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Abstract:
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DT-MRI techniques such as DTI and HARDI are popular in vivo methods of measuring directional diffusion in the brain at a 3D grid of locations. As the means of tracking neural pathways, these methods make use of the signal response under an applied magnetic field to measure the degree to which water is diffusing in a given direction. Since water molecules diffuse primarily along axonal fibers, their location can be estimated from HARDI data. We consider a completely nonparametric approach to modeling of fibers based on HARDI data to address concerns regarding the form of the imaging signal model. Instead of representing the imaging signal through a diffusion tensor or a vector field we leave it as unknown function. We show that the proposed methods are mathematically and statistically rigorous and have good asymptotic properties. More precisely, the resulting fiber estimators are asymptotically normal, with optimal convergence rates. They are based on a combination of kernel smoothing technique and Simpson's rule for approximate integration. Our method is computationally intense but it avoids the typical limitations of deterministic and probabilistic tractography methods.
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