Introduction to diffusion tensor imaging mathematics: Part II. Anisotropy, diffusion-weighting factors, and gradient encoding schemes

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 II, different formulas for measuring diffusion anisotropy are compared in two and three dimensions. The use of magnetic field gradients to measure diffusion is explained, including calculation of the diffusion-weighting b factor. Selection of gradient directions is discussed, with the focus on directions defined by the regular polyhedra (Platonic solids). (C) 2006 Wiley Periodicals, Inc.