An introduction to computational diffusion MRI: the diffusion tensor and beyond

This chapter gives an introduction to the principles of diffusion magnetic resonance imaging (MRI) with emphasis on the computational aspects. It introduces the philosophies underlying the technique and shows how to sensitize MRI measurements to the motion of particles within a sample material. The main body of the chapter is a technical review of diffusion MRI reconstruction algorithms, which determine features of the material microstructure from diffusion MRI measurements. The focus is on techniques developed for biomedical diffusion MRI, but most of the methods discussed are applicable beyond this domain. The review begins by showing how the standard reconstruction algorithms in biomedical diffusion MRI, diffusion-tensor MRI and diffusion spectrum imaging, arise from the principles of the measurement process. The discussion highlights the weaknesses of the standard approaches to motivate the development of a new generation of reconstruction algorithms and reviews the current state-of-the-art. The chapter concludes with a brief discussion of diffusion MRI applications, in particular fibre tracking, followed by a summary and a glimpse into the future of diffusion MRI acquisition and reconstruction.