Surface-Based Vector Analysis Using Heat Equation Interpolation: A New Approach to Quantify Local Hippocampal Volume Changes

Analysis of surface-based displacement vectors using spherical harmonic description (SPHARM) localizes shape changes accurately. However, it does not allow differentiating volume variations from shifting and/or bending. We propose a new approach to quantify local volume changes by computing the surface-based Jacobian determinant. This measurement is computed on the displacement vector fields estimated by a heat equation interpolation on the displacement vectors produced by SPHARM. Data simulation showed that the surface-based Jacobian determinant enables accurate quantification of local volume changes without interference of shifting/bending. In patients with temporal lobe epilepsy and left hippocampal atrophy, SPHARM detected widespread inward deformation related to atrophy in the hippocampal head and body, and showed areas of mirrored inward/outward deformations mostly at the level of the hippocampal tail. In these areas, the surface-based Jacobian determinant showed atrophy. Our method facilitates the interpretation of SPHARM because it allows decomposing volume changes and shifting/bending. Furthermore, it provides a better delineation of the extent of hippocampal atrophy.