Disentangling the Effects of Restriction and Exchange With Diffusion Exchange Spectroscopy

Abstract

Diffusion exchange spectroscopy (DEXSY) is a multidimensional NMR technique that can reveal how water molecules exchange between compartments within heterogeneous media, such as biological tissue. Data from DEXSY experiments is typically processed using numerical inverse Laplace transforms (ILTs) to produce a diffusion-diffusion spectrum. A tacit assumption of this ILT approach is that the signal behavior is Gaussian—i.e., the spin echo intensity decays exponentially with the degree of diffusion weighting. The assumptions that underlie Gaussian signal behavior may be violated, however, depending on the gradient strength applied and the sample under study. We argue that non-Gaussian signal behavior due to restrictions is to be expected in the study of biological tissue using diffusion NMR. Further, we argue that this signal behavior can produce confounding features in the diffusion-diffusion spectra obtained from numerical ILTs of DEXSY data—entangling the effects of restriction and exchange. Specifically, restricted signal behavior can result in broadening of peaks and in the appearance of illusory exchanging compartments with distributed diffusivities, which pearl into multiple peaks if not highly regularized. We demonstrate these effects on simulated data. That said, we suggest the use of features in the signal acquisition domain that can be used to rapidly probe exchange without employing an ILT. We also propose a means to characterize the non-Gaussian signal behavior due to restrictions within a sample using DEXSY measurements with a near zero mixing time or storage interval. We propose a combined acquisition scheme to independently characterize restriction and exchange with various DEXSY measurements, which we term Restriction and Exchange from Equally-weighted Double and Single Diffusion Encodings (REEDS-DE). We test this method on ex vivo neonatal mouse spinal cord—a sample consisting primarily of gray matter—using a low-field, static gradient NMR system. In sum, we highlight critical shortcomings of prevailing DEXSY analysis methods that conflate the effects of restriction and exchange, and suggest a viable experimental approach to disentangle them.

The interplay between exchange and microscopic kurtosis as measured by diffusion MRI with double diffusion encoding: Theory and simulations

“…Recent work has also shown sensitivity also to blood-brain-barrier exchange 69,73,74 . Other studies have applied diffusion-exchange spectroscopy (DEXSY) to measure relatively high exchange rates in the ex-vivo mouse brain 75,76 . A new class of models based on a combination of the standard model and the Ka rger model has been recently developed and applied to map exchange in the rat brain using SDE with variable diffusion times 77,78 .…”

Water exchange rates measure active transport and homeostasis in neural tissue

“…Prior to our finding on ex vivo fixed spinal cords (41), there were no reliable measurements of transcy-tolemmal exchange rates this fast in biological systems. Perhaps this is because low-field, high-gradient DEXSY is the first method capable of reliably measuring diffusive exchange in and out of water pools restricted on length scales smaller than a micron (33). Large membrane surface-to-volume (SV) ratios, in combination with high levels of active exchange, leads to the high turnover rates.…”

“…A promising alternative MR method for measuring active water exchange is Diffusion Exchange SpectroscopY (DEXSY) (30). DEXSY is a multidimensional MR method (31) that combines two diffusion encoding times separated by a mixing time which can be varied independently to isolate and measure exchange unaffected by restriction (32, 33), over-coming limitations of one-dimensional diffusion measurements. DEXSY and variants of DEXSY have been used to non-invasively measure water exchange rates using only the endogenous tissue water as a reporter, without requiring the introduction of exogenous contrast agents, making this methodology amenable to translational MR imaging applications without the attendant disadvantages of DCE (32–42).…”

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

“…Nonetheless, according to the dichotomous view above, the non-Gaussian signal can be lumped into some effective decay with 𝜌 2 , irrespective of the actual distribution of ℓ 𝑠 and the mixture of motionally-averaged and localized signal that may arise as a result. The ensemble signal can be approximated as a Gaussian signal fraction decaying with 𝜌 6 and a non-Gaussian fraction decaying with 𝜌 2 , as suggested by Cai et al [81], and which is similar in principle to the combined hindered and restricted (CHARMED) model [82]. Ignoring exchange for the time being, we can write the following quasi-biexponential model:…”