Exchange between structurally-disordered compartments

Which signatures of the diffusion signal are responsible for non-Gaussian diffusion inside cells or extra-cellular space, and which ones are the hallmark of the exchange between compartments? Answering this unresolved question is vital for mapping tissue microstructure in brain (especially in gray matter) and body. Here we employ the effective medium formalism to extend the multi-site exchange approach onto the case when diffusion in each tissue compartment is arbitrarily complex. We find the time-dependent diffusivity and kurtosis of a general system of exchanging non-Gaussian compartments for all times, validate with Monte Carlo simulations, and discuss practical implications.