Thickness profile generation for the corpus callosum using Laplace's equation

Abstract

The corpus callosum facilitates communication between the cerebral hemispheres. Morphological abnormalities of the corpus callosum have been identified in numerous psychiatric and neurological disorders. To quantitatively analyze the thickness profile of the corpus callosum, we adapted an automatic thickness measurement method, which was originally used on magnetic resonance (MR) images of the cerebral cortex (Hutton et al. [2008]: NeuroImage 40:1701-10; Jones et al. [2002]: Hum Brain Mapp 11:12-32; Schmitt and Böhme [2002]: NeuroImage 16:1103-9; Yezzi and Prince [2003]: IEEE Trans Med Imaging 22:1332-9), to MR images of the corpus callosum. The thickness model was derived by computing a solution to Laplace's equation evaluated on callosal voxels. The streamlines from this solution form non-overlapping, cross-sectional contours the lengths of which are modeled as the callosal thickness. Apart from the semi-automated segmentation and endpoint selection procedures, the method is fully automated, robust, and reproducible. We compared the Laplace method with the orthogonal projection technique previously published (Walterfang et al. [2009a]: Psych Res Neuroimaging 173:77-82; Walterfang et al. [2008a]: Br J Psychiatry 192:429-34; Walterfang et al. [2008b]: Schizophr Res 103:1-10) on a cohort of 296 subjects, composed of 86 patients with chronic schizophrenia (CSZ), 110 individuals with first-episode psychosis, 100 individuals at ultra-high risk for psychosis (UHR; 27 of whom later developed psychosis, UHR-P, and 73 who did not, UHR-NP), and 55 control subjects (CTL). We report similar patterns of statistically significant differences in regional callosal thickness with respect to the comparisons CSZ vs. CTL, UHR vs. CTL, UHR-P vs. UHR-NP, and UHR vs. CTL.

Corpus callosum thickness on mid-sagittal MRI as a marker of brain volume: a pilot study in children with HIV-related brain disease and controls

“…A number of recent papers describe methods for semi-automated and fully automated measurement of corpus callosum thickness on MRI. Most notable are those by Adamson in 2011 [40] and Herron in 2012 [41]. Herron describes a variety of techniques that are either semi-automated, which like our method require manual outlining of the corpus callosum , or fully automated including the boundary-based and rule-based approaches.…”

Impact of Early and Late Visual Deprivation on the Structure of the Corpus Callosum: A Study Combining Thickness Profile with Surface Tensor-Based Morphometry

“…Compared with prior work on solving the Laplace’s equation (e.g. (Jones et al 2000; Adamson et al 2011)), this approach may overcome numerical inaccuracies issues caused by the limited resolution of the 3D grid in standard voxel-based thickness computations.…”

“…The right panel shows a zoomed-in result after a cut along the sagittal direction. Similar to prior work (Jones et al 2000; Adamson et al 2011), the streamlines are computed by tracing the normal directions to the surface level sets (as shown by the red lines in the zoom-in picture in Fig. 4 (d)).…”

“…4 (d)). Finally, the computed streamline lengths define the thickness profile on the callosal surface (Jones et al 2000; Adamson et al 2011). Fig.…”

“…Intuitively, thickness and mTBM are complementary, as thickness describes distances roughly along the surface’s normal direction, while mTBM detects surface dissimilarities, including differences in the surface metric tensor induced by the particular surface parameterization. So we hypothesize that the combination of thickness and mTBM will offer a complete set of surface statistics for callosal morphometry and that it may boost statistical power to detect the impacts of visual experience in the CC compared to 2D mid-sagittal analyses (Thompson et al 2003; Luders et al 2006; Luders et al 2010; Tepest et al 2010; Adamson et al 2011; Di Paola et al 2012; Herron et al 2012). …”