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.

Figure 1

Laplace equation thickness model (A) and orthogonal projection method thickness model (B) shown on an idealized corpus callosum. The 39 sampled streamlines in (A) and (B) are colored according to callosal thickness and are annotated with their indices, which were chosen to increase caudally. (A) (Inset) Magnification of the streamlines (not colored according to callosal thickness), constructed from a denser sampling of the midline, near the splenium. A comparison of the node locations and resultant regional thickness profiles of the two methods are shown in (C) and (D), respectively.

Figure 2

(A) Idealized callosum with the contours colored according to the number of callosi, as a percentage, in the dataset in which that contour intersected with at least one other contour. (B) Graphical representation of (A) with the non‐intersecting nodes, across the entire dataset, omitted.

Figure 3

Four selected callosi with overlapping streamlines produced by the orthogonal projection method. In each figure, the top panel shows the streamlines produced by the orthogonal projection method, whereas the lower panel shows the streamlines produced by the Laplace equation method.

Figure 4

Mean thickness and variance values for the Laplace and Orthogonal projection thickness measurement methods for the CTL group. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 5

Comparison of statistical analysis results using the orthogonal projection callosal thickness measure (first row) and the Laplace method callosal thickness measure (second row). The columns of the figure denote the CSZ vs. CTL (A), FEP vs. CTL (B), and the UHR‐P vs. UHR‐NP (C) contrasts.