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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.
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“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).”
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Metadata
- 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
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