Fuzzy anatomical connectedness of the brain using single and multiple fibre orientations estimated from diffusion MRI

Fast approximate stochastic tractography

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.

Brain tractography using Q-ball imaging and graph theory: Improved connectivities through fibre crossings via a model-based approach

Brain tractography techniques utilize a set of diffusion-weighted magnetic resonance images to reconstruct white matter tracts, non-invasively and in-vivo. Streamline tracking techniques propagate curves from a seed to imply connectivity to distal voxels. Alternative approaches have been developed that attempt to quantify connection strength between all voxels and the seed. Tractography based on graph theory is amongst them. Despite its potential, graph-based tracking through complex fibre configurations has not been extensively studied and existing methods have inherent limitations. Anatomically unlikely connections may be identified in fibre crossing regions, by assigning relatively high connection strengths to all crossing populations. In this study, we discuss these limitations and present a new approach for robustly propagating through fibre crossings, as described by the orientation distribution functions (ODFs) derived from Q-ball imaging. Each image voxel is treated as a graph node and graph arcs connect neighbouring voxels. Weights representative of both structural and diffusivity features are assigned to each arc. To account for the existence of crossing fibre populations within a voxel, complex ODFs are decomposed into components representative of single-fibre populations and an image multigraph is created. The multigraph is searched exhaustively, but efficiently, to find the strongest paths and assign connectivity strengths between a seed and all the other image voxels. A comparison with the existing graph-based tractography as well as Q-ball driven front evolution tractography is performed on simulated data, and on human Q-ball imaging data acquired from five healthy volunteers. The new approach improves the connection strengths through fibre crossing regions, reducing the strengths of paths that are less anatomically plausible.