Multiple-subjects connectivity-based parcellation using hierarchical Dirichlet process mixture models

We propose a hierarchical infinite mixture model approach to address two issues in connectivity-based parcellations: (i) choosing the number of clusters, and (ii) combining data from different subjects. In a Bayesian setting, we model voxel-wise anatomical connectivity profiles as an infinite mixture of multivariate Gaussian distributions, with a Dirichlet process prior on the cluster parameters. This type of prior allows us to conveniently model the number of clusters and estimate its posterior distribution directly from the data. An important benefit of using Bayesian modelling is the extension to multiple subjects clustering via a hierarchical mixture of Dirichlet processes. Data from different subjects are used to infer on class parameters and the number of classes at individual and group level. Such a method accounts for inter-subject variability, while still benefiting from combining different subjects data to yield more robust estimates of the individual clusterings.

[1]  Heidi Johansen-Berg,et al.  Two‐dimensional population map of cortical connections in the human internal capsule , 2007, Journal of magnetic resonance imaging : JMRI.

[2]  Yaniv Assaf,et al.  Virtual definition of neuronal tissue by cluster analysis of multi-parametric imaging (virtual-dot-com imaging) , 2007, NeuroImage.

[3]  Desmond J. Higham,et al.  Connectivity-based parcellation of human cortex using diffusion MRI: Establishing reproducibility, validity and observer independence in BA 44/45 and SMA/pre-SMA , 2007, NeuroImage.

[4]  Katrin Amunts,et al.  Cortical Folding Patterns and Predicting Cytoarchitecture , 2007, Cerebral cortex.

[5]  Jerry Nedelman,et al.  Book review: “Bayesian Data Analysis,” Second Edition by A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Chapman & Hall/CRC, 2004 , 2005, Comput. Stat..

[6]  Terry M. Peters,et al.  Segmentation of thalamic nuclei using a modified k-means clustering algorithm and high-resolution quantitative magnetic resonance imaging at 1.5 T , 2007, NeuroImage.

[7]  Timothy Edward John Behrens,et al.  Diffusion-Weighted Imaging Tractography-Based Parcellation of the Human Lateral Premotor Cortex Identifies Dorsal and Ventral Subregions with Anatomical and Functional Specializations , 2007, The Journal of Neuroscience.

[8]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[9]  Stephen M. Smith,et al.  A global optimisation method for robust affine registration of brain images , 2001, Medical Image Anal..

[10]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[11]  Karl J. Friston,et al.  Non-invasive mapping of corticofugal fibres from multiple motor areas--relevance to stroke recovery. , 2006, Brain : a journal of neurology.

[12]  A. Schleicher,et al.  Broca's region revisited: Cytoarchitecture and intersubject variability , 1999, The Journal of comparative neurology.

[13]  Nikos Makris,et al.  Automatically parcellating the human cerebral cortex. , 2004, Cerebral cortex.

[14]  Timothy Edward John Behrens,et al.  Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging , 2003, Nature Neuroscience.

[15]  S. Leh,et al.  Fronto-striatal connections in the human brain: A probabilistic diffusion tractography study , 2007, Neuroscience Letters.

[16]  Michael I. Jordan,et al.  Hierarchical Dirichlet Processes , 2006 .

[17]  Jean-Francois Mangin,et al.  High Level Group Analysis of FMRI Data Based on Dirichlet Process Mixture Models , 2007, IPMI.

[18]  Stephen M. Smith,et al.  Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm , 2001, IEEE Transactions on Medical Imaging.

[19]  Timothy Edward John Behrens,et al.  A Bayesian framework for global tractography , 2007, NeuroImage.

[20]  Timothy Edward John Behrens,et al.  Functional-anatomical validation and individual variation of diffusion tractography-based segmentation of the human thalamus. , 2005, Cerebral cortex.

[21]  T. Peters,et al.  Visualization of thalamic nuclei on high resolution, multi‐averaged T1 and T2 maps acquired at 1.5 T , 2005, Human brain mapping.

[22]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[23]  Guy M. McKhann,et al.  Non-invasive Mapping of Connections Between Human Thalamus and Cortex Using Diffusion Imaging , 2004 .

[24]  Radford M. Neal Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[25]  T. Ferguson A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[26]  Mark W. Woolrich,et al.  Mixture models with adaptive spatial regularization for segmentation with an application to FMRI data , 2005, IEEE Transactions on Medical Imaging.

[27]  A. Anwander,et al.  Connectivity-Based Parcellation of Broca's Area. , 2006, Cerebral cortex.

[28]  Klaas E. Stephan,et al.  The anatomical basis of functional localization in the cortex , 2002, Nature Reviews Neuroscience.

[29]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[30]  P. Müller,et al.  Bayesian curve fitting using multivariate normal mixtures , 1996 .

[31]  A. R. Ferreira da Silva A Dirichlet process mixture model for brain MRI tissue classification. , 2007, Medical image analysis.

[32]  B. Schölkopf,et al.  Hierarchical Dirichlet Processes with Random Effects , 2007 .

[33]  Timothy Edward John Behrens,et al.  Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Timothy Edward John Behrens,et al.  Connection patterns distinguish 3 regions of human parietal cortex. , 2006, Cerebral cortex.

[35]  C. Antoniak Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[36]  S. Lehéricy,et al.  3-D diffusion tensor axonal tracking shows distinct SMA and pre-SMA projections to the human striatum. , 2004, Cerebral cortex.