Cortical thickness computation by solving tetrahedron-based harmonic field

Cortical thickness computation in magnetic resonance imaging (MRI) is an important method to study the brain morphological changes induced by neurodegenerative diseases. This paper presents an algorithm of thickness measurement based on a volumetric Laplacian operator (VLO), which is able to capture accurately the geometric information of brain images. The proposed algorithm is a novel three-step method: 1) The rule of parity and the shrinkage strategy are combined to detect and fix the intersection error regions between the cortical surface meshes separated by FreeSurfer software and the tetrahedral mesh is constructed which reflects the original morphological features of the cerebral cortex, 2) VLO and finite element method are combined to compute the temperature distribution in the cerebral cortex under the Dirichlet boundary conditions, and 3) the thermal gradient line is determined based on the constructed local isothermal surfaces and linear geometric interpolation results. Combined with half-face data storage structure, the cortical thickness can be computed accurately and effectively from the length of each gradient line. With the obtained thickness, we set experiments to study the group differences among groups of Alzheimer's disease (AD, N = 110), mild cognitive impairment (MCI, N = 101) and healthy control people (CTL, N = 128) by statistical analysis. The results show that the q-value associated with the group differences is 0.0458 between AD and CTL, 0.0371 between MCI and CTL, and 0.0044 between AD and MCI. Practical tests demonstrate that the algorithm of thickness measurement has high efficiency and is generic to be applied to various biological structures that have internal and external surfaces.