Constant gradient FEXSY: A time-efficient method for measuring exchange

Compartmental anisotropy of filtered exchange imaging (FEXI) in human white matter: What is happening in FEXI?

PURPOSE

To investigate the effects of compartmental anisotropy on filtered exchange imaging (FEXI) in white matter (WM).

THEORY AND METHODS

FEXI signals were measured using multiple combinations of diffusion filter and detection directions in five healthy volunteers. Additional filters, including a trace-weighted diffusion filter with trapezoidal gradients, a spherical b-tensor encoded diffusion filter, and a T2 filter, were tested with trace-weighted diffusion detection.

RESULTS

A large range of apparent exchange rates (AXR) and both positive and negative filter efficiencies (σ) were found depending on the mutual orientation of the filter and detection gradients relative to WM fiber orientation. The data demonstrated that the fast-diffusion compartment suppressed by diffusional filtering is not exclusively extra-cellular, but also intra-cellular. While not comprehensive, a simple two-compartment diffusion tensor model with water exchange was able to account qualitatively for the trends in positive and negative filtering efficiencies, while standard model imaging (SMI) without exchange could not. This two-compartment diffusion tensor model also demonstrated smaller AXR variances across subjects. When employing trace-weighted diffusion detection, AXR values were on the order of the R1 (=1/T1) of water at 3T for crossing fibers, while being less than R1 for parallel fibers.

CONCLUSION

Orientation-dependent AXR and σ values were observed when using multi-orientation filter and detection gradients in FEXI, indicating that WM FEXI models need to account for compartmental anisotropy. When using trace-weighted detection, AXR values were on the order of or less than R1, complicating the interpretation of FEXI results in WM in terms of biological exchange properties. These findings may contribute toward better understanding of FEXI results in WM.

Tuned exchange imaging: Can the filter exchange imaging pulse sequence be adapted for applications with thin slices and restricted diffusion?

Filter exchange imaging (FEXI) is a double diffusion-encoding (DDE) sequence that is specifically sensitive to exchange between sites with different apparent diffusivities. FEXI uses a diffusion-encoding filtering block followed by a detection block at varying mixing times to map the exchange rate. Long mixing times enhance the sensitivity to exchange, but they pose challenges for imaging applications that require a stimulated echo sequence with crusher gradients. Thin imaging slices require strong crushers, which can introduce significant diffusion weighting and bias exchange rate estimates. Here, we treat the crushers as an additional encoding block and consider FEXI as a triple diffusion-encoding sequence. This allows the bias to be corrected in the case of multi-Gaussian diffusion, but not easily in the presence of restricted diffusion. Our approach addresses challenges in the presence of restricted diffusion and relies on the ability to independently gauge sensitivities to exchange and restricted diffusion for arbitrary gradient waveforms. It follows two principles: (i) the effects of crushers are included in the forward model using signal cumulant expansion; and (ii) timing parameters of diffusion gradients in filter and detection blocks are adjusted to maintain the same level of restriction encoding regardless of the mixing time. This results in the tuned exchange imaging (TEXI) protocol. The accuracy of exchange mapping with TEXI was assessed through Monte Carlo simulations in spheres of identical sizes and gamma-distributed sizes, and in parallel hexagonally packed cylinders. The simulations demonstrate that TEXI provides consistent exchange rates regardless of slice thickness and restriction size, even with strong crushers. However, the accuracy depends on b-values, mixing times, and restriction geometry. The constraints and limitations of TEXI are discussed, including suggestions for protocol adaptations. Further studies are needed to optimize the precision of TEXI and assess the approach experimentally in realistic, heterogeneous substrates.

Measuring water exchange on a preclinical MRI system using filter exchange and diffusion time dependent kurtosis imaging

PURPOSE

Filter exchange imaging (FEXI) and diffusion time (t)-dependent diffusion kurtosis imaging (DKI(t)) are both sensitive to water exchange between tissue compartments. The restrictive effects of tissue microstructure, however, introduce bias to the exchange rate obtained by these two methods, as their interpretation conventionally rely on the Kärger model of barrier limited exchange between Gaussian compartments. Here, we investigated whether FEXI and DKI(t) can provide comparable exchange rates in ex vivo mouse brains.

THEORY AND METHODS

FEXI and DKI(t) data were acquired from ex vivo mouse brains on a preclinical MRI system. Phase cycling and negative slice prewinder gradients were used to minimize the interferences from imaging gradients.

RESULTS

In the corpus callosum, apparent exchange rate (AXR) from FEXI correlated with the exchange rate (the inverse of exchange time, 1/τex ) from DKI(t) along the radial direction. In comparison, discrepancies between FEXI and DKI(t) were found in the cortex due to low filter efficiency and confounding effects from tissue microstructure.

CONCLUSION

The results suggest that FEXI and DKI(t) are sensitive to the same exchange processes in white matter when separated from restrictive effects of microstructure. The complex microstructure in gray matter, with potential exchange among multiple compartments and confounding effects of microstructure, still pose a challenge for FEXI and DKI(t).

Diffusion NMR for Measuring Dynamic Ligand Exchange on Colloidal Nanocrystals

Ligand exchange is fundamentally related to the surface chemistry of nanoparticles in solution and is also an essential procedure for their synthesis and solution processing. The solution of ligand-bearing nanoparticles can be regarded as a dynamic equilibrium of bound and free ligands depending on the concentration and temperature. The direct experimental calibration of the ligand exchange dynamics relies on the in situ and real-time quantification of bound and free ligands. However, existing analytical strategies are often with limited applicability considering the requirement of special functional groups or the indirect detection of photoluminescence or reaction heat. In this work, we explore diffusion-based methods of solution-state nuclear magnetic resonance (NMR) as a general strategy to probe ligand exchange. Using comprehensive numerical simulations, we show that diffusion NMR with designable time sequences can effectively distinguish bound and free ligands and measure the exchange rate constants from 0.5 to 200 s^-1 under typical instrumental settings. These methods are demonstrated experimentally on colloidal CdSe nanocrystal systems with carboxylate or amine ligands whose exchange rates were previously undetectable. The kinetic rate constants, activation energies, and thermodynamic parameters of ligand exchange have been obtained under variable temperature conditions. We expect the diffusion NMR strategies to be generally applicable for calibrating the exchange of organic ligands on various nanoparticle systems.

Disentangling the effects of restriction and exchange with diffusion exchange spectroscopy

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.

Apparent exchange rate imaging: On its applicability and the connection to the real exchange rate

PURPOSE

Water exchange between the intracellular and extracellular space can be measured using apparent exchange rate (AXR) imaging. The aim of this study was to investigate the relationship between the measured AXR and the geometry of diffusion restrictions, membrane permeability, and the real exchange rate, as well as to explore the applicability of AXR for typical human measurement settings.

METHODS

The AXR measurements and the underlying exchange rates were simulated using the Monte Carlo method with different geometries, size distributions, packing densities, and a broad range of membrane permeabilities. Furthermore, the influence of SNR and sequence parameters was analyzed.

RESULTS

The estimated AXR values correspond to the simulated values and show the expected proportionality to membrane permeability, except for fast exchange (ie, AXR > 20 - 30 s - 1 ) and small packing densities. Moreover, it was found that the duration of the filter gradient must be shorter than 2 · AX R - 1 . In cell size and permeability distributions, AXR depends on the average surface-to-volume ratio, permeability, and the packing density. Finally, AXR can be reliably determined in the presence of orientation dispersion in axon-like structures with sufficient gradient sampling (ie, 30 gradient directions).

CONCLUSION

Currently used experimental settings for in vivo human measurements are well suited for determining AXR, with the exception of single-voxel analysis, due to limited SNR. The detection of changes in membrane permeability in diseased tissue is nonetheless challenging because of the AXR dependence on further factors, such as packing density and geometry, which cannot be disentangled without further knowledge of the underlying cell structure.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

Real-time measurement of diffusion exchange rate in biological tissue

Diffusion exchange spectroscopy (DEXSY) provides a means to isolate the signal attenuation associated with exchange from other sources of signal loss. With the total diffusion weighting b₁+b₂=b_s held constant, DEXSY signals acquired with b₁=0 or b₂=0 have no exchange weighting, while a DEXSY signal acquired with b₁=b₂ has maximal exchange weighting. The exchange rate can be estimated by fitting a diffusion exchange model to signals acquired with variable mixing times. Conventionally, acquired signals are normalized by a signal with b₁=0 and b₂=0 to remove the decay due to spin-lattice relaxation. Instead, division by a signal with equal b_s but b₁=0 or b₂=0 reduces spin-lattice relaxation weighting of the apparent exchange rate (AXR). Furthermore, apparent diffusion-weighted R₁ relaxation rates can be estimated from non-exchange-weighted DEXSY signals. Estimated R₁ values are utilized to remove signal decay due to spin-lattice relaxation from exchange-weighted signals, permitting a more precise estimate of AXR with less data. Data reduction methods are proposed and tested with regards to statistical accuracy and precision of AXR estimates on simulated and experimental data. Simulations show that the methods are capable of accurately measuring the ground-truth exchange rate. The methods remain accurate even when the assumption that DEXSY signals attenuate with b is violated, as occurs for restricted diffusion. Experimental data was collected from fixed neonatal mouse spinal cord samples at 25 and 7°C using the strong static magnetic field gradient produced by a single-sided permanent magnet (i.e., an NMR MOUSE). The most rapid method for exchange measurements requires only five data points (an 80 s experiment as implemented) and achieves a similar level of accuracy and precision to the baseline method using 44 data points. This represents a significant improvement in acquisition speed, overcoming a barrier which has limited the use of DEXSY on living specimen.