Inferring functional connectivity in fMRI using minimum partial correlation
- 384 Downloads
Functional connectivity has emerged as a promising approach to study the functional organisation of the brain and to define features for prediction of brain state. The most widely used method for inferring functional connectivity is Pearson-s correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by computing the partial correlation between two regions controlling all other regions, but this method suffers from Berkson-s paradox. Some advanced methods, such as regularised inverse covariance, have been applied. However, these methods usually depend on some parameters. Here we propose use of minimum partial correlation as a parameter-free measure for the skeleton of functional connectivity in functional magnetic resonance imaging (fMRI). The minimum partial correlation between two regions is the minimum of absolute values of partial correlations by controlling all possible subsets of other regions. Theoretically, there is a direct effect between two regions if and only if their minimum partial correlation is non-zero under faithfulness and Gaussian assumptions. The elastic PC-algorithm is designed to efficiently approximate minimum partial correlation within a computational time budget. The simulation study shows that the proposed method outperforms others in most cases and its application is illustrated using a resting-state fMRI dataset from the human connectome project.
KeywordsFunctional connectivity functional magnetic resonance imaging (fMRI) network modelling partial correlation PC-algorithm resting-state networks
Data were provided by the human connectome project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil, 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research, and by the McDonnell Center for Systems Neuroscience at Washington University. Paul M. Matthews gratefully acknowledges support from the Imperial College NIHR Biomedical Research Centre and personal support from the Edmond Safra Foundation and Lily Safra.
- D. J. Hawellek, J. F. Hipp, C. M. Lewis, M. Corbetta, A. K. Engel. Increased functional connectivity indicates the severity of cognitive impairment in multiple sclerosis. Proceedings of the National Academy of Sciences of the United States of America, vol. 108, no. 47, pp. 19066–19071, 2011.CrossRefGoogle Scholar
- A. M. Hermundstad, D. S. Bassett, K. S. Brown, E. M. Aminoff, D. Clewett, S. Freeman, A. Frithsen, A. Johnson, C. M. Tipper, M. B. Miller, S. T. Grafton, J. M. Carlson. Structural foundations of resting-state and task-based functional connectivity in the human brain. Proceedings of the National Academy of Sciences of the United States of America, vol. 110, no. 15, pp. 6169–6174, 2013.CrossRefGoogle Scholar
- S. M. Smith, D. Vidaurre, C. F. Beckmann, M. F. Glasser, M. Jenkinson, K. L. Miller, T. E. Nichols, E. C. Robinson, G. Salimi-Khorshidi, M. W. Woolrich, D. M. Barch, K. Uğurbil, D. C. Van Essen. Functional connectomics from resting-state fMRI. Trends in Cognitive Sciences, vol. 17, no. 12, pp. 666–682, 2013.CrossRefGoogle Scholar
- S. M. Smith, T. E. Nichols, D. Vidaurre, A. M. Winkler, T. E. J. Behrens, M. F. Glasser, K. Ugurbil, D. M. Barch, D. C. Van Essen, K. L. Miller. A positive-negative mode of population covariation links brain connectivity, demographics and behavior. Nature Neuroscience, vol. 18, no. 11, pp. 1565–1567, 2015.CrossRefGoogle Scholar
- G. Varoquaux, A. Gramfort, J. B. Poline, B. Thirion. Brain covariance selection: Better individual functional connectivity models using population prior. In Proceedings of Neural Information Processing Systems, NIPS, Vancouver, Canada, pp. 2334–2342, 2010.Google Scholar
- M. G. G’Sell, J. Taylor, R. Tibshirani. Adaptive testing for the graphical lasso, [Online], Available: https://arxiv.org/abs/1307.4765, 2013.Google Scholar
- S. M. Smith, C. F. Beckmann, J. Andersson, E. J. Auerbach, J. Bijsterbosch, G. Douaud, E. Duff, D. A. Feinberg, L. Griffanti, M. P. Harms, M. Kelly, T. Laumann, K. L. Miller, S. Moeller, S. Petersen, J. Power, G. Salimi-Khorshidi, A. Z. Snyder, A. T. Vu, M. W. Woolrich, J. Q. Xu, E. Yacoub, K. Ugŭrbil, D. C. Van Essen, M. F. Glasser. Resting-state fMRI in the Human Connectome Project. NeuroImage, vol. 80, pp. 144–168, 2013.CrossRefGoogle Scholar
- L. Nie, X. Yang, P. M. Matthews, Z. X. Xu, Y. K. Guo. Minimum partial correlation: An accurate and parameterfree measure of functional connectivity in fMRI. In Proceedings of International Conference on Brain Informatics and Health, Springer, Cham, Switzerland, pp. 125–134, 2015.Google Scholar
- C. Bielza, P. Larra˜naga. Bayesian networks in neuroscience: A survey. Frontiers in Computational Neuroscience, vol.8, Article number 131, 2014.Google Scholar
- R. A. Fisher. The distribution of the partial correlation coefficient. Metron, vol. 3, pp. 329–332, 1924.Google Scholar
- Z. X. Wang, L. W. Chan. Learning Bayesian networks from Markov random fields: An efficient algorithm for linear models. ACM Transactions on Knowledge Discovery from Data (TKDD), vol. 6, no. 3, Article number 10, 2012.Google Scholar
- R. Han, L. Nie, M. M. Ghanem, Y. K. Guo. Elastic algorithms for guaranteeing quality monotonicity in big data mining. In Proceedings of IEEE International Conference on Big Data, IEEE, Silicon Valley, USA, pp. 45–50, 2013.Google Scholar
- L. Griffanti, G. Salimi-Khorshidi, C. F. Beckmann, E. J. Auerbach, G. Douaud, C. E. Sexton, E. Zsoldos, K. P. Ebmeier, N. Filippin, C. E. Mackay, S. Moeller, J. Q. Xu, E. Yacoub, G. Baselli, K. Ugurbil, K. L. Miller, S. M. Smith. ICA-based artefact removal and accelerated fMRI acquisition for improved resting state network imaging. NeuroImage, vol. 95, no. 4, pp. 232–247, 2014.CrossRefGoogle Scholar
- N. Tzourio-Mazoyer, B. Landeau, D. Papathanassiou, F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, M. Joliot. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, vol. 15, no. 1, pp. 273–289, 2002.CrossRefGoogle Scholar
- M. L. Stanley, M. N. Moussa, B. M. Paolini, R. G. Lyday, J. H. Burdette, P. J. Laurienti. Defining nodes in complex brain networks. Frontiers in Computational Neuroscience, vol. 7, Article number 169, 2013.Google Scholar
- M. R. Xia, J. H. Wang, Y. He. BrainNet Viewer: A network visualization tool for human brain connectomics. PLoS One, vol. 8, no. 7, Article number e68910, 2013.Google Scholar
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.