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The Bloch equation describes the evolution of classical particles tagged witha magnetisation vector in a strong magnetic field and is fundamental to manyNMR and MRI contrast methods. The equation can be generalised to include theeffects of spin motion by including a spin flux, which typically contains aFickian diffusive term and/or a coherent velocity term. This form is known asthe Bloch-Torrey equation, and is fundamental to MR modalities which aresensitive to spin dynamics such as diffusion MRI. Such modalities have receiveda great deal of interest in the research literature over the last few years,resulting in a huge range of models and methods.  In this work we make make use of a more general Bloch-Torrey equation with ageneralised flux term. We show that many commonly employed approaches inDiffusion MRI may be viewed as different choices for the flux terms in thisequation. This viewpoint, although obvious theoretically, is not usuallyemphasised in the diffusion MR literature and points to interesting newdirections for methods development.  In the interests of completeness, we describe all the necessary mathematicaland physical framework -- including the method used to solve the variousBloch-Torrey equations. We then review the relevant portions of the diffusionMRI literature and show how different flux choices lead to different models.All the models considered here are continuum-based but we also discuss theirrelationship to so-called microstructure methods and other more advanced ideassuch as time-dependent diffusivities.

Continuity, the Bloch-Torrey equation, and Diffusion MRI