for measuring complex interactions and multi-dimensional patterns. However, whether sophisticated measures of emergent phenomena can be traced back to simpler, low-dimensional statistics is largely unknown. To explore this question, we examined resting-state functional magnetic resonance imaging (rs-fMRI) data using complex topology measures from network neuroscience. Here we show that spatial and temporal autocorrelation are reliable statistics that explain numerous measures of network topology. Surrogate time series with subject-matched spatial and temporal autocorrelation capture nearly all reliable individual and regional variation in these topology measures. Network topology changes during aging are driven by spatial autocorrelation, and multiple serotonergic drugs causally induce the same topographic change in temporal autocorrelation. This reductionistic interpretation of widely used complexity measures may help link them to neurobiology.

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Fig. 1: SA and TA are important features of rs-fMRI time series.
Fig. 2: A spatiotemporal model captures connectome topology.
Fig. 3: Correlation of model and data graph metrics for all models.
Fig. 4: SA links functional connectome topology to neurobiology during aging.
Fig. 5: Pharmacological administration of serotonergic drugs causes changes in TA.

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Data availability

The HCP data are available at https://www.humanconnectome.org/study/hcp-young-adult. The Yale-TRT data are available at http://fcon_1000.projects.nitrc.org/indi/retro/yale_trt.html. The Cam-CAN data are available at https://www.cam-can.org/index.php?content=dataset. The LSD data and psilocybin data are available upon reasonable request.

Code availability

We prepared a software package that allows the principal analyses in this paper to be performed quickly and easily. The ‘spatiotemporal’ Python package, which can be installed through pip or downloaded at https://github.com/murraylab/spatiotemporal, offers a more user-friendly way of applying the analyses described here.

The raw source code used to perform the analyses in this paper can be downloaded at https://github.com/murraylab/spatial_and_temporal_paper. Code was implemented using the standard Python stack99,100 and other libraries101,102. Source code was checked for correctness using software verification techniques103.

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Acknowledgements

We thank J. Burt for help with plotting; A. Howell for assistance with HCP data; and T. Ito and J. C. C. Vila for helpful discussions. Funding was provided by European Molecular Biology Organization grant ALTF 712-2021, the Winston Churchill Foundation of the United States and the Gruber Foundation (M.S.); National Institute of Mental Health (NIMH) grant K00MH122372 (S.N.); the Swiss National Science Foundation (P2ZHP1\161626) (K.H.P.); Agence Nationale de la Recherche (ANR-20-NEUC-003-01) and MIAI@Grenoble Alpes (ANR-19-P3IA-0003) (S.A.); the Usona Institute (2015-2056), the Heffter Research Institute (1-190420), the Swiss Neuromatrix Foundation (2015-103 and 2016-0111) and the Swiss National Science Foundation under the framework of Neuron Cofund (01EW1908) (F.X.V.); the National Institute for Health and Care Research (NIHR) (Senior Investigator Award) and the NIHR Cambridge Biomedical Research Centre (E.T.B.); SFARI (Pilot Award) (A.A. and J.D.M.); and the NIMH (R01MH112746) (J.D.M.). Data collection and sharing for this project were provided, in part, by the Cambridge Centre for Ageing and Neuroscience (Cam-CAN). Cam-CAN funding was provided by the UK Biotechnology and Biological Sciences Research Council (grant BB/H008217/1), together with support from the UK Medical Research Council and the University of Cambridge.

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Author notes

  1. These authors contributed equally: Edward T. Bullmore, John D. Murray.

Authors and Affiliations

  1. Interdepartmental Neuroscience Program, Yale University, New Haven, CT, USA

    Maxwell Shinn, Dustin Scheinost, R. Todd Constable, Alan Anticevic & John D. Murray

  2. Department of Psychiatry, Yale University, New Haven, CT, USA

    Maxwell Shinn, Katrin H. Preller, Jie Lisa Ji, John H. Krystal, Alan Anticevic & John D. Murray

  3. Yale College, Yale University, New Haven, CT, USA

    Amber Hu & Laurel Turner

  4. Department of Radiology and Biomedical Imaging, Yale University, New Haven, CT, USA

    Stephanie Noble, Dustin Scheinost & R. Todd Constable

  5. Department of Psychiatry, Psychotherapy and Psychosomatics, University Hospital for Psychiatry, Zurich, Switzerland

    Katrin H. Preller, Flora Moujaes & Franz X. Vollenweider

  6. University of Grenoble Alpes, CNRS, Inria, Grenoble INP, LJK, Grenoble, France

    Sophie Achard

  7. Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, MD, USA

    Daeyeol Lee

  8. Kavli Discovery Neuroscience Institute, Johns Hopkins University, Baltimore, MD, USA

    Daeyeol Lee

  9. Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, USA

    Daeyeol Lee

  10. Department of Neuroscience, Johns Hopkins University, Baltimore, MD, USA

    Daeyeol Lee

  11. Department of Psychiatry, University of Cambridge, Cambridge, UK

    Edward T. Bullmore

  12. Department of Physics, Yale University, New Haven, CT, USA

    John D. Murray

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Contributions

M.S. and E.T.B. conceived the research. M.S. designed the experiments. M.S. and A.H. performed the experiments. M.S. and J.D.M. analyzed and interpreted results. K.H.P., J.L.J., F.M., S.N., D.S., R.T.C., J.H.K., F.X.V. and A.A. contributed data, methodology and resources. M.S., L.T. and S.A. performed the mathematical analysis. D.L., E.T.B. and J.D.M. provided supervision and funding. M.S., A.H. and L.T. wrote the first draft of the manuscript. All authors edited, revised and approved the manuscript.

Corresponding author

Correspondence to John D. Murray.

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K.H.P. is currently an employee of Hoffmann-La Roche. J.H.K. has consulting agreements (less than $5,000 per year) with the following: Aptinyx; Atai Life Sciences; AstraZeneca Pharmaceuticals; Biogen; Biomedisyn Corporation; Bionomics; Boehringer Ingelheim; Cadent Therapeutics; Clexio Bioscience; COMPASS Pathways; Concert Pharmaceuticals; Epiodyne; EpiVario; Greenwich Biosciences; Heptares Therapeutics; Janssen Research & Development; Jazz Pharmaceuticals; Otsuka America Pharmaceutical; Perception Neuroscience Holdings; Spring Care; Sunovion Pharmaceuticals; Takeda Industries; and Taisho Pharmaceutical Company. J.H.K. serves on the scientific advisory boards of Biohaven Pharmaceuticals; BioXcel Therapeutics (Clinical Advisory Board); Cadent Therapeutics (Clinical Advisory Board); Cerevel Therapeutics; EpiVario; Eisai; Jazz Pharmaceuticals; Lohocla Research Corporation; Novartis Pharmaceuticals Corporation; PsychoGenics; Neumora Therapeutics; Tempero Bio; and Terran Biosciences. J.H.K. is on the board of directors of Freedom Biosciences. J.H.K. has stock and/or stock options in Biohaven Pharmaceuticals; Sage Pharmaceuticals; Spring Care; Biohaven Pharmaceuticals Medical Sciences; EpiVario; Neumora Therapeutics; Terran Biosciences; and Tempero Bio. J.H.K. is editor of Biological Psychiatry with income greater than $10,000. D.L. is a co-founder of Neurogazer. A.A. and J.D.M. are co-founders of Manifest Technologies and serve on the technical advisory board of Neumora Therapeutics. E.T.B. serves on the scientific advisory board of Sosei Heptares and as a consultant for GlaxoSmithKline. The remaining authors declare no competing interests.

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Extended data

Extended Data Fig. 1 SA and TA are important features of rs-fMRI.

Data from the HCP-GSR (a-h, N=850 subjects), Yale-TRT (i-p, N=12 subjects, 4 sessions each), and Cam-CAN (q-t, N=646 subjects) datasets. For all subpanels, unless otherwise indicated, * indicates p < 0.05 and ** indicates P < 0.01 on a two-sided test, and boxplots indicate the median, first/third quartiles, and range, with outliers hidden for visualization. (a,i,q) Correlation across all subjects in the HCP dataset, with Bonferroni FWER corrected two-sided P-values. (b,i) Test-retest reliability of graph metrics, quantified by intraclass correlation coefficient (ICC). Error bars indicate 95% CI. Following each bar is a string of three characters indicating significance: the first indicates significantly less than SA-λ, the second SA-\(\infty\), and the third global TA-Δ1, where # indicates P < .01, + indicates P < .05, and — indicates P > .05, by a one-sided bootstrap resampling procedure. Inset scatterplots show correlation across subjects for two example sessions. (c,k,r) Correlation across subjects between graph metrics and SA-λ, SA-\(\infty\), or global TA-Δ1. ‘SA-λ + SA-\(\infty\)’ and ‘all’ indicate a cross-validated linear model with two or three terms, respectively, using Bonferroni FWER corrected two-sided P-values. (d,l,s) The brain map depicting regional TA-Δ1, averaged across all subjects. (e,m) Distribution of reliability for each brain region. (f,n) Mean fraction of subjects correctly identified by a fingerprinting analysis. Points indicate identification performance on each of six possible test-retest pairs from the four sessions. (g,o,t) Correlation across regions of regional TA-Δ1 with nodal graph metrics for each subject. (k) The regional TA-Δ1 for each region plotted against its reliability.

Extended Data Fig. 2 Correlation of motion and parcel size with spatial and temporal autocorrelation.

(a-c) For each dataset, the mean framewise displacement (‘motion’) is compared to (a) SA-λ, (b) SA-\(\infty\), and (c) TA-Δ1, with inset Spearman correlation (rs). (d) The average regional TA-Δ1 across all subjects is plotted against the region’s parcel size, with inset Spearman correlation. Parcel size is measured in surface area for HCP and HCP-GSR, and number of voxels for Yale-TRT and Cam-CAN. (e) Subject’s mean framewise displacement (‘motion’) is plotted against the subject’s age. * indicates Spearman correlation two-sided P < .05, and ** indicates P < .01. HCP: N=883, HCP-GSR: N=850, Yale-TRT: N=12 subjects, 4 sessions each, Cam-CAN: N=646, LSD: N=24, Psilocybin: N=23 subjects.

Extended Data Fig. 3 TA-Δ1 captures individual variation in long memory dynamics.

(a-c,h-j) TA-Δ1, the first lag term in the ACF, is more reliable than higher lag terms. (a,h) For each lag k, we computed the reliability of the corresponding term in the ACF, ACFx(k), as measured by ICC. The median reliability across brain regions decreased as k increased, and regional TA-Δ1 (that is, ACFx(1)) maximized median reliability. Additionally, d had similar reliability to regional TA-Δ1. (b,i) To confirm this occurs for each brain region individually, we found the difference in reliability between the ACFx(1) and ACFx(k) (ΔICC), which also decreased across lags. d was similar to regional TA-Δ1. (c,j) Global TA-Δ1 reliability also decreased with increasing lag, and d averaged across regions had similar reliability to global TA-Δ1, as measured by ICC. Error bars indicate 95% confidence interval. Thus, the reliability at short compared to long time lags, and the similarity to d, motivate a prioritization for TA-Δ1 over higher lags. (d,k,o) TA-Δ1 is predictive of higher terms of the ACF. TA-Δ1 was used to predict higher ACF terms in a regression model (see Methods). Mean cross-validated R2 is shown, where error bars (sometimes hidden under the line) indicate maximum and minimum cross-validated R2. (e-g,l-n,p-r) Individual variation in d, the long-memory or fractional integration term from an ARFIMA(0,d,0) model, can be captured by individual variation in TA-Δ1. (e,l,p) regional TA-Δ1 averaged across subjects is highly correlated with regional d averaged across subjects. (e: P=0, l: P=10−260, p: P=.10) (f,m,q) Global TA-Δ1 is highly correlated with d averaged across regions within a subject. (f: P=0, m: P=10−101 q: 10−61) (g,n,r) Without averaging, across regions and subjects, d is correlated with TA-Δ1. (g: P=0, n: P=0, r: P=0) For all figures, unless otherwise indicated, rs indicates Spearman correlation, where * indicates two-sided P < .05, and ** indicates P < .01, N=883 subjects.

Extended Data Fig. 4 Relationship between regional TA-Δ1 and regional homogeneity.

Comparisons are shown for the HCP (a-c, N=883) and Yale-TRT (d-f, N=12, 4 sessions each) datasets. (a,d) The global TA-Δ1 averaged across subjects, compared to the regional homogeneity (ReHo) averaged across subjects. Each point represents a parcel. ** indicates two-sided Spearman correlation P < .01. (a: P=10−18, d: P=10−39) (b,e) Distribution of correlations of global TA-Δ1 and regional homogeneity. Compare to Fig. 1j. (c,f) Average fingerprinting performance of regional homogeneity, compared to global TA-Δ1 and chance. Points are overlaid for each pair of datasets compared. Compare to Fig. 1i.

Extended Data Fig. 5 Correlation of model and data graph metrics for all models.

For each model, each subject’s empirical graph metrics are plotted against model graph metrics for metrics from Fig. 2e. Spearman correlation (rs) and Lin’s concordance (Lin) are inset. * indicates Spearman correlation two-sided P < .05, and ** indicates P < .01, N=883 subjects. Zalesky matching operates at the level of the FC matrix, and thus, TA-Δ1 could not be computed. Edge reshuffle operates at the level of the graph, preventing any of these measures from being computed.

Extended Data Fig. 6 Schematics of all models.

All models considered are described in their corresponding schematics. The spatiotemporal model is shown in Fig. 2a.

Extended Data Fig. 7 Model fitting under geodesic distance.

We analyzed the data and model using geodesic instead of Euclidean distance in the right hemisphere. (a-b) We computed SA-λ and SA-\(\infty\) under geodesic distance for the right hemisphere. The geodesic and Euclidean distances lead to highly correlated measurements for SA-λ (a) and SA-\(\infty\) (b). * indicates Spearman correlation two-sided P < .05, and ** indicates P < .01. (a: P=0, b: P=0) (c) Comparison of reliability of graph measures to SA-λ and SA-\(\infty\) when computed using geodesic distance, as measured using ICC. Following each bar is a string of three characters: the first indicates significantly less than SA-λ, the second SA-\(\infty\), and the third global TA-Δ1, where # indicates P < .01, + indicates P < .05, and - indicates P > .05 by a bootstrap resampling procedure on a one-sided test. Compare to Fig. 1d. (d) Correlation of graph metrics with SA-λ, SA-\(\infty\), a linear model of both (‘SA-λ + SA-\(\infty\)’), and a linear model incorporating both of these plus global TA-Δ1 (‘all’), when computed using geodesic distance instead of Euclidean distance. Compare to Fig. 1e. * indicates Spearman correlation two-sided P < .05, and ** indicates P < .01. (e-g) The spatiotemporal model and all comparison models were fit using geodesic instead of Euclidean distance. (e) The similarity of graph metrics in the model and data, as measured by Lin’s concordance, under geodesic distance. Compare to Fig. 2e. (f) The similarity of degree distribution in the model and data under geodesic distance. Compare to Fig. 2f. (g) The similarity of nodal graph metrics in the model and data under geodesic distance. Compare to Fig. 2g. For all panels, N=883 subjects.

Extended Data Fig. 8 Comparison of model fits for all datasets.

(a,d,g) Lin’s concordance between model and data for each model. Bars represent the mean across four (HCP-GSR), six (Yale-TRT), or one (Cam-CAN) scanning sessions, and points indicate the Lin’s concordance between the model and data for each session. For comparison, black indicates Lin’s concordance between separate sessions from the same subject in the HCP-GSR and Yale-TRT datasets, where dots indicate pairs of sessions. (b,e,h) Log-log degree distribution for each model compared to the data (black). (c,f,i) Distribution of Lin’s concordance of nodal metrics between model and data for each region. Boxplots show median, first/third quartiles, and range, with outliers hidden for visualization, N=883 subjects. Compare to Fig. 2e-g. Statistics of these fits can be found in Table S1.

Extended Data Fig. 9 Relationship between the spatiotemporal model and economical clustering (EC) model.

(a) For three given values of the EC cluster parameter (γ), the distance parameter (η) was varied and the TA-\({\Delta }_{1}^{{{{\rm{gen}}}}}\) parameter of the best fit spatiotemporal model is shown. (b) For three given values of the EC distance parameter, the EC cluster parameter was varied and the SA-λgen parameter of the best fit spatiotemporal model is shown. Error bars show standard error across 10 simulations of the EC model. (e-g) The Homogeneous variant of the model was simulated for different values of parameters SA-λgen and TA-\({\Delta }_{1}^{{{{\rm{gen}}}}}\). For each timeseries metric (e), weighted graph metric (f), and unweighted graph metric (g), the metric value is plotted as a heatmap. (h) The economical clustering (EC) model was simulated for different values of its distance and cluster parameters. The value of each of the graph metrics is plotted as a heatmap. For all panels, N=883 subjects.

Extended Data Fig. 10 SA and TA under serotonergic modulation.

(a-c,e) Analysis of scans after administration of LSD (top) or psilocybin (bottom). (a) Correlation of graph metrics across all subjects, with Bonferroni FWER corrected two-sided P-values, * indicates P < .05, ** indicates P < .01. Compare to Figure 1b. (b) Correlation across subjects between graph metrics and SA-λ, SA-\(\infty\), or global TA-Δ1. ‘SA-λ+SA-\(\infty\)’ and ‘all’ columns indicate a linear model with leave-one-out cross-validation and Bonferroni FWER corrected two-sided P-values, * indicates P < .05, ** indicates P < .01. Compare to Figure 1e. (c) The brain map depicting regional TA-Δ1, averaged across all subjects. (d) Correlation of regional TA-Δ1 in HCP with those under LSD (top) or psilocybin (bottom). Spearman correlation > .85, two-sided significance P < .0001 of the correlation of HCP and LSD or psilocybin regional TA-Δ1 determined with SA-preserving scrambles11. Gray points indicate the placebo condition. (e) Correlation across regions of regional TA-Δ1 with nodal graph metrics for each subject. Boxplots show the median, first/third quartiles, and outlier-excluded minimum and maximum of the distribution Compare to Figure 1j. (f-j) Difference between drug and control across subjects for LSD (blue), psilocybin (pink), and LSD with ketanserin (green), for both early and late scans. Metrics plotted are TA as quantified by TA-Δ1 (f), SA as quantified by SA-λ and SA-\(\infty\) (g), the residual of a regression model using motion to predict TA-Δ1, subject motion as quantified by mean framewise displacement (i), and graph metrics (j). * indicates P < .05, ** indicates P < .01, two-sided Wilcoxon sign-rank test. Boxplots show the median, first/third quartiles, and outlier-excluded minimum and maximum of the distribution. For all panels, LSD: N=24, Psilocybin: N=23 subjects.

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Shinn, M., Hu, A., Turner, L. et al. Functional brain networks reflect spatial and temporal autocorrelation. Nat Neurosci 26, 867–878 (2023). https://doi.org/10.1038/s41593-023-01299-3

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