  The importance of studying the brain microstructure is described and the
existing and state of the art non-invasive methods for the investigation of the
brain microstructure using Diffusion Weighted Magnetic Resonance Imaging (DWI)
is studied. In the next step, Cramer-Rao Lower Bound (CRLB) analysis is
described and utilised for assessment of the minimum estimation error and
uncertainty level of different Diffusion Weighted Magnetic Resonance (DWMR)
signal decay models. The analyses are performed considering the best scenario
through which, we assume that the models are the appropriate representation of
the measured phenomena. This includes the study of the sensitivity of the
estimations to the measurement and model parameters. It is demonstrated that
none of the existing models can achieve a reasonable minimum uncertainty level
under typical measurement setup. At the end, the practical obstacles for
achieving higher performance in clinical and experimental environments are
studied and their effects on feasibility of the methods are discussed.
