Unifying Transverse Relaxation and Diffusion: An Effective Medium Approach

Dmitry S. Novikov¹, Valerij G. Kiselev²

MR signal is massively volume-averaged. Which parameters of tissue microstructure can survive this averaging, and be quantified by MRI? An answer is given by the effective medium description of tissues yielding the voxel-averaged equation for the magnetization. Heterogeneous diffusivity, relaxation rate and Larmor frequency offset give rise to corrections to the magnetization dynamics. The quantifiable tissue parameters are the distinct length scales on which the local diffusivity, relaxation rate and Larmor frequency vary. The effective medium approach unifies diffusion and relaxation, focussing on the single quantity whose frequency and wavevector dependence contains all measurable information about tissue heterogeneity.