, Volume 10, Issue 1, pp 5–17 | Cite as

Fast Approximate Stochastic Tractography

  • Juan Eugenio IglesiasEmail author
  • Paul M. Thompson
  • Cheng-Yi Liu
  • Zhuowen Tu
Original Article


Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: i) lack of quantitative connectivity information; and ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e. visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore enabling interactive probabilistic tractography: the user can quickly modify the seed region if he is not satisfied with the output without having to wait on average 7 min.


Probabilistic tractography Diffusion-weighted MRI Markov chain 



This work was funded by the National Science Foundation (grant no. 0844566), the Office of Naval Research (grant no. N000140910099), and the National Institutes of Health through grants U54 RR021813 (Center for Computational Biology), 1U01MH093765 (The Human Connectome Project) and 5P41RR013642 (Computational Anatomy and Multidimensional Modeling). The authors would like to thank Greig de Zubicaray, Kathie McMahon, Margaret Wright from the Center for Magnetic Resonance at the University of Queensland for acquiring the data. The first author would also like to thank the U.S. Department of State's Fulbright program for the funding.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Juan Eugenio Iglesias
    • 1
    Email author
  • Paul M. Thompson
    • 1
  • Cheng-Yi Liu
    • 1
  • Zhuowen Tu
    • 1
  1. 1.UCLALos AngelesUSA

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