Relating Brain Functional Connectivity to Anatomical Connections: Model Selection

We aim to learn across several subjects a mapping from brain anatomical connectivity to functional connectivity. Following [1], we formulate this problem as estimating a multivariate autoregressive (MAR) model with sparse linear regression. We introduce a model selection framework based on cross-validation. We select the appropriate sparsity of the connectivity matrices and demonstrate that choosing an ordering for the MAR that lends to sparser models is more appropriate than a random. Finally, we suggest randomized Least Absolute Shrinkage and Selective Operator (LASSO) in order to identify relevant anatomo-functional links with better recovery of ground truth.

[1]  C. J. Honeya,et al.  Predicting human resting-state functional connectivity from structural connectivity , 2009 .

[2]  M. Raichle,et al.  Disease and the brain's dark energy , 2010, Nature Reviews Neurology.

[3]  J. Burns.  An evolutionary theory of schizophrenia: Cortical connectivity, metarepresentation, and the social brain , 2004, Behavioral and Brain Sciences.

[4]  M. P. van den Heuvel,et al.  Microstructural Organization of the Cingulum Tract and the Level of Default Mode Functional Connectivity , 2008, The Journal of Neuroscience.

[5]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[6]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[7]  George Zouridakis,et al.  Information Communication Networks in Severe Traumatic Brain Injury , 2010, Brain Topography.

[8]  Daniel Rueckert,et al.  Identifying population differences in whole-brain structural networks: A machine learning approach , 2010, NeuroImage.

[9]  Mark W. Woolrich,et al.  Advances in functional and structural MR image analysis and implementation as FSL , 2004, NeuroImage.

[10]  Nassir Navab,et al.  Medical Image Computing and Computer-Assisted Intervention - MICCAI 2010, 13th International Conference, Beijing, China, September 20-24, 2010, Proceedings, Part III , 2010, MICCAI.

[11]  Tso-Jung Yen,et al.  Discussion on "Stability Selection" by Meinshausen and Buhlmann , 2010 .

[12]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[13]  Daniel Rueckert,et al.  A Probabilistic Framework to Infer Brain Functional Connectivity from Anatomical Connections , 2011, IPMI.

[14]  Timothy Edward John Behrens,et al.  Characterization and propagation of uncertainty in diffusion‐weighted MR imaging , 2003, Magnetic resonance in medicine.

[15]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[16]  N. Meinshausen,et al.  Stability selection , 2008, 0809.2932.

[17]  Gaël Varoquaux,et al.  Detection of Brain Functional-Connectivity Difference in Post-stroke Patients Using Group-Level Covariance Modeling , 2010, MICCAI.

[18]  Cun-Hui Zhang,et al.  The sparsity and bias of the Lasso selection in high-dimensional linear regression , 2008, 0808.0967.

[19]  Jean-Baptiste Poline,et al.  Brain covariance selection: better individual functional connectivity models using population prior , 2010, NIPS.

[20]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[21]  Olaf Sporns,et al.  The Non-Random Brain: Efficiency, Economy, and Complex Dynamics , 2010, Front. Comput. Neurosci..

[22]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[23]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[24]  M. Greicius,et al.  Resting-state functional connectivity reflects structural connectivity in the default mode network. , 2009, Cerebral cortex.

[25]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[26]  R. Müller.  The study of autism as a distributed disorder. , 2007, Mental retardation and developmental disabilities research reviews.

[27]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[28]  Daniel Rueckert,et al.  Multi-atlas based segmentation of brain images: Atlas selection and its effect on accuracy , 2009, NeuroImage.