BVAR-Connect: A Variational Bayes Approach to Multi-Subject Vector Autoregressive Models for Inference on Brain Connectivity Networks
Tóm tắt
In this paper we propose BVAR-connect, a variational inference approach to a Bayesian multi-subject vector autoregressive (VAR) model for inference on effective brain connectivity based on resting-state functional MRI data. The modeling framework uses a Bayesian variable selection approach that flexibly integrates multi-modal data, in particular structural diffusion tensor imaging (DTI) data, into the prior construction. The variational inference approach we develop allows scalability of the methods and results in the ability to estimate subject- and group-level brain connectivity networks over whole-brain parcellations of the data. We provide a brief description of a user-friendly MATLAB GUI released for public use. We assess performance on simulated data, where we show that the proposed inference method can achieve comparable accuracy to the sampling-based Markov Chain Monte Carlo approach but at a much lower computational cost. We also address the case of subject groups with imbalanced sample sizes. Finally, we illustrate the methods on resting-state functional MRI and structural DTI data on children with a history of traumatic injury.
Tài liệu tham khảo
Friston, K.J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling. NeuroImage, 19(4), 1273–1302.
Mclntosh, A., & Gonzalez-Lima, F. (1994). Structural equation modeling and its application to network analysis in functional brain imaging. Human brain mapping, 2(1-2), 2–22.
Li, J., Wang, Z.J., Palmer, S.J., & McKeown, M.J. (2008). Dynamic Bayesian network modeling of fMRI: a comparison of group-analysis methods. NeuroImage, 41(2), 398–407.
Rajapakse, J., & Zhou, J. (2007). Learning effective brain connectivity with dynamic Bayesian networks. NeuroImage, 37(3), 749–760.
Granger, C.W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society 424–438.
Roebroeck, A., Formisano, E., & Goebel, R. (2005). Mapping directed influence over the brain using granger causality and fmri. NeuroImage, 25(1), 230–242.
Friston, K.J. (2011). Functional and effective connectivity: a review. Brain connectivity, 1(1), 13–36.
Wen, X., Rangarajan, G., & Ding, M. (2013). Is Granger causality a viable technique for analyzing fMRI data?. Plos One, 8(7), e67428.
Deshpande, G., LaConte, S., James, G., Peltier, S., & Hu, X. (2009). Multivariate Granger causality analysis of fMRI data. Human B,rain Mapping, 30(4), 1361–1373.
Gorrostieta, C., Ombao, H., Bédard, P., & Sanes, J. (2012). Investigating brain connectivity using mixed effects vector autoregressive models. NeuroImage, 59(4), 3347–3355.
Gorrostieta, C., Fiecas, M., Ombao, H., Burke, E., & Cramer, S. (2013). Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity. Frontiers in Computational Neuroscience, 7, 1–11.
Yu, Z., Ombao, H., Prado, R., Quinlan, E., & Cramer, S. (2016). Understanding the impact of stroke on brain motor function: A hierarchical Bayesian approach. Journal of the American Statistical Association, 111, 549–563.
Chiang, S., Guindani, M., Yeh, H.J., Haneef, Z., Stern, J., & Vannucci, M. (2017). Bayesian vector autoregressive model for multi-subject effective connectivity inference using multi-modal neuroimaging data. Human Brain Mapping, 38, 1311–1332. https://doi.org/10.1002/hbm.23456.
Calhoun, V., Adali, T., Pearlson, G., & Pekar, J. (2001). A method for making group inferences from functional MRI data using independent component analysis. Human Brain Mapping, 14(3), 140–151.
Polson, N.G., Scott, J.G., & Windle, J. (2013). Bayesian inference for logistic models using pólya–gamma latent variables. Journal of the American Statistical Association, 108(504), 1339–1349. https://doi.org/10.1080/01621459.2013.829001.
George, E., & McCulloch, R. (1997). Approaches for Bayesian variable selection. Statistica Sinica, 7(2), 339–373.
Brown, P., Vannucci, M., & Fearn, T. (1998). Multivariate bayesian variable selection and prediction. Journal of the Royal Statistical Society Series B, 60(3), 627–641.
Banerjee, S., Gelfand, A.E., & Carlin, B.P. (2003). Hierarchical modeling and analysis for spatial data, Monographs on statistics and applied probability. Boca Raton: CRC Press.
Greicius, M.D., Supekar, K., Menon, V., & Dougherty, R.F. (2009). Resting-state functional connectivity reflects structural connectivity in the default mode network. Cerebral Cortex, 19(1), 72–78.
Deco, G., Jirsa, V.K., & McIntosh, A.R. (2011). Emerging concepts for the dynamical organization of resting-state activity in the brain. Nature Reviews Neuroscience, 12(1), 43–56.
Kang, H., Ombao, H., Fonnesbeck, C., & Morgan, V. (2017). A Bayesian double fusion model for resting state brain connectivity using joint functional and structural data. Brain Connectivity, 7(4), 219– 227.
Higgins, I., Kundu, S., & Guo, Y. (2018). Integrative Bayesian analysis of brain functional networks incorporating anatomical knowledge. NeuroImage, 181, 263–278.
Bishop, C.M., & Tipping, M.E. Variational relevance vector machines, CoRR abs/1301.3838.arXiv:1301.3838.
Beal, M.J. (2003). Variational algorithms for approximate bayesian inference, Ph.D. thesis, Gatsby Computational Neuroscience Unit University College London.
Blei, D.M., Kucukelbir, A., & McAuliffe, J.D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877. https://doi.org/10.1080/01621459.2017.1285773.
Bishop, C.M. (2006). Pattern recognition and machine learning springer.
Penny, W., Kiebel, S., & Friston, K. (2003). Variational Bayesian Inference for fMRI time series. NeuroImage, 19(3), 727–741.
Flandin, G., & Penny, W. (2007). Bayesian fMRI, data analysis with sparse spatial basis function priors. NeuroImage, 34(3), 1108–1125.
Woolrich, M.W., Behrens, T.E.J., & Smith, S.M. (2004). Constrained linear basis sets for HRF, modelling using Variational Bayes. NeuroImage, 21(4), 1748–1761.
Zhang, L., Guindani, M., Versace, F., Englemann, J., Vannucci, M., & spatiotemporal nonparametric, A. (2016). BAyesian model of multi-subject fMRI data. Annals of Applied Statistics, 10(2), 638–666.
Kook, J., Guindani, M., Zhang, L., & Vannucci, M. (2019). NPBAyes-fMRI: Nonparametric bayesian general linear models for single- and multi-subject fMRI data. Statistics in Biosciences, 11(1), 3–21.
Titsias, M.K., & Lázaro-Gredilla, M. Shawe-Taylor, J., Zemel, R. S., Bartlett, P. L., Pereira, F., & Weinberger, K. Q. (Eds.). (2011). Spike and slab variational inference for multi-task and multiple kernel learning, (Vol. 24. New York: Curran Associates Inc.
Scott, J., & Berger, J. (2010). Bayes and empirical-bayes multiplicity adjustment in the variable-selection problem. The Annals of Statistics, 38(5), 2587–2619.
Teasdale, G., & Jennett, B. (1974). Assessment of coma and impaired consciousness. The Lancet, 304, 81–84.
Whitfield-Gabrieli, S., Nieto-Castanon, A., & Ghosh, S. (2011). Artifact detection tools (art), Camb., Ma. Release Version, 7, 11.
Behrens, T.E., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M., & Smith, S.M. (2003). Characterization and propagation of uncertainty in diffusion-weighted mr imaging. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 50(5), 1077–1088.
Andersson, J.L., Skare, S., & Ashburner, J. (2003). How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging. NeuroImage, 20(2), 870– 888.
Andersson, J.L., & Sotiropoulos, S.N. (2015). Non-parametric representation and prediction of single-and multi-shell diffusion-weighted MRI data using Gaussian processes. NeuroImage, 122, 166–176.
Andersson, J.L., & Sotiropoulos, S.N. (2016). An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging. NeuroImage, 125, 1063–1078.
Andersson, J.L., Graham, M.S., Zsoldos, E., & Sotiropoulos, S.N. (2016). Incorporating outlier detection and replacement into a non-parametric framework for movement and distortion correction of diffusion MR images. NeuroImage, 141, 556–572.
Graham, M.S., Drobnjak, I., & Zhang, H. (2016). Realistic simulation of artefacts in diffusion mri for validating post-processing correction techniques. NeuroImage, 125, 1079–1094.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.
Goelman, G., Gordon, N., & Bonne, O. (2014). Maximizing negative correlations in resting-state functional connectivity MRI by time-lag, PloS One 9(11).
Gu, Z., Gu, L., Eils, R., Schlesner, M., & Brors, B. (2014). circlize implements and enhances circular visualization in R. Bioinformatics, 30(19), 2811–2812.
Ewing-Cobbs, L., Johnson, C.P., Juranek, J., DeMaster, D., Prasad, M., Duque, G., Kramer, L., Cox, C.S., & Swank, P.R. (2016). Longitudinal diffusion tensor imaging after pediatric traumatic brain injury: Impact of age at injury and time since injury on pathway integrity. Human brain mapping, 37(11), 3929– 3945.
Watson, C.G., DeMaster, D., & Ewing-Cobbs, L. (2019). Graph theory analysis of dti tractography in children with traumatic injury. NeuroImage: Clinical, 21, 101673.
Wilde, E.A., Ayoub, K.W., Bigler, E.D., Chu, Z.D., Hunter, J.V., Wu, T.C., McCauley, S.R., & Levin, H.S. (2012). Diffusion tensor imaging in moderate-to-severe pediatric traumatic brain injury: changes within an 18 month post-injury interval. Brain imaging and Behavior, 6(3), 404–416.
Henson, R., Rugg, M., & Friston, K.J. (2001). The choice of basis functions in event-related fMRI. NeuroImage, 13, 149.
Chang, C., & Glover, G. (2010). Time-frequency dynamics of resting-state brain connectivity measured with fMRI. NeuroImage, 50(1), 81–98.
Calhoun, V., Miller, R., Pearlson, G., & Adali, T. (2014). The chronnectome: time-varying connectivity networks as the next frontier in fMRI data discovery. Neuron, 84(2), 262– 274.
Ryali, S., Supekar, K., Chen, T., Kochalka, J., Cai, W., Nicholas, J., & et al. Temporal dynamics and developmental maturation of salience, default and central-executive network interactions revealed by variational Bayes hidden Markov modeling PLoS Comput Biol 12(12): e1005138.
Chiang, S., Vankov, E., Yeh, H., Guindani, M., Vannucci, M., Haneef, Z., & Stern, J. Temporal and spectral characteristics of dynamic functional connectivity between resting-state networks reveal information beyond static connectivity, PLoS ONE 13(1): e0190220.
Warnick, R., Guindani, M., Erhardt, E., Allen, E., Calhoun, V., & Vannucci, M. (2018). A Bayesian Approach for Estimating Dynamic Functional Network Connectivity in fMRI Data. Journal of the American Statistical Association, 113(521), 134–151.
Ewing-Cobbs, L., DeMaster, D., Watson, C.G., Prasad, M.R., Cox, C.S., Kramer, L.A., Fischer, J.T., Duque, G., & Swank, P.R. (2019). Post-traumatic stress symptoms after pediatric injury: Relation to pre-frontal limbic circuitry. Journal of neurotrauma, 36(11), 1738–1751.