A large deformation diffeomorphic metric mapping solution for diffusion spectrum imaging datasets.

Spatial transformation for diffusion spectrum imaging (DSI) is an important step for group analyses of DSI datasets. In this study, we developed a transformation method for DSI datasets under the framework of large deformation diffeomorphic metric mapping (LDDMM), which is termed LDDMM-DSI. The proposed method made use of the fact that a DSI dataset is 6D, and generalized the original 2D/3D LDDMM algorithm to the 6D case with some modifications made for the DSI datasets. In this manner, the conventional reorientation problem that arises from transforming diffusion-weighted datasets was avoided by making the DSI datasets capable of being freely deformed in the q-space. The algorithm treated the data-matching task as a variational problem under the LDDMM framework and sought optimal velocity fields from which the generated transformations were diffeomorphic and the transformation curve was a geodesic. The mathematical materials and numerical implementation are detailed in the paper, and experiments were performed to analyze the proposed method on real brain DSI datasets. The results showed that the method was capable of registering different DSI datasets in both global structural shapes and local diffusion profiles. In conclusion, the proposed method can facilitate group analyses of DSI datasets and the generation of a DSI template.