Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Mapping tissue microstructure across the human brain on a clinical scanner with soma and neurite density image metrics

Soma and neurite density image (SANDI) is an advanced diffusion magnetic resonance imaging biophysical signal model devised to probe in vivo microstructural information in the gray matter (GM). This model requires acquisitions that include b values that are at least six times higher than those used in clinical practice. Such high b values are required to disentangle the signal contribution of water diffusing in soma from that diffusing in neurites and extracellular space, while keeping the diffusion time as short as possible to minimize potential bias due to water exchange. These requirements have limited the use of SANDI only to preclinical or cutting-edge human scanners. Here, we investigate the potential impact of neglecting water exchange in the SANDI model and present a 10-min acquisition protocol that enables to characterize both GM and white matter (WM) on 3 T scanners. We implemented analytical simulations to (i) evaluate the stability of the fitting of SANDI parameters when diminishing the number of shells; (ii) estimate the bias due to potential exchange between neurites and extracellular space in such reduced acquisition scheme, comparing it with the bias due to experimental noise. Then, we demonstrated the feasibility and assessed the repeatability and reproducibility of our approach by computing microstructural metrics of SANDI with AMICO toolbox and other state-of-the-art models on five healthy subjects. Finally, we applied our protocol to five multiple sclerosis patients. Results suggest that SANDI is a practical method to characterize WM and GM tissues in vivo on performant clinical scanners.

Comparison of different neurite density metrics with brain asymmetry evaluation

The standard diffusion MRI model with intra- and extra-axonal water pools offers a set of microstructural parameters describing brain white matter architecture. However, non-linearities in the standard model and diffusion data contamination by noise and imaging artefacts make estimation of diffusion metrics challenging. In order to develop reliable diffusion approaches and to avoid computational model degeneracy, additional theoretical assumptions allowing stable numerical implementations are required. Advanced diffusion approaches allow for estimation of intra-axonal water fraction (AWF), describing a key structural characteristic of brain tissue. AWF can be interpreted as an indirect measure or proxy of neurite density and has a potential as useful clinical biomarker. Established diffusion approaches such as white matter tract integrity, neurite orientation dispersion and density imaging (NODDI), and spherical mean technique provide estimates of AWF within their respective theoretical frameworks. In the present study, we estimated AWF metrics using different diffusion approaches and compared measures of brain asymmetry between the different metrics in a sub-sample of 182 subjects from the UK Biobank. Multivariate decomposition by mean of linked independent component analysis revealed that the various AWF proxies derived from the different diffusion approaches reflect partly non-overlapping variance of independent components, with distinct anatomical distributions and sensitivity to age. Further, voxel-wise analysis revealed age-related differences in AWF-based brain asymmetry, indicating less apparent left-right hemisphere difference with higher age. Finally, we demonstrated that NODDI metrics suffer from a quite strong dependence on used numerical algorithms and post-processing pipeline. The analysis based on AWF metrics strongly depends on the used diffusion approach and leads to poorly reproducible results.

Extra-axonal contribution to double diffusion encoding-based pore size estimates in the corticospinal tract

OBJECTIVE

To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates.

MATERIALS AND METHODS

Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann-Whitney U test.

RESULTS

Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ([Formula: see text]).

CONCLUSION

The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.

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

PURPOSE

Tensor-valued diffusion encoding can probe more specific features of tissue microstructure than what is available by conventional diffusion weighting. In this work, we investigate the technical feasibility of tensor-valued diffusion encoding at high b-values with q-space trajectory imaging (QTI) analysis, in the human heart in vivo.

METHODS

Ten healthy volunteers were scanned on a 3T scanner. We designed time-optimal gradient waveforms for tensor-valued diffusion encoding (linear and planar) with second-order motion compensation. Data were analyzed with QTI. Normal values and repeatability were investigated for the mean diffusivity (MD), fractional anisotropy (FA), microscopic FA (μFA), isotropic, anisotropic and total mean kurtosis (MKi, MKa, and MKt), and orientation coherence (Cc ). A phantom, consisting of two fiber blocks at adjustable angles, was used to evaluate sensitivity of parameters to orientation dispersion and diffusion time.

RESULTS

QTI data in the left ventricular myocardium were MD = 1.62 ± 0.07 μm2 /ms, FA = 0.31 ± 0.03, μFA = 0.43 ± 0.07, MKa = 0.20 ± 0.07, MKi = 0.13 ± 0.03, MKt = 0.33 ± 0.09, and Cc  = 0.56 ± 0.22 (mean ± SD across subjects). Phantom experiments showed that FA depends on orientation dispersion, whereas μFA was insensitive to this effect.

CONCLUSION

We demonstrated the first tensor-valued diffusion encoding and QTI analysis in the heart in vivo, along with first measurements of myocardial μFA, MKi, MKa, and Cc . The methodology is technically feasible and provides promising novel biomarkers for myocardial tissue characterization.

Multi-tensor diffusion abnormalities of gray matter in an animal model of cortical dysplasia

Focal cortical dysplasias are a type of malformations of cortical development that are a common cause of drug-resistant focal epilepsy. Surgical treatment is a viable option for some of these patients, with their outcome being highly related to complete surgical resection of lesions visible in magnetic resonance imaging (MRI). However, subtle lesions often go undetected on conventional imaging. Several methods to analyze MRI have been proposed, with the common goal of rendering subtle cortical lesions visible. However, most image-processing methods are targeted to detect the macroscopic characteristics of cortical dysplasias, which do not always correspond to the microstructural disarrangement of these cortical malformations. Quantitative analysis of diffusion-weighted MRI (dMRI) enables the inference of tissue characteristics, and novel methods provide valuable microstructural features of complex tissue, including gray matter. We investigated the ability of advanced dMRI descriptors to detect diffusion abnormalities in an animal model of cortical dysplasia. For this purpose, we induced cortical dysplasia in 18 animals that were scanned at 30 postnatal days (along with 19 control animals). We obtained multi-shell dMRI, to which we fitted single and multi-tensor representations. Quantitative dMRI parameters derived from these methods were queried using a curvilinear coordinate system to sample the cortical mantle, providing inter-subject anatomical correspondence. We found region- and layer-specific diffusion abnormalities in experimental animals. Moreover, we were able to distinguish diffusion abnormalities related to altered intra-cortical tangential fibers from those associated with radial cortical fibers. Histological examinations revealed myelo-architectural abnormalities that explain the alterations observed through dMRI. The methods for dMRI acquisition and analysis used here are available in clinical settings and our work shows their clinical relevance to detect subtle cortical dysplasias through analysis of their microstructural properties.

Comparison of two types of microscopic diffusion anisotropy in mouse brain

Two distinct types of microscopic diffusion anisotropy (MA) are compared in brain for both normal control and transgenic (3xTg-AD) mice, which develop Alzheimer's disease pathology. The first type of MA is the commonly used microscopic fractional anisotropy (μFA), and the second is a new MA measure referred to as μFA'. These two MA parameters have different symmetry properties that are central to their physical interpretations. Specifically, μFA is invariant with respect to local rotations of compartmental diffusion tensors while μFA' is invariant with respect to global diffusion tensor deformations. A key distinction between μFA and μFA' is that μFA is affected by the same type of orientationally coherent diffusion anisotropy as the conventional fractional anisotropy (FA) while μFA' is not. Furthermore, μFA can be viewed as having independent contributions from FA and μFA', as is quantified by an equation relating all three anisotropies. The normal control and transgenic mice are studied at ages ranging from 2 to 15 months, with double diffusion encoding MRI being used to estimate μFA and μFA'. μFA and μFA' are nearly identical in low FA brain regions, but they show notable differences when FA is large. In particular, μFA and FA are found to be strongly correlated in the fimbria, but μFA' and FA are not. In addition, both μFA and μFA' are seen to increase with age in the corpus callosum and external capsule, and modest differences between normal control and transgenic mice are observed for μFA and μFA' in the corpus callosum and for μFA in the fimbria. The triad of FA, μFA, and μFA' is proposed as a useful combination of parameters for assessing diffusion anisotropy in brain.

Differentiating False Positive Lesions from Clinically Significant Cancer and Normal Prostate Tissue Using VERDICT MRI and Other Diffusion Models

False positives on multiparametric MRIs (mp-MRIs) result in many unnecessary invasive biopsies in men with clinically insignificant diseases. This study investigated whether quantitative diffusion MRI could differentiate between false positives, true positives and normal tissue non-invasively. Thirty-eight patients underwent mp-MRI and Vascular, Extracellular and Restricted Diffusion for Cytometry in Tumors (VERDICT) MRI, followed by transperineal biopsy. The patients were categorized into two groups following biopsy: (1) significant cancer—true positive, 19 patients; (2) atrophy/inflammation/high-grade prostatic intraepithelial neoplasia (PIN)—false positive, 19 patients. The clinical apparent diffusion coefficient (ADC) values were obtained, and the intravoxel incoherent motion (IVIM), diffusion kurtosis imaging (DKI) and VERDICT models were fitted via deep learning. Significant differences (p < 0.05) between true positive and false positive lesions were found in ADC, IVIM perfusion fraction (f) and diffusivity (D), DKI diffusivity (DK) (p < 0.0001) and kurtosis (K) and VERDICT intracellular volume fraction (fIC), extracellular−extravascular volume fraction (fEES) and diffusivity (dEES) values. Significant differences between false positives and normal tissue were found for the VERDICT fIC (p = 0.004) and IVIM D. These results demonstrate that model-based diffusion MRI could reduce unnecessary biopsies occurring due to false positive prostate lesions and shows promising sensitivity to benign diseases.

Diffusion Kurtosis Imaging of Neonatal Spinal Cord in Clinical Routine

Diffusion kurtosis imaging (DKI) has undisputed advantages over the more classical diffusion magnetic resonance imaging (dMRI) as witnessed by the fast-increasing number of clinical applications and software packages widely adopted in brain imaging. However, in the neonatal setting, DKI is still largely underutilized, in particular in spinal cord (SC) imaging, because of its inherently demanding technological requirements. Due to its extreme sensitivity to non-Gaussian diffusion, DKI proves particularly suitable for detecting complex, subtle, fast microstructural changes occurring in this area at this early and critical stage of development, which are not identifiable with only DTI. Given the multiplicity of congenital anomalies of the spinal canal, their crucial effect on later developmental outcome, and the close interconnection between the SC region and the brain above, managing to apply such a method to the neonatal cohort becomes of utmost importance. This study will (i) mention current methodological challenges associated with the application of advanced dMRI methods, like DKI, in early infancy, (ii) illustrate the first semi-automated pipeline built on Spinal Cord Toolbox for handling the DKI data of neonatal SC, from acquisition setting to estimation of diffusion measures, through accurate adjustment of processing algorithms customized for adult SC, and (iii) present results of its application in a pilot clinical case study. With the proposed pipeline, we preliminarily show that DKI is more sensitive than DTI-related measures to alterations caused by brain white matter injuries in the underlying cervical SC.

Diffusion time dependence, power-law scaling, and exchange in gray matter

Characterizing neural tissue microstructure is a critical goal for future neuroimaging. Diffusion MRI (dMRI) provides contrasts that reflect diffusing spins' interactions with myriad microstructural features of biological systems. However, the specificity of dMRI remains limited due to the ambiguity of its signals vis-à-vis the underlying microstructure. To improve specificity, biophysical models of white matter (WM) typically express dMRI signals according to the Standard Model (SM) and have more recently in gray matter (GM) taken spherical compartments into account (the SANDI model) in attempts to represent cell soma. The validity of the assumptions underlying these models, however, remains largely undetermined, especially in GM. To validate these assumptions experimentally, observing their unique, functional properties, such as the b-1/2 power-law associated with one-dimensional diffusion, has emerged as a fruitful strategy. The absence of this signature in GM, in turn, has been explained by neurite water exchange, non-linear morphology, and/or by obscuring soma signal contributions. Here, we present diffusion simulations in realistic neurons demonstrating that curvature and branching does not destroy the stick power-law behavior in impermeable neurites, but also that their signal is drowned by the soma signal under typical experimental conditions. Nevertheless, by studying the GM dMRI signal's behavior as a function of diffusion weighting as well as time, we identify an attainable experimental regime in which the neurite signal dominates. Furthermore, we find that exchange-driven time dependence produces a signal behavior opposite to that which would be expected from restricted diffusion, thereby providing a functional signature that disambiguates the two effects. We present data from dMRI experiments in ex vivo rat brain at ultrahigh field of 16.4T and observe a time dependence that is consistent with substantial exchange but also with a GM stick power-law. The first finding suggests significant water exchange between neurites and the extracellular space while the second suggests a small sub-population of impermeable neurites. To quantify these observations, we harness the Kärger exchange model and incorporate the corresponding signal time dependence in the SM and SANDI models.

Resolution and b value dependent Structural Connectome in ex vivo Mouse Brain

Diffusion magnetic resonance imaging has been widely used in both clinical and preclinical studies to characterize tissue microstructure and structural connectivity. The diffusion MRI protocol for the Human Connectome Project (HCP) has been developed and optimized to obtain high-quality, high-resolution diffusion MRI (dMRI) datasets. However, such efforts have not been fully explored in preclinical studies, especially for rodents. In this study, high quality dMRI datasets of mouse brains were acquired at 9.4T system from two vendors. In particular, we acquired a high-spatial resolution dMRI dataset (25 μm isotropic with 126 diffusion encoding directions), which we believe to be the highest spatial resolution yet obtained; and a high-angular resolution dMRI dataset (50 μm isotropic with 384 diffusion encoding directions), which we believe to be the highest angular resolution compared to the dMRI datasets at the microscopic resolution. We systematically investigated the effects of three important parameters that affect the final outcome of the connectome: b value (1000s/mm² to 8000 s/mm²), angular resolution (10 to 126), and spatial resolution (25 μm to 200 μm). The stability of tractography and connectome increase with the angular resolution, where more than 50 angles is necessary to achieve consistent results. The connectome and quantitative parameters derived from graph theory exhibit a linear relationship to the b value (R² > 0.99); a single-shell acquisition with b value of 3000 s/mm² shows comparable results to the multi-shell high angular resolution dataset. The dice coefficient decreases and both false positive rate and false negative rate gradually increase with coarser spatial resolution. Our study provides guidelines and foundations for exploration of tradeoffs among acquisition parameters for the structural connectome in ex vivo mouse brain.

In vivo Correlation Tensor MRI reveals microscopic kurtosis in the human brain on a clinical 3T scanner

Diffusion MRI (dMRI) has become one of the most important imaging modalities for noninvasively probing tissue microstructure. Diffusional Kurtosis MRI (DKI) quantifies the degree of non-gaussian diffusion, which in turn has been shown to increase sensitivity towards, e.g., disease and orientation mapping in neural tissue. However, the specificity of DKI is limited as different sources can contribute to the total intravoxel diffusional kurtosis, including: variance in diffusion tensor magnitudes (K_iso), variance due to diffusion anisotropy (K_aniso), and microscopic kurtosis (μK) related to restricted diffusion, microstructural disorder, and/or exchange. Interestingly, μK is typically ignored in diffusion MRI signal modeling as it is assumed to be negligible in neural tissues. However, recently, Correlation Tensor MRI (CTI) based on Double-Diffusion-Encoding (DDE) was introduced for kurtosis source separation, revealing non negligible μK in preclinical imaging. Here, we implemented CTI for the first time on a clinical 3T scanner and investigated the sources of total kurtosis in healthy subjects. A robust framework for kurtosis source separation in humans is introduced, followed by estimation of μK (and the other kurtosis sources) in the healthy brain. Using this clinical CTI approach, we find that μK significantly contributes to total diffusional kurtosis both in gray and white matter tissue but, as expected, not in the ventricles. The first μK maps of the human brain are presented, revealing that the spatial distribution of μK provides a unique source of contrast, appearing different from isotropic and anisotropic kurtosis counterparts. Moreover, group average templates of these kurtosis sources have been generated for the first time, which corroborated our findings at the underlying individual-level maps. We further show that the common practice of ignoring μK and assuming the multiple gaussian component approximation for kurtosis source estimation introduces significant bias in the estimation of other kurtosis sources and, perhaps even worse, compromises their interpretation. Finally, a twofold acceleration of CTI is discussed in the context of potential future clinical applications. We conclude that CTI has much potential for future in vivo microstructural characterizations in healthy and pathological tissue.

Diffusion MRI signal cumulants and hepatocyte microstructure at fixed diffusion time: Insights from simulations, 9.4T imaging, and histology

Purpose

Relationships between diffusion‐weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following question: Can cell size and diffusivity be estimated at fixed diffusion time, realistic SNR, and negligible contribution from extracellular/extravascular water and exchange?

Methods

Monte Carlo simulations were performed within synthetic hepatocytes for varying cell size/diffusivity L/D0, and clinical protocols (single diffusion encoding; maximum b‐value: {1000, 1500, 2000} s/mm²; 5 unique gradient duration/separation pairs; SNR = {∞, 100, 80, 40, 20}), accounting for heterogeneity in (D0,L) and perfusion contamination. Diffusion (D) and kurtosis (K) coefficients were calculated, and relationships between (D0,L) and (D,K) were visualized. Functions mapping (D,K) to (D0,L) were computed to predict unseen (D0,L) values, tested for their ability to classify discrete cell‐size contrasts, and deployed on 9.4T ex vivo MRI‐histology data of fixed mouse livers

Results

Relationships between (D,K) and (D0,L) are complex and depend on the diffusion encoding. Functions mapping D,K to (D0,L) captures salient characteristics of D0(D,K) and L(D,K) dependencies. Mappings are not always accurate, but they enable just under 70% accuracy in a three‐class cell‐size classification task (for SNR = 20, bmax = 1500 s/mm², δ = 20 ms, and Δ = 75 ms). MRI detects cell‐size contrasts in the mouse livers that are confirmed by histology, but overestimates the largest cell sizes.

Conclusion

Salient information about liver cell size and diffusivity may be retrieved from minimal diffusion encodings at fixed diffusion time, in experimental conditions and pathological scenarios for which extracellular, extravascular water and exchange are negligible.

Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds the potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent studies use powder averaging to account for complex white matter architectures, but these have not been validated for real axonal geometries from regions that contain fibre crossings. Here, we present 120-304μm long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, are larger and exhibit a wider distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. For strong gradients available on human Connectom and preclinical scanners, Monte Carlo simulations of diffusion confirm that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of sequence parameters and diffusion times, even in complex white matter architectures. At relatively low b-values, the diameter estimate becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.

Test-retest reproducibility of in vivo oscillating gradient and microscopic anisotropy diffusion MRI in mice at 9.4 Tesla

BACKGROUND AND PURPOSE

Microstructure imaging with advanced diffusion MRI (dMRI) techniques have shown increased sensitivity and specificity to microstructural changes in various disease and injury models. Oscillating gradient spin echo (OGSE) dMRI, implemented by varying the oscillating gradient frequency, and microscopic anisotropy (μA) dMRI, implemented via tensor valued diffusion encoding, may provide additional insight by increasing sensitivity to smaller spatial scales and disentangling fiber orientation dispersion from true microstructural changes, respectively. The aims of this study were to characterize the test-retest reproducibility of in vivo OGSE and μA dMRI metrics in the mouse brain at 9.4 Tesla and provide estimates of required sample sizes for future investigations.

METHODS

Twelve adult C57Bl/6 mice were scanned twice (5 days apart). Each imaging session consisted of multifrequency OGSE and μA dMRI protocols. Metrics investigated included μA, linear diffusion kurtosis, isotropic diffusion kurtosis, and the diffusion dispersion rate (Λ), which explores the power-law frequency dependence of mean diffusivity. The dMRI metric maps were analyzed with mean region-of-interest (ROI) and whole brain voxel-wise analysis. Bland-Altman plots and coefficients of variation (CV) were used to assess the reproducibility of OGSE and μA metrics. Furthermore, we estimated sample sizes required to detect a variety of effect sizes.

RESULTS

Bland-Altman plots showed negligible biases between test and retest sessions. ROI-based CVs revealed high reproducibility for most metrics (CVs < 15%). Voxel-wise CV maps revealed high reproducibility for μA (CVs ~ 10%), but low reproducibility for OGSE metrics (CVs ~ 50%).

CONCLUSION

Most of the μA dMRI metrics are reproducible in both ROI-based and voxel-wise analysis, while the OGSE dMRI metrics are only reproducible in ROI-based analysis. Given feasible sample sizes (10-15), μA metrics and OGSE metrics may provide sensitivity to subtle microstructural changes (4-8%) and moderate changes (> 6%), respectively.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain - from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

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.

Toward more robust and reproducible diffusion kurtosis imaging

PURPOSE

The general utility of diffusion kurtosis imaging (DKI) is challenged by its poor robustness to imaging artifacts and thermal noise that often lead to implausible kurtosis values.

THEORY AND METHODS

A robust scalar kurtosis index can be estimated from powder-averaged diffusion-weighted data. We introduce a novel DKI estimator that uses this scalar kurtosis index as a proxy for the mean kurtosis to regularize the fit.

RESULTS

The regularized DKI estimator improves the robustness and reproducibility of the kurtosis metrics and results in parameter maps with enhanced quality and contrast.

CONCLUSION

Our novel DKI estimator promotes the wider use of DKI in clinical research and potentially diagnostics by improving the reproducibility and precision of DKI fitting and, as such, enabling enhanced visual, quantitative, and statistical analyses of DKI parameters.

SPHERIOUSLY? The challenges of estimating sphere radius non-invasively in the human brain from diffusion MRI

The Soma and Neurite Density Imaging (SANDI) three-compartment model was recently proposed to disentangle cylindrical and spherical geometries, attributed to neurite and soma compartments, respectively, in brain tissue. There are some recent advances in diffusion-weighted MRI signal encoding and analysis (including the use of multiple so-called 'b-tensor' encodings and analysing the signal in the frequency-domain) that have not yet been applied in the context of SANDI. In this work, using: (i) ultra-strong gradients; (ii) a combination of linear, planar, and spherical b-tensor encodings; and (iii) analysing the signal in the frequency domain, three main challenges to robust estimation of sphere size were identified: First, the Rician noise floor in magnitude-reconstructed data biases estimates of sphere properties in a non-uniform fashion. It may cause overestimation or underestimation of the spherical compartment size and density. This can be partly ameliorated by accounting for the noise floor in the estimation routine. Second, even when using the strongest diffusion-encoding gradient strengths available for human MRI, there is an empirical lower bound on the spherical signal fraction and radius that can be detected and estimated robustly. For the experimental setup used here, the lower bound on the sphere signal fraction was approximately 10%. We employed two different ways of establishing the lower bound for spherical radius estimates in white matter. The first, examining power-law relationships between the DW-signal and diffusion weighting in empirical data, yielded a lower bound of 7μm, while the second, pure Monte Carlo simulations, yielded a lower limit of 3μm and in this low radii domain, there is little differentiation in signal attenuation. Third, if there is sensitivity to the transverse intra-cellular diffusivity in cylindrical structures, e.g., axons and cellular projections, then trying to disentangle two diffusion-time-dependencies using one experimental parameter (i.e., change in frequency-content of the encoding waveform) makes spherical radii estimates particularly challenging. We conclude that due to the aforementioned challenges spherical radii estimates may be biased when the corresponding sphere signal fraction is low, which must be considered.

Comparative analysis of signal models for microscopic fractional anisotropy estimation using q-space trajectory encoding

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.

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

PURPOSE

The 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 METHODS

CTI 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.

RESULTS

The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside K_aniso and K_iso 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 K_iso and K_aniso .

CONCLUSIONS

Correlation 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.

Diffusional Kurtosis Imaging in the Diffusion Imaging in Python Project

Diffusion-weighted magnetic resonance imaging (dMRI) measurements and models provide information about brain connectivity and are sensitive to the physical properties of tissue microstructure. Diffusional Kurtosis Imaging (DKI) quantifies the degree of non-Gaussian diffusion in biological tissue from dMRI. These estimates are of interest because they were shown to be more sensitive to microstructural alterations in health and diseases than measures based on the total anisotropy of diffusion which are highly confounded by tissue dispersion and fiber crossings. In this work, we implemented DKI in the Diffusion in Python (DIPY) project-a large collaborative open-source project which aims to provide well-tested, well-documented and comprehensive implementation of different dMRI techniques. We demonstrate the functionality of our methods in numerical simulations with known ground truth parameters and in openly available datasets. A particular strength of our DKI implementations is that it pursues several extensions of the model that connect it explicitly with microstructural models and the reconstruction of 3D white matter fiber bundles (tractography). For instance, our implementations include DKI-based microstructural models that allow the estimation of biophysical parameters, such as axonal water fraction. Moreover, we illustrate how DKI provides more general characterization of non-Gaussian diffusion compatible with complex white matter fiber architectures and gray matter, and we include a novel mean kurtosis index that is invariant to the confounding effects due to tissue dispersion. In summary, DKI in DIPY provides a well-tested, well-documented and comprehensive reference implementation for DKI. It provides a platform for wider use of DKI in research on brain disorders and in cognitive neuroscience.

Comparison of Neurite Orientation Dispersion and Density Imaging and Two-Compartment Spherical Mean Technique Parameter Maps in Multiple Sclerosis

Background: Neurite orientation dispersion and density imaging (NODDI) and the spherical mean technique (SMT) are diffusion MRI methods providing metrics with sensitivity to similar characteristics of white matter microstructure. There has been limited comparison of changes in NODDI and SMT parameters due to multiple sclerosis (MS) pathology in clinical settings.

Purpose: To compare group-wise differences between healthy controls and MS patients in NODDI and SMT metrics, investigating associations with disability and correlations with diffusion tensor imaging (DTI) metrics.

Methods: Sixty three relapsing-remitting MS patients were compared to 28 healthy controls. NODDI and SMT metrics corresponding to intracellular volume fraction (v_in), orientation dispersion (ODI and ODE), diffusivity (D) (SMT only) and isotropic volume fraction (v_iso) (NODDI only) were calculated from diffusion MRI data, alongside DTI metrics (fractional anisotropy, FA; axial/mean/radial diffusivity, AD/MD/RD). Correlations between all pairs of MRI metrics were calculated in normal-appearing white matter (NAWM). Associations with expanded disability status scale (EDSS), controlling for age and gender, were evaluated. Patient-control differences were assessed voxel-by-voxel in MNI space controlling for age and gender at the 5% significance level, correcting for multiple comparisons. Spatial overlap of areas showing significant differences were compared using Dice coefficients.

Results: NODDI and SMT show significant associations with EDSS (standardised beta coefficient −0.34 in NAWM and −0.37 in lesions for NODDI v_in; 0.38 and −0.31 for SMT ODE and v_in in lesions; p < 0.05). Significant correlations in NAWM are observed between DTI and NODDI/SMT metrics. NODDI v_in and SMT v_in strongly correlated (r = 0.72, p < 0.05), likewise NODDI ODI and SMT ODE (r = −0.80, p < 0.05). All DTI, NODDI and SMT metrics detect widespread differences between patients and controls in NAWM (12.57% and 11.90% of MNI brain mask for SMT and NODDI v_in, Dice overlap of 0.42).

Data Conclusion: SMT and NODDI detect significant differences in white matter microstructure between MS patients and controls, concurring on the direction of these changes, providing consistent descriptors of tissue microstructure that correlate with disability and show alterations beyond focal damage. Our study suggests that NODDI and SMT may play a role in monitoring MS in clinical trials and practice.

Cytosolic diffusivity and microscopic anisotropy of N-acetyl aspartate in human white matter with diffusion-weighted MRS at 7 T

Metabolite diffusion measurable in humans in vivo with diffusion-weighted spectroscopy (DW-MRS) provides a window into the intracellular morphology and state of specific cell types. Anisotropic diffusion in white matter is governed by the microscopic properties of the individual cell types and their structural units (axons, soma, dendrites). However, anisotropy is also markedly affected by the macroscopic orientational distribution over the imaging voxel, particularly in DW-MRS, where the dimensions of the volume of interest (VOI) are much larger than those typically used in diffusion-weighted imaging. One way to address the confound of macroscopic structural features is to average the measurements acquired with uniformly distributed gradient directions to mimic a situation where fibers present in the VOI are orientationally uniformly distributed. This situation allows the extraction of relevant microstructural features such as transverse and longitudinal diffusivities within axons and the related microscopic fractional anisotropy. We present human DW-MRS data acquired at 7 T in two different white matter regions, processed and analyzed as described above, and find that intra-axonal diffusion of the neuronal metabolite N-acetyl aspartate is in good correspondence to simple model interpretations, such as multi-Gaussian diffusion from disperse fibers where the transverse diffusivity can be neglected. We also discuss the implications of our approach for current and future applications of DW-MRS for cell-specific measurements.

In vivo diffusion-weighted MRS using semi-LASER in the human brain at 3 T: Methodological aspects and clinical feasibility

Diffusion-weighted (DW-) MRS investigates non-invasively microstructural properties of tissue by probing metabolite diffusion in vivo. Despite the growing interest in DW-MRS for clinical applications, little has been published on the reproducibility of this technique. In this study, we explored the optimization of a single-voxel DW-semi-LASER sequence for clinical applications at 3 T, and evaluated the reproducibility of the method under different experimental conditions. DW-MRS measurements were carried out in 10 healthy participants and repeated across three sessions. Metabolite apparent diffusion coefficients (ADCs) were calculated from mono-exponential fits (ADC_exp ) up to b = 3300 s/mm² , and from the diffusional kurtosis approach (ADC_K ) up to b = 7300 s/mm² . The inter-subject variabilities of ADCs of N-acetylaspartate + N-acetylaspartylglutamate (tNAA), creatine + phosphocreatine, choline containing compounds, and myo-inositol were calculated in the posterior cingulate cortex (PCC) and in the corona radiata (CR). We explored the effect of physiological motion on the DW-MRS signal and the importance of cardiac gating and peak thresholding to account for signal amplitude fluctuations. Additionally, we investigated the dependence of the intra-subject variability on the acquisition scheme using a bootstrapping resampling method. Coefficients of variation were lower in PCC than CR, likely due to the different sensitivities to motion artifacts of the two regions. Finally, we computed coefficients of repeatability for ADC_exp and performed power calculations needed for designing clinical studies. The power calculation for ADC_exp of tNAA showed that in the PCC seven subjects per group are sufficient to detect a difference of 5% between two groups with an acquisition time of 4 min, suggesting that ADC_exp of tNAA is a suitable marker for disease-related intracellular alteration even in small case-control studies. In the CR, further work is needed to evaluate the voxel size and location that minimize the motion artifacts and variability of the ADC measurements.

Rapid microscopic fractional anisotropy imaging via an optimized linear regression formulation

Water diffusion anisotropy in the human brain is affected by disease, trauma, and development. Microscopic fractional anisotropy (μFA) is a diffusion MRI (dMRI) metric that can quantify water diffusion anisotropy independent of neuron fiber orientation dispersion. However, there are several different techniques to estimate μFA and few have demonstrated full brain imaging capabilities within clinically viable scan times and resolutions. Here, we present an optimized spherical tensor encoding (STE) technique to acquire μFA directly from the 2nd order cumulant expansion of the powder averaged dMRI signal obtained from direct linear regression (i.e. diffusion kurtosis) which requires fewer powder-averaged signals than other STE fitting techniques and can be rapidly computed. We found that the optimal dMRI parameters for white matter μFA imaging were a maximum b-value of 2000 s/mm² and a ratio of STE to LTE tensor encoded acquisitions of 1.7 for our system specifications. We then compared two implementations of the direct regression approach to the well-established gamma model in 4 healthy volunteers on a 3 Tesla system. One implementation used mean diffusivity (D) obtained from a 2nd order fit of the cumulant expansion, while the other used a linear estimation of D from the low b-values. Both implementations of the direct regression approach showed strong linear correlations with the gamma model (ρ = 0.97 and ρ = 0.90) but mean biases of -0.11 and - 0.02 relative to the gamma model were also observed, respectively. All three μFA measurements showed good test-retest reliability (ρ ≥ 0.79 and bias = 0). To demonstrate the potential scan time advantage of the direct approach, 2 mm isotropic resolution μFA was demonstrated over a 10 cm slab using a subsampled data set with fewer powder-averaged signals that would correspond to a 3.3-min scan. Accordingly, our results introduce an optimization procedure that has enabled nearly full brain μFA in only several minutes.

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.

Beyond the diffusion standard model in fixed rat spinal cord with combined linear and planar encoding

Information about tissue on the microscopic and mesoscopic scales can be accessed by modelling diffusion MRI signals, with the aim of extracting microstructure-specific biomarkers. The standard model (SM) of diffusion, currently the most broadly adopted microstructural model, describes diffusion in white matter (WM) tissues by two Gaussian components, one of which has zero radial diffusivity, to represent diffusion in intra- and extra-axonal water, respectively. Here, we reappraise these SM assumptions by collecting comprehensive double diffusion encoded (DDE) MRI data with both linear and planar encodings, which was recently shown to substantially enhance the ability to estimate SM parameters. We find however, that the SM is unable to account for data recorded in fixed rat spinal cord at an ultrahigh field of 16.4 T, suggesting that its underlying assumptions are violated in our experimental data. We offer three model extensions to mitigate this problem: first, we generalize the SM to accommodate finite radii (axons) by releasing the constraint of zero radial diffusivity in the intra-axonal compartment. Second, we include intracompartmental kurtosis to account for non-Gaussian behaviour. Third, we introduce an additional (third) compartment. The ability of these models to account for our experimental data are compared based on parameter feasibility and Bayesian information criterion. Our analysis identifies the three-compartment description as the optimal model. The third compartment exhibits slow diffusion with a minor but non-negligible signal fraction (∼12%). We demonstrate how failure to take the presence of such a compartment into account severely misguides inferences about WM microstructure. Our findings bear significance for microstructural modelling at large and can impact the interpretation of biomarkers extracted from the standard model of diffusion.

Gradient waveform design for tensor-valued encoding in diffusion MRI

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.

Towards in vivo g-ratio mapping using MRI: Unifying myelin and diffusion imaging

BACKGROUND

The g-ratio, quantifying the comparative thickness of the myelin sheath encasing an axon, is a geometrical invariant that has high functional relevance because of its importance in determining neuronal conduction velocity. Advances in MRI data acquisition and signal modelling have put in vivo mapping of the g-ratio, across the entire white matter, within our reach. This capacity would greatly increase our knowledge of the nervous system: how it functions, and how it is impacted by disease.

NEW METHOD

This is the second review on the topic of g-ratio mapping using MRI.

RESULTS

This review summarizes the most recent developments in the field, while also providing methodological background pertinent to aggregate g-ratio weighted mapping, and discussing pitfalls associated with these approaches.

COMPARISON WITH EXISTING METHODS

Using simulations based on recently published data, this review reveals caveats to the state-of-the-art calibration methods that have been used for in vivo g-ratio mapping. It highlights the need to estimate both the slope and offset of the relationship between these MRI-based markers and the true myelin volume fraction if we are really to achieve the goal of precise, high sensitivity g-ratio mapping in vivo. Other challenges discussed in this review further evidence the need for gold standard measurements of human brain tissue from ex vivo histology.

CONCLUSIONS

We conclude that the quest to find the most appropriate MRI biomarkers to enable in vivo g-ratio mapping is ongoing, with the full potential of many novel techniques yet to be investigated.

Probing tissue microstructure by diffusion skewness tensor imaging

Probing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.

Free-water DTI estimates from single b-value data might seem plausible but must be interpreted with care

PURPOSE

Free-water elimination DTI (FWE-DTI) has been used widely to distinguish increases of free-water partial-volume effects from tissue's diffusion in healthy aging and degenerative diseases. Because the FWE-DTI fitting is only well-posed for multishell acquisitions, a regularized gradient descent (RGD) method was proposed to enable application to single-shell data, more common in the clinic. However, the validity of the RGD method has been poorly assessed. This study aims to quantify the specificity of FWE-DTI procedures on single-shell and multishell data.

METHODS

Different FWE-DTI fitting procedures were tested on an open-source in vivo diffusion data set and single-shell and multishell synthetic signals, including the RGD and standard nonlinear least-squares methods. Single-voxel simulations were carried out to compare initialization approaches. A multivoxel phantom simulation was performed to evaluate the effect of spatial regularization when comparing between methods. To test the algorithms' specificity, phantoms with two different types of lesions were simulated: with altered mean diffusivity or with modified free water.

RESULTS

Plausible parameter maps were obtained with RGD from single-shell in vivo data. The plausibility of these maps was shown to be determined by the initialization. Tests with simulated lesions inserted into the in vivo data revealed that the RGD approach cannot distinguish free water from tissue mean-diffusivity alterations, contrarily to the nonlinear least-squares algorithm.

CONCLUSION

The RGD FWE-DTI method has limited specificity; thus, its results from single-shell data should be carefully interpreted. When possible, multishell acquisitions and the nonlinear least-squares approach should be preferred instead.

Accuracy and precision of statistical descriptors obtained from multidimensional diffusion signal inversion algorithms

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.

Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module

The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.

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.

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.

Tensor-valued diffusion MRI differentiates cortex and white matter in malformations of cortical development associated with epilepsy

Objective:

Delineation of malformations of cortical development (MCD) is central in presurgical evaluation of drug-resistant epilepsy. Delineation using magnetic resonance imaging (MRI) can be ambiguous, however, because the conventional T₁- and T₂-weighted contrasts depend strongly on myelin for differentiation of cortical tissue and white matter. Variations in myelin content within both cortex and white matter may cause MCD findings on MRI to change size, become undetectable, or disagree with histopathology. The novel tensor-valued diffusion MRI (dMRI) technique maps microscopic diffusion anisotropy, which is sensitive to axons rather than myelin. This work investigated whether tensor-valued dMRI may improve differentiation of cortex and white matter in the delineation of MCD.

Methods:

Tensor-valued dMRI was performed on a 7 T MRI scanner in 13 MCD patients (age = 32 ± 13 years) featuring periventricular heterotopia, subcortical heterotopia, focal cortical dysplasia, and polymicrogyria. Data analysis yielded maps of microscopic anisotropy that were compared with T₁-weighted and T₂-fluid-attenuated inversion recovery images and with the fractional anisotropy from diffusion tensor imaging.

Results:

Maps of microscopic anisotropy revealed large white matter-like regions within MCD that were uniformly cortex-like in the conventional MRI contrasts. These regions were seen particularly in the deep white matter parts of subcortical heterotopias and near the gray-white boundaries of focal cortical dysplasias and polymicrogyrias.

Significance:

By being sensitive to axons rather than myelin, mapping of microscopic anisotropy may yield a more robust differentiation of cortex and white matter and improve MCD delineation in presurgical evaluation of epilepsy.

Disentangling white-matter damage from physiological fibre orientation dispersion in multiple sclerosis

Multiple sclerosis leads to diffuse damage of the central nervous system, affecting also the normal-appearing white matter. Demyelination and axonal degeneration reduce regional fractional anisotropy in normal-appearing white matter, which can be routinely mapped with diffusion tensor imaging. However, the standard fractional anisotropy metric is also sensitive to physiological variations in orientation dispersion of white matter fibres. This complicates the detection of disease-related damage in large parts of cerebral white matter where microstructure physiologically displays a high degree of fibre dispersion. To resolve this ambiguity, we employed a novel tensor-valued encoding method for diffusion MRI, which yields a microscopic fractional anisotropy metric that is unaffected by regional variations in orientation dispersion. In 26 patients with relapsing-remitting multiple sclerosis, 14 patients with primary-progressive multiple sclerosis and 27 age-matched healthy controls, we compared standard fractional anisotropy mapping with the novel microscopic fractional anisotropy mapping method, focusing on normal-appearing white matter. Mean microscopic fractional anisotropy and standard fractional anisotropy of normal-appearing white matter were significantly reduced in both patient groups relative to healthy controls, but microscopic fractional anisotropy yielded a better reflection of disease-related white-matter alterations. The reduction in mean microscopic fractional anisotropy showed a significant positive linear relationship with physical disability, as reflected by the expanded disability status scale. Mean reduction of microscopic fractional anisotropy in normal-appearing white matter also scaled positively with individual cognitive dysfunction, as measured with the symbol digit modality test. Mean microscopic fractional anisotropy reduction in normal-appearing white matter also showed a positive relationship with total white-matter lesion load as well as lesion load in specific tract systems. None of these relationships between normal-appearing white-matter microstructure and clinical, cognitive or structural measures emerged when using mean fractional anisotropy. Together, the results provide converging evidence that microscopic fractional anisotropy mapping substantially advances the assessment of cerebral white matter in multiple sclerosis by disentangling microstructure damage from variations in physiological fibre orientation dispersion at the stage of data acquisition. Since tensor-valued encoding can be implemented in routine diffusion MRI, microscopic fractional anisotropy mapping bears considerable potential for the future assessment of disease progression in normal-appearing white matter in both relapsing-remitting and progressive forms of multiple sclerosis as well as other white-matter-related brain diseases.

SANDI: A compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI

This work introduces a compartment-based model for apparent cell body (namely soma) and neurite density imaging (SANDI) using non-invasive diffusion-weighted MRI (DW-MRI). The existing conjecture in brain microstructure imaging through DW-MRI presents water diffusion in white (WM) and gray (GM) matter as restricted diffusion in neurites, modelled by infinite cylinders of null radius embedded in the hindered extra-neurite water. The extra-neurite pool in WM corresponds to water in the extra-axonal space, but in GM it combines water in the extra-cellular space with water in soma. While several studies showed that this microstructure model successfully describe DW-MRI data in WM and GM at b ​≤ ​3,000 ​s/mm² (or 3 ​ms/μm²), it has been also shown to fail in GM at high b values (b≫3,000 ​s/mm² or 3 ​ms/μm²). Here we hypothesise that the unmodelled soma compartment (i.e. cell body of any brain cell type: from neuroglia to neurons) may be responsible for this failure and propose SANDI as a new model of brain microstructure where soma of any brain cell type is explicitly included. We assess the effects of size and density of soma on the direction-averaged DW-MRI signal at high b values and the regime of validity of the model using numerical simulations and comparison with experimental data from mouse (b_max ​= ​40,000 ​s/mm², or 40 ​ms/μm²) and human (b_max ​= ​10,000 ​s/mm², or 10 ​ms/μm²) brain. We show that SANDI defines new contrasts representing complementary information on the brain cyto- and myelo-architecture. Indeed, we show maps from 25 healthy human subjects of MR soma and neurite signal fractions, that remarkably mirror contrasts of histological images of brain cyto- and myelo-architecture. Although still under validation, SANDI might provide new insight into tissue architecture by introducing a new set of biomarkers of potential great value for biomedical applications and pure neuroscience.

Portable simulation framework for diffusion MRI

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite element discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite element discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite element software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Diffusion dispersion imaging: Mapping oscillating gradient spin-echo frequency dependence in the human brain

PURPOSE

Oscillating gradient spin-echo (OGSE) diffusion MRI provides information about the microstructure of biological tissues by means of the frequency dependence of the apparent diffusion coefficient (ADC). ADC dependence on OGSE frequency has been explored in numerous rodent studies, but applications in the human brain have been limited and have suffered from low contrast between different frequencies, long scan times, and a limited exploration of the nature of the ADC dependence on frequency.

THEORY AND METHODS

Multiple frequency OGSE acquisitions were acquired in healthy subjects at 7T to explore the power-law frequency dependence of ADC, the "diffusion dispersion." Furthermore, a method for optimizing the estimation of the ADC difference between different OGSE frequencies was developed, which enabled the design of a highly efficient protocol for mapping diffusion dispersion.

RESULTS

For the first time, evidence of a linear dependence of ADC on the square root of frequency in healthy human white matter was obtained. Using the optimized protocol, high-quality, full-brain maps of apparent diffusion dispersion rate were also demonstrated at an isotropic resolution of 2 mm in a scan time of 6 min.

CONCLUSIONS

This work sheds light on the nature of diffusion dispersion in the healthy human brain and introduces full-brain diffusion dispersion mapping at clinically relevant scan times. These advances may lead to new biomarkers of pathology or improved microstructural modeling.

Evaluation of white matter microstructure in patients with Parkinson's disease using microscopic fractional anisotropy

PURPOSE

Micro fractional anisotropy (μFA) is more accurate than conventional fractional anisotropy (FA) for assessing microscopic tissue properties and can overcome limitations related to crossing white matter fibres. We compared μFA and FA for evaluating white matter changes in patients with Parkinson's disease (PD).

METHODS

We compared FA and μFA measures between 25 patients with PD and 25 age- and gender-matched healthy controls using tract-based spatial statistics (TBSS) analysis. We also examined potential correlations between changes, revealed by conventional FA or μFA, and disease duration or Unified Parkinson's Disease Rating Scale (UPDRS)-III scores.

RESULTS

Compared with healthy controls, patients with PD had significantly reduced μFA values, mainly in the anterior corona radiata (ACR). In the PD group, μFA values (primarily those from the ACR) were significantly negatively correlated with UPDRS-III motor scores. No significant changes or correlations with disease duration or UPDRS-III scores with tissue properties were detected using conventional FA.

CONCLUSION

μFA can evaluate microstructural changes that occur during white matter degeneration in patients with PD and may overcome a key limitation of FA.

Tensor-valued diffusion MRI in under 3 minutes: an initial survey of microscopic anisotropy and tissue heterogeneity in intracranial tumors

PURPOSE

To evaluate the feasibility of a 3-minutes protocol for assessment of the microscopic anisotropy and tissue heterogeneity based on tensor-valued diffusion MRI in a wide range of intracranial tumors.

METHODS

B-tensor encoding was performed in 42 patients with intracranial tumors (gliomas, meningiomas, adenomas, and 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 3-minutes 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 ± 0.06 vs. 0.45 ± 0.08, P = 0.003). Metastases had higher tissue heterogeneity (MK_I = 0.57 ± 0.07) than both the glioblastomas (0.44 ± 0.06, P < 0.001) and meningiomas (0.46 ± 0.06, P = 0.03).

CONCLUSION

Evaluation of the microscopic anisotropy and tissue heterogeneity in intracranial tumor patients is feasible in clinically relevant times frames.

Tensor-valued diffusion encoding for diffusional variance decomposition (DIVIDE): Technical feasibility in clinical MRI systems

Microstructure imaging techniques based on tensor-valued diffusion encoding have gained popularity within the MRI research community. Unlike conventional diffusion encoding-applied along a single direction in each shot-tensor-valued encoding employs diffusion encoding along multiple directions within a single preparation of the signal. The benefit is that such encoding may probe tissue features that are not accessible by conventional encoding. For example, diffusional variance decomposition (DIVIDE) takes advantage of tensor-valued encoding to probe microscopic diffusion anisotropy independent of orientation coherence. The drawback is that tensor-valued encoding generally requires gradient waveforms that are more demanding on hardware; it has therefore been used primarily in MRI systems with relatively high performance. The purpose of this work was to explore tensor-valued diffusion encoding on clinical MRI systems with varying performance to test its technical feasibility within the context of DIVIDE. We performed whole-brain imaging with linear and spherical b-tensor encoding at field strengths between 1.5 and 7 T, and at maximal gradient amplitudes between 45 and 80 mT/m. Asymmetric gradient waveforms were optimized numerically to yield b-values up to 2 ms/μm2. Technical feasibility was assessed in terms of the repeatability, SNR, and quality of DIVIDE parameter maps. Variable system performance resulted in echo times between 83 to 115 ms and total acquisition times of 6 to 9 minutes when using 80 signal samples and resolution 2×2×4 mm3. As expected, the repeatability, signal-to-noise ratio and parameter map quality depended on hardware performance. We conclude that tensor-valued encoding is feasible for a wide range of MRI systems-even at 1.5 T with maximal gradient waveform amplitudes of 33 mT/m-and baseline experimental design and quality parameters for all included configurations. This demonstrates that tissue features, beyond those accessible by conventional diffusion encoding, can be explored on a wide range of MRI systems.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Purpose

Microscopic 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.

Methods

SDE 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.

Results

µFA, 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).

Conclusion

Powder‐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.