Corpus callosum is the largest inter-hemispheric fiber bundle in the human brain [1, 2]. Most of the fibers interconnect homologue cortical areas in roughly mirror image sites but a large number of the fibers have heterotypic connections ending in asymmetrical areas . Previous studies have mainly investigated effects of various pathologies on the corpus callosum [4–7]. However, a fully automated, fast, and accurate method for segmenting corpus callosum without penetrating into irrelevant neighboring structures, using data acquired in routine clinical protocols, is still lacking.
Previously, image processing methods have been proposed for segmenting corpus callosum in anatomical magnetic resonance images (MRI) [8–10]. These methods rely on intensity information of two-dimensional images and their results may need pruning. Recently, attention has been oriented towards diffusion tensor imaging (DTI) to segment white matter tracts of the brain [11, 12]. Although the tensor model fails to describe higher order anisotropies in heterogeneous areas where more than one fiber population exists, it is practically useful for extracting major white matter tracts, particularly the ones with predominant diffusivity pattern such as corpus callosum. When using DTI data, the fiber bundles can be extracted by: a) clustering of fibers resulting from tractography into fiber bundles [13–19]; or b) segmenting fiber bundles via hyper-surface propagation based on local properties of diffusion tensor, diffusion signal, or orientation distribution function (ODF) [20–27]. Since clustering methods rely on the tractography results, they do not work properly if the tractography results are inaccurate. On the other hand, segmentation methods based on hyper-surface propagation do not use the tractography results and are thus more robust to noise.
In a region-based segmentation framework, a similarity measure between successive tensors is typically used. Some of the hyper-surface propagating methods in the literature concentrated on scalar quantities derived from the tensor data which do not reflect complete tensor information . Other methods benefit from the entire information contained in the DTI data [21–30]. Wang and Vemuri  proposed a statistical level-set segmentation method. However, the tensors derived in this framework are not necessarily positive semi-definite, leading to inappropriate results especially when consecutive tensors are much different. Metrics like Kullback-Leibler divergence and J-divergence [23, 24] have also been proposed. One of the most promising methods is introduced by Jonasson et al. . They defined a new similarity measure called normalized tensor scalar product (NTSP). Comparing NTSP with other similarity measures, they demonstrated superiority of their proposed measure. To segment brain structures like thalamic nuclei, they modified their framework to favor the propagation of multiple hyper surfaces without overlapping . Lenglet et al.  defined a dissimilarity measure and statistics between tensors based on the Riemannian distances. Although improving the segmentation results, this approach is computationally expensive. Defining a Log-Euclidean distance, another metric was defined by Arsigny et al.  which has lower computational burden. Weldeselassie and Hamarneh  used their proposed similarity measure in an energy minimization framework. Awate et al.  used the similarity measure in a Markov random field framework.
In terms of quantitative evaluation of diffusion parameters, previous studies have compared DTI-based indices in normal appearing white matter and corpus callosum in multiple sclerosis , stroke , schizophrenia , and Huntington's  and also studied the DTI methods to assess corpus callosum regions across the human lifespan . For segmenting corpus callosum and its subdivisions in these studies, however, two-dimensional (2D) methods were applied and DTI-based indices compared in the mid-sagittal plane. However, without recruiting a three dimensional (3D) method to segment the whole corpus callosum and its subdivisions, the extracted quantities may be inaccurate.
Since the tensor model is not capable of describing heterogeneous diffusion behavior in the crossing fiber bundles, some studies used High Angular Resolution Diffusion Imaging (HARDI) data to segment specific bundles [32–38]. However, the HARDI data is not widely acquired in clinical centers and hence, the tensor-based methods are still of more practical use in clinical research.
In this manuscript, we present a 3D method to segment corpus callosum. Based on tensor and anisotropy values of neighboring voxels, a similarity measure is proposed and used as a speed function in the proposed level-set method. In this method, the principal diffusion direction (PDD) and prior information about the diffusivity pattern in corpus callosum are used to avoid inclusion of neighboring fiber bundles. Then, the Witelson subdivisions of corpus callosum are automatically identified . The idea of using diffusivity pattern in corpus callosum has been used by Lee et al. . However, they performed a 2D segmentation on the mid-sagittal plane. Moreover, since their method uses the left-right component of PDD to delineate corpus callosum boundaries, it is not applicable in more lateral sagittal planes, where corpus callosum connects to minor and major forceps and considerable anterior-posterior component of PDD exists.
The proposed segmentation method can be identically used for segmenting corpus callosum of control subjects as well as patients with glioblastoma. However, since we use the geometric information of the diffusivity pattern in corpus callosum and the glioblastoma tumor may change the original shape and diffusivity pattern of corpus callosum, we validate the reproducibility of the proposed method through realistic simulations of corpus callosum rotations under glioblastoma tumor pressure. We study the effects of rotation by different Euler angles (azimuth, elevation and skew) quantitatively and demonstrate that even in extreme cases with large rotations, brain tumors do not have major effects on the segmentation results generated by our proposed method. We apply the method to the DTI data of normal subjects and brain cancer patients with glioblastoma and show its superiority to some of the previously published methods in the literature.