Introduction to diffusion tensor imaging mathematics: Part III. Tensor calculation, noise, simulations, and optimization

Abstract 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. Part III begins with a comparison of different ways to calculate the tensor from diffusion‐weighted imaging data. Next, the effects of noise on signal intensities and diffusion tensor measurements are discussed. In MRI signal intensities as well as DTI parameters, noise can introduce a bias (systematic deviation) as well as scatter (random deviation) in the data. Propagation‐of‐error formulas are explained with examples. Step‐by‐step procedures for simulating diffusion tensor measurements are presented. Finally, methods for selecting the optimal b factor and number of b = 0 images for measuring several properties of the diffusion tensor, including the trace (or mean diffusivity) and anisotropy, are presented. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 155–179, 2006