A probabilistic framework to infer brain functional connectivity from anatomical connections

Authors:
Fani Deligianni;Gael Varoquaux;Bertrand Thirion;Emma Robinson;David J. Sharp;A. David Edwards;Daniel Rueckert
Affiliations:
Department of Computing, Imperial College London, UK;INSERM, CEA, Saclay, France and INRIA, Saclay, France;INRIA, Saclay, France;Department of Computing, Imperial College London, UK;C3NL, The Division of Experimental Medicine, Imperial College London, UK;Institute of Clinical Sciences, Imperial College London, UK;Department of Computing, Imperial College London, UK
Venue:
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Year:
2011

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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.