Background and mathematical analysis of diffusion MRI methods

Abstract

The addition of a pair of magnetic field gradient pulses had initially enabled the measurement of spin motion to nuclear magnetic resonance (NMR) experiments. In the adaptation of diffusion weighted (DW)-NMR techniques to magnetic resonance imaging (MRI), the taxonomy of mathematical models is divided in two categories: model matching and spectral methods. In this review, the methods are summarized starting from early DW NMR models followed up with their adaptation to DW MRI. Finally, a newly introduced Fourier analysis based unifying theory, so-called Complete Fourier Direct MRI, is included to explain the mechanisms of existing methods. (c) 2012 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 22, 4452, 2012