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Monitoring time-dependence with diffusion MRI yields observables sensitive tocompartment sizes (restricted diffusion) and membrane permeability (waterexchange). However, restricted diffusion and exchange have opposite effects onthe diffusion-weighted signal, which can confound parameter estimates. In thiswork, we present a signal representation that captures the effects of bothrestricted diffusion and exchange up to second order in b-value and iscompatible with gradient waveforms of arbitrary shape. The representationfeatures mappings from a gradient waveform to two scalars that separatelycontrol the sensitivity to restriction and exchange. We demonstrate that thesescalars span a two-dimensional space that can be used to choose waveforms thatselectively probe restricted diffusion or exchange, in order to eliminate thecorrelation between the two phenomena. We found that waveforms with specificbut unconventional shapes provide an advantage over conventional pulsed andoscillating gradient acquisitions. We also show that parametrisation ofwaveforms into a two-dimensional space can be used to understand protocols fromother approaches that probe restricted diffusion and exchange. For example, wefind that the variation of mixing time in filter-exchange imaging correspondsto variation of our exchange-weighting scalar at a fixed value of therestriction-weighting scalar. Numerical evaluation of the proposed signalrepresentation using Monte Carlo simulations on a synthetic substrate showedthat the theory is applicable to sizes in the range 2 - 7 micrometres andbarrier-limited exchange in the range 0 - 20 s$^{-1}$. The presented theoryconstitutes a simple and intuitive description of how restricted diffusion andexchange influence the signal as well as how to design a protocol to separatethe two effects.

Probing restricted diffusion and exchange using free gradient waveforms: validation by numerical simulations