Introduction to Diffusion Tensor Imaging Mathematics: Part I. Tensors, Rotations, and Eigenvectors
نویسنده
چکیده
The mathematical aspects of diffusion tensor magnetic resonance imaging (DTMRI, or DTI), the measurement of the diffusion tensor by magnetic resonance imaging (MRI), are discussed in this three-part series. In part I, some general features of diffusion imaging are presented briefly, including the relationship between the diffusion ellipsoid and the diffusion tensor. Rotations of vectors and tensors are explained for both two and three dimensions. Rotationally invariant properties of the diffusion tensor are discussed. Calculation of the eigenvectors and eigenvalues of the diffusion tensor, which correspond to the directions of the diffusion ellipsoid axes and the squares of the hemiaxis lengths, is explained. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 101–122, 2006
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