  Heterogeneous diffusion processes occur in many different fields such as
transport in living cells or diffusion in porous media. A characterization of
the transport parameters of such processes can be achieved by ensemble-based
methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or
by trajectory-based methods obtained from single-particle tracking (SPT)
experiments. In this paper, we study the general relationship between both
methods and its application to heterogeneous systems. We derive analytical
expressions for the distribution of diffusivities from SPT and further relate
it to NMR spin-echo diffusion attenuation functions. To exemplify the
applicability of this approach, we employ a well-established two-region
exchange model, which has widely been used in the context of PFG NMR studies of
multiphase systems subjected to interphase molecular exchange processes. This
type of systems, which can also describe a layered liquid with layer-dependent
self-diffusion coefficients, has also recently gained attention in SPT
experiments. We reformulate the results of the two-region exchange model in
terms of SPT-observables and compare its predictions to that obtained using the
exact transformation which we derived.
