A Bayesian approach for stochastic white matter tractography

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile

[1]  J Sijbers,et al.  Estimation of the noise in magnitude MR images. , 1998, Magnetic resonance imaging.

[2]  Leonidas J. Guibas,et al.  Robust Monte Carlo methods for light transport simulation , 1997 .

[3]  M. Raichle,et al.  Tracking neuronal fiber pathways in the living human brain. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[4]  C. Beaulieu,et al.  The basis of anisotropic water diffusion in the nervous system – a technical review , 2002, NMR in biomedicine.

[5]  Kalvis M. Jansons,et al.  Persistent angular structure: new insights from diffusion magnetic resonance imaging data , 2003 .

[6]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[7]  P. Basser,et al.  Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. , 1996, Journal of magnetic resonance. Series B.

[8]  Isabelle Bloch,et al.  Towards inference of human brain connectivity from MR diffusion tensor data , 2001, Medical Image Anal..

[9]  Takashi Kawashima,et al.  Topography of commissural fibers in the corpus callosum of the cat: a study using WGA-HRP method , 1994, Neuroscience Research.

[10]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

[11]  H. Kleinert.  Path Integrals in Quantum Mechanics Statistics and Polymer Physics , 1990 .

[12]  V. Wedeen,et al.  Fiber crossing in human brain depicted with diffusion tensor MR imaging. , 2000, Radiology.

[13]  Andrew L. Alexander,et al.  An error analysis of white matter tractography methods: synthetic diffusion tensor field simulations , 2003, NeuroImage.

[14]  Carl-Fredrik Westin,et al.  Processing and visualization for diffusion tensor MRI , 2002, Medical Image Anal..

[15]  P. Basser,et al.  Estimation of the effective self-diffusion tensor from the NMR spin echo. , 1994, Journal of magnetic resonance. Series B.

[16]  David G. Norris,et al.  An Investigation of Functional and Anatomical Connectivity Using Magnetic Resonance Imaging , 2002, NeuroImage.

[17]  Carl-Fredrik Westin,et al.  Regularized Stochastic White Matter Tractography Using Diffusion Tensor MRI , 2002, MICCAI.

[18]  Stephen G. Lomber,et al.  The spatial relationship between the cerebral cortex and fiber trajectory through the corpus callosum of the cat , 1994, Behavioural Brain Research.

[19]  Alan Connelly,et al.  Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution , 2004, NeuroImage.

[20]  A. Macovski.  Noise in MRI , 1996, Magnetic resonance in medicine.

[21]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[22]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[23]  Derek K. Jones,et al.  Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI , 2003, Magnetic resonance in medicine.

[24]  Carl-Fredrik Westin,et al.  Uncertainty in White Matter Fiber Tractography , 2005, MICCAI.

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

[26]  Carlo Pierpaoli,et al.  Confidence mapping in diffusion tensor magnetic resonance imaging tractography using a bootstrap approach , 2005, Magnetic resonance in medicine.

[27]  Daniel C Alexander,et al.  Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[28]  Geoffrey J M Parker,et al.  A framework for a streamline‐based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements , 2003, Journal of magnetic resonance imaging : JMRI.

[29]  P. Basser,et al.  Water Diffusion Changes in Wallerian Degeneration and Their Dependence on White Matter Architecture , 2000 .

[30]  Susumu Mori,et al.  Fiber tracking: principles and strategies – a technical review , 2002, NMR in biomedicine.

[31]  Andrew L. Alexander,et al.  Bootstrap white matter tractography (BOOT-TRAC) , 2005, NeuroImage.

[32]  Daniel C. Alexander,et al.  An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond , 2006, Visualization and Processing of Tensor Fields.

[33]  V. Wedeen,et al.  Mapping fiber orientation spectra in cerebral white matter with Fourier-transform diffusion MRI , 2000 .

[34]  G. Pearlson,et al.  Diffusion Tensor Imaging and Axonal Tracking in the Human Brainstem , 2001, NeuroImage.

[35]  Zhizhou Wang,et al.  A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex DWI , 2004, IEEE Transactions on Medical Imaging.

[36]  Nicholas Ayache,et al.  Fast and Simple Calculus on Tensors in the Log-Euclidean Framework , 2005, MICCAI.

[37]  Jean-Philippe Thiran,et al.  DTI mapping of human brain connectivity: statistical fibre tracking and virtual dissection , 2003, NeuroImage.

[38]  M. Horsfield,et al.  Optimal strategies for measuring diffusion in anisotropic systems by magnetic resonance imaging , 1999, Magnetic resonance in medicine.

[39]  D. Tuch.  Diffusion MRI of complex tissue structure , 2002 .

[40]  E. Bullmore,et al.  Formal characterization and extension of the linearized diffusion tensor model , 2005, Human brain mapping.

[41]  Jean-Francois Mangin,et al.  Fiber Tracking in q-Ball Fields Using Regularized Particle Trajectories , 2005, IPMI.

[42]  S. Arridge,et al.  Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data , 2002, Magnetic resonance in medicine.

[43]  P. V. van Zijl,et al.  Three‐dimensional tracking of axonal projections in the brain by magnetic resonance imaging , 1999, Annals of neurology.

[44]  P. Basser,et al.  In vivo fiber tractography using DT‐MRI data , 2000, Magnetic resonance in medicine.