Diffusion phase-imaging in anisotropic media using non-linear gradients for diffusion encoding

Diffusion MRI classically uses gradient fields that vary linearly in space to encode the diffusion of water molecules in the signal magnitude by tempering its intensity. In spin ensembles, a presumably equal number of particles move in positive and negative direction, resulting in approximately zero change in net phase. Hence, in classical diffusion weighted MRI with a linear gradient field, the phase does not carry any information as the incoherent motion of the spins only impacts the magnitude of the signal. Conversely, when the linear gradient field is replaced with one that varies quadratically over space, the diffusion of water molecules in anisotropic media does give rise to a change in net phase and preserves large portion of the signal around the saddle point of the gradient field. In this work, the phase evolution of anisotropic fibre phantoms in the presence of quadratic gradient fields was studied in Monte Carlo simulations and diffusion MRI experiments. The simulations confirm the dependence of the phase change on the degree of anisotropy of the media and the diffusion weighting, as predicted by the derived analytic model. First MR experiments show a phase change depending on the diffusion time in an anisotropic synthetic fibre phantom, and approximately zero phase change for the experiment repeated in an isotropic agar phantom. As predicted by the analytic model, an increase of the diffusion time by approximately a factor of two leads to an increase of approximately a factor of two in the signal phase.