Diffusion MRI with pulsed and free gradient waveforms: Effects of restricted diffusion and exchange

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 lead to errors in parameter estimates. In this work, we propose a signal representation that incorporates 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, eliminating 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 parametrization 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 found 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. The proposed signal representation was evaluated using Monte Carlo simulations in identical parallel cylinders with hexagonal and random packing as well as parallel cylinders with gamma‐distributed radii. Results showed that the approach is sensitive to sizes in the interval 4–12 μm and exchange rates in the simulated range of 0 to 20 s−1, but also that there is a sensitivity to the extracellular geometry. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as a guide to protocol design capable of separating the two effects.

Diffusional kurtosis time dependence and the water exchange rate for the multi‐compartment Kärger model

“…References 10, 11 used oscillating gradient spin echo sequences rather than conventional pulsed gradient spin echo sequences to acquire diffusion data for the shortest two diffusion times (1.9 ms and 3.8 ms for Reference 1, 10, and 1.8 ms and 3.6 ms for Reference 11). As discussed by Chakwizira et al 23 this difference could affect the sensitivity to water exchange. While data points for these short diffusion times do appear in some of the figures in this paper, they are not part of our quantitative analysis.…”

Cardiac q‐space trajectory imaging by motion‐compensated tensor‐valued diffusion encoding in human heart in vivo

“…Furthermore, we observed that MD increased, and FA decreased, with mean frequency of the power spectrum of q ( t ), demonstrating clear diffusion time effects in contrast to the in vivo data. This difference may appear due to the longer diffusion times used at the clinical scanner (a consequence of the relatively low gradient system performance in human MRI systems) and may be indicative of a higher permeability in myocardium compared with the plastic used in the phantom 64,65 . Here, we were limited by the size of the phantom; therefore, a preclinical scanner with high gradient performance was used.…”

“…This difference may appear due to the longer diffusion times used at the clinical scanner (a consequence of the relatively low gradient system performance in human MRI systems) and may be indicative of a higher permeability in myocardium compared with the plastic used in the phantom. 64 , 65 Here, we were limited by the size of the phantom; therefore, a preclinical scanner with high gradient performance was used. Further development of more sophisticated phantoms, coupled with evaluation on clinical scanners, will add further insight.…”

Ultra-strong diffusion-weighted MRI reveals cerebellar grey matter abnormalities in movement disorders

“…( Olesen et al, 2022 ) As a consequence, we expect the values of to be lower than expected from histology and protocol dependent, as different gradient waveforms have different sensitivity to exchange, as well as there being potential bias due to microscopic GM kurtosis. ( Chakwizira et al, 2023 , Novello et al, 2022 ) The former point also indicates that a change in can be interpreted either as a change in its corresponding volume fraction or a change in the membrane permeability of the related cell population. The coarse spatial resolution was adopted to maintain acceptable signal-to-noise ratio (SNR) in the diffusion-weighted data, and despite the highly curved structure of the cerebellar GM, partial volume mixture with CSF and WM was minimised by the use of cerebellar segmentation, free-water elimination, and high b-value STE.…”