Clinical neuroimaging studies increasingly rely on diffusion tensor imaging (DTI) for new insights into the tissue structure of brain white matter in vivo
. Traditional structural magnetic resonance imaging (MRI) provides little contrast within white matter, which is displayed as a homogeneous volume without information about the underlying tissue orientation and microstructure. DTI, on the other hand, provides information about the axon bundles of brain white matter such as preferred orientation, myeli-nation, and density as reflected in measures of the diffusion tensor for each voxel (Basser and Pierpaoli, 1996
). The diffusion tensor incorporates information about the preferred fiber orientation in the principal eigenvector as well as information about local tissue structure in measures of anisotropy and norm. This paper addresses the problem of normalizing geometric models of white matter bundles and making statistical inference about differences in diffusion properties.
Most approaches to group analysis in the clinical DTI literature have relied on voxel based analysis or manually drawn regions of interest (ROI). An overview of the differences between voxel based and ROI analysis in DTI population studies was described by Snook et al (2007)
. Voxel based analysis methods are characterized by alignment of images to a template followed by independent hypothesis tests per voxel which are smoothed and corrected for multiple comparisons. Voxelwise analysis has been applied in DTI studies including autism (Barnea-Goraly et al., 2004
) and schizophrenia (Burns et al., 2003
). The major challenge in voxel based analysis is the need for multiple comparison correction and smoothing which can make localization of changes challenging to interpret (Jones et al., 2005a
). Other studies have used manually drawn ROIs for group comparison of DTI properties. Within the ROIs, diffusion properties such as FA or mean diffusivity (MD) are averaged to create a single statistic. Examples of studies using ROI methods can be found in normal development (Bonekamp et al., 2007
; Hermoye et al., 2006
), schizophrenia (Kubicki et al., 2005
), and Krabbe disease (Guo et al., 2001
). The major drawback of ROI analysis is the time consuming nature of manual identification of regions, especially the ability to identify the long curved structures common in DTI fiber tracts. Our method improves on previous methods in the ability to perform automatic processing through the use of high dimensional deformable registration as well as the ability to focus on testing specific hypotheses regarding tracts of interest using a novel method for joint analysis of multivariate tensor measures in a tract model.
Segmenting anatomically known fiber bundles remains an important challenge for DTI analysis. The most common approach, fiber tractography, integrates the field of tensor principal eigenvector to create streamlines which sample anatomical fiber bundles (Basser et al., 2000
). Corouge et al. (2006)
, Jones et al. (2005b)
, Maddah et al. (2008)
, and Lin et al. (2006)
proposed to analyze diffusion properties as a function sampled along arc length of fiber bundles. More recent work has focused on volumetric segmentation methods which also allow data within the tract to be reduced to a function of arc length (Fletcher et al., 2007
; Melonakos et al., 2007
). These methods emphasize the need to understand diffusion properties in the context of geometric models of fiber bundles.
The major challenge in implementing tract oriented statistics in population studies is finding a consistent spatial parametrization within and between populations. Defining anatomically equivalent ROIs to seed tractography for large population studies is time consuming, error prone, and often requires significant post-processing such as cleaning and clustering (Gilmore et al., 2007
). Furthermore, even given tractography seeds for each image, the natural variability of brain size and shape prohibits a naturally consistent parametrization for arc length models of diffusion. To solve both the needs for tract segmentation in individual cases as well as shape normalization for fiber tracts, we apply a population based registration method. Jones et al. (2002)
and Xu et al. (2003)
described the advantages of spatial normalization for DTI population studies. Recent work has focused on the use of unbiased methods for mapping tensor images to a common coordinate system (Zhang et al., 2007
; Peyrat et al., 2007
). A reference atlas of fiber bundles visible in DTI was produced by Mori et al. (2005)
. Xu et al. (2008)
highlighted the need for smooth invertible mappings in a registration framework. Other work on DTI atlas building has used the geometry information contained within tractography results rather than image registration to build a population model (O’Donnell and Westin, 2007
). In our framework, atlas building for DTI creates a global spatial normalization which can be used to parametrize tract oriented measures across a population.
In work closely related to the proposed methodology, Yushkevich et al. (2008)
propose a method for statistical analysis along the two-dimensional medial manifolds of fiber tracts for specific tracts of interest after unbiased group alignment. On the tract medial axis, permutation tests are applied to detect clusters of pointwise differences between MD of groups. Another approach proposed by Smith et al. (2006)
, tract-based spatial statistics, is a global approach for analysis of diffusion properties using non-linear registration to a template combined with a skeletonization of FA voxels. FA values are globally projected onto the skeleton followed by pointwise hypothesis tests on the skeleton. O’Donnell et al. (2007)
used tracts obtained through clustering and performs pointwise statistics along tract-oriented functions. Our method differs from these primarily in the use of statistical analysis that incorporate multivariate tensor measure and tract-oriented statistics for a single hypothesis test per tract.
This paper presents a method for group comparison of DTI that combines a method for high-dimensional diffeomorphic registration with a statistical framework for detecting and understanding differences between the diffusion properties of fiber tracts. The emphasis of the DTI atlas building procedure is to model and normalize the geometry of fiber bundles to analyze differences of diffusion properties between groups. A schematic overview of the procedure is shown in . Atlas building is performed based on a feature which is sensitive to the medial location of brain white matter. The diffusion properties of fiber bundles are modeled as continuous functions of arc length, where the tract functions are multivariate functions which map arc length to orthogonal tensor invariants. Statistics appropriate to populations of continuous functions is applied for hypothesis testing and discrimination. The proposed methodology is applicable to general DTI population comparisons. For this paper, the methodology was evaluated on a large pediatric study of normal development and comparison of neonate controls to MVMs who are at higher risk for mental illness.
Fig. 1 All images in a study are used to compute an atlas. Fiber tractography in the atlas produces a template atlas fiber tract. Inverse transformations are used to map the template tract back into the individual subjects to collect along tract measurements (more ...)