Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data
Open accessAbstract
Increasing interest in understanding dynamic interactions of brain neural networks leads to formulation of sophisticated connectivity analysis methods. Recent studies have applied Granger causality based on standard multivariate autoregressive (MAR) modeling to assess the brain connectivity. Nevertheless, one important flaw of this commonly proposed method is that it requires the analyzed time series to be stationary, whereas such assumption is mostly violated due to the weakly nonstationary nature of functional magnetic resonance imaging (fMRI) time series. Therefore, we propose an approach to dynamic Granger causality in the frequency domain for evaluating functional network connectivity in fMRI data. The effectiveness and robustness of the dynamic approach was significantly improved by combining a forward and backward Kalman filter that improved estimates compared to the standard time-invariant MAR modeling. In our method, the functional networks were first detected by independent component analysis (ICA), a computational method for separating a multivariate signal into maximally independent components. Then the measure of Granger causality was evaluated using generalized partial directed coherence that is suitable for bivariate as well as multivariate data. Moreover, this metric provides identification of causal relation in frequency domain, which allows one to distinguish the frequency components related to the experimental paradigm. The procedure of evaluating Granger causality via dynamic MAR was demonstrated on simulated time series as well as on two sets of group fMRI data collected during an auditory sensorimotor (SM) or auditory oddball discrimination (AOD) tasks. Finally, a comparison with the results obtained from a standard time-invariant MAR model was provided.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
There is no reason why exactly the same approach could not be applied to the activity of distributed modes, such as those from principal or independent component analysis.
“Although we have illustrated the approach using region specific summaries of fMRI data from an activation study, there is no reason why exactly the same approach could not be applied to the activity of distributed modes, such as those from principal or independent component analysis (cf, Havlicek et al., 2010).”
From Network discovery with DCM (2011) · cites this paper as Havlicek et al., 2010
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A new look at the statistical model identification
Akaike, H. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100705 · Cited by 51,879 · see citing works
Estimating the Dimension of a Model
Schwarz, G. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344136 · Cited by 47,033 · see citing works
A New Approach to Linear Filtering and Prediction Problems
Kalman, R. E. (1960) · Journal of Basic Engineering · doi:10.1115/1.3662552 · Cited by 31,751 · see citing works
Investigating causal relations by econometric models and cross-spectral methods
Granger, C. W. J. (1969) · Econometrica · doi:10.2307/1912791 · Cited by 22,989 · see citing works
Haykin, S. (1986) · Cited by 12,603 · see citing works
Rogers, S. (1996) · Control Engineering Practice · doi:10.1016/0967-0661(96)82838-3 · Cited by 10,013 · see citing works
An Information-Maximization Approach to Blind Separation and Blind Deconvolution
Bell, A. J., & Sejnowski, T. J. (1995) · Neural Computation · doi:10.1162/neco.1995.7.6.1129 · Cited by 8,986 · see citing works
New Introduction to Multiple Time Series Analysis
Lütkepohl, H. (2005) · Springer eBooks · doi:10.1007/978-3-540-27752-1 · Cited by 5,972 · see citing works
Friston, K. J., Harrison, L., & Penny, W. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00202-7 · Cited by 4,583 · see citing works
A method for making group inferences from functional MRI data using independent component analysis
Calhoun, V. D., Adali, T., Pearlson, G. D., & Pekar, J. J. (2001) · Human Brain Mapping · doi:10.1002/hbm.1048 · Cited by 2,994 · see citing works
Self-citationFunctional and effective connectivity in neuroimaging: a synthesis
Friston, K. J. (1994) · Human Brain Mapping · doi:10.1002/hbm.460020107 · Cited by 2,452 · see citing works
Measurement of Linear Dependence and Feedback between Multiple Time Series
Geweke, J. (1982) · Journal of the American Statistical Association · doi:10.1080/01621459.1982.10477803 · Cited by 2,060 · see citing works
Maximum likelihood estimates of linear dynamic systems
Rauch, H. E., Tung, F., & Striebel, C. T. (1965) · AIAA Journal · doi:10.2514/3.3166 · Cited by 1,976 · see citing works
Partial directed coherence: a new concept in neural structure determination
Baccalá, L. A., & Sameshima, K. (2001) · Biological Cybernetics · doi:10.1007/pl00007990 · Cited by 1,791 · see citing works
Frequencies contributing to functional connectivity in the cerebral cortex in "resting-state" data.
Cordes, D., Haughton, V. M., Arfanakis, K., Carew, J. D., Turski, P. A., Moritz, C. H., Quigley, M., & Meyerand, M. E. (2001) · PubMed Central · Cited by 1,402 · see citing works
The Variability of Human, BOLD Hemodynamic Responses
Aguirre, G. K., Zarahn, E., & D’Esposito, M. (1998) · NeuroImage · doi:10.1006/nimg.1998.0369 · Cited by 1,224 · see citing works
A Parametric Manipulation of Factors Affecting Task-induced Deactivation in Functional Neuroimaging
McKiernan, K. A., Kaufman, J. N., Kucera-Thompson, J., & Binder, J. R. (2003) · Journal of Cognitive Neuroscience · doi:10.1162/089892903321593117 · Cited by 1,080 · see citing works
A new method of the description of the information flow in the brain structures
Kaminski, M. J., & Blinowska, K. J. (1991) · Biological Cybernetics · doi:10.1007/bf00198091 · Cited by 1,047 · see citing works
Mapping directed influence over the brain using Granger causality and fMRI
Roebroeck, A. F., Formisano, E., & Goebel, R. (2005) · NeuroImage · doi:10.1016/j.neuroimage.2004.11.017 · Cited by 1,012 · see citing works
Handwerker, D. A., Ollinger, J. M., & D’Esposito, M. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2003.11.029 · Cited by 993 · see citing works
Kamiński, M., Ding, M., Truccolo, W., & Bressler, S. L. (2001) · Biological Cybernetics · doi:10.1007/s004220000235 · Cited by 990 · see citing works
Analyzing brain networks with PCA and conditional Granger causality
Zhou, Z., Chen, Y., Ding, M., Wright, P. K., Lu, Z., & Liu, Y. (2008) · Human Brain Mapping · doi:10.1002/hbm.20661 · Cited by 978 · see citing works
Jafri, M. J., Pearlson, G. D., Stevens, M. C. G., & Calhoun, V. D. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.11.001 · Cited by 976 · see citing works
Self-citationEstimating the number of independent components for functional magnetic resonance imaging data
Li, Y., Adalı, T., & Calhoun, V. D. (2007) · Human Brain Mapping · doi:10.1002/hbm.20359 · Cited by 912 · see citing works
Self-citationMeasures of Conditional Linear Dependence and Feedback Between Time Series
Geweke, J. F. (1984) · Journal of the American Statistical Association · doi:10.1080/01621459.1984.10477110 · Cited by 769 · see citing works
A MATLAB toolbox for Granger causal connectivity analysis
Seth, A. K. (2009) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2009.11.020 · Cited by 746 · see citing works
Calhoun, V. D., Adalı, T., Pearlson, G. D., & Pekar, J. J. (2001) · Human Brain Mapping · doi:10.1002/hbm.1024 · Cited by 697 · see citing works
Self-citationGoebel, R., Roebroeck, A. F., Kim, D., & Formisano, E. (2003) · Magnetic Resonance Imaging · doi:10.1016/j.mri.2003.08.026 · Cited by 678 · see citing works
van de Ven, V. G., Formisano, E., Prvulovic, D., Röder, C. H., & Linden, D. E. J. (2004) · Human Brain Mapping · doi:10.1002/hbm.20022 · Cited by 538 · see citing works
Identifying neural drivers with functional MRI: an electrophysiological validation
David, O., Guillemain, I., Saillet, S., Reyt, S., Deransart, C., Segebarth, C., & Depaulis, A. (2008) · PLoS Biology · doi:10.1371/journal.pbio.0060315 · Cited by 533 · see citing works
Towards a network theory of cognition
McIntosh, A. R. (2000) · Neural Networks · doi:10.1016/s0893-6080(00)00059-9 · Cited by 500 · see citing works
Kernel Method for Nonlinear Granger Causality
Marinazzo, D., Pellicoro, M., & Stramaglia, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.144103 · Cited by 409 · see citing works
Sun, F. T., Miller, L. M., & D’Esposito, M. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2003.09.056 · Cited by 406 · see citing works
Analyzing information flow in brain networks with nonparametric Granger causality
Dhamala, M., Rangarajan, G., & Ding, M. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.02.020 · Cited by 386 · see citing works
Schneider, T., & Neumaier, A. (2001) · ACM Transactions on Mathematical Software · doi:10.1145/382043.382316 · Cited by 386 · see citing works
Hesse, W., Möller, E., Arnold, M., & Schack, B. (2003) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(02)00366-7 · Cited by 382 · see citing works
The optimum linear smoother as a combination of two optimum linear filters
Fraser, D. C., & Potter, J. M. (1969) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1969.1099196 · Cited by 377 · see citing works
Korzeniewska, A., Mańczak, M., Kamiński, M., Blinowska, K. J., & Kasicki, S. (2003) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(03)00052-9 · Cited by 375 · see citing works
Handbook of Time Series Analysis
(2006) · Wiley eBooks · doi:10.1002/9783527609970 · Cited by 362 · see citing works
Chen, Y., Bressler, S. L., & Ding, M. (2005) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2005.06.011 · Cited by 344 · see citing works
Unmixing fMRI with independent component analysis
Calhoun, V. D., & Adalı, T. (2006) · IEEE Engineering in Medicine and Biology Magazine · doi:10.1109/memb.2006.1607672 · Cited by 309 · see citing works
Self-citationAdaptive AR modeling of nonstationary time series by means of Kalman filtering
Arnold, M., Milner, X. H. R., Witte, H., Bauer, R., & Braun, C. (1998) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.668741 · Cited by 306 · see citing works
Responses to Rare Visual Target and Distractor Stimuli Using Event-Related fMRI
Clark, V. P., Fannon, S. P., Lai, S., Benson, R. R., & Bauer, L. O. (2000) · Journal of Neurophysiology · doi:10.1152/jn.2000.83.5.3133 · Cited by 297 · see citing works
Generalized Partial Directed Coherence
Baccalá, L. A., Sameshima, K., & Takahashi, D. Y. (2007) · doi:10.1109/icdsp.2007.4288544 · Cited by 260 · see citing works
Kiehl, K. A., Stevens, M. C. G., Laurens, K. R., Pearlson, G. D., Calhoun, V. D., & Liddle, P. F. (2005) · NeuroImage · doi:10.1016/j.neuroimage.2004.12.035 · Cited by 248 · see citing works
Self-citationMultivariate Granger causality analysis of fMRI data
Deshpande, G., LaConte, S., James, G. A., Peltier, S., & Hu, X. P. (2008) · Human Brain Mapping · doi:10.1002/hbm.20606 · Cited by 238 · see citing works
Roebroeck, A. F., Formisano, E., & Goebel, R. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.09.036 · Cited by 237 · see citing works
Radial basis function approach to nonlinear Granger causality of time series
Ancona, N., Marinazzo, D., & Stramaglia, S. (2004) · Physical Review E · doi:10.1103/physreve.70.056221 · Cited by 228 · see citing works
Evaluating the effective connectivity of resting state networks using conditional Granger causality
Liao, W., Mantini, D., Zhang, Z., Pan, Z., Ding, J., Gong, Q., Yang, Y., & Chen, H. (2009) · Biological Cybernetics · doi:10.1007/s00422-009-0350-5 · Cited by 208 · see citing works
Partial Granger causality—Eliminating exogenous inputs and latent variables
Guo, S., Seth, A. K., Kendrick, K. M., Zhou, C., & Feng, J. (2008) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2008.04.011 · Cited by 205 · see citing works
NEW INTRODUCTION TO MULTIPLE TIME SERIES ANALYSIS , by Helmut Lütkepohl, Springer, 2005
Kilian, L. (2006) · Econometric Theory · doi:10.1017/s0266466606000442 · Cited by 190 · see citing works
Effect of hemodynamic variability on Granger causality analysis of fMRI
Deshpande, G., Sathian, K., & Hu, X. P. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.11.060 · Cited by 190 · see citing works
A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals
Riera, J. J., Watanabe, J., Iwata, K., Miura, N., Aubert, E., Ozaki, T., & Kawashima, R. (2003) · NeuroImage · doi:10.1016/j.neuroimage.2003.09.052 · Cited by 186 · see citing works
Deshpande, G., Hu, X. P., Stilla, R. F., & Sathian, K. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.01.044 · Cited by 151 · see citing works
The effect of filtering on Granger causality based multivariate causality measures
Florin, E., Groß, J., Pfeifer, J., Fink, G. R., & Timmermann, L. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.12.050 · Cited by 134 · see citing works
Freiwald, W. A., Valdes-Sosa, P. A., Bosch, J., Biscay, R., Jiménez, J. C., Rodriguez, L. M., Rodrı́guez, V., Kreiter, A. K., & Singer, W. (1999) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(99)00129-6 · Cited by 129 · see citing works
Demirci, O., Stevens, M. C., Andreasen, N. C., Michael, A., Liu, J., White, T., Pearlson, G. D., Clark, V. P., & Calhoun, V. D. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.02.014 · Cited by 126 · see citing works
Self-citationMapping and correction of vascular hemodynamic latency in the BOLD signal
Chang, C., Thomason, M. E., & Glover, G. H. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.06.030 · Cited by 121 · see citing works
Sato, J. R., Amaro, E., Takahashi, D. Y., Felix, M. D. M., Brammer, M. J., & Morettin, P. A. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2005.11.039 · Cited by 121 · see citing works
Frequency domain connectivity identification: An application of partial directed coherence in fMRI
Sato, J. R., Takahashi, D. Y., Arcuri, S. M., Sameshima, K., Morettin, P. A., & Baccalá, L. A. (2007) · Human Brain Mapping · doi:10.1002/hbm.20513 · Cited by 119 · see citing works
Impact of Working Memory Load on fMRI Resting State Pattern in Subsequent Resting Phases
Pyka, M., Beckmann, C. F., Schöning, S., Hauke, S., Heider, D., Kugel, H., Arolt, V., & Konrad, C. (2009) · PLoS ONE · doi:10.1371/journal.pone.0007198 · Cited by 108 · see citing works
Al‐Mehdi, A., Patel, M., Haroon, A., Reed, D., Ohlsson‐Wilhelm, B. M., Muirhead, K. A., & Gray, B. D. (2006) · International Journal of Biomedical Imaging · doi:10.1155/ijbi/2006/37470 · Cited by 103 · see citing works
Calhoun, V. D., Adalı, T., Pekar, J. J., & Pearlson, G. D. (2003) · NeuroImage · doi:10.1016/s1053-8119(03)00411-7 · Cited by 83 · see citing works
Self-citationA Kalman filter based methodology for EEG spike enhancement
Oikonomou, V. P., Tzallas, A. T., & Fotiadis, D. I. (2006) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2006.10.003 · Cited by 83 · see citing works
Liu, J., Kiehl, K. A., Pearlson, G. D., Perrone‐Bizzozero, N. I., Eichele, T., & Calhoun, V. D. (2009) · NeuroImage · doi:10.1016/j.neuroimage.2009.02.045 · Cited by 62 · see citing works
Self-citationA new method for detecting causality in fMRI data of cognitive processing
Londei, A., D'Ausilio, A., Basso, D., & Belardinelli, M. O. (2006) · Cognitive Processing · doi:10.1007/s10339-005-0019-5 · Cited by 49 · see citing works
Berns, G. S., Song, A. W., & Mao, H. (1999) · Journal of Neuroscience · doi:10.1523/jneurosci.19-14-j0003.1999 · Cited by 40 · see citing works
A criterion for adaptive autoregressive models
Schlögl, A., Roberts, S., & Pfurtscheller, G. (2002) · doi:10.1109/iembs.2000.898046 · Cited by 40 · see citing works
Gaschler‐Markefski, B., Baumgart, F., Tempelmann, C., Schindler, F., Stiller, D., Heinze, H., & Scheich, H. (1997) · Magnetic Resonance in Medicine · doi:10.1002/mrm.1910380518 · Cited by 37 · see citing works
BOLD Noise Assumptions in fMRI
Wink, A. M., & Roerdink, J. B. T. M. (2006) · International Journal of Biomedical Imaging · doi:10.1155/ijbi/2006/12014 · Cited by 37 · see citing works
Computer Intensive Testing for the Influence Between Time Series
Baccalá, L. A., Takahashi, D. Y., & Sameshima, K. (2006) · doi:10.1002/9783527609970.ch16 · Cited by 36 · see citing works
Brain network for passive word listening as evaluated with ICA and Granger causality
Londei, A., D’Ausilio, A., Basso, D., Sestieri, C., Gratta, C. D., Romani, G. L., & Belardinelli, M. O. (2007) · Brain Research Bulletin · doi:10.1016/j.brainresbull.2007.01.008 · Cited by 36 · see citing works
Inferring neural activity from BOLD signals through nonlinear optimization
Vakorin, V. A., Krakovska, O., Borowsky, R., & Sarty, G. E. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.06.033 · Cited by 24 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Functional and Effective Connectivity: A Review
Friston, K. J. (2011) · Brain Connectivity · doi:10.1089/brain.2011.0008 · Cited by 3,415 · see citing works
Network modelling methods for FMRI
Smith, S. M., Miller, K. L., Salimi-Khorshidi, G., Webster, M., Beckmann, C. F., Nichols, T. E., Ramsey, J. D., & Woolrich, M. W. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.08.063 · Cited by 1,878 · see citing works
Effective connectivity: Influence, causality and biophysical modeling
Valdes-Sosa, P. A., Roebroeck, A. F., Jean Daunizeau, A., & Friston, K. J. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.03.058 · Cited by 392 · see citing works
Friston, K. J., Li, B., Daunizeau, J., & Stephan, K. E. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.12.039 · Cited by 283 · see citing works
Wu, G., Liao, W., Stramaglia, S., Ding, J.-R., Chen, H., & Marinazzo, D. (2013) · Medical Image Analysis · doi:10.1016/j.media.2013.01.003 · Cited by 279 · see citing works
Granger causality for state-space models
Barnett, L., & Seth, A. K. (2015) · Physical Review E · doi:10.1103/physreve.91.040101 · Cited by 208 · see citing works
Classification of schizophrenia patients based on resting-state functional network connectivity
Arbabshirani, M. R., Kiehl, K. A., Pearlson, G. D., & Calhoun, V. D. (2013) · Frontiers in Neuroscience · doi:10.3389/fnins.2013.00133 · Cited by 181 · see citing works
Self-citationCausal inference with multiple time series: principles and problems
Eichler, M. (2013) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2011.0613 · Cited by 136 · see citing works
Dynamic brain connectivity is a better predictor of PTSD than static connectivity
Jin, C., Jia, H., Lanka, P., Rangaprakash, D., Li, L., Liu, T., Hu, X. P., & Deshpande, G. (2017) · Human Brain Mapping · doi:10.1002/hbm.23676 · Cited by 135 · see citing works
Functional network connectivity during rest and task conditions: A comparative study
Arbabshirani, M. R., Havlíček, M., Kiehl, K. A., Pearlson, G. D., & Calhoun, V. D. (2012) · Human Brain Mapping · doi:10.1002/hbm.22118 · Cited by 116 · see citing works
Self-citationA short history of causal modeling of fMRI data
Stephan, K. E., & Roebroeck, A. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.01.034 · Cited by 112 · see citing works
Multivariate dynamical systems models for estimating causal interactions in fMRI
Ryali, S., Supekar, K., Chen, T., & Menon, V. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.09.052 · Cited by 110 · see citing works
Extracting neuronal functional network dynamics via adaptive Granger causality analysis
Sheikhattar, A., Miran, S., Liu, J., Fritz, J. B., Shamma, S., Kanold, P. O., & Babadi, B. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1718154115 · Cited by 95 · see citing works
The Connected Brain: Causality, models, and intrinsic dynamics
Razi, A., & Friston, K. J. (2016) · IEEE Signal Processing Magazine · doi:10.1109/msp.2015.2482121 · Cited by 85 · see citing works
Dysconnectivity of neurocognitive networks at rest in very-preterm born adults
White, T. P., Symington, I., Castellanos, N. P., Brittain, P. J., Froudist‐Walsh, S., Nam, K.-W., Sato, J. R., Allin, M. P. G., Shergill, S. S., Murray, R. M., et al. (2014) · NeuroImage Clinical · doi:10.1016/j.nicl.2014.01.005 · Cited by 83 · see citing works
van Mierlo, P., Carrette, E., Hallez, H., Vonck, K. E. J., Roost, D. V., Boon, P., & Staelens, S. G. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.02.009 · Cited by 83 · see citing works
Shoeibi, A., Ghassemi, N., Khodatars, M., Moridian, P., Khosravi, A., Zare, A., Górriz, J. M., Chale-Chale, A. H., Khadem, A. A., & Acharya, U. R. (2022) · Cognitive Neurodynamics · doi:10.1007/s11571-022-09897-w · Cited by 77 · see citing works
Bayesian models for functional magnetic resonance imaging data analysis
Zhang, L., Guindani, M., & Vannucci, M. (2014) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.1339 · Cited by 72 · see citing works
Estimating Dynamic Connectivity States in fMRI Using Regime-Switching Factor Models
Ting, C., Ombao, H., Samdin, S. B., & Salleh, S. (2017) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2017.2780185 · Cited by 72 · see citing works
Hagan, D. F. T., Wang, G., Liang, X. S., & Dolman, A. J. (2019) · Journal of Climate · doi:10.1175/jcli-d-18-0881.1 · Cited by 72 · see citing works
Time, frequency, and time‐varying Granger‐causality measures in neuroscience
Cekic, S., Grandjean, D., & Renaud, O. (2018) · Statistics in Medicine · doi:10.1002/sim.7621 · Cited by 71 · see citing works
Signal quality and Bayesian signal processing in neurofeedback based on real-time fMRI
Koush, Y., Zvyagintsev, M., Dyck, M., Mathiak, K. A., & Mathiak, K. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.07.076 · Cited by 62 · see citing works
Statistical models for brain signals with properties that evolve across trials
Ombao, H., Fiecas, M. J. A., Ting, C., & Low, Y. F. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.11.061 · Cited by 54 · see citing works
Real-time fMRI-based neurofeedback reinforces causality of attention networks
Lee, J., Kim, J., & Yoo, S. (2012) · Neuroscience Research · doi:10.1016/j.neures.2012.01.002 · Cited by 54 · see citing works
Pisapia, N. D., Turatto, M., Lin, P., Jovicich, J., & Caramazza, A. (2011) · Cerebral Cortex · doi:10.1093/cercor/bhr146 · Cited by 52 · see citing works
A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity
Samdin, S. B., Ting, C., Ombao, H., & Salleh, S. (2016) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2016.2580738 · Cited by 52 · see citing works
Modeling time-varying brain networks with a self-tuning optimized Kalman filter
Pascucci, D., Rubega, M., & Plomp, G. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007566 · Cited by 50 · see citing works
Effective connectivity analysis of fMRI and MEG data collected under identical paradigms
Plis, S., Weisend, M. P., Damaraju, E., Eichele, T., Mayer, A., Clark, V. P., Lane, T. D. R., & Calhoun, V. D. (2011) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2011.04.011 · Cited by 47 · see citing works
Self-citationSpatio-temporal Granger causality: A new framework
Luo, Q., Lu, W., Cheng, W., Valdes-Sosa, P. A., Wen, X., Ding, M., & Feng, J. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.04.091 · Cited by 45 · see citing works
A Comprehensive Analysis of Connectivity and Aging Over the Adult Life Span
Archer, J. A., Lee, A., Qiu, A., & Chen, S. A. (2015) · Brain Connectivity · doi:10.1089/brain.2015.0345 · Cited by 44 · see citing works
Li, Z., Ouyang, G., Li, D., & Li, X. (2011) · Physical Review E · doi:10.1103/physreve.84.021929 · Cited by 42 · see citing works
Rangaprakash, D., Tadayonnejad, R., Deshpande, G., O’Neill, J., & Feusner, J. D. (2020) · Brain Imaging and Behavior · doi:10.1007/s11682-020-00358-8 · Cited by 41 · see citing works
Gaglianese, A., Costagli, M., Bernardi, G., Ricciardi, E., & Pietrini, P. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.01.093 · Cited by 39 · see citing works
Stramaglia, S., Angelini, L., Wu, G., Cortés, J. M., Faes, L., & Marinazzo, D. (2016) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2016.2559578 · Cited by 38 · see citing works
Chiang, S., Guindani, M., Yeh, H. J., Haneef, Z., Stern, J. M., & Vannucci, M. (2016) · Human Brain Mapping · doi:10.1002/hbm.23456 · Cited by 36 · see citing works
Wheelock, M. D., Rangaprakash, D., Harnett, N. G., Wood, K. H., Orem, T. R., Mrug, S., Granger, D. A., Deshpande, G., & Knight, D. C. (2018) · Behavioral Neuroscience · doi:10.1037/bne0000276 · Cited by 35 · see citing works
Callara, A. L., Sebastiani, L., Vanello, N., Scilingo, E. P., & Greco, A. (2021) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2021.3060867 · Cited by 35 · see citing works
Searching Multiregression Dynamic Models of Resting-State fMRI Networks Using Integer Programming
da Costa, L. C. C., Smith, J. Q., Nichols, T. E., Cussens, J., Duff, E. P., & Makin, T. R. (2015) · Bayesian Analysis · doi:10.1214/14-ba913 · Cited by 34 · see citing works
Robust Nonlinear Causality Analysis of Nonstationary Multivariate Physiological Time Series
Schäck, T., Muma, M., Feng, M., Guan, C., & Zoubir, A. M. (2017) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2017.2708609 · Cited by 32 · see citing works
Switching state-space modeling of neural signal dynamics
He, M., Das, P., Hotan, G. C., & Purdon, P. L. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011395 · Cited by 27 · see citing works
Causal time series analysis of functional magnetic resonance imaging data
Roebroeck, A. F., Seth, A. K., & Valdes-Sosa, P. A. (2009) · Research Publications (Maastricht University) · Cited by 27 · see citing works
Rodrigues, J., & Andrade, A. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.10.029 · Cited by 26 · see citing works
Protopapa, F., Siettos, C. I., Evdokimidis, I., & Smyrnis, N. (2014) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2014.00146 · Cited by 26 · see citing works
Smith, J. F., Pillai, A. S., Chen, K., & Horwitz, B. (2012) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2011.00104 · Cited by 25 · see citing works
Wei, H., An, J., Shen, H., Zeng, L., Qiu, S., & Hu, D. (2016) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2016.00447 · Cited by 25 · see citing works
Mao, J.-W., Ye, X., Li, Y.-H., Liang, P.-J., Xu, J., & Zhang, P.-M. (2016) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2016.00113 · Cited by 25 · see citing works
Wang, Y., Katwal, S. B., Rogers, B. P., Gore, J. C., & Deshpande, G. (2017) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2016.2593655 · Cited by 24 · see citing works
GMAC: A Matlab toolbox for spectral Granger causality analysis of fMRI data
Tana, M. G., Sclocco, R., & Bianchi, A. M. (2012) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2012.07.003 · Cited by 22 · see citing works
Youssofzadeh, V., Prasad, G., Naeem, M., & Wong‐Lin, K. (2015) · Neuroinformatics · doi:10.1007/s12021-015-9281-6 · Cited by 19 · see citing works
Granger causality analysis of rat cortical functional connectivity in pain
Guo, X., Zhang, Q., Singh, A., Wang, J., & Chen, Z. S. (2020) · Journal of Neural Engineering · doi:10.1088/1741-2552/ab6cba · Cited by 18 · see citing works
Zhao, S., Rangaprakash, D., Venkataraman, A., Liang, P., & Deshpande, G. (2017) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2017.00211 · Cited by 18 · see citing works
Frequency-based approach to the study of semantic brain networks connectivity
Bianchi, A. M., Marchetta, E., Tana, M. G., Tettamanti, M., & Rizzo, G. (2012) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2012.10.005 · Cited by 17 · see citing works
Zhang, H., Chen, H., Wang, H., Li, D., Jia, B., Tan, Z., Zheng, B., & Weng, Z. (2015) · Journal of Traditional Chinese Medical Sciences · doi:10.1016/j.jtcms.2015.10.001 · Cited by 16 · see citing works
New Levels of Language Processing Complexity and Organization Revealed by Granger Causation
Gow, D. W., & Caplan, D. N. (2012) · Frontiers in Psychology · doi:10.3389/fpsyg.2012.00506 · Cited by 16 · see citing works
The altered Granger causality connection among pain-related brain networks in migraine
Ning, Y., Zheng, R., Li, K., Zhang, Y., Lyu, D., Jia, H., Ren, Y., & Zou, Y. (2018) · Medicine · doi:10.1097/md.0000000000010102 · Cited by 16 · see citing works
Rangaprakash, D., Barry, R. L., & Deshpande, G. (2023) · Frontiers in Neuroscience · doi:10.3389/fnins.2023.934138 · Cited by 15 · see citing works
Estimating Time-Dependent Structures in a Multivariate Causality for Land–Atmosphere Interactions
Zhou, F., Hagan, D. F. T., Wang, G., Liang, X. S., Li, S., Shao, Y., Yeboah, E., & Wei, X. (2024) · Journal of Climate · doi:10.1175/jcli-d-23-0207.1 · Cited by 15 · see citing works
Shim, W. H., Baek, K., Kim, J. K., Chae, Y., Suh, J., Rosen, B. R., Jeong, J., & Kim, Y. R. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00332.2012 · Cited by 13 · see citing works
Li, Y., Wu, K., Hu, X., Xu, T., Li, Z., Zhang, Y., & Li, K. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2022.858833 · Cited by 13 · see citing works
Multi-Level Clustering of Dynamic Directional Brain Network Patterns and Their Behavioral Relevance
Deshpande, G., & Jia, H. (2020) · Frontiers in Neuroscience · doi:10.3389/fnins.2019.01448 · Cited by 13 · see citing works
Granger causality in the frequency domain: derivation and applications
Lima, V., Dellajustina, F. J., Shimoura, R. O., Girardi‐Schappo, M., Kamiji, N. L., Pena, R. F. O., & Roque, A. C. (2020) · Revista Brasileira de Ensino de Física · doi:10.1590/1806-9126-rbef-2020-0007 · Cited by 13 · see citing works
Parcel-Based Connectivity Analysis of fMRI Data for the Study of Epileptic Seizure Propagation
Tana, M. G., Bianchi, A. M., Sclocco, R., Franchin, T., Cerutti, S., & Leal, A. (2012) · Brain Topography · doi:10.1007/s10548-012-0225-2 · Cited by 12 · see citing works
Sidulova, M., & Park, C. H. (2023) · Bioengineering · doi:10.3390/bioengineering10101209 · Cited by 10 · see citing works
Network analysis of multivariate time series data in biological systems: methods and applications
Mei, H., Wang, Z., Yang, H., Li, X., & Xu, Y. (2025) · Briefings in Bioinformatics · doi:10.1093/bib/bbaf223 · Cited by 10 · see citing works
How ignoring physiological noise can bias the conclusions from fMRI simulation results
Welvaert, M., & Rosseel, Y. (2012) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2012.08.022 · Cited by 9 · see citing works
Ning, Y., Li, K., Zhang, Y., Chen, P., Yin, D., Zhu, H., & Jia, H. (2020) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2020.00780 · Cited by 9 · see citing works
Optimal stimulus scheduling for active estimation of evoked brain networks
Kafashan, M., & Ching, S. (2015) · Journal of Neural Engineering · doi:10.1088/1741-2560/12/6/066011 · Cited by 9 · see citing works
Detecting effective connectivity in networks of coupled neuronal oscillators
Boykin, E. R., Khargonekar, P. P., Carney, P. R., Ogle, W. O., & Talathi, S. S. (2011) · Journal of Computational Neuroscience · doi:10.1007/s10827-011-0367-3 · Cited by 8 · see citing works
Studying the effective brain connectivity using multiregression dynamic models
da Costa, L. C. C., Nichols, T. E., & Smith, J. Q. (2017) · Brazilian Journal of Probability and Statistics · doi:10.1214/17-bjps375 · Cited by 8 · see citing works
Samdin, S. B., Ting, C., Salleh, S. H. S., Hamedi, M., & Noor, A. M. (2015) · World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany · doi:10.1007/978-981-10-0266-3_50 · Cited by 8 · see citing works
Management of Epilepsy - Research, Results and Treatment
Günel, M. K. (2011) · InTech eBooks · doi:10.5772/1139 · Cited by 8 · see citing works
Roebroeck, A. F. (2015) · Elsevier eBooks · doi:10.1016/b978-0-12-397025-1.00337-7 · Cited by 8 · see citing works
Anwar, A. R., Muthalib, M., Perrey, S., Galka, A., Granert, O., Wolff, S., Deuschl, G., Raethjen, J., Heute, U., & Muthuraman, M. (2012) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc.2012.6346419 · Cited by 7 · see citing works
Smith, J. F., Chen, K., Pillai, A. S., & Horwitz, B. (2013) · Frontiers in Neuroscience · doi:10.3389/fnins.2013.00070 · Cited by 7 · see citing works
Spatiotemporal Neural Network for Sublexical Information Processing: An Intracranial SEEG Study
Zhao, C., Liu, Y., Zeng, J., Luo, X., Sun, W., Luan, G., Liu, Y., Zhang, Y., Shi, G., Guan, Y., et al. (2024) · Journal of Neuroscience · doi:10.1523/jneurosci.0717-24.2024 · Cited by 6 · see citing works
Zeng, J., Liu, Y., Zhao, C., Cui, Z., Jiao, S., Liu, Y., Liu, D., Zhang, X., Wu, J., Luo, Y., et al. (2025) · Journal of Neuroscience · doi:10.1523/jneurosci.0307-25.2025 · Cited by 6 · see citing works
Pidnebesna, A., Fajnerová, I., Horáček, J., & Hlinka, J. (2022) · Applied Mathematical Modelling · doi:10.1016/j.apm.2022.11.034 · Cited by 6 · see citing works
Deshpande, G., & Wang, Y. (2022) · Brain Sciences · doi:10.3390/brainsci12101361 · Cited by 5 · see citing works
Investigating dynamic causal network with unified Granger causality analysis
Li, F., Cheng, M., Chu, L., Zhang, Y., Zhao, X., Lin, Q., & Hu, Z. (2022) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2022.109720 · Cited by 5 · see citing works
Avcu, E., Newman, O., Ahlfors, S. P., & Gow, D. W. (2022) · Cognition · doi:10.1016/j.cognition.2022.105322 · Cited by 5 · see citing works
Causal inference in neuronal time-series using adaptive decomposition
Rodrigues, J., & Andrade, A. (2015) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2015.02.013 · Cited by 5 · see citing works
EEG source localization based on multivariate autoregressive models using Kalman filtering
Buriticá, J. I. P., Giraldo, E., & Castellanos-Dominguez, G. (2011) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/iembs.2011.6091807 · Cited by 4 · see citing works
McFarlin, D. R., Kerr, D. L., & Nitschke, J. B. (2012) · Brain Connectivity · doi:10.1089/brain.2012.0093 · Cited by 4 · see citing works
Analyzing epileptic network dynamics via time-variant partial directed coherence
Liu, B., Mao, J.-W., Shi, Y.-J., Lu, Q.-C., Liang, P.-J., & Zhang, P.-M. (2016) · IEEE International Conference on Bioinformatics and Biomedicine (BIBM) · doi:10.1109/bibm.2016.7822547 · Cited by 4 · see citing works
Dynamic neural reconfiguration for distinct strategies during competitive social interactions
Yang, R., Ma, Y., Pan, B., Bhatt, M. A., Lohrenz, T. M., Gu, H., Kanen, J. W., Camerer, C. F., Montague, P. R., & Luo, Q. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119585 · Cited by 3 · see citing works
Chuang, C., Fang, S.-X., Huang, C.-S., & Ding, W. (2024) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2024.109347 · Cited by 3 · see citing works
Neurovascular deconvolution of optical signals as a proxy for the true neuronal inputs
Dubeau, S., Havlíček, M., Beaumont, É., Ferland, G., Lesage, F., & Pouliot, P. (2012) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2012.07.008 · Cited by 3 · see citing works
A Review on Dependence Measures in Exploring Brain Networks from fMRI Data
Pruttiakaravanich, A., & Songsiri, J. (2016) · Engineering Journal · doi:10.4186/ej.2016.20.3.207 · Cited by 3 · see citing works
Causality of Spike Trains Based on Entropy
Li, Z., & Xiaoli Li, A. (2016) · Springer eBooks · doi:10.1007/978-981-10-1822-0_3 · Cited by 2 · see citing works
Sadeghi, A. Z., Oghabian, M. A., Zare-Bidoky, M., Batouli, S. A. H., & Ekhtiari, H. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/678961 · Cited by 2 · see citing works
Pidnebesna, A., Fajnerová, I., Horáček, J., & Hlinka, J. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2019.12.19.876508 · Cited by 2 · see citing works
Mapping effective connectivity
Reyes, R. G., & Valdes-Sosa, P. A. (2024) · Elsevier eBooks · doi:10.1016/b978-0-12-820480-1.00184-4 · Cited by 2 · see citing works
Hedlin, H., Boatman, D. F., & Caffo, B. S. (2010) · Collection of Biostatistics Research Archive · Cited by 1 · see citing works
Karameh, F. N., & Nahas, Z. H. (2018) · Brain Topography · doi:10.1007/s10548-018-0666-3 · Cited by 1 · see citing works
Decision thresholding on fMRI activation maps using the Hilbert–Huang transform
Kuo, P., & Liou, M. (2022) · Journal of Neural Engineering · doi:10.1088/1741-2552/ac7f5e · Cited by 1 · see citing works
Ma, Y., Liang, X., Wu, H., Lu, H., Li, Y., Liu, C., Gao, Y., Xiang, M., Yu, D., & Ning, X. (2024) · Bioengineering · doi:10.3390/bioengineering11121258 · Cited by 1 · see citing works
EEG-fMRI Multimodal Integration for Epilepsy Research
Anna, M., Franchin, T., & Maria, G. D. (2011) · InTech eBooks · doi:10.5772/21891
Arbabshirani, M. R. (2014) · UNM’s Digital Repository (University of New Mexico)
Optimally estimating Granger causalityPreprint
Luo, Q., Lu, W., Cheng, W., Valdes-Sosa, P. A., Wen, X., Ding, M., & Feng, J. (2012) · arXiv (Cornell University)
Causality analysis of P300 recordings focused on the localization of active brain areas
Padilla, B. J. I., Avendao, J., & Castellanos, D. G. (2014) · Symposium on Image, Signal Processing and Artificial Vision (STSIVA) · doi:10.1109/stsiva.2014.7010127
- Authors
- Havlicek, M., Jan, J., Brazdil, M., & Calhoun, V. D.
- Affiliations
- Mind Research Network (US)
- ORCID
- Calhoun, Vince D.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2010-10
- Volume
- 53
- Issue
- 1
- Pages
- 65-77
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC4347842
- OpenAlex
- W1963526411
- Cited by
- 106
- References
- 74
- Citations by year
- 2025: 2 · 2024: 5 · 2023: 4 · 2022: 8 · 2021: 1 · 2020: 7 · 2019: 3 · 2018: 5 · 2017: 9 · 2016: 10 · 2015: 9 · 2014: 6 · 2013: 6 · 2012: 15
- FWCI
- 6.96
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- Ministerstvo Školství, Mládeže a Tělovýchovy
- National Institutes of Health (R01EB000840)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- Kalman filter, functional network connectivity, fMRI time series, non-stationary time series, generalized partial directed coherence, frequency domain causality, independent component analysis, brain neural networks
- MeSH terms
- Adult, Algorithms, Auditory Cortex, Auditory Perception, Evoked Potentials, Auditory, Female, Humans, Image Enhancement, Image Interpretation, Computer-Assisted, Magnetic Resonance Imaging, Male, Nerve Net, Sensitivity and Specificity, Signal Processing, Computer-Assisted, Reproducibility of Results
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
