1. Introduction. Vasileios Megalooikonomou James Gee

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1 Reducing the Computational Cost for Statistical Medical Image Analysis: An MRI Study on the Sexual Morphological Differentiation of the Corpus Callosum Despina Kontos Data Engineering Laboratory (DEnLab) Department of Computer and Information Sciences Temple University Philadelphia, USA Vasileios Megalooikonomou James Gee Data Engineering Department of Radiology Laboratory (DEnLab) University of Pennsylvania Department of Computer Philadelphia, USA and Information Sciences Temple University Philadelphia, USA Abstract We illustrate the application of intelligent medical image analysis techniques in order to reduce the computational cost of statistical voxel-wise analysis for detecting discriminative regions of morphological variability among different populations. We demonstrate that novel statistical image processing techniques that operate selectively on groups of pixels are suitable for morphological analysis of anatomical structures visualized by modern medical imaging modalities. We also show that the proposed methodology effectively decreases the number of statistical tests performed, alleviating the effect of the multiple comparison problem. We show that our approach detects regions of statistically significant morphological variability. Our results validate previous findings, while being robust across a wide range of experimental settings. 1. Introduction Visualizing human physiology with modern tomographic methods has offered valuable insight to understanding anatomy, function and the development of several diseases. Especially in the field of brain imaging [1], intelligent image analysis techniques [2] have broaden our understanding of how anatomical structures are associated to function [3]. Moreover, knowledge has been gained on how the cognitive process is generated [4] as well as the effects of development [5], pathology and aging [6]. A lot of research has also been conducted in identifying functional or anatomical differences between different populations, such as healthy individuals and patients [7, 8]. One of the most common approaches currently in use for this type of analysis with brain image data is Statistical Parametric Mapping (SPM) [9]. SPM can be applied to detect functional differences among groups of subjects by analyzing each voxel s changes independently of the others and building a corresponding map of statistical values. The significance of each voxel is ascertained statistically by means of Student s t-test, F-test, correlation coefficient, or other univariate statistical parametric tests. The multiple comparison problem, which occurs when computing a statistic for many pairwise tests (introducing significant computational overhead), is usually handled by estimating corrected p-values for clusters. Other voxel-wise approaches have also been employed in neuroimaging research in order to detect morphological variability among populations [10].

2 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 mid-sagittal section of the brain. It 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 the claim that the corpus callosum is critically engaged in the development of disorders such as schizophrenia [11] and Alzheimer s disease [12]. Research on the sexual dimorphism of the corpus callosum has also raised significant discussion during the past decades [13]. Being critical to interhemispheric communication, the corpus callosum has often been accounted for differences in cognition between males and females. Many investigators have seeked to identify variation on the overall size of the corpus callosum when examining male and female populations [14]. More recent studies have investigated local morphological sex-based differentiation using template deformation morphometry and voxel-based analysis [15-17]. In this paper, we demonstrate that novel statistical image processing techniques that operate selectively on groups of pixels are suitable for morphological analysis of anatomical structures visualized by modern medical imaging modalities. We illustrate that the proposed methods effectively reduce the computational cost (i.e. number of statistical tests) required for this type of analysis by the standard voxel-based approaches. The effect of the multiple comparison problem is also effectively reduced. We apply the proposed analysis framework on MRI images of the corpus callosum in order to detect morphological variation among healthy male and female subjects. We show that our approach detects regions of statistically significant morphological variability among the two populations. Our results validate previous findings, while being robust across a wide range of experimental settings. We also extract quantitative feature vectors that reflect the discriminative morphological variability and can be used for classification purposes. 2. Methods We illustrate a method that reduces the statistical tests performed by voxel-wise approaches and is effectively applicable for morphometric analysis of anatomical structures. The proposed approach reduces the computational cost of voxel-based morphological analysis and can be employed to detect discriminative morphological variations among groups of subjects. In this work, we apply the proposed approach in order to detect gender-based local shape differentiation in the corpus callosum of the human brain. Our groups of subjects 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 [17]. The MRI images were acquired on a 1.5T GE scanner (TR=35, TE=6, flip=35, slices= 1 x 1mm, FOV=24cm). Transaxial images were in planes parallel to the orbitomeatal line, with resolution of x mm2. We used template deformation morphometry (TDM) [15, 17] to compute the template deformation vector fields arising when spatially normalizing (registering) the 2D MRI images to a standard anatomical template for the corpus callosum. TDM has the advantage of providing information with respect to local morphological properties of anatomical structures, rather than overall shape characteristics. To further compensate for the overall size variation between female and male callosum, we applied a normalization with respect to the total crosssectional callosal area [17]. This allows the applied analysis to focus on local morphometric differentiation among the different populations, rather than differences attributed to overall callosum size variation and scaling. For applying the proposed statistical image analysis techniques, we utilized the Jacobian determinants of the transformation[17], computed from

3 the template deformation field vectors. Normalization (scaling) is also applied at each pixel to correct for global variability. These Jacobian determinants provide a quantitative measurement for the degree of expansion or contraction at each pixel [16]. For the morphological analysis, we modified 3D medical image analysis tools [8, 18] to be applicable on 2D MRI images. The main idea of our methodology is to adaptively partition the 2D image space into progressively smaller regions until areas are found that have highly significant morphological differentiation among the groups of subjects. The advantage of the proposed technique over voxel-based approaches is that the partitioning process is guided by statistical tests which are applied on selected groups of pixels, rather than on each individual pixel independently. This effectively reduces the number of statistical tests that are required by most of the voxel-based approaches for this type of morphometric analysis. More specifically, the entire image is initially treated as one hyper-rectangle. An adaptive quad-tree splitting of the 2D space into smaller hyper-rectangles is performed guided by statistical tests. We consider as a candidate attribute for every hyper-rectangle the median V J median of the corresponding Jacobian determinant matrix elements. A particular hyperrectangle is partitioned if the V J median does not have high discriminative power with respect to morphological differentiation among the different populations, since the Jacobian elements quantify the degree of expansion or shrinkage at each voxel. Considering the median of the Jacobian determinants for a group of voxels accounts for the morphological variability in the image regions formed by the corresponding pixels. Hence, the proposed approach operates in a coarse-to-fine grain basis, focusing on successively smaller discriminative local regions of morphological sex-based differentiation. The discriminative power of a hyper-rectangle is determined by applying a statistical test (chi-square/fisher's exact, t-test, Wilcoxon rank sum test) on the corresponding V J median attributes of the distinct groups of subjects (classes). A p- value threshold is assigned in order to define the desired level of discriminatory significance and guide the selectivity of the splitting. The procedure progresses recursively until all remaining hyper-rectangles are discriminative or a hyper-rectangle becomes so small that it cannot be further partitioned, given the resolution of the image. Figure 1 illustrates the main idea of the adaptive partitioning process. We utilize information from the detected highly discriminative regions in order to perform classification. We construct feature vectors by selecting as attributes the V J median measurements of the final discriminative hyper-rectangles. These discriminative hyperrectangles can be of various sizes. We employ these feature vectors as inputs to linear or quadratic Bayes Normal classifiers in order to evaluate class label assignment based on the indicated regions of morphological variability. Classification in this type of analysis can be used to validate the significance of the detected discriminative regions. In several cases such as the specific study of possible sex-based dimorphism in the corpus callosum, the differentiation might not be so deterministic in order to suffice for effective classification. p-value > 0.05 Split! p-value > 0.05 Split! Discriminatory significance threshold: p-value<0.05 p-value > 0.05 Split! p-value 0.05 Discriminative Region! Figure 1. The main idea of our proposed approach for adaptive partitioning of the space guided by statistical tests, the detection of discriminative hyper-rectangles and the extraction of discriminative features to perform classification.

4 3. Results We applied the proposed technique on the 2D MRI groups of male and female subjects, using t-test, ranksum test and kolmogorov-smirnoff test to ascertain statistical divergence. We experimented with p-value threshold of 0.01 and the most commonly used p-value threshold of The detected regions of morphological differentiation among the female and male subjects were consistent with findings from other studies [15-17]. Significant morphological shape differentiation was detected in the posterior corpus callosum region also known as the splenium. This specific region was identified as significant in all the different experimental settings (i.e., combination of statistical test and p-value threshold). Besides the splenium, structural variability was also identified for specific experimental settings in parts of the isthmus and the anterior corpus callosum. Figure 2.a shows discriminative regions of morphological dimorphism that were identified by our proposed approach, overlaid on the anatomical template. Darker regions correspond to higher discriminatory significance. We compare these findings with the ones obtained when applying voxel-wise statistical analysis on the same dataset using t-test, ranksum test and kolmogorov-smirnoff test to access pixel significance. Our approach significantly reduced the number of statistical tests performed compared to voxel-wise analysis by more than 50% for all experimental settings. Table 1 shows the number of statistical tests performed by our approach compared to voxelwise analysis. Figure 2.b illustrates the corresponding regions identified by voxel-wise analysis for the same experimental settings. As shown in the figures, our approach is able to detect regions comparable to those of voxel-wise analysis, while reducing the number of required statistical tests by more than 50%. Also, the proposed methodology is less prone to outliers since it operates on groups of pixels. We used the V J median attributes extracted from the morphologically discriminative regions to train linear and quadratic Bayes Normal classifiers. We experimented with training set sizes ranging from 55% to 65% of the available data. The classification performance reached up to 60%-65% accuracy. These classification results comply with previous attempts to classify corpus callosum data based on attributes extracted from sexually dimorphic regions [16]. They also validate the general belief that despite being able to detect regions of genderbased morphologic variability in the corpus callosum, the differentiation is not that prevalent in order to rely on these regions for sex classification. Table 1. Comparison of the number of statistical tests performed by the proposed methodology and voxel-wise analysis. Method DRP Voxel wise analysis Experimental Settings Statistical test P-Value Threshold Statistical tests performed t-test ranksum k-s test correlation 0.05/ t-test 0.05/ ranksum 0.05/

5 (a) (b) Figure 2. Areas of discriminative sexual morphological differentiation indicated by applying (a) the proposed approach and (b) the voxel-wise statistical analysis with ranksum-test (p-value threshold 0.05). 4. Conclusions We demonstrated the applicability of intelligent statistical medical image processing techniques to the analysis of deformation fields obtained from 2D MRI images. The proposed methodology effectively reduces the number of statistical tests performed alleviating the effect of the multiple comparison problem. This particular advantage makes the proposed analysis framework very suitable for processing large amounts of medical images. Our technique also eliminates the clustering step required by the second analysis level of SPM, by automatically extracting quantitative features from regions of morphological variability among different populations. Moreover, by operating on groups of voxels and considering the entire image space through the adaptive partitioning process, our method has the ability to detect spatially diffused and subtle morphometric variations. Standard voxel-based approaches have been criticized in the literature as being highly localized and linear in nature [19], which can produce misleading results in cases with limited number of subjects. We applied our approach on 2D MRI midsagittal slices of the corpus callosum seeking to identify regions of morphological differentiation between female and male subjects. The analysis was performed on the Jacobian determinants of the template deformation fields. We detected gender-based local morphological variability in the corpus callosum. The number of statistical tests was effectively reduced by more than 50% while the indicated discriminative regions were consistent with other studies. Acknowledgements This work was supported in part by NIH Research Grant #1 R01 MH funded by NIMH, NINDS and NIA, and by NSF Research Grant IIS and Infrastructure Grant ANI The funding agencies specifically disclaim responsibility for any analyses, interpretations and conclusions. References [1] S. H. Koslow and M. F. Huerta, "Neuroinformatics: An Overview of the Human Brain Project." Mahway, NJ: Erlbaum, [2] V. Megalooikonomou, J. Ford, L. Shen, F. Makedon, and A. Saykin, "Data mining in brain imaging," Statistical Methods in Medical Research, vol. 9, pp , [3] S. I. Letovsky, S. H. Whitehead, C. H. Paik, G. A. Miller, J. Gerber, E. H. Herskovits, T. K. Fulton, and R. N. Bryan, "A brain image database for structure-function analysis," American Journal of Neuroradiology, vol. 19, pp , [4] M. Grossman, P. Koenig, C. DeVita, G. Glosser, D. Alsop, J. Detre, and J. Gee, "Neural representation of verb meaning: an fmri study," Humman Brain Mapping, vol. 15, pp , 2002.

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