A Global Probabilistic Approach to Fiber Tractography with Diffusion Tensor MRI

S. Inati, H. Farid, K. Sherwin, and S. Grafton

Human Brain Mapping, Brighton, UK, 2001

Introduction
Coherently organized tissue has a high degree of diffusional anisotropy which can be observed non-invasively using diffusion weighted MRI. DT-MRI has been applied with some success to the in vivo tracing of white-matter fiber pathways in the brain. Current approaches[1,2,3] "grow" pathways by taking steps in the direction indicated by the diffusion tensor at each point. The noise inherent in DT-MRI data limits the ability of these stepwise techniques to trace long fibers in their entirety. In contrast to these local approaches, we describe a global approach that employs Expectation Maximization[4] (EM). EM is a statistical technique that has been used in computer vision to estimate parametric models from 2-D motion vector fields[5]. Here, we apply EM to the estimation of neuronal pathways from 3-D tensor fields. EM is an iterative two stage process for simultaneous data segmentation and model estimation. In order to employ EM, a set of models are first defined to describe the data. In the E-step the probability of every data point belonging to each model is computed. In the M-step the probabilities are used to re-estimate the model parameters. The E- and M-steps are repeatedly performed until the probabilities and model parameters converge to a solution.

Methods
Subjects were scanned using a 1.5T GE Signa Echospeed (LX8.3) equipped with 4 G/cm gradients. Diffusion weighted images were acquired using a single-shot, diffusion-weighted, spin echo EPI sequence with 6 gradient encoding directions (b=1000). In our case, the data consisted of a volume of vector-valued data points (the principle eigenvectors of the apparent diffusion tensor). The model was taken to be a low-order Bezier curve. A single run of EM yielded a parametric description of a pathway and a probability of each point belonging to the pathway. Multiple pathways were classified after repeated runs with different random starting conditions.

Results/Discussion
Using the global probabilistic methods outlined above, we have successfully traced white matter fiber pathways. The global nature of this technique provides several advantages over local approaches: 1) Fiber tracts can be traced through noisy regions. 2) Longer fiber tracts can be traced because EM is insensitive to the accumulation of error found in stepwise solutions. 3) EM provides a measure of the likelihood of each pathway given the underlying data. 4) Finally, by fixing both endpoints, pathways connecting two brain regions can be easily found. We have presented a method for fiber tracking using EM. This global approach can be tailored and extended to provide a valuable tool in neuroimaging, separately or in concert with existing methods.

References
[1] P.J. Basser, et al., MRM 44:625-632, 2000
[2] T.E. Conturo, et al., PNAS 96:10422-10427, 1999
[3] S. Mori, et al., Ann Neurol 45:265-269, 1999
[4] G.J. McLachlan et al., "Mixture Models: Inference and Applications to Clustering", 1988
[5] A. Jepson et al., Proc CVPR 760-761, 1993

Acknowledgments This work was supported in part by NSF Grant P50-NS-17778 (Inati), NSF CAREER Award IIS-99-83806 (Farid), NSF Grant EIA-98-02068 (Farid), PHS Grant NS-33504 (Grafton).