Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Abstract

Effects of diffusion on the magnetic resonance (MR) signal carry a wealth of information regarding the microstructure of the medium. Characterizing such effects is immensely important for quantitative studies aiming to obtain microstructural parameters using diffusionMR acquisitions. Studies in recent years have demonstrated the potential of sophisticated gradient waveforms to provide novel information inaccessible by traditional measurements. There are mainly two approaches that can be used to incorporate the influence of restricted diffusion, particularly on experiments featuring general gradient waveforms. The multiple propagator framework essentially reduces the problem to a path integral, which can be evaluated analytically or approximated via a matrix representation. The multiple correlation function method tackles the Bloch–Torrey equation, and employs an alternative matrix formulation. In this work, we present the two techniques in a unified fashion and link the two approaches. We provide an explanation for why the multiple correlation function is computationally more efficient in the case of waveforms featuring piecewise constant gradients.