Diffusion tensor imaging (DTI)

^{1}has emerged as a unique MRI-based probe of brain microstructure able to sensitively distinguish heterogeneous tissue types and detect structural abnormalities in human populations and experimental disease models. DTI maps are constructed from estimation of the diffusion tensor (DT), which describes the 3-dimensional self-diffusion of water, at every MRI voxel (Basser et al., 1994). The eigenvalues (λ_{1}, λ_{2}and λ_{3}) and eigenvectors (ε_{1}, ε_{2}and ε_{3}) of the DT can be used to characterize differences in magnitude and shape of diffusion in DTI index maps, such as fractional anisotropy (FA) and mean diffusion (MD). Although FA and MD are the primary DTI indices employed in brain research, the diffusion tensor is a rich source of structural information with the potential to provide additional metrics relevant to a range of neurobiological questions including alterations in tissue orientation properties consistent with developmental or pathological reorganizatiht on of circuitry.In conventional analysis, the orientation of ε

_{1}has been depicted by directionally encoded color (DEC) maps (Pajevic & Pierpaoli, 1999) enabling qualitative visual comparisons. While this type of subjective observation can provide qualitative insight into the nature of tissue abnormality, there is a general need for quantitative statistcal methods to assess the likelihood that any observed alterations differ from random variation. A range of approaches have been suggested for this purpose (Jones et al., 2002), however the existing frameworks (Wu et al., 2004; Wang et al., 2008) are based on the coherence and dispersion of ε_{1}, and hemispheric symmetry of white matter tracts and do not make possible groupwise statistical comparison of regional orientation information.The objective of this work was to develop a straightforward statistical approach for the quantitative analysis of directional DTI information and to interrogate robust subjective visual observations of abnormal tissue orientation on DEC maps in the hilus region of the hippocampal dentate gyrus following injury. The Fisher probability density function (Fisher, 1953), which is the spherical coordinate system analogue of the familiar Gaussian probability density function, was chosen as the basis for this framework. Historically, Fisher statistics have been widely implemented in the field of paleomagnetism (Butler & Butler, 1992; Tauxe, 2010) to characterize magnetization vectors measured from rock samples and used to determine the history of the Earth's magnetic field. Here we report for the first time the theoretical and practical application of Fisher statistics for analysis of DTI directional information and demonstrate the utility of this approach to detect directional abnormalities in the dentate gyrus following injury.