Double Diffusion Encoding Research Articles

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.

Compensation of concomitant field effects in double diffusion encoding by means of added oscillating gradients

Maxwell or concomitant fields imprint additional phases on the transverse magnetization. This concomitant phase may cause severe image artifacts like signal voids or distort the quantitative parameters due to the induced intravoxel dephasing. In particular, double diffusion encoding (DDE) schemes with two pairs of bipolar diffusion-weighting gradients separated by a refocusing radiofrequency (RF) pulse are prone to concomitant field-induced artifacts. In this work, a method for reducing concomitant field effects in these DDE sequences based on additional oscillating gradients is presented. These oscillating gradient pulses obtained by constrained optimization were added to the original gradient waveforms. The modified sequences reduced the accumulated concomitant phase without significant changes in the original sequence characteristics. The proposed method was applied to a DDE acquisition scheme consisting of 60 pairs of diffusion wave vectors. For phantom as well as for in vivo experiments, a considerable increase in the signal-to-noise ratio (SNR) was obtained. For phantom measurements with a diffusion weighting of b = 2000 s/mm2 for each of the gradient pairs, an SNR increase of up to 40% was observed for a transversal slice that had a distance of 5 cm from the isocenter. For equivalent slice parameters, in vivo measurements in the brain of a healthy volunteer exhibited an increase in SNR of up to 35% for b = 750 s/mm2 for each weighting. These findings are supported by corresponding simulations, which also predict a positive effect on the SNR. In summary, the presented method leads to an SNR gain without additional RF refocusing pulses.

On the sampling strategies and models for measuring diffusion exchange with a double diffusion encoding sequence

Water exchange between the different compartments of a heterogeneous specimen can be characterized via diffusion magnetic resonance imaging (dMRI). Many analysis frameworks using dMRI data have been proposed to describe exchange, often using a double diffusion encoding (DDE) stimulated echo sequence. Techniques such as diffusion exchange weighted imaging (DEWI) and the filter exchange and rapid exchange models, use a specific subset of the full space DDE signal. In this work, a general representation of the DDE signal was employed with different sampling schemes (namely constant b1, diagonal and anti-diagonal) from the data reduction models to estimate exchange. A near-uniform sampling scheme was proposed and compared with the other sampling schemes. The filter exchange and rapid exchange models were also applied to estimate exchange with their own subsampling schemes. These subsampling schemes and models were compared on both simulated data and experimental data acquired with a benchtop MR scanner. In synthetic data, the diagonal and near-uniform sampling schemes performed the best due to the consistency of their estimates with the ground truth. In experimental data, the shifted diagonal and near-uniform sampling schemes outperformed the others, yielding the most consistent estimates with the full space estimation. The results suggest the feasibility of measuring exchange using a general representation of the DDE signal along with variable sampling schemes. In future studies, algorithms could be further developed for the optimization of sampling schemes, as well as incorporating additional properties, such as geometry and diffusion anisotropy, into exchange frameworks.

Microscopic Fractional Anisotropy Detects Cognitive Training-Induced Microstructural Brain Changes.

Cognitive training-induced neuroplastic brain changes have been reported. This prospective study evaluated whether microscopic fractional anisotropy (μFA) derived from double diffusion encoding (DDE) MRI could detect brain changes following a 4 week cognitive training. Twenty-nine healthy volunteers were recruited and randomly assigned into the training (n = 21) and control (n = 8) groups. Both groups underwent brain MRI including DDE MRI and 3D-T1-weighted imaging twice at an interval of 4–6 weeks, during which the former underwent the training. The training consisted of hour-long dual N-back and attention network tasks conducted five days per week. Training and time-related changes of DDE MRI indices (μFA, fractional anisotropy (FA), and mean diffusivity (MD)) and the gray and white matter volume were evaluated using mixed-design analysis of variance. In addition, any significant imaging indices were tested for correlation with cognitive training-induced task performance changes, using partial correlation analyses. μFA in the left middle frontal gyrus decreased upon the training (53 voxels, uncorrected p < 0.001), which correlated moderately with response time changes in the orienting component of attention (r = −0.521, uncorrected p = 0.032). No significant training and time-related changes were observed for other imaging indices. Thus, μFA can become a sensitive index to detect cognitive training-induced neuroplastic changes.

Correlation Tensor MRI deciphers underlying kurtosis sources in stroke

Noninvasively detecting and characterizing modulations in cellular scale micro-architecture remains a desideratum for contemporary neuroimaging. Diffusion MRI (dMRI) has become the mainstay methodology for probing microstructure, and, in ischemia, its contrasts have revolutionized stroke management. Diffusion kurtosis imaging (DKI) has been shown to significantly enhance the sensitivity of stroke detection compared to its diffusion tensor imaging (DTI) counterparts. However, the interpretation of DKI remains ambiguous as its contrast may arise from competing kurtosis sources related to the anisotropy of tissue components, diffusivity variance across components, and microscopic kurtosis (e.g., arising from cross-sectional variance, structural disorder, and restriction). Resolving these sources may be fundamental for developing more specific imaging techniques for stroke management, prognosis, and understanding its pathophysiology. In this study, we apply Correlation Tensor MRI (CTI) – a double diffusion encoding (DDE) methodology recently introduced for deciphering kurtosis sources based on the unique information captured in DDE's diffusion correlation tensors – to investigate the underpinnings of kurtosis measurements in acute ischemic lesions. Simulations for the different kurtosis sources revealed specific signatures for cross-sectional variance (representing neurite beading), edema, and cell swelling. Ex vivo CTI experiments at 16.4 T were then performed in an experimental photothrombotic stroke model 3 h post-stroke (N = 10), and successfully separated anisotropic, isotropic, and microscopic non-Gaussian diffusion sources in the ischemic lesions. Each of these kurtosis sources provided unique contrasts in the stroked area. Particularly, microscopic kurtosis was shown to be a primary “driver” of total kurtosis upon ischemia; its large increases, coupled with decreases in anisotropic kurtosis, are consistent with the expected elevation in cross-sectional variance, likely linked to beading effects in small objects such as neurites. In vivo experiments at 9.4 T at the same time point (3 h post ischemia, N = 5) demonstrated the stability and relevance of the findings and showed that fixation is not a dominant confounder in our findings. In future studies, the different CTI contrasts may be useful to address current limitations of stroke imaging, e.g., penumbra characterization, distinguishing lesion progression form tissue recovery, and elucidating pathophysiological correlates.

Prediction of dMRI signals with neural architecture search

BackgroundThere is growing interest in the neuroscience community in estimating and mapping microscopic properties of brain tissue non-invasively using magnetic resonance measurements. Machine learning methods are actively investigated to predict the signals measured in diffusion magnetic resonance imaging (dMRI). New methodWe applied the neural architecture search (NAS) to train a recurrent neural network to generate a multilayer perceptron to predict the dMRI data of unknown signals based on the different acquisition parameters and training data. The search space of NAS is the number of neurons in each layer of the multilayer perceptron network. To our best knowledge, this is the first time to apply NAS to solve the dMRI signal prediction problem. ResultsThe experimental results demonstrate that the proposed NAS method can achieve fast training and predict dMRI signals accurately. For dMRI signals with four acquisition strategies of double diffusion encoding (DDE), double oscillating diffusion encoding (DODE), multi-shell and DSI-like pulsed gradient spin-echo (PGSE), the mean squared errors of the multilayer perceptron network designed by NAS are 0.0043, 0.0034, 0.0147 and 0.0199, respectively. Comparison with existing method(s)We also compared NAS with other machine learning prediction methods, such as support vector regression (SVR), decision tree (DT) and random forest (RF), k-nearest neighbors (KNN), adaboost regressor (AR), gradient boosting regressor (GBR) and extra-trees regressor (ET). NAS achieved the better prediction performance in most cases. ConclusionIn this study, NAS was developed for the prediction of dMRI signals and could become an effective prediction tool.

Diffusion-Weighted Imaging: Recent Advances and Applications

Quantitative diffusion imaging techniques enable the characterization of tissue microstructural properties of the human brain "in vivo", and are widely used in neuroscientific and clinical contexts. In this review, we present the basic physical principles behind diffusion imaging and provide an overview of the current diffusion techniques, including standard and advanced techniques as well as their main clinical applications. Standard diffusion tensor imaging (DTI) offers sensitivity to changes in microstructure due to diseases and enables the characterization of single fiber distributions within a voxel as well as diffusion anisotropy. Nonetheless, its inability to represent complex intravoxel fiber topologies and the limited biological specificity of its metrics motivated the development of several advanced diffusion MRI techniques. For example, high-angular resolution diffusion imaging (HARDI) techniques enabled the characterization of fiber crossing areas and other complex fiber topologies in a single voxel and supported the development of higher-order signal representations aiming to decompose the diffusion MRI signal into distinct microstructure compartments. Biophysical models, often known by their acronym (e.g., CHARMED, WMTI, NODDI, DBSI, DIAMOND) contributed to capture the diffusion properties from each of such tissue compartments, enabling the computation of voxel-wise maps of axonal density and/or morphology that hold promise as clinically viable biomarkers in several neurological and neuroscientific applications; for example, to quantify tissue alterations due to disease or healthy processes. Current challenges and limitations of state-of-the-art models are discussed, including validation efforts. Finally, novel diffusion encoding approaches (e.g., b-tensor or double diffusion encoding) may increase the biological specificity of diffusion metrics towards intra-voxel diffusion heterogeneity in clinical settings, holding promise in neurological applications.

Evidence for microscopic kurtosis in neural tissue revealed by correlation tensor MRI.

PurposeThe impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, correlation tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a‐priori multi‐gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state‐of‐the‐art methods ignoring µK.Theory and MethodsCTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre‐clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis.ResultsThe improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher‐order‐term biases, thus enabling robust µK estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non‐negligible µK substantially were found to bias prior MGC analyses of Kiso and Kaniso.ConclusionsCorrelation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non‐negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.

Mapping complex cell morphology in the grey matter with double diffusion encoding MR: A simulation study

This paper investigates the impact of cell body (namely soma) size and branching of cellular projections on diffusion MR imaging (dMRI) and spectroscopy (dMRS) signals for both standard single diffusion encoding (SDE) and more advanced double diffusion encoding (DDE) measurements using numerical simulations. The aim is to investigate the ability of dMRI/dMRS to characterize the complex morphology of brain cells focusing on these two distinctive features of brain grey matter.To this end, we employ a recently developed computational framework to create three dimensional meshes of neuron-like structures for Monte Carlo simulations, using diffusion coefficients typical of water and brain metabolites. Modelling the cellular structure as realistically connected spherical soma and cylindrical cellular projections, we cover a wide range of combinations of sphere radii and branching order of cellular projections, characteristic of various grey matter cells. We assess the impact of spherical soma size and branching order on the b-value dependence of the SDE signal as well as the time dependence of the mean diffusivity (MD) and mean kurtosis (MK). Moreover, we also assess the impact of spherical soma size and branching order on the angular modulation of DDE signal at different mixing times, together with the mixing time dependence of the apparent microscopic anisotropy (μA), a promising contrast derived from DDE measurements.The SDE results show that spherical soma size has a measurable impact on both the b-value dependence of the SDE signal and the MD and MK diffusion time dependence for both water and metabolites. On the other hand, we show that branching order has little impact on either, especially for water. In contrast, the DDE results show that spherical soma size has a measurable impact on the DDE signal's angular modulation at short mixing times and the branching order of cellular projections significantly impacts the mixing time dependence of the DDE signal's angular modulation as well as of the derived μA, for both water and metabolites.Our results confirm that SDE based techniques may be sensitive to spherical soma size, and most importantly, show for the first time that DDE measurements may be more sensitive to the dendritic tree complexity (as parametrized by the branching order of cellular projections), paving the way for new ways of characterizing grey matter morphology, non-invasively using dMRS and potentially dMRI.

Compartmental diffusion and microstructural properties of human brain gray and white matter studied with double diffusion encoding magnetic resonance spectroscopy of metabolites and water

Double diffusion encoding (DDE) of the water signal offers a unique ability to separate the effect of microscopic anisotropic diffusion in structural units of tissue from the overall macroscopic orientational distribution of cells. However, the specificity in detected microscopic anisotropy is limited as the signal is averaged over different cell types and across tissue compartments. Performing side-by-side water and metabolite DDE spectroscopic (DDES) experiments provides complementary measures from which intracellular and extracellular microscopic fractional anisotropies (μFA) and diffusivities can be estimated. Metabolites are largely confined to the intracellular space and therefore provide a benchmark for intracellular μFA and diffusivities of specific cell types. By contrast, water DDES measurements allow examination of the separate contributions to water μFA and diffusivity from the intra- and extracellular spaces, by using a wide range of b values to gradually eliminate the extracellular contribution. Here, we aimed to estimate tissue and compartment specific human brain microstructure by combining water and metabolites DDES experiments. We performed our DDES measurements in two brain regions that contain widely different amounts of white matter (WM) and gray matter (GM): parietal white matter (PWM) and occipital gray matter (OGM) in a total of 20 healthy volunteers at 7 Tesla. Metabolite DDES measurements were performed at b = 7199 s/mm2, while water DDES measurements were performed with a range of b values from 918 to 7199 s/mm2. The experimental framework we employed here resulted in a set of insights pertaining to the morphology of the intracellular and extracellular spaces in both gray and white matter. Results of the metabolite DDES experiments in both PWM and OGM suggest a highly anisotropic intracellular space within neurons and glia, with the possible exception of gray matter glia. The water μFA obtained from the DDES results at high b values in both regions converged with that of the metabolite DDES, suggesting that the signal from the extracellular space is indeed effectively suppressed at the highest b value. The μFA measured in the OGM significantly decreased at lower b values, suggesting a considerably lower anisotropy of the extracellular space in GM compared to WM. In PWM, the water μFA remained high even at the lowest b value, indicating a high degree of organization in the interstitial space in WM. Tortuosity values in the cytoplasm for water and tNAA, obtained with correlation analysis of microscopic parallel diffusivity with respect to GM/WM tissue fraction in the volume of interest, are remarkably similar for both molecules, while exhibiting a clear difference between gray and white matter, suggesting a more crowded cytoplasm and more complex cytomorphology of neuronal cell bodies and dendrites in GM than those found in long-range axons in WM.

Characterizing extracellular diffusion properties using diffusion-weighted MRS of sucrose injected in mouse brain.

Brain water and some critically important energy metabolites, such as lactate or glucose, are present in both intracellular and extracellular spaces (ICS/ECS) at significant levels. This ubiquitous nature makes diffusion MRI/MRS data sometimes difficult to interpret and model. While it is possible to glean information on the diffusion properties in ICS by measuring the diffusion of purely intracellular endogenous metabolites (such as NAA), the absence of endogenous markers specific to ECS hampers similar analyses in this compartment. In past experiments, exogenous probes have therefore been injected into the brain to assess their apparent diffusion coefficient (ADC) and thus estimate tortuosity in ECS. Here, we use a similar approach in mice by injecting sucrose, a well‐known ECS marker, in either the lateral ventricles or directly in the prefrontal cortex. For the first time, we propose a thorough characterization of ECS diffusion properties encompassing (1) short‐range restriction by looking at signal attenuation at high b values, (2) tortuosity and long‐range restriction by measuring ADC time‐dependence at long diffusion times and (3) microscopic anisotropy by performing double diffusion encoding (DDE) measurements. Overall, sucrose diffusion behavior is strikingly different from that of intracellular metabolites. Acquisitions at high b values not only reveal faster sucrose diffusion but also some sensitivity to restriction, suggesting that the diffusion in ECS is not fully Gaussian at high b. The time evolution of the ADC at long diffusion times shows that the tortuosity regime is not reached yet in the case of sucrose, while DDE experiments suggest that it is not trapped in elongated structures. No major difference in sucrose diffusion properties is reported between the two investigated routes of injection and brain regions. These original experimental insights should be useful to better interpret and model the diffusion signal of molecules that are distributed between ICS and ECS compartments.

Brain White-Matter Degeneration Due to Aging and Parkinson Disease as Revealed by Double Diffusion Encoding.

Microstructure imaging by means of multidimensional diffusion encoding is increasingly applied in clinical research, with expectations that it yields a parameter that better correlates with clinical disability than current methods based on single diffusion encoding. Under the assumption that diffusion within a voxel can be well described by a collection of diffusion tensors, several parameters of this diffusion tensor distribution can be derived, including mean size, variance of sizes, orientational dispersion, and microscopic anisotropy. The information provided by multidimensional diffusion encoding also enables us to decompose the sources of the conventional fractional anisotropy and mean kurtosis. In this study, we explored the utility of the diffusion tensor distribution approach for characterizing white-matter degeneration in aging and in Parkinson disease by using double diffusion encoding. Data from 23 healthy older subjects and 27 patients with Parkinson disease were analyzed. Advanced age was associated with greater mean size and size variances, as well as smaller microscopic anisotropy. By analyzing the parameters underlying diffusion kurtosis, we found that the reductions of kurtosis in aging and Parkinson disease reported in the literature are likely driven by the reduction in microscopic anisotropy. Furthermore, microscopic anisotropy correlated with the severity of motor impairment in the patients with Parkinson disease. The present results support the use of multidimensional diffusion encoding in clinical studies and are encouraging for its future clinical implementation.

Double Diffusion Encoding for Probing Radiation-Induced Microstructural Changes in a Tumor Model: A Proof-of-Concept Study With Comparison to the Apparent Diffusion Coefficient and Histology.

Microstructure analyses are gaining interest in cancer MRI as an alternative to the conventional apparent diffusion coefficient (ADC), of which the determinants remain unclear. To assess the sensitivity of parameters calculated from a double diffusion encoding (DDE) sequence to changes in a tumor's microstructure early after radiotherapy and to compare them with ADC and histology. Cohort study on experimental tumors. Sixteen WAG/Rij rats grafted with one rhabdomyosarcoma fragment in each thigh. Thirty-one were imaged at days 1 and 4, of which 17 tumors received a 20 Gy radiation dose after the first imagery. 3T. Diffusion-weighted imaging, DDE with flow compensated, and noncompensated measurements. 1) To compare, after irradiation, DDE-derived parameters (intracellular fraction, cell size, and cell density) to their histological counterparts (fraction of stained area, minimal Feret diameter, and nuclei count, respectively). 2) To compare percentage changes in DDE-derived parameters and ADC. 3) To evaluate the evolution of DDE-derived parameters describing perfusion. Wilcoxon rank sum test. 1) Intracellular fraction, cell size, and cell density were respectively lower (-24%, P < 0.001), higher (+7.5%, P < 0.001) and lower (-38%, P < 0.001) in treated tumors as compared to controls. Fraction of stained area, minimal Feret diameter, and nuclei count were respectively lower (-20%, P < 0.001), higher (+28%, P < 0.001), and lower (-34%, P < 0.001) in treated tumors. 2) The magnitude of ADC's percentage change due to irradiation (16.4%) was superior to the one of cell size (8.4%, P < 0.01) but inferior to those of intracellular fraction (35.5%, P < 0.001) and cell density (42%, P < 0.001). 3) After treatment, the magnitude of the vascular fraction's decrease was higher than the increase of flow velocity (33.3%, vs. 13.3%, P < 0.001). The DDE sequence allows quantitatively monitoring the effects of radiotherapy on a tumor's microstructure, whereas ADC only reveals global changes. 2. Stage 4. J. Magn. Reson. Imaging 2020;52:941-951.

Correlation tensor magnetic resonance imaging

Diffusional Kurtosis Magnetic Resonance Imaging (DKI) quantifies the extent of non-Gaussian water diffusion, which has been shown to be a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property per se since kurtosis may emerge from several different sources. Q-space trajectory encoding schemes have been proposed for decoupling kurtosis arising from the variance of mean diffusivities (isotropic kurtosis) from kurtosis driven by microscopic anisotropy (anisotropic kurtosis). Still, these methods assume that the system is comprised of multiple Gaussian diffusion components with vanishing intra-compartmental kurtosis (associated with restricted diffusion). Here, we develop a more general framework for resolving the underlying kurtosis sources without relying on the multiple Gaussian diffusion approximation. We introduce Correlation Tensor MRI (CTI) – an approach harnessing the versatility of double diffusion encoding (DDE) and its sensitivity to displacement correlation tensors capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted (and time-dependent) diffusion. Additionally, we show that, by subtracting these isotropic and anisotropic kurtosis components from the total diffusional kurtosis, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI experiments in ex vivo mouse brains at ultrahigh field of 16.4 T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different synthetic microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher order terms that were not taken into account in this study. CTI measurements were then extended to in vivo settings and used to map heathy rat brains at 9.4 T. These in vivo CTI results were found to be consistent with our ex vivo findings. Although future studies are still required to assess and mitigate the higher order effects on the intra-compartmental kurtosis index, our results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future in vivo studies, which can have significant impact our understanding of the mechanisms underlying diffusion metrics extracted in health and disease.

Revisiting double diffusion encoding MRS in the mouse brain at 11.7T: Which microstructural features are we sensitive to?

Brain metabolites, such as N-acetylaspartate or myo-inositol, are constantly probing their local cellular environment under the effect of diffusion. Diffusion-weighted NMR spectroscopy therefore presents unparalleled potential to yield cell-type specific microstructural information. Double diffusion encoding (DDE) consists in applying two diffusion blocks, where gradient’s direction in the second block is varied during the course of the experiment. Unlike single diffusion encoding, DDE measurements at long mixing time display some angular modulation of the signal amplitude which reflects microscopic anisotropy (μA), while requiring relatively low gradient strength. This angular dependence has been formerly used to quantify cell fiber diameter using a model of isotropically oriented infinite cylinders. However, how additional features of the cell microstructure (such as cell body diameter, fiber length and branching) may also influence the DDE signal has been little explored. Here, we used a cryoprobe as well as state-of-the-art post-processing to perform DDE acquisitions with high accuracy and precision in the mouse brain at 11.7 ​T. We then compared our results to simulated DDE datasets obtained in various 3D cell models in order to pinpoint which features of cell morphology may influence the most the angular dependence of the DDE signal. While the infinite cylinder model poorly fits our experimental data, we show that incorporating branched fiber structure in our model allows more realistic interpretation of the DDE signal. Lastly, data acquired in the short mixing time regime suggest that some sensitivity to cell body diameter might be retrieved, although additional experiments would be required to further support this statement.

Validation and noise robustness assessment of microscopic anisotropy estimation with clinically feasible double diffusion encoding MRI.

Double diffusion encoding (DDE) MRI enables the estimation of microscopic diffusion anisotropy, yielding valuable information on tissue microstructure. A recent study proposed that the acquisition of rotationally invariant DDE metrics, typically obtained using a spherical "5-design," could be greatly simplified by assuming Gaussian diffusion, facilitating reduced acquisition times that are more compatible with clinical settings. Here, we aim to validate the new minimal acquisition scheme against the standard DDE 5-design, and to quantify the proposed method's noise robustness to facilitate future clinical use. DDE MRI experiments were performed on both ex vivo and in vivo rat brains at 9.4 T using the 5-design and the proposed minimal design and taking into account the difference in the number of acquisitions. The ensuing microscopic fractional anisotropy (μFA) maps were compared over a range of b-values up to 5000 s/mm2 . Noise robustness was studied using analytical calculations and numerical simulations. The minimal protocol quantified μFA at an accuracy comparable to the estimates obtained by means of the more theoretically robust DDE 5-design. μFA's sensitivity to noise was found to strongly depend on compartment anisotropy and tensor magnitude in a nonlinear manner. When μFA < 0.75 or when mean diffusivity is particularly low, very high signal-to-noise ratio is required for precise quantification of µFA. Our work supports using DDE for quantifying microscopic diffusion anisotropy in clinical settings but raises hitherto overlooked precision issues when measuring μFA with DDE and typical clinical signal-to-noise ratio.

Single‐ and double‐Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

Resolving degeneracy in diffusion MRI biophysical model parameter estimation using double diffusion encoding.

PurposeBiophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill‐conditioned even when very high b‐values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill‐posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation.MethodsWe analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions.ResultsWe prove analytically that DDE provides invariant information non‐accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space.ConclusionsDDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI.

PurposeMicroscopic fractional anisotropy (µFA) can disentangle microstructural information from orientation dispersion. While double diffusion encoding (DDE) MRI methods are widely used to extract accurate µFA, it has only recently been proposed that powder‐averaged single diffusion encoding (SDE) signals, when coupled with the diffusion standard model (SM) and a set of constraints, could be used for µFA estimation. This study aims to evaluate µFA as derived from the spherical mean technique (SMT) set of constraints, as well as more generally for powder‐averaged SM signals.MethodsSDE experiments were performed at 16.4 T on an ex vivo mouse brain (Δ/δ = 12/1.5 ms). The µFA maps obtained from powder‐averaged SDE signals were then compared to maps obtained from DDE‐MRI experiments (Δ/τ/δ = 12/12/1.5 ms), which allow a model‐free estimation of µFA. Theory and simulations that consider different types of heterogeneity are presented for corroborating the experimental findings.ResultsµFA, as well as other estimates derived from powder‐averaged SDE signals produced large deviations from the ground truth in both gray and white matter. Simulations revealed that these misestimations are likely a consequence of factors not considered by the underlying microstructural models (such as intercomponent and intracompartmental kurtosis).ConclusionPowder‐averaged SMT and (2‐component) SM are unable to accurately report µFA and other microstructural parameters in ex vivo tissues. Improper model assumptions and constraints can significantly compromise parameter specificity. Further developments and validations are required prior to implementation of these models in clinical or preclinical research.

In vivo microscopic diffusional kurtosis imaging with symmetrized double diffusion encoding EPI.

Diffusional kurtosis imaging (DKI) measures the deviation of the displacement probability from a normal distribution, complementing the data commonly acquired by diffusion MRI. It is important to elucidate the sources of kurtosis contrast, particularly in biological tissues where microscopic kurtosis (intrinsic kurtosis) and diffusional heterogeneity may co-exist. We have developed a technique for microscopic kurtosis MRI, dubbed microscopic diffusional kurtosis imaging (µDKI), using a symmetrized double diffusion encoding (s-DDE) EPI sequence. We compared this newly developed µDKI to conventional DKI methods in both a triple compartment phantom and in vivo. Our results showed that whereas conventional DKI and µDKI provided similar measurements in a compartment of monosphere beads, kurtosis measured by µDKI was significantly less than that measured by conventional DKI in a compartment of mixed Gaussian pools. For in vivo brain imaging, µDKI showed small yet significantly lower kurtosis measurement in regions of the cortex, CSF, and internal capsule compared to the conventional DKI approach. Our study showed that µDKI is less susceptible than conventional DKI to sub-voxel diffusional heterogeneity. Our study also provided important preliminary demonstration of our technique in vivo, warranting future studies to investigate its diagnostic use in examining neurological disorders.