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Advancing functional connectivity research from association to causation

Abstract

Cognition and behavior emerge from brain network interactions, such that investigating causal interactions should be central to the study of brain function. Approaches that characterize statistical associations among neural time series—functional connectivity (FC) methods—are likely a good starting point for estimating brain network interactions. Yet only a subset of FC methods (‘effective connectivity’) is explicitly designed to infer causal interactions from statistical associations. Here we incorporate best practices from diverse areas of FC research to illustrate how FC methods can be refined to improve inferences about neural mechanisms, with properties of causal neural interactions as a common ontology to facilitate cumulative progress across FC approaches. We further demonstrate how the most common FC measures (correlation and coherence) reduce the set of likely causal models, facilitating causal inferences despite major limitations. Alternative FC measures are suggested to immediately start improving causal inferences beyond these common FC measures.

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Fig. 1: Ontological levels relevant to mechanistic interpretation of FC, defining the pathway from neural mechanisms (neural level) to imaging measurements (observational level) to inferences about target theoretical properties (inferential level).
Fig. 2: The conceptual structure of the FC framework.
Fig. 3: A systematic approach to validate mechanistic interpretations of FC measures.

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References

  1. Valdes-Sosa, P. A., Roebroeck, A., Daunizeau, J. & Friston, K. Effective connectivity: influence, causality and biophysical modeling. Neuroimage 58, 339–361 (2011).

    Article  PubMed  Google Scholar 

  2. Ramsey, J. D. et al. Six problems for causal inference from fMRI. Neuroimage 49, 1545–1558 (2010).

    Article  CAS  PubMed  Google Scholar 

  3. Mill, R. D., Ito, T. & Cole, M. W. From connectome to cognition: The search for mechanism in human functional brain networks. Neuroimage 160, 124–139 (2017).

    Article  PubMed  Google Scholar 

  4. Cole, M. W., Yang, G. J., Murray, J. D., Repovš, G. & Anticevic, A. Functional connectivity change as shared signal dynamics. J. Neurosci. Methods 259, 22–39 (2016).

    Article  PubMed  Google Scholar 

  5. Smith, S. M. The future of FMRI connectivity. Neuroimage 62, 1257–1266 (2012).

    Article  PubMed  Google Scholar 

  6. Friston, K. J. Functional and effective connectivity: a review. Brain Connect. 1, 13–36 (2011).

    Article  PubMed  Google Scholar 

  7. Horwitz, B. The elusive concept of brain connectivity. Neuroimage 19, 466–470 (2003).

    Article  PubMed  Google Scholar 

  8. Korzybski, A. Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. (Institute of General Semantics, 1933).

  9. Yeo, B. T. T. et al. The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J. Neurophysiol. 106, 1125–1165 (2011).

    Article  PubMed  Google Scholar 

  10. Power, J. D. et al. Functional network organization of the human brain. Neuron 72, 665–678 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Power, J. D. & Petersen, S. E. Control-related systems in the human brain. Curr. Opin. Neurobiol. 23, 223–228 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Smith, S. M. et al. Correspondence of the brain’s functional architecture during activation and rest. Proc. Natl Acad. Sci. USA 106, 13040–13045 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  13. Power, J. D., Barnes, K. A., Snyder, A. Z., Schlaggar, B. L. & Petersen, S. E. Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. Neuroimage 59, 2142–2154 (2012).

    Article  PubMed  Google Scholar 

  14. Van Dijk, K. R. A., Sabuncu, M. R. & Buckner, R. L. The influence of head motion on intrinsic functional connectivity MRI. Neuroimage 59, 431–438 (2012).

    Article  PubMed  Google Scholar 

  15. Satterthwaite, T. D. et al. Impact of in-scanner head motion on multiple measures of functional connectivity: relevance for studies of neurodevelopment in youth. Neuroimage 60, 623–632 (2012).

    Article  PubMed  Google Scholar 

  16. Mehler, D.M.A. & Kording, K.P. The lure of causal statements: rampant mis-inference of causality in estimated connectivity. Preprint at arXiv https://arxiv.org/abs/1812.03363 (2018).

  17. Pearl, J. A probabilistic calculus of actions. in Uncertainty Proceedings 1994 (eds. de Mantaras, R. L. & Poole, D.) 454–462 (Morgan Kaufmann, 1994).

  18. Pearl, J. & Mackenzie, D. The Book of Why: The New Science of Cause and Effect. (Basic Books, 2018).

  19. Pearl, J., Glymour, M. & Jewell, N. P. Causal Inference in Statistics: A Primer. (Wiley, 2016).

  20. Robins, J. A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect. Math. Model. 7, 1393–1512 (1986).

    Article  Google Scholar 

  21. Spirtes, P., Glymour, C. & Scheines, R. Causation, Prediction, and Search. (MIT Press, 2000).

  22. Marinescu, I. E., Lawlor, P. N. & Kording, K. P. Quasi-experimental causality in neuroscience and behavioural research. Nat. Hum. Behav. 2, 891–898 (2018).

    Article  PubMed  Google Scholar 

  23. Hume, D. An enquiry concerning human understanding (originally published 1748). in The Clarendon Edition of the Works of David Hume: An Enquiry Concerning Human Understanding (eds. Beauchamp, T. L., Hume, D. & Beauchamp, T. L.) 134–198 (Oxford University Press, 2000).

  24. Pearl, J., Robins, J. M. & Greenland, S. Confounding and collapsibility in causal inference. Stat. Sci. 14, 29–46 (1999).

    Article  Google Scholar 

  25. Friston, K. J. Functional and effective connectivity in neuroimaging: a synthesis. Hum. Brain Mapp. 2, 56–78 (1994).

    Article  Google Scholar 

  26. Friston, K. J. et al. Psychophysiological and modulatory interactions in neuroimaging. Neuroimage 6, 218–229 (1997).

    Article  CAS  PubMed  Google Scholar 

  27. Roebroeck, A., Formisano, E. & Goebel, R. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25, 230–242 (2005).

    Article  PubMed  Google Scholar 

  28. Klahr, D. & Dunbar, K. Dual space search during scientific reasoning. Cogn. Sci. 12, 1–48 (1988).

    Article  Google Scholar 

  29. Lee, H. S., Betts, S. & Anderson, J. R. Learning problem-solving rules as search through a hypothesis space. Cogn. Sci. 40, 1036–1079 (2016).

    Article  PubMed  Google Scholar 

  30. Smith, S. M. et al. Network modelling methods for FMRI. Neuroimage 54, 875–891 (2011).

    Article  PubMed  Google Scholar 

  31. Mill, R. D., Bagic, A., Bostan, A., Schneider, W. & Cole, M. W. Empirical validation of directed functional connectivity. Neuroimage 146, 275–287 (2017).

    Article  PubMed  Google Scholar 

  32. Wang, H. E. et al. A systematic framework for functional connectivity measures. Front. Neurosci. 8, 405 (2014).

    PubMed  PubMed Central  Google Scholar 

  33. Illari, P. M. & Williamson, J. What is a mechanism? Thinking about mechanisms across the sciences. Eur. J. Philos. Sci. 2, 119–135 (2012).

    Google Scholar 

  34. Hutchison, R. M. et al. Dynamic functional connectivity: promise, issues, and interpretations. Neuroimage 80, 360–378 (2013).

    Article  PubMed  Google Scholar 

  35. Lurie, D. et al. On the nature of resting fMRI and time-varying functional connectivity. Preprint at PsyArXiv https://doi.org/10.31234/osf.io/xtzre (2018).

  36. Smith, S. M. et al. A positive-negative mode of population covariation links brain connectivity, demographics and behavior. Nat. Neurosci. 18, 1565–1567 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Schultz, D. H. & Cole, M. W. Higher intelligence is associated with less task-related brain network reconfiguration. J. Neurosci. 36, 8551–8561 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Cole, M. W., Yarkoni, T., Repovs, G., Anticevic, A. & Braver, T. S. Global connectivity of prefrontal cortex predicts cognitive control and intelligence. J. Neurosci. 32, 8988–8999 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Friston, K. J., Harrison, L. & Penny, W. Dynamic causal modelling. Neuroimage 19, 1273–1302 (2003).

    Article  CAS  PubMed  Google Scholar 

  40. Frässle, S. et al. A generative model of whole-brain effective connectivity. Neuroimage 179, 505–529 (2018).

    Article  PubMed  Google Scholar 

  41. Honey, C. J., Kötter, R., Breakspear, M. & Sporns, O. Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Natl Acad. Sci. USA 104, 10240–10245 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Lohmann, G., Erfurth, K., Müller, K. & Turner, R. Critical comments on dynamic causal modelling. Neuroimage 59, 2322–2329 (2012).

    Article  PubMed  Google Scholar 

  43. Lewontin, R. C. The Genetic Basis of Evolutionary Change. (Columbia University Press, 1974).

  44. Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.) 117, 500–544 (1952).

    Article  CAS  Google Scholar 

  45. Hines, M. L. & Carnevale, N. T. The NEURON simulation environment. Neural Comput. 9, 1179–1209 (1997).

    Article  CAS  PubMed  Google Scholar 

  46. Goodman, D. & Brette, R. Brian: a simulator for spiking neural networks in python. Front. Neuroinform. 2, 5 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  47. Ramsey, J. D., Hanson, S. J. & Glymour, C. Multi-subject search correctly identifies causal connections and most causal directions in the DCM models of the Smith et al. simulation study. Neuroimage 58, 838–848 (2011).

    Article  PubMed  Google Scholar 

  48. Hyttinen, A., Plis, S., Järvisalo, M., Eberhardt, F. & Danks, D. Causal discovery from subsampled time series data by constraint optimization. JMLR 52, 216–227 (2016).

    PubMed  Google Scholar 

  49. Schubert, N. et al. 3D reconstructed cyto-, muscarinic M2 receptor, and Fiber architecture of the rat brain registered to the Waxholm Space Atlas. Front. Neuroanat. 10, 51 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Eickhoff, S. B. et al. A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data. Neuroimage 25, 1325–1335 (2005).

    Article  PubMed  Google Scholar 

  51. Craddock, R. C., James, G. A., Holtzheimer, P. E. III, Hu, X. P. & Mayberg, H. S. A whole brain fMRI atlas generated via spatially constrained spectral clustering. Hum. Brain Mapp. 33, 1914–1928 (2012).

    Article  PubMed  Google Scholar 

  52. Buzsáki, G., Anastassiou, C. A. & Koch, C. The origin of extracellular fields and currents—EEG, ECoG, LFP and spikes. Nat. Rev. Neurosci. 13, 407–420 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Potjans, T. C. & Diesmann, M. The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model. Cereb. Cortex 24, 785–806 (2014).

    Article  PubMed  Google Scholar 

  54. Logothetis, N. K. The neural basis of the blood-oxygen-level-dependent functional magnetic resonance imaging signal. Philos. Trans. R. Soc. Lond. B 357, 1003–1037 (2002).

    Article  Google Scholar 

  55. Buxton, R. B., Wong, E. C. & Frank, L. R. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39, 855–864 (1998).

    Article  CAS  PubMed  Google Scholar 

  56. Birn, R. M., Saad, Z. S. & Bandettini, P. A. Spatial heterogeneity of the nonlinear dynamics in the FMRI BOLD response. Neuroimage 14, 817–826 (2001).

    Article  CAS  PubMed  Google Scholar 

  57. Jellema, W. T. et al. Heterogeneity and prediction of hemodynamic responses to dobutamine in patients with septic shock. Crit. Care Med. 34, 2392–2398 (2006).

    Article  CAS  PubMed  Google Scholar 

  58. Tarantini, S., Tran, C. H. T., Gordon, G. R., Ungvari, Z. & Csiszar, A. Impaired neurovascular coupling in aging and Alzheimer’s disease: Contribution of astrocyte dysfunction and endothelial impairment to cognitive decline. Exp. Gerontol. 94, 52–58 (2017).

    Article  CAS  PubMed  Google Scholar 

  59. Handwerker, D. A., Ollinger, J. M. & D’Esposito, M. Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage 21, 1639–1651 (2004).

    Article  PubMed  Google Scholar 

  60. Di, X., Kannurpatti, S. S., Rypma, B. & Biswal, B. B. Calibrating BOLD fMRI activations with neurovascular and anatomical constraints. Cereb. Cortex 23, 255–263 (2013).

    Article  PubMed  Google Scholar 

  61. Rangaprakash, D., Wu, G.-R., Marinazzo, D., Hu, X. & Deshpande, G. Hemodynamic response function (HRF) variability confounds resting-state fMRI functional connectivity. Magn. Reson. Med. 80, 1697–1713 (2018).

    Article  CAS  PubMed  Google Scholar 

  62. Calhoun, V. D., Stevens, M. C., Pearlson, G. D. & Kiehl, K. A. fMRI analysis with the general linear model: removal of latency-induced amplitude bias by incorporation of hemodynamic derivative terms. Neuroimage 22, 252–257 (2004).

    Article  CAS  PubMed  Google Scholar 

  63. Schoffelen, J.-M. & Gross, J. Source connectivity analysis with MEG and EEG. Hum. Brain Mapp. 30, 1857–1865 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  64. Salimi-Khorshidi, G. et al. Automatic denoising of functional MRI data: combining independent component analysis and hierarchical fusion of classifiers. Neuroimage 90, 449–468 (2014).

    Article  PubMed  Google Scholar 

  65. Sochat, V. et al. A robust classifier to distinguish noise from fMRI independent components. PLoS One 9, e95493 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  66. Acharjee, P. P., Phlypo, R., Wu, L., Calhoun, V. D. & Adali, T. Independent vector analysis for gradient artifact removal in concurrent EEG-fMRI Data. IEEE Trans. Biomed. Eng. 62, 1750–1758 (2015).

    Article  PubMed  Google Scholar 

  67. Du, Y. et al. Artifact removal in the context of group ICA: A comparison of single-subject and group approaches. Hum. Brain Mapp. 37, 1005–1025 (2016).

    Article  PubMed  Google Scholar 

  68. Glasser, M. F. et al. Using temporal ICA to selectively remove global noise while preserving global signal in functional MRI data. Neuroimage 181, 692–717 (2018).

    Article  PubMed  Google Scholar 

  69. Buibas, M. & Silva, G. A. A framework for simulating and estimating the state and functional topology of complex dynamic geometric networks. Neural Comput. 23, 183–214 (2011).

    Article  PubMed  Google Scholar 

  70. Fuentes, L., Aldana, J.F. & Troya, J.M. GENESIS: an object-oriented framework for simulation of neural network models. in Artificial Neural Nets and Genetic Algorithms (eds. Pearson, D. W., Steele, N. C. & Albrecht, R. F.) 321–324 (Springer Vienna, 1995).

  71. Ritter, P., Schirner, M., McIntosh, A. R. & Jirsa, V. K. The virtual brain integrates computational modeling and multimodal neuroimaging. Brain Connect. 3, 121–145 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  72. Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M. & Friston, K. The dynamic brain: from spiking neurons to neural masses and cortical fields. PLOS Comput. Biol. 4, e1000092 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  73. David, O., Cosmelli, D. & Friston, K. J. Evaluation of different measures of functional connectivity using a neural mass model. Neuroimage 21, 659–673 (2004).

    Article  PubMed  Google Scholar 

  74. Gourévitch, B., Bouquin-Jeannès, R. L. & Faucon, G. Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. Biol. Cybern. 95, 349–369 (2006).

    Article  PubMed  Google Scholar 

  75. Wang, Y., Katwal, S., Rogers, B., Gore, J. & Deshpande, G. Experimental validation of dynamic granger causality for inferring stimulus-evoked sub-100 ms timing differences from fMRI. IEEE Trans. Neural Syst. Rehabil. Eng. 25, 539–546 (2017).

    Article  PubMed  Google Scholar 

  76. Nee, D. E. & D’Esposito, M. Causal evidence for lateral prefrontal cortex dynamics supporting cognitive control. eLife 6, e28040 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  77. Wheeler, M. E., Petersen, S. E. & Buckner, R. L. Memory’s echo: vivid remembering reactivates sensory-specific cortex. Proc. Natl Acad. Sci. USA 97, 11125–11129 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. David, O. et al. Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol. 6, 2683–2697 (2008).

    Article  CAS  PubMed  Google Scholar 

  79. Smith, V. A., Yu, J., Smulders, T. V., Hartemink, A. J. & Jarvis, E. D. Computational inference of neural information flow networks. PLOS Comput. Biol. 2, e161 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Ryali, S. et al. Combining optogenetic stimulation and fMRI to validate a multivariate dynamical systems model for estimating causal brain interactions. Neuroimage 132, 398–405 (2016).

    Article  PubMed  Google Scholar 

  81. Lee, J. H. Informing brain connectivity with optogenetic functional magnetic resonance imaging. Neuroimage 62, 2244–2249 (2012).

    Article  PubMed  Google Scholar 

  82. Power, J. D., Schlaggar, B. L. & Petersen, S. E. Recent progress and outstanding issues in motion correction in resting state fMRI. Neuroimage 105, 536–551 (2015).

    Article  PubMed  Google Scholar 

  83. Power, J. D. et al. Methods to detect, characterize, and remove motion artifact in resting state fMRI. Neuroimage 84, 320–341 (2014).

    Article  PubMed  Google Scholar 

  84. Cole, M. W. et al. Task activations produce spurious but systematic inflation of task functional connectivity estimates. Neuroimage 189, 1–18 (2019).

    Article  PubMed  Google Scholar 

  85. Mumford, J. A. & Ramsey, J. D. Bayesian networks for fMRI: a primer. Neuroimage 86, 573–582 (2014).

    Article  PubMed  Google Scholar 

  86. Friston, K., Moran, R. & Seth, A. K. Analysing connectivity with Granger causality and dynamic causal modelling. Curr. Opin. Neurobiol. 23, 172–178 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Aertsen, A. M., Gerstein, G. L., Habib, M. K. & Palm, G. Dynamics of neuronal firing correlation: modulation of “effective connectivity”. J. Neurophysiol. 61, 900–917 (1989).

    Article  CAS  PubMed  Google Scholar 

  88. Cole, M. W., Ito, T., Bassett, D. S. & Schultz, D. H. Activity flow over resting-state networks shapes cognitive task activations. Nat. Neurosci. 19, 1718–1726 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Barnett, L. & Seth, A. K. The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. J. Neurosci. Methods 223, 50–68 (2014).

    Article  PubMed  Google Scholar 

  90. Bishop, C. M. Pattern Recognition and Machine Learning. (Springer, New York, 2016).

  91. Rebane, G. & Pearl, J. The recovery of causal poly-trees from statistical data. Proceedings of the Third Workshop on Uncertainty in AI 222–228 (1987).

  92. Schiefer, J. et al. From correlation to causation: Estimating effective connectivity from zero-lag covariances of brain signals. PLoS Comput. Biol. 14, e1006056 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Ramsey, J., Glymour, M., Sanchez-Romero, R. & Glymour, C. A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images. Int. J. Data Sci. Anal. 3, 121–129 (2017).

    Article  PubMed  Google Scholar 

  94. Sanchez-Romero, R. et al. Estimating feedforward and feedback effective connections from fMRI time series: assessments of statistical methods. Netw. Neurosci. 3, 274–306 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

The authors acknowledge the following support: National Institutes of Health grant R01MH107549 to L.Q.U.; National Institutes of Health grants R01MH109520 and R01AG055556 to M.W.C.; National Institutes of Health grants P20GM103472, R01EB020407, and NSF National Science Foundation grant 1539067 to V.C. The content is solely the responsibility of the authors and does not necessarily represent the official views of any of the funding agencies. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Reid, A.T., Headley, D.B., Mill, R.D. et al. Advancing functional connectivity research from association to causation. Nat Neurosci 22, 1751–1760 (2019). https://doi.org/10.1038/s41593-019-0510-4

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