Morphometric analysis of brain images with reduced number of statistical tests: A study on the gender-related differentiation of the corpus callosum
Introduction
Visualizing human physiology with modern imaging technologies has offered valuable insight into understanding anatomy, function and the development of several diseases. Considering in particular the advances in brain imaging [1], great progress has been achieved during the recent years in understanding how anatomical structures are associated to function [2], [3] and how the cognitive process is generated [4]. Fascinating insight has been gained by interpreting the process of development [5], and identifying the effects of pathology and aging [6]. To date, most of the research in brain imaging has been based on computerized analysis of brain imaging modalities [2], such as magnetic resonance imaging (MRI), functional magnetic resonance imaging (fMRI), and diffusion tensor imaging (DTI). The goal of many studies has been to identify anatomical or functional differences between different populations, such as healthy individuals and patients [7], [8].
Statistical parametric mapping (SPM) analysis is one of the most common approaches that has been used for brain image analysis [8], [9], [10], [11], [12]. SPM analysis can be performed to detect differences between images of separate groups of subjects by analyzing each pixel's changes independently and building a corresponding map of statistical values. To ascertain the discriminatory significance of each pixel, a statistical test such as the t-test, rank-sum test, or the F-test is applied. A P-value is obtained for each pixel that indicates how likely it is that the pixel's variability across classes is observed by chance. Clustering is often employed in the process to construct highly informative regions with respect to classification.
One of the drawbacks of SPM analysis is that pixel-wise analysis usually requires a large number of statistical tests to be performed. The increased number of statistical tests increases the probability that certain tests will appear positive simply due to chance (i.e., type-I error); this effect is usually referred to as the multiple comparison problem. Consider, for example, a 256 × 190 two-dimensional (2D) MRI image acquired with approximately 0.9 × 0.9 mm2 pixel resolution: with a standard 0.01 type-I error, the required 48,640 pixel-wise statistical tests could result to approximately 486 false positives; depending on the spatial distribution of these falsely detected pixels, the spatial extent of the effect could be considerable.
Several approaches have been proposed in the literature for controlling the false-positive rate [13]. Perhaps the most commonly used approach is the Bonferroni correction [14], which is a rather conservative procedure: the nominal significance level α is replaced with the level α/n for each test, where n is equal to the total number of statistical tests performed; it can be shown that the Bonferroni correction has strong control of type-I error. In practice, when applied to brain image analysis, Bonferroni correction tends to eliminate several true positives along with the false positives. For this reason heuristic modifications such as the sequential Bonferroni correction have been proposed [15]. Clustering is usually applied to detect and discard outlier pixels when constructing discriminative regions. In addition to the multiple comparison problem, pixel-wise statistics appear to be significantly biased toward distribution differences that are highly localized in space [16].
SPM analysis has been used in combination with template deformation morphometry (TDM) for quantifying structural variations in anatomical structures of the human brain. In TDM, registration of a template brain image is performed to match each individual subject in the dataset [17], [18], [19]; pixel-wise information is extracted about the degree of expansion or contraction of each pixel during the registration process. Essentially, each image is mapped to a deformation vector field, which can be quantified to a scalar measurement by computing the corresponding Jacobians in the template space. By applying pixel-wise statistics on the Jacobians, an SPM can be generated and a significance threshold can be applied to detect discriminative morphometric variations.
One of the structures in the human brain that has attracted a lot of research in the past decades is the corpus callosum. The corpus callosum can be easily identified as a white matter structure in the midsagittal section of the brain [20]. It is a structure that facilitates primarily the communication between the two cerebral hemispheres of the human brain, being of critical importance when interpreting the neurological process of cognitive tasks. Studies have supported that the corpus callosum is critically engaged in the development of disorders such as schizophrenia [21] and Alzheimer's disease [22]. Research on the gender-based dimorphism of the corpus callosum has also raised significant discussion during the past decades [23]; being critical to interhemispheric communication, the corpus callosum has often been accounted for differences in cognition between males and females. Many investigators have sought to identify variation on the overall size of the corpus callosum when examining male and female populations [24]. More recent studies have investigated local morphological gender-related differentiation using TDM and pixel-based analysis [18], [25], [26].
In this article we evaluate the feasibility of applying dynamic recursive partitioning (DRP), an image analysis technique suitable for detecting discriminative image regions between groups of subjects, to perform morphometric analysis. The main idea of DRP is to partition the image adaptively into progressively smaller subregions until statistically significant discriminative regions are detected. The partitioning process is guided by statistical tests that are applied to groups of pixels rather than to individual pixels; for this reason the number of statistical tests is effectively reduced compared to SPM analysis. Depending on the required degree of control for type-I error, P-value correction methods can also be incorporated to further restrict the effect of the multiple comparison problem.
The algorithmic outline of DRP was initially introduced and evaluated primarily with synthetic and realistic images [27], [28]. Preliminary evaluation of DRP with functional brain images showed its potential to be used effectively for medical image analysis; DRP was able to reduce the number of statistical tests by two orders of magnitude compared to pixel-wise statistics, while also improving classification accuracy by 15% [8], [27]. Here, we evaluate the feasibility of DRP for anatomical imaging, and particularly for performing morphometric analysis. Morphometry introduces different challenges than functional imaging. While patterns of functional activity are usually analyzed within the entire image region in functional imaging, in morphometry, template deformation statistics are usually computed from well-defined anatomical structures as a necessary first level of analysis; DRP can then be applied as a postprocessing second level of analysis. A preliminary report on this study was previously presented by Kontos et al. [29].
Section snippets
Data and preprocessing
Our dataset included 2D MRI midsagittal slices acquired from 93 healthy female and 93 healthy male right-handed individuals. The images were obtained from the Schizophrenia Center database of the University of Pennsylvania [26]. The MRI images were acquired on a 1.5 T GE scanner (TR = 35, TE = 6, flip = 35, slices = 1 × 1 mm, FOV = 24 cm). Transaxial images were in planes parallel to the orbitomeatal line, with resolution of 0.9375 × 0.9375 mm2. A k-means clustering algorithm which groups image voxels into k
Results
We applied DPR to the Jacobian determinants computed from the template deformation fields of the male and female callosum images. Due to the nature of our dataset, it was reasonable to assume that the two populations (i.e., male and female images) are most likely to have been generated by normal distributions with equal within class variance; under this assumption, the unpaired t-test could safely be applied. To validate this assumption, we examined the cross-subject pixel-wise value
Discussion
The results demonstrate that DRP could potentially provide an alternative viable technique for morphometric analysis of anatomical brain structures, particularly when the reduction of statistical tests is a desirable parameter in the application at hand. A potential concern for the applicability of DRP is the rectangular shape of the regions on which the adaptive partitioning process operates. However, the rectangular shape of the DRP regions is not as restrictive as one could suspect. For
Conclusions
We evaluated the feasibility of applying DRP for detecting discriminative morphometric characteristics between anatomical brain structures of different groups of subjects. In DRP, the image is adaptively partitioned into progressively smaller subregions, until regions of significant morphological differentiation are detected. The partitioning process is guided by statistical tests applied on groups of pixels, resulting in significant reduction of statistical tests, compared to the commonly used
Acknowledgments
This work was supported in part by NIH Research Grant #1 R01 MH68066-04 funded by NIMH, NINDS and NIA, and by NSF Research Grant IIS-0237921 and Infrastructure Grant ANI-0124390. The funding agencies specifically disclaim responsibility for any analyses, interpretations and conclusions. The authors would also like to thank the anonymous reviewers for their very constructive comments and suggestions.
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