Probabilistic diffusion tractography with multiple fibre orientations: What can we gain?
Section snippets
Signal model
We use the model described in Behrens et al. (2003b) and Hosey et al. (2005). It is a partial volume model, where the diffusion-weighted MR signal is split into an infinitely anisotropic component for each fibre orientation, and a single isotropic component. Unlike Behrens et al. (2003b), here, we will infer on multiple fibre orientations.
The predicted signal for each diffusion-weighted measurement at each voxel is:where S0 is the
Probabilistic tractography in a multi-fibre field
We perform tractography using the same sampling scheme that was shown to sample from the global probability of connection in Behrens et al. (2003b), and has also been used in Parker and Alexander (2003), Hagmann et al. (2003), Jones and Pierpaoli (2005), and Lazar and Alexander (2005).
This scheme amounts to streamline tractography except, at each step, instead of progressing along the most likely principal diffusion direction, we draw a sample from the posterior distribution on principal
60 direction data
Diffusion-weighted data were acquired on a 1.5 T Siemens Sonata scanner by using echo planar imaging (72 × 2 mm thick axial slices, matrix size 128 × 104, field of view 256 × 208 mm2, giving a voxel size of 2 × 2 × 2 mm). The diffusion weighting was isotropically distributed along 60 directions by using a b-value of 1000 s mm− 2, allowing an echo time of 89 ms and a repetition time of 9 s, For each set of diffusion-weighted data, 5 volumes with no diffusion weighting were acquired at points throughout the
Local fitting of the complex fibre model
Fig. 2 shows typical examples of the probabilistic multi-fibre fit to the 60 direction data set. Note the wide extent of complex fibre architecture in Fig. 2(a). In this case, the diffusion data at one third of voxels with Fractional Anisotropy > 0.1 were able to support more than one fibre orientation, but no single voxel in the data set supported more than two orientations. In the 12 direction set, no single voxel supported more than a single fibre orientation. Note that the method is general
Discussion
We have presented a direct extension of Behrens et al. (2003b) to the case of complex fibre architecture, and shown that, using this modelling approach, it is possible to detect white matter regions of complex fibre architecture that have previously been identified by model-free inversion approaches (Tuch et al., 2003, Tuch et al., 2005, Jansons and Alexander, 2003, Tournier et al., 2004, Ozarslan et al., 2005). Furthermore, by inferring on a model of local diffusion, we are able to limit the
Acknowledgments
The authors would like to acknowledge funding from the UK Medical Research Council (TEJB, HJB), the Royal Society (MFSR), the UK Engineering and Physical Sciences Research Council (MWW), the Dr. Hadwen Trust (SJ) and the Wellcome Trust (HJB). We would also like to thank Professor Paul Matthews and the Isle of Islay for providing their combined support for this work.
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