Theoretical models of the diffusion weighted MR signal

Diffusion MRI plays a very important role in studying biological tissue structure and functioning both in health and disease. Proper interpretation of experimental data requires development of theoretical models that connect the diffusion MRI signal to salient features of tissue microstructure at the cellular level. In this review, we present some models (mostly, relevant to the brain) for describing diffusion attenuated MR signals. These range from the simplest approach, where the signal is described in terms of an apparent diffusion coefficient, to rather complicated models, where consideration is given to signals originating from extra- and intracellular spaces and where account is taken of the specific geometry and orientation distribution of cells. To better understand the characteristics of the diffusion attenuated MR signal arising from the complex structure of whole tissue, it is instructive to appreciate first the characteristics of the signal arising from simple single-cell-like structures. For this purpose, we also present here a theoretical analysis of models allowing exact analytical calculation of the MR signal, specifically, a single-compartment model with impermeable boundaries and a periodic structure of identical cells separated by permeable membranes. Such pure theoretical models give important insights into mechanisms contributing to the MR signal formation in the presence of diffusion. In this review we targeted both scientists just entering the MR field and more experienced MR researchers interested in applying diffusion methods to study biological tissues.