Post-mortem and neuroimaging studies suggest that there is evidence of neuroanatomical abnormalities of the cerebral cortex in neurodegenerative diseases and psychiatric disorders. Thus methods for measuring the cortical structure in living human beings, including cortical shape, volume, cortical area, and thickness, are needed directly from MRI images.

We study the cortical thickness for some cortical submanifolds, such as cingulate, planum temporale, and central sulcus, by labeled cortical mantle distance mapping (LCMDM). LCMDM generates a profile of gray matter occurrence as a function of normal distance to the coritcal surface indexed locally over the gray/white cortical surface. The continuous smooth representation of cortical thickness is reconstructed by the orthonormal bases of the Laplace-Beltrami operator with Neumann boundary conditions. Shown in the figure above are examples of the orthonormal basis on the central sulcus manifold. The top row shows the first orthonormal basis function on the 3D central sulcus manifold. The two bottom rows illustrate the first four orthonormal bases on the flattened map of the central sulcus for visualization purposes.

Shown below is the representation of cortical thickness using the LCMDM of the central sulcus. The bottom left panel depicts the original LCMDM on the flattened manifold for visualization purposes. The bottom right panel depicts smoothed versions of these profiles generated in the orthonormal basis of the Laplace-Beltrami operator using the first four basis functions. As denoted via the color bars, dark color means thin, and light means thick; the valley of the central sulcus is the thinnest part with thickness increasing toward the border.