Abstract
We present a novel probabilistic framework to learn across several subjects a mapping from brain anatomical connectivity to functional connectivity, i.e. the covariance structure of brain activity. This prediction problem must be formulated as a structured-output learning task, as the predicted parameters are strongly correlated. We introduce a model selection framework based on cross-validation with a parametrization-independent loss function suitable to the manifold of covariance matrices. Our model is based on constraining the conditional independence structure of functional activity by the anatomical connectivity. Subsequently, we learn a linear predictor of a stationary multivariate autoregressive model. This natural parameterization of functional connectivity also enforces the positive-definiteness of the predicted covariance and thus matches the structure of the output space. Our results show that functional connectivity can be explained by anatomical connectivity on a rigorous statistical basis, and that a proper model of functional connectivity is essential to assess this link.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aljabar, P., Heckemann, R., Hammers, A., Hajnal, J., Rueckert, D.: Multi-atlas based segmentation of brain images: atlas selection and its effect on accuracy. Neuroimage 46(3), 726–738 (2009)
Behrens, T., Woolrich, M., Jenkinson, M., Johansen-Berg, H., Nunes, R., Clare, S., Matthews, P., Brady, J., Smith, S.: Characterization and propagation of uncertainty in diffusion-weighted mr imaging. Magnet Reson Med. 50(5), 1077–1088 (2003)
Burns, J.: An evolutionary theory of schizophrenia: Cortical connectivity, metarepresentation, and the social brain. Behavioral and Brain Sciences 27(6), 831 (2004)
Damoiseaux, J., Greicius, M.: Greater than the sum of its parts: a review of studies combining structural connectivity and resting-state functional connectivity. Brain Struct. Funct. 213(6), 525–533 (2009)
Deligianni, F., Robinson, E., Beckmann, C., Sharp, D., Edwards, A., Rueckert, D.: Inference of functional connectivity from structural brain connectivity. In: ISBI, pp. 1113–1116 (2010)
Donoho, D.: For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59(6), 797–829 (2006)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)
Ferrarelli, F., Massimini, M., Sarasso, S., Casali, A., Riedner, B., Angelini, G., Tononi, G., Pearce, R.: Breakdown in cortical effective connectivity during midazolam-induced loss of consciousness. P. Natl. Acad. Sci. Usa 107(6), 2681–2686 (2010)
Förstner, W., Moonen, B.: A metric for covariance matrices. Qua. Vadis Geodesia, 113–128 (1999)
Fransson, P., Marrelec, G.: The precuneus/posterior cingulate cortex plays a pivotal role in the default mode network: Evidence from a partial correlation network analysis. Neuroimage 42, 1178–1184 (2008)
Friston, K.: Statistical parametric mapping: the analysis of functional brain images. Academic Press, London (2007)
Greicius, M., Supekar, K., Menon, V., Dougherty, R.: Resting-state functional connectivity reflects structural connectivity in the default mode network. Cereb. Cortex (2008)
van den Heuvel, M.P., Mandl, R.C.W., Kahn, R.S., Pol, H.E.H.: Functionally linked resting-state networks reflect the underlying structural connectivity architecture of the human brain. Human Brain Mapping 30(10), 3127–3141 (2009)
Honey, C., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. P. Natl. Acad. Sci. Usa 106(6), 2035–2040 (2009)
Honey, C., Kötter, R., Breakspear, M., Sporns, O.: Network structure of cerebral cortex shapes functional connectivity on multiple time scales. P. Natl. Acad. Sci. Usa 104(24), 10240 (2007)
Lauritzen, S.: Graphical models. Oxford University Press, USA (1996)
LeCun, Y., Chopra, S., Hadsell, R., Ranzato, M., Huang, F.L.: Energy-based models. In: BakIr, G., Hofmann, T., Schölkopf, B. (eds.) Predicting Structured Data, pp. 191–245. MIT Press, Cambridge (2007)
Ledoit, O., Wolf, M.: A well-conditioned estimator for large-dimensional covariance matrices. J. Multivar. Anal. 88, 365–411 (2004)
Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.: Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor MRI processing. J. Math. Imaging Vis. 25, 423–444 (2006)
Morcom, A., Fletcher, P.: Does the brain have a baseline? why we should be resisting a rest. Neuroimage 37(4), 1073–1082 (2007)
Müller, R.: The study of autism as a distributed disorder. Ment. Retard. Dev. Disabil. Res. 13(1), 85–95 (2007)
Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. Int. J. Comput. Vision 66, 41–66 (2006)
Pollonini, L., Pophale, S., Situ, N., Wu, M.H., Frye, R., Leon-Carrion, J., Zouridakis, G.: Information communication networks in severe traumatic brain injury. Brain Topogr. 23(2), 221–226 (2010)
Robinson, E., Hammers, A., Ericsson, A., Edwards, A., Rueckert, D.: Identifying population differences in whole-brain structural networks: a machine learning approach. Neuroimage 50(3), 910–919 (2010)
Rueckert, D., Sonoda, L., Hayes, C., Hill, D.: Non-rigid registration using free-form deformations: application to breast mr images. IEEE Trans. Med. Imag. 18, 712–721 (1999)
Smith, S., Jenkinson, M., Woolrich, M., Beckmann, C., Behrens, T., Johansen-Berg, H., Bannister, P., Luca, M.D., Drobnjak, I., Flitney, D., Niazy, R., Saunders, J., Vickers, J., Zhang, Y., Stefano, N.D., Brady, J., Matthews, P.: Advances in functional and structural mr image analysis and implementation as fsl. Neuroimage 23, 208–219 (2004)
Smith, S., Miller, K., Salimi-Khorshidi, G., Webster, M., Beckmann, C., Nichols, T., Ramsey, J., Woolrich, M.: Network modelling methods for fMRI. Neuroimage (2010) (in press)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58(1), 267–288 (1996)
Varoquaux, G., Gramfort, A., Poline, J.B., Thirion, B.: Brain covariance selection: better individual functional connectivity models using population prior. In: NIPS (2010)
Venkataraman, A., Rathi, Y., Kubicki, M., Westin, C.F., Golland, P.: Joint generative model for fmri/dwi and its application to population studies. Med. Image Comput. Comput. Assist Interv. 13(pt. 1), 191–199 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deligianni, F. et al. (2011). A Probabilistic Framework to Infer Brain Functional Connectivity from Anatomical Connections. In: Székely, G., Hahn, H.K. (eds) Information Processing in Medical Imaging. IPMI 2011. Lecture Notes in Computer Science, vol 6801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22092-0_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-22092-0_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22091-3
Online ISBN: 978-3-642-22092-0
eBook Packages: Computer ScienceComputer Science (R0)