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

TL;DR

This paper introduces a new signal representation for diffusion MRI that separates the effects of restricted diffusion and water exchange, enabling more precise parameter estimation through optimized gradient waveforms.

Contribution

The work presents a novel two-scalar representation of diffusion MRI signals that isolates restriction and exchange effects, guiding the design of waveforms to selectively probe each phenomenon.

Findings

Unconventional waveforms outperform traditional ones in sensitivity.

The two-scalar space helps interpret existing protocols.

Simulation confirms applicability for sizes 2-7 micrometres and exchange rates 0-20 s$^{-1}$.

Abstract

Monitoring time-dependence with diffusion MRI yields observables sensitive to compartment sizes (restricted diffusion) and membrane permeability (water exchange). However, restricted diffusion and exchange have opposite effects on the diffusion-weighted signal, which can confound parameter estimates. In this work, we present a signal representation that captures the effects of both restricted diffusion and exchange up to second order in b-value and is compatible with gradient waveforms of arbitrary shape. The representation features mappings from a gradient waveform to two scalars that separately control the sensitivity to restriction and exchange. We demonstrate that these scalars span a two-dimensional space that can be used to choose waveforms that selectively probe restricted diffusion or exchange, in order to eliminate the correlation between the two phenomena. We found that waveforms with specific but unconventional shapes provide an advantage over conventional pulsed and oscillating gradient acquisitions. We also show that parametrisation of waveforms into a two-dimensional space can be used to understand protocols from other approaches that probe restricted diffusion and exchange. For example, we find that the variation of mixing time in filter-exchange imaging corresponds to variation of our exchange-weighting scalar at a fixed value of the restriction-weighting scalar. Numerical evaluation of the proposed signal representation using Monte Carlo simulations on a synthetic substrate showed that the theory is applicable to sizes in the range 2 - 7 micrometres and barrier-limited exchange in the range 0 - 20 s$^{-1}$. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as how to design a protocol to separate the two effects.