Abstract
Time-varying Granger causality refers to patterns of causal relationships that vary over time between brain functional time series at distinct source and target regions. It provides rich information about the spatiotemporal structure of brain activity that underlies behavior. Current methods for this problem fail to quantify nonlinear relationships in source-target relationships, and require ad hoc setting of relationship time lags. This paper proposes deep stacking networks (DSNs), with adaptive convolutional kernels (ACKs) as component parts, to address these challenges. The DSNs use convolutional neural networks to estimate nonlinear source-target relationships, ACKs allow these relationships to vary over time, and time lags are estimated by analysis of ACKs coefficients. When applied to synthetic data and data simulated by the STANCE fMRI simulator, the method identified ground-truth time-varying causal relationships and time lags more robustly than competing methods. The method also identified more biologically-plausible causal relationships in a real-world task fMRI dataset than a competing method. Our method is promising for modeling complex functional relationships within brain networks.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Friston, K.: Functional and effective connectivity: a review. Brain connectivity 1(1), 13–36 (2011)
Deshpande, G., et al.: Multivariate Granger causality analysis of fMRI data. Hum. Brain Mapp. 30(4), 1361–1373 (2009)
Seth, A.K., Barrett, A.B., Barnett, L.: Granger causality analysis in neuroscience and neuroimaging. J. Neurosci. 35(8), 3293–3297 (2015)
Friston, K., Moran, R., Seth, A.K.: Analysing connectivity with Granger causality and dynamic causal modelling. Curr. Opin. Neurobiol. 23(2), 172–178 (2013)
Goebel, R., et al.: Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn. Reson. Imaging 21(10), 1251–1261 (2003)
Granger, C.W.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica: J. Econometric Society 424–438 (1969)
Liao, W., et al.: Kernel Granger causality mapping effective connectivity on fMRI data. IEEE Trans. Med. Imaging 28(11), 1825–1835 (2009)
Zhou, Z., et al.: A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging. Magn. Reson. Imaging 29(3), 418–433 (2011)
Ambrosi, P., et al.: Modeling Brain Connectivity Dynamics in Functional Magnetic Resonance Imaging via Particle Filtering. bioRxiv (2021)
Marcinkevičs, R., Vogt, J.E.: Interpretable Models for Granger Causality Using Self-explaining Neural Networks. arXiv preprint arXiv:2101.07600 (2021)
Sato, J.R., et al.: A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality. Neuroimage 31(1), 187–196 (2006)
Cekic, S., Grandjean, D., Renaud, O.: Time, frequency, and time-varying Granger-causality measures in neuroscience. Stat. Med. 37(11), 1910–1931 (2018)
Marinazzo, D., et al.: Nonlinear connectivity by Granger causality. Neuroimage 58(2), 330–338 (2011)
Príncipe, J.C., Liu, W., Haykin, S.: Kernel adaptive filtering: a comprehensive introduction. John Wiley & Sons (2011)
Schoukens, J., Ljung, L.: Nonlinear system identification: a user-oriented road map. IEEE Control Syst. Mag. 39(6), 28–99 (2019)
Ge, X., Lin, A.: Dynamic causality analysis using overlapped sliding windows based on the extended convergent cross-mapping. Nonlinear Dyn. 104(2), 1753–1765 (2021)
Schiecke, K., et al.: Brain–heart interactions considering complex physiological data: processing schemes for time-variant, frequency-dependent, topographical and statistical examination of directed interactions by convergent cross mapping. Physiol. Meas. 40(11), 114001 (2019)
Paus, T.: Inferring causality in brain images: a perturbation approach. Philosophical Trans. Royal Society B: Biological Sci. 360(1457), 1109–1114 (2005)
Antonacci, Y., et al.: Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators. PeerJ Computer Science 7, e429 (2021)
Tank, A., et al.: Neural granger causality. arXiv preprint arXiv:1802.05842 (2018)
Wismüller, A., et al.: Large-scale nonlinear Granger causality for inferring directed dependence from short multivariate time-series data. Sci. Rep. 11(1), 1–11 (2021)
Leonardi, N., Van De Ville, D.: On spurious and real fluctuations of dynamic functional connectivity during rest. Neuroimage 104, 430–436 (2015)
Chuang, K.-C., Ramakrishnapillai, S., Bazzano, L., Carmichael, O.T.: Deep stacking networks for conditional nonlinear granger causal modeling of fMRI data. In: Abdulkadir, A., et al. (eds.) MLCN 2021. LNCS, vol. 13001, pp. 113–124. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-87586-2_12
Jia, X., et al.: Dynamic filter networks. Adv. Neural. Inf. Process. Syst. 29, 667–675 (2016)
Zamora Esquivel, J., et al. Adaptive convolutional kernels. in Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops. 2019
Abadi, M., et al.: Tensorflow: A system for large-scale machine learning. In: 12th {USENIX} Symposium on Operating Systems Design and Implementation ({OSDI} 16) (2016)
Chollet, F.: keras (2015)
Koprowski, R.: Image processing. In: Processing of Hyperspectral Medical Images. SCI, vol. 682, pp. 39–82. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-50490-2_4
Murphy, K., Bodurka, J., Bandettini, P.A.: How long to scan? the relationship between fMRI temporal signal to noise ratio and necessary scan duration. Neuroimage 34(2), 565–574 (2007)
Triantafyllou, C., et al.: Comparison of physiological noise at 1.5 T, 3 T and 7 T and optimization of fMRI acquisition parameters. Neuroimage 26(1), 243–250 (2005)
Berenson, G.S.: Bogalusa Heart Study: a long-term community study of a rural biracial (black/white) population. Am. J. Med. Sci. 322(5), 267–274 (2001)
Carmichael, O., et al.: High-normal adolescent fasting plasma glucose is associated with poorer midlife brain health: bogalusa heart study. J. Clin. Endocrinol. Metab. 104(10), 4492–4500 (2019)
Glover, G.H., Li, T.Q., Ress, D.: Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR. Magnetic Resonance in Medicine: An Official J. Int. Society for Magnetic Resonance in Medicine 44(1), 162–167 (2000)
Sheu, L.K., Jennings, J.R., Gianaros, P.J.: Test–retest reliability of an fMRI paradigm for studies of cardiovascular reactivity. Psychophysiology 49(7), 873–884 (2012)
Guido, W.: Development, form, and function of the mouse visual thalamus. J. Neurophysiol. 120(1), 211–225 (2018)
Usrey, W.M., Alitto, H.J.: Visual functions of the thalamus. Annual Review of Vision Sci. 1, 351–371 (2015)
Duggento, A., Guerrisi, M., Toschi, N.: Echo state network models for nonlinear granger causality. Phil. Trans. R. Soc. A 379(2212), 20200256 (2021)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
1 Electronic supplementary material
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Chuang, KC., Ramakrishnapillai, S., Bazzano, L., Carmichael, O. (2022). Nonlinear Conditional Time-Varying Granger Causality of Task fMRI via Deep Stacking Networks and Adaptive Convolutional Kernels. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds) Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. MICCAI 2022. Lecture Notes in Computer Science, vol 13431. Springer, Cham. https://doi.org/10.1007/978-3-031-16431-6_26
Download citation
DOI: https://doi.org/10.1007/978-3-031-16431-6_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-16430-9
Online ISBN: 978-3-031-16431-6
eBook Packages: Computer ScienceComputer Science (R0)