New Approaches to Estimation of White Matter Connectivity in Diffusion Tensor MRI: Elliptic PDEs and Geodesics in a Tensor-Warped Space

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Summary

Here we investigate new approaches to quantifying the white matter connectivity in the brain, as discernible from Diffusion Tensor Magnetic Resonance Imaging data. Our frst approach nds a steady-state concentration/heat distribution using the three-dimensional tensor eld as di usion/conductivity tensors. Our second approach casts the problem in a Riemannian framework, considering each tensor as a local warping of space, and nding geodesic paths in the space. Both approaches use the information from the whole tensor, and can provide numerical measures of connectivity as well as estimated tracts for visualization. Previous work has employed an iterative technique to create time-of-arrival maps of a heat diffusion front. Instead, we solve directly for the steady state concentration, u, which can also be thought of as a heat distribution in the tensor feld:

Results of solving Equation 5 for the steady-state heat distribution. The temperature (left) and the steady-state flow magnitude (center) demonstrate the flow from the source to the sink. (The source is bright in the temperature image and the sink is dark; in the center flow image, dark means high ow magnitude.) The grayscale image on the right, a non-diffusion-weighted image, shows the corresponding anatomy.

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Bibtex entry

@InProceedings{odonnellMICCAI02,
  author         = {L. O'Donnell and S. Haker and C.-F. Westin},               
  title          = {New Approaches to Estimation of White Matter Connectivity  
                   in  Diffusion Tensor {MRI}: Elliptic PDEs and Geodesics in a
                    Tensor-Warped Space},                                      
  booktitle      = {Fifth International Conference on Medical Image Computing  
                   and  Computer-Assisted Intervention (MICCAI'02)},           
  pages          = {459--466},                                                 
  year           = 2002,                                                       
  address        = {Tokyo, Japan}
}                                             

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