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Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte-Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the intrinsic kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as $\mu$MGE (MGE incorporating intrinsic kurtosis) that accounts for both effects, by exploiting the distinct signatures of exchange and intrinsic kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while intrinsic kurtosis arguably has a much faster dependence. We find that applying $\mu$MGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may allow estimation of the exchange rate as well as the isotropic, anisotropic, and intrinsic kurtosis.

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms that are selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of gradient waveforms with different sensitivities to restricted diffusion and exchange (150 samples), our results reveal unique time-dependence signatures in grey and white matter, where the former is characterised by both restricted diffusion and exchange and the latter predominantly exhibits restricted diffusion. Furthermore, we show that gradient waveforms with independently varying sensitivities to restricted diffusion and exchange can be used to map exchange in the human brain. We consistently find that exchange in grey matter is at least twice as fast as in white matter, across all subjects and all gradient strengths. The shortest exchange times observed in this study were in the cerebellar cortex (115 ms). We also assess the feasibility of future clinical applications of the method used in this work, where we find that the grey-white matter exchange contrast obtained with a 25-minute 300 mT/m protocol is preserved by a 4-minute 300 mT/m and a 10-minute 80 mT/m protocol. Our work underlines the utility of free waveforms for detecting time-dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

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., Comment: 31 pages, 8 figures, 1 table, Submitted to NMR in Biomedicine

Diffusion weighted imaging techniques permit us to infer microstructural detail in biological tissue in vivo and noninvasively. Modern sequences are based on advanced diffusion encoding schemes, allowing probing of more revealing measures of tissue microstructure than the standard apparent diffusion coefficient or fractional anisotropy. Though these methods may result in faster or more revealing acquisitions, they generally demand prior knowledge of sequence-specific parameters for which there is no accepted sharing standard. Here, we present a metadata labelling scheme suitable for the needs of developers and users within the diffusion neuroimaging community alike: a lightweight, unambiguous parametric map relaying acqusition parameters. This extensible scheme supports a wide spectrum of diffusion encoding methods, from single diffusion encoding to highly complex sequences involving arbitrary gradient waveforms. Built under the brain imaging data structure (BIDS), it allows storage of advanced diffusion MRI data comprehensively alongside any other neuroimaging information, facilitating processing pipelines and multimodal analyses. We illustrate the usefulness of this BIDS-extension with a range of example data, and discuss the extension's impact on pre- and post-processing software.

Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is that it unlocks the "shape of the b-tensor" as a new encoding dimension. By modulating the b-tensor shape, we can control the sensitivity to microscopic diffusion anisotropy which can be used as a contrast mechanism; a feature that is inaccessible by conventional diffusion encoding. Since imaging methods based on tensor-valued diffusion encoding are finding an increasing number of applications we are prompted to highlight the challenge of designing the optimal gradient waveforms for any given application. In this review, we first establish the basic design objectives in creating field gradient waveforms for tensor-valued diffusion MRI. We also survey additional design considerations related to limitations imposed by hardware and physiology, potential confounding effects that cannot be captured by the b-tensor, and artifacts related to the diffusion encoding waveform. Throughout, we discuss the expected compromises and tradeoffs with an aim to establish a more complete understanding of gradient waveform design and its impact on accurate measurements and interpretations of data., Comment: Invited review, submitted in May 2020 to the Journal of Neuroscience Methods. 46 pages, 9 figures, 35 equations

We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the K\"arger model, and a modified K\"arger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The K\"arger model and the modified K\"arger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.

Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modelling axons as straight cylinders. Axons do not, however, run in straight trajectories and so far, the impact of the axonal trajectory on diameter estimation has not been systematically investigated. Here, we employ a toy-model of axons, which we refer to as undulating thin-fiber model, to analyze the impact of undulating trajectories on the diffusion-time dependence represented by the diffusion spectrum. We analyze the spectrum by its height (diffusivity at high frequencies), width (half width at half maximum), and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin-fibers is the main parameter that determines the characteristics of the diffusion spectra. Straight cylinders and undulating thin-fibers have virtually identical spectra at lower frequencies. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and the microscopic orientation dispersion. At high frequencies (short diffusion times), spectra from cylinders and undulating thin-fibers differ. The spectra from the undulating thin-fibers can also differ from that of cylinders by exhibiting power law behaviors with exponents below two. In conclusion, we argue that the non-straight nature of axonal trajectories should not be ignored when analyzing dMRI data and that careful experiments may enable separation of diffusion within straight cylinders and diffusion in undulating thin-fibers.

Purpose: Asymmetric gradient waveforms are attractive for diffusion encoding due to their superior efficiency, however, the asymmetry may cause a residual gradient moment at the end of the encoding. Depending on the experiment setup, this residual moment may cause significant signal bias and image artifacts. The purpose of this study was to develop an asymmetric gradient waveform design for tensor-valued diffusion encoding that is not affected by concomitant gradient. Methods: The Maxwell index was proposed as a scalar invariant that captures the effect of concomitant gradients and was constrained in the numerical optimization to 100 (mT/m)$^2$ms to yield Maxwell-compensated waveforms. The efficacy of this design was tested in an oil phantom, and in a healthy human brain. For reference, waveforms from literature were included in the analysis. Simulations were performed to investigate if the design was valid for a wide range of experiments and if it could predict the signal bias. Results: Maxwell-compensated waveforms showed no signal bias in oil or in the brain. By contrast, several waveforms from literature showed gross signal bias. In the brain, the bias was large enough to markedly affect both signal and parameter maps, and the bias could be accurately predicted by theory. Conclusion: Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient tensor-valued encoding with concomitant gradients that have a negligible effect on the signal. This waveform design is especially relevant in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition and large/oblique FOVs.

Purpose: To evaluate the feasibility of a 3-minute b-tensor encoding protocol for diffusion MRI-based assessment of the microscopic anisotropy and tissue heterogeneity in a wide range of intracranial tumors. Methods: B-tensor encoding was performed in 42 patients with intracranial tumors (gliomas, meningiomas, adenomas, metastases). Microscopic anisotropy and tissue heterogeneity were evaluated by estimating the anisotropic kurtosis ($MK_A$) and isotropic kurtosis ($MK_I$), respectively. An extensive imaging protocol was compared with a faster 3-minute protocol. Results: The fast imaging protocol yielded parameters with characteristics in terms of bias and precision similar to the full protocol. Glioblastomas had lower microscopic anisotropy than meningiomas $(MK_A = 0.29 \pm 0.06$ versus $0.45\pm0.08, p = 0.003)$. Metastases had higher tissue heterogeneity $(MK_I = 0.57\pm0.07)$ than both the glioblastomas $(0.44\pm0.06, p < 0.001)$ and meningiomas $(0.46\pm0.06, p = 0.03)$. Conclusion: Evaluation of the microscopic anisotropy and tissue heterogeneity in intracranial tumor patients is feasible in clinically relevant times frames., Comment: Submitted to Magnetic Resonance in Medicine

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced ($\sim$5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/$\mu$m$^2$, increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.

Diffusion magnetic resonance imaging (diffusion MRI) is a non-invasive microstructure assessment technique. Scalar measures, such as FA (fractional anisotropy) and MD (mean diffusivity), quantifying micro-structural tissue properties can be obtained using diffusion models and data processing pipelines. However, it is costly and time consuming to collect high quality diffusion data. Here, we therefore demonstrate how Generative Adversarial Networks (GANs) can be used to generate synthetic diffusion scalar measures from structural T1-weighted images in a single optimized step. Specifically, we train the popular CycleGAN model to learn to map a T1 image to FA or MD, and vice versa. As an application, we show that synthetic FA images can be used as a target for non-linear registration, to correct for geometric distortions common in diffusion MRI.

In vivo mapping of the neurite density with diffusion MRI (dMRI) is a high but challenging aim. First, it is unknown whether all neurites exhibit completely anisotropic ('stick-like') diffusion. Second, the 'density' of tissue components may be confounded by non-diffusion properties such as T2 relaxation. Third, the domain of validity for the estimated parameters to serve as indices of neurite density is incompletely explored. We investigated these challenges by acquiring data with 'b-tensor encoding' and multiple echo times in both healthy brain and white matter lesions. Results showed that microscopic anisotropy from b-tensor data is associated with myelinated axons but not with dendrites. Furthermore, b-tensor and multi-echo data showed that unbiased density estimates in white matter lesions require data-driven estimates of compartment-specific T2 times. Finally, the 'stick' fractions of different biophysical models could generally not serve as neurite density indices across the healthy brain and white matter lesions, where outcomes of comparisons depended on the choice of constraints. In particular, constraining compartment-specific T2 times was ambiguous in the healthy brain and had a large impact on estimated values. In summary, estimating neurite density may require accounting for different diffusion and/or T2 properties between axons and dendrites. Constrained 'index' parameters could be valid within limited domains that should be delineated by future studies., Comment: 48 pages including 5 figures and supplementary material

Purpose: To assess the technical feasibility of whole-brain diffusional variance decomposition (DIVIDE) based on q-space trajectory encoding (QTE) at clinical MRI systems with varying performance. DIVIDE is used to separate diffusional heterogeneity into components that arise due to isotropic and anisotropic tissue structures. Methods: We designed imaging protocols for DIVIDE using numerically optimized gradient waveforms for diffusion encoding. Imaging was performed at systems with magnetic field strengths between 1.5 and 7 T, and gradient amplitudes between 33 and 80 mT/m. Technical feasibility was assessed from signal characteristics and quality of parameter maps in a single volunteer scanned at all systems. Results: The technical feasibility of QTE and DIVIDE was demonstrated at all systems. The system with the highest performance allowed whole-brain DIVIDE at 2 mm isotropic voxels. The system with the lowest performance required a spatial resolution of 2.5x2.5x4 mm3 to yield a sufficient signal-to-noise ratio. Conclusions: Whole-brain DIVIDE based on QTE is feasible at the investigated MRI systems. This demonstration indicates that tissue features beyond those accessible by conventional diffusion encoding may be explored on a wide range of MRI systems., Comment: 13 pages, 7 figures

A large number of mathematical models have been proposed to describe the measured signal in diffusion-weighted (DW) magnetic resonance imaging (MRI) and infer properties about the white matter microstructure. However, a head-to-head comparison of DW-MRI models is critically missing in the field. To address this deficiency, we organized the "White Matter Modeling Challenge" during the International Symposium on Biomedical Imaging (ISBI) 2015 conference. This competition aimed at identifying the DW-MRI models that best predict unseen DW data. in vivo DW-MRI data was acquired on the Connectom scanner at the A.A.Martinos Center (Massachusetts General Hospital) using gradients strength of up to 300 mT/m and a broad set of diffusion times. We focused on assessing the DW signal prediction in two regions: the genu in the corpus callosum, where the fibres are relatively straight and parallel, and the fornix, where the configuration of fibres is more complex. The challenge participants had access to three-quarters of the whole dataset, and their models were ranked on their ability to predict the remaining unseen quarter of data. In this paper we provide both an overview and a more in-depth description of each evaluated model, report the challenge results, and infer trends about the model characteristics that were associated with high model ranking. This work provides a much needed benchmark for DW-MRI models. The acquired data and model details for signal prediction evaluation are provided online to encourage a larger scale assessment of diffusion models in the future.