Gibbs tracking: A novel approach for the reconstruction of neuronal pathways

Reconstruction of neuronal fibers using diffusion‐weighted (DW) MRI is an emerging method in biomedical research. Existing fiber‐tracking algorithms are commonly based on the “walker principle.” Fibers are reconstructed as trajectories of “walkers,” which are guided according to local diffusion properties. In this study, a new method of fiber tracking is proposed that does not engage any “walking” algorithm. It resolves a number of inherent problems of the “walking” approach, in particular the reconstruction of crossing and spreading fibers. In the proposed method, the fibers are built with small line elements. Each line element contributes an anisotropic term to the simulated DW signal, which is adjusted to the measured signal. This method demonstrates good results for simulated fibers. A single in vivo result demonstrates the successful reconstruction of the dominant neuronal pathways. A comparison with the diffusion tensor imaging (DTI)‐based fiber assignment with continuous tracking (FACT) method and the probabilistic index of connectivity (PICo) method based on a multitensor model is performed for the callosal fibers. The result shows a strong increase in the number of reconstructed fibers. These almost fill the total white matter (WM) volume and connect a large area of the cortex. The method is very computationally expensive. Possible ways to address this problem are discussed. Magn Reson Med 60:953–963, 2008. © 2008 Wiley‐Liss, Inc.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  J. E. Tanner,et al.  Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient , 1965 .

[3]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[4]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[5]  J. Tsuruda,et al.  Diffusion-weighted MR imaging of anisotropic water diffusion in cat central nervous system. , 1990, Radiology.

[6]  M.N.M. vanLieshout Stochastic annealing for nearest-neighbour point processes with application to object recognition , 1993 .

[7]  van Marie-Colette Lieshout,et al.  Stochastic annealing for nearest-neighbour point processes with application to object recognition , 1994, Advances in Applied Probability.

[8]  C. Geyer,et al.  Simulation Procedures and Likelihood Inference for Spatial Point Processes , 1994 .

[9]  P. Green Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

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

[11]  van Marie-Colette Lieshout,et al.  Markov Point Processes and Their Applications , 2000 .

[12]  Radu Stoica,et al.  The Candy model: properties and inference , 2003 .

[13]  D. Le Bihan,et al.  Diffusion tensor imaging: Concepts and applications , 2001, Journal of magnetic resonance imaging : JMRI.

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

[15]  L. Frank Characterization of anisotropy in high angular resolution diffusion‐weighted MRI , 2002, Magnetic resonance in medicine.

[16]  V. Wedeen,et al.  Diffusion MRI of Complex Neural Architecture , 2003, Neuron.

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

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

[19]  Paul J. Laurienti,et al.  An automated method for neuroanatomic and cytoarchitectonic atlas-based interrogation of fMRI data sets , 2003, NeuroImage.

[20]  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.

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

[22]  Josiane Zerubia,et al.  A Gibbs Point Process for Road Extraction from Remotely Sensed Images , 2004, International Journal of Computer Vision.

[23]  M. Moseley,et al.  Magnetic Resonance in Medicine 51:924–937 (2004) Characterizing Non-Gaussian Diffusion by Using Generalized Diffusion Tensors , 2022 .

[24]  Matthew A. Lambon Ralph,et al.  Lateralization of ventral and dorsal auditory-language pathways in the human brain , 2005, NeuroImage.

[25]  B W Kreher,et al.  Multitensor approach for analysis and tracking of complex fiber configurations , 2005, Magnetic resonance in medicine.

[26]  Daniel C Alexander,et al.  Multiple‐Fiber Reconstruction Algorithms for Diffusion MRI , 2005, Annals of the New York Academy of Sciences.

[27]  Guy B. Williams,et al.  Inference of multiple fiber orientations in high angular resolution diffusion imaging , 2005, Magnetic resonance in medicine.

[28]  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.

[29]  Josiane Zerubia,et al.  Adaptive Simulated Annealing for Energy Minimization Problem in a Marked Point Process Application , 2005, EMMCVPR.

[30]  P. Hagmann,et al.  Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging , 2005, Magnetic resonance in medicine.

[31]  Josiane Zerubia,et al.  Point processes for unsupervised line network extraction in remote sensing , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Jürgen Hennig,et al.  FiberTools : A Complete Toolbox for DTI Calculation , Fiber Tracking , and Combined Evaluation , 2005 .

[33]  P. Szeszko,et al.  MRI atlas of human white matter , 2006 .

[34]  Daniel C. Alexander,et al.  Camino: Open-Source Diffusion-MRI Reconstruction and Processing , 2006 .

[35]  Carl-Fredrik Westin,et al.  A Bayesian approach for stochastic white matter tractography , 2006, IEEE Transactions on Medical Imaging.

[36]  Thomas R. Knösche,et al.  Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging , 2007, NeuroImage.

[37]  Charles J. Geyer,et al.  Likelihood inference for spatial point processes , 2019, Stochastic Geometry.