Volume can be considered as a simple, coarse and intuitive anatomical descriptor, which is independent of the patient position within the scanner. Many previous ROI-based volumetry studies focused on structures such as entorhinal cortex, hippocampus, and amygdala, which are known to present the largest atrophy at the earliest stages of the neurodegenerative process (Laakso et al., 1996
; Apostolova and Thompson, 2008
). However, it is known that neurodegeneration spreads over many other regions, in particular over the structures of the limbic system, such as thalami, which are reported less frequently. The statistical techniques to assess significant volume differences are simple univariate hypothesis tests, and correction for multiple comparisons is not an issue. However, volume is an unspecific anatomical descriptor. Recent works show that the shape of a brain structure can be more useful than the volume for population studies (Styner et al., 2004
; Csernansky et al., 2000
More complex shape descriptors typically involve vectors of large dimensionality. For example, shape analysis of a single structure, such as the hippocampus using coordinates of point sets on the surface as shape descriptor, requires thousands of parameters. Statistical analysis on such high dimensional feature space with relatively small sample size (a few hundreds in the best cases) is problematic.
Relative pose information can be regarded as an interesting trade-off for the following reasons. First, the dimensionality required in pose characterization is not very high, just 7 parameters for each structure. Accordingly, the multiple comparison corrections will not be very severe. Second, the pose information3
can be considered as a generalization of volume measurements, because in addition to volume, it provides information about the location and orientation of each object. Third, the pose information is complementary to shape, because the relative pose between structures is typically disregarded in the alignment stage performed in single-structure shape studies.
In this paper a methodology for analysis of the relative pose information from a set of brain structures has been presented. A
general framework allowed us to compare several approaches to perform statistical analysis: pseudo-Riemannian metrics, that were proposed in Woods (2003)
in the context of linear transformations and in Park (1995)
; Zefran et al. (1996
) for SE
(3) group; Log– Euclidean framework (Arsigny et al., 2006b
); left-invariant Rieman-nian metrics on the similarity group, which is, to our knowledge, a novel contribution; and bi-invariant metrics on the group of centered transformations. The first approach can be related to our previous work (Bossa and Olmos, 2006
), while the latter approach to Styner et al. (2006)
; Gorczowski et al. (2010)
. The comparison of the geodesics induced us to select the bi-invariant centered transformation approach for the following reasons: it avoids the undesirable effect of the non-monotonic trajectories of the scale parameter (see and discussion below). Moreover, this approach allows a more clear interpretation of the results because the contribution of each natural category, either rotation or translation or scale, are independent. It should be also noted that, to our knowledge, this is the first work where the pose information provides positive results with clinical data, because the pose was useless in a longitudinal study of autism (Styner et al., 2006
; Gorczowski et al., 2010
) and only normal subjects were considered in our previous work (Bossa and Olmos, 2006
The application of the methodology was performed in order to illustrate the usefulness of the pose information compared to the volume information in a particular case. To our knowledge, this is the first study considering the whole set of pose parameters of the subcortical nuclei as a potential MRI marker of AD. Although the focus of the paper was devoted to the methodological aspects rather than extracting of clinical useful knowledge from the analyzed data, some interesting results were obtained which deserve discussion.
Regarding the group analysis, it can be seen from that the pattern of significant pose differences was different at each group comparison. At the earliest stage of the disease, represented here by the NOR–MCIs comparison, statistical differences were found only for the scale parameter of bilateral hippocampi and thalami. When comparing NOR–MCIc groups, in addition to the previous differences, an important asymmetry was found in the left hemisphere because all subcortical nuclei showed statistically significant translations. It is interesting to note that this left-hemisphere asymmetry was also recently reported in Cherbuin et al. (2010)
. At the latest stage, when comparing NOR–AD patients, a larger number of subcortical structures showed significant differences in the scale parameter, but also interestingly, translations and rotations were significant in both hemispheres. These pose differences were nicely illustrated in , showing that while some subcortical structures show pose differences along the complete time-course of the disease, such as the hippocampus with an atrophic behavior or caudate nuclei with translations, other structures only experience pose differences at specific stages. Even though pose differences in the MCIs–MCIc comparison were not statistically significant after the correction for multiple comparisons in this dataset, noticeable pose differences can be observed in several subcortical structures in , in some cases almost as large as the ones in the NOR–AD comparison.
On the other hand, confirms that the volume of all subcortical structures were smaller in the pathological than in the NOR group, confirming that neurodegeneration is linked to atrophy of subcortical structures. The magnitude of the atrophy increases along the neurodegenerative process, especially of the hippocampi, with cross-sectional atrophy values ranging from 8 to 16%, which are in agreement with the atrophy values reported in the literature (Apostolova and Thompson, 2008
). In contrast, caudate nuclei did not show significant volume differences at any disease stage, while presenting significant translation in the left hemisphere for the NOR– MCIc comparison and translations and rotations in both hemispheres for the NOR–AD comparison.
Brain morphometry techniques with better spatial resolution, such as tensor-based morphometry (Bossa et al., 2010
; Hua et al., 2008
) have shown significant patterns of local atrophy affecting several cortical and subcortical structures. These anatomical changes may be the origin of the observed significant translation and rotation differences of structures such as the hippocampi, in addition to the volume differences. Similarly, significant differences in the translation of structures such as the caudate nuclei, do not experience significant atrophy.
Regarding the classification analysis, a very recent study (Cuingnet et al., in press) compared 10 different methods using the ADNI database (150 subjects for training and 150 for testing). The methods included the assessment of cortical thickness, voxel-based methods, and hippocampus-based approaches. The highest accuracy score for the NOR–AD classification was achieved by whole-brain methods, up to 0.81 sensitivity and 0.95 specificity. The hippocampus-based strategies obtained a similar sensitivity but a lower specificity (between 0.63 for volume based methods and 0.84 for shape based methods). In the case of NOR–MCIc, the sensitivity was substantially lower. In this work, the average accuracy for the NOR–AD classification was equal to 0.78 for the pose parameters, and 0.80 when gender, age and genotype information are considered. The assessment of accuracy was performed in Cuingnet et al. (in press) and in this work with independent training and testing datasets. While Cuingnet et al. (in press) used only a single random allocation of subjects with 50% for training and testing, 100 random allocations with 65% training were used here.
Several limitations of this study can be mentioned. Firstly, as the segmentation of the subcortical nuclei is the starting point, the segmentation errors will have an important influence in the results. Secondly, the current work only looked across individuals at a single snapshot of the evolving process. A longitudinal analysis of the pose changes would be much more convenient in order to get more accurate information about the time-course of the disease. Future studies will be devoted to assess statistical differences between temporal pose changes between different patient groups. Finally, as the pose information is only a coarse descriptor of the anatomy and complementary to shape, better classification results may be obtained with a method with a joint pose + shape statistical analysis, following our preliminary work (Bossa and Olmos, 2007