Abstract: A transformation method for diffusion spectrum imaging includes: receiving an original DSI dataset and a template DSI dataset; computing an energy function; computing, for each time point, first-order and second-order derivatives of the energy function with respect to velocity fields in an image space and in a q-space; computing, for each time point, the velocity fields in the image space and in the q-space based upon the first-order and second-order derivatives; performing integration on the velocity fields over time to obtain a deformation field; and generating a transformed DSI dataset according to the deformation field.

Abstract: A voxel-based transformation method includes: a) obtaining a MRI dataset in a subject space associated with subject voxel coordinates, subject sampling directions, and subject voxel spin amounts, and a dataset of a co-registration template associated with template voxel coordinates, each subject voxel coordinate corresponding to a template voxel coordinate according to a mapping function; b) through an inverse of the mapping function, obtaining subject voxel coordinates and a Jacobian matrix; and c) obtaining template voxel spin amounts, each being a function of a template sampling direction and a template voxel coordinate, using the Jacobian matrix and image data.

Abstract: A transformation method for diffusion spectrum imaging includes: receiving an original DSI dataset and a template DSI dataset; computing an energy function; computing, for each time point, first-order and second-order derivatives of the energy function with respect to velocity fields in an image space and in a q-space; computing, for each time point, the velocity fields in the image space and in the q-space based upon the first-order and second-order derivatives; performing integration on the velocity fields over time to obtain a deformation field; and generating a transformed DSI dataset according to the deformation field.

Abstract: A method is adapted for providing microstructural information of a biological target from a plurality of diffusion weighted MR images corresponding to a specific area of the biological target. Each of the diffusion weighted MR images is obtained using a respective q-space sampling vector and is sampled at a plurality of sample points thereof to obtain a group of diffusion weighted MR image data. The diffusion weighted MR image data are processed to obtain a spin distribution function from which the microstructural information of the biological target can be obtained.

Abstract: A voxel-based transformation method includes: a) obtaining a MRI dataset in a subject space associated with subject voxel coordinates, subject sampling directions, and subject voxel spin amounts, and a dataset of a co-registration template associated with template voxel coordinates, each subject voxel coordinate corresponding to a template voxel coordinate according to a mapping function; b) through an inverse of the mapping function, obtaining subject voxel coordinates and a Jacobian matrix; and c) obtaining template voxel spin amounts, each being a function of a template sampling direction and a template voxel coordinate, using the Jacobian matrix and image data.

Abstract: A method of analyzing a diffusion-weighted magnetic resonance image is adapted to analyze an orientation distribution function ?0 of nerve fibers at a vector in space. The method includes the following steps: (A) finding an orientation {circumflex over (?)}a with the largest probability in the ODF ?0; (B) maximizing a single fiber ODF ??; (C) analyzing the maximized single fiber ODF ?? to obtain quantitative information; (D) deducting the maximized single fiber ODF ?? obtained in step (B) from the entire ODF ?0; and (E) stopping computation if the result obtained in step (D) is determined to be smaller than a predetermined value, and repeating steps (A), (B), (C), and (D) if otherwise.

Abstract: A method is adapted for providing microstructural information of a biological target from a plurality of diffusion weighted MR images corresponding to a specific area of the biological target. Each of the diffusion weighted MR images is obtained using a respective q-space sampling vector and is sampled at a plurality of sample points thereof to obtain a group of diffusion weighted MR image data. The diffusion weighted MR image data are processed to obtain a spin distribution function from which the microstructural information of the biological target can be obtained.

Abstract: A method of analyzing a diffusion-weighted magnetic resonance image is adapted to analyze an orientation distribution function ?0 of nerve fibers at a vector in space. The method includes the following steps: (A) finding an orientation {circumflex over (?)}a with the largest probability in the ODF ?0; (B) maximizing a single fiber ODF ??; (C) analyzing the maximized single fiber ODF ?? to obtain quantitative information; (D) deducting the maximized single fiber ODF ?? obtained in step (B) from the entire ODF ?0; and (E) stopping computation if the result obtained in step (D) is determined to be smaller than a predetermined value, and repeating steps (A), (B), (C), and (D) if otherwise.