Progress Report:Diffusion Tensor Statistics

Collaborators: Tom Fletcher (Utah), Isabelle Corouge (UNC), Ross Whitaker (Utah), Guido Gerig (UNC)

Description

We have been developing a software framework for statistical analysis of diffusion tensor data. In order to take into account the physical properties of diffusion tensors, namely that they are symmetric and have positive eigenvalues, the diffusion tensor space is treated as a nonlinear manifold. Statistics such as the mean, covariance, and modes of variation are computed in this space, see [1] for details. The work of Corouge et al. [2] has involved analysis of diffusion tensors along white matter fiber tracts using the nonlinear manifold statistics (Fig. 1 & 2). The nonlinear averaging method also provides a means for interpolating tensor data (Fig. 3), as shown in [3].

Fig. 1. Fiber tracts from the genu in a neonatal DT image overlaid on an axial section of an FA image. (Image from Corouge et al. [2])

Fig. 2. Average tensors from the bundle cross-sections displayed along the central spine of the bundle. (Image from Corouge et al. [2])

Fig. 3. Interpolation from a coronal slice of a DTI using the nonlinear averaging. Original data is on the left; the right image is created by up-sampling the image by two. (Image from Fletcher and Joshi [3])

Code Progress

Software for computing diffusion tensor statistics (mean, covariance, modes of variation) has been completed using ITK and is a part of the NA-MIC Sandbox. Development of the code was finished during the NA-MIC Programmer's Week.

Publications

This work has led to two new papers under the NA-MIC project. The paper by Corouge et al. [2] is accepted as an oral presentation at MICCAI. The paper by Fletcher and Joshi [3] is under review. (The first paper is a previous publication and included for reference).

[1] Fletcher, P.T., Joshi, S. Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors, Presented at ECCV 2004 Workshop on Computer Vision Approaches to Medical Image Analysis (CVAMIA), LNCS 3117, Springer-Verlag, pp. 87-98, 2004.

[2] Corouge, I., Fletcher, P.T., Joshi, S., Gilmore, J.H., Gerig, G. Fiber Tract-Oriented Statistics for Quantitative Diffusion Tensor MRI Analysis, To appear at MICCAI 2005.

[3] Fletcher, P.T., Joshi, S. Statistical Analysis of Diffusion Tensor Data. Submitted to Signal Processing.