Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

Oscillating-gradient spin-echo diffusion-weighted imaging (OGSE-DWI) with a limited number of oscillations: I. Signal equation

The oscillating-gradient spin-echo (OGSE) sequence has been promoted as a promising diffusion-weighted magnetic resonance imaging (DWI) technique for probing in vivo tissue microstructure in the frequency domain. However, due to practical restrictions on the duration and number of oscillations that a motion-probing gradient can have, the technique has limited spectral resolution and range. This work re-examines the OGSE-DWI method to clarify how these limitations are reflected in the signal model. There are several aspects of the revised framework that distinguish it from the conventional description employed for OGSE DWI. In particular, while the conventional OGSE signal model implies that the spectral density of molecular diffusion may be directly sampled in experiments, in practice information about the spectral density can be only indirectly obtained.

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.

Can MRI measure myelin? Systematic review, qualitative assessment, and meta-analysis of studies validating microstructural imaging with myelin histology

Recent years have seen an increased understanding of the importance of myelination in healthy brain function and neuropsychiatric diseases. Non-invasive microstructural magnetic resonance imaging (MRI) holds the potential to expand and translate these insights to basic and clinical human research, but the sensitivity and specificity of different MR markers to myelination is a subject of debate. To consolidate current knowledge on the topic, we perform a systematic review and meta-analysis of studies that validate microstructural imaging by combining it with myelin histology. We find meta-analytic evidence for correlations between various myelin histology metrics and markers from different MRI modalities, including fractional anisotropy, radial diffusivity, macromolecular pool, magnetization transfer ratio, susceptibility and longitudinal relaxation rate, but not mean diffusivity. Meta-analytic correlation effect sizes range widely, between R2 = 0.26 and R2 = 0.82. However, formal comparisons between MRI-based myelin markers are limited by methodological variability, inconsistent reporting and potential for publication bias, thus preventing the establishment of a single most sensitive strategy to measure myelin with MRI. To facilitate further progress, we provide a detailed characterisation of the evaluated studies as an online resource. We also share a set of 12 recommendations for future studies validating putative MR-based myelin markers and deploying them in vivo in humans.

In vivo tensor-valued diffusion MRI of focal demyelination in white and deep grey matter of rodents

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We performed in-vivo tensor-valued diffusion MRI in demyelinating rodents.

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Lysolecithin was injected in white and deep grey matter to cause focal demyelination.

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Focal demyelination reduced microscopic fractional anisotropy (µFA).

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Isotropic kurtosis may be particularly sensitive to deep grey matter lesions.

Background

Multiple sclerosis (MS) is a chronic inflammatory demyelinating disease leading to damage of white matter (WM) and grey matter (GM). Magnetic resonance imaging (MRI) is the modality of choice to assess brain damage in MS, but there is an unmet need in MRI for achieving higher sensitivity and specificity to MS-related microstructural alterations in WM and GM.

Objective

To explore whether tensor-valued diffusion MRI (dMRI) can yield sensitive microstructural read-outs for focal demyelination in cerebral WM and deep GM (DGM).

Methods

Eight rats underwent L-α-Lysophosphatidylcholine (LPC) injections in the WM and striatum to introduce focal demyelination. Multimodal MRI was performed at 7 Tesla after 7 days. Tensor-valued dMRI was complemented by diffusion tensor imaging, quantitative MRI and proton magnetic resonance spectroscopy (MRS).

Results

Quantitative MRI and MRS confirmed that LPC injections caused inflammatory demyelinating lesions in WM and DGM. Tensor-valued dMRI illustrated a significant decline of microscopic fractional anisotropy (µFA) in both LPC-treated WM and DGM (P < 0.005) along with a marked increase of isotropic kurtosis (MK_I) in DGM (P < 0.0001).

Conclusion

Tensor-valued dMRI bears considerable potential for microstructural imaging in MS, suggesting a regional µFA decrease may be a sensitive indicator of MS lesions, while a regional MK_I increase may be particularly sensitive in detecting DGM lesions of MS.

GAMER-MRI in Multiple Sclerosis Identifies the Diffusion-Based Microstructural Measures That Are Most Sensitive to Focal Damage: A Deep-Learning-Based Analysis and Clinico-Biological Validation

Conventional magnetic resonance imaging (cMRI) in multiple sclerosis (MS) patients provides measures of focal brain damage and activity, which are fundamental for disease diagnosis, prognosis, and the evaluation of response to therapy. However, cMRI is insensitive to the damage to the microenvironment of the brain tissue and the heterogeneity of MS lesions. In contrast, the damaged tissue can be characterized by mathematical models on multishell diffusion imaging data, which measure different compartmental water diffusion. In this work, we obtained 12 diffusion measures from eight diffusion models, and we applied a deep-learning attention-based convolutional neural network (CNN) (GAMER-MRI) to select the most discriminating measures in the classification of MS lesions and the perilesional tissue by attention weights. Furthermore, we provided clinical and biological validation of the chosen metrics-and of their most discriminative combinations-by correlating their respective mean values in MS patients with the corresponding Expanded Disability Status Scale (EDSS) and the serum level of neurofilament light chain (sNfL), which are measures of disability and neuroaxonal damage. Our results show that the neurite density index from neurite orientation and dispersion density imaging (NODDI), the measures of the intra-axonal and isotropic compartments from microstructural Bayesian approach, and the measure of the intra-axonal compartment from the spherical mean technique NODDI were the most discriminating (respective attention weights were 0.12, 0.12, 0.15, and 0.13). In addition, the combination of the neurite density index from NODDI and the measures for the intra-axonal and isotropic compartments from the microstructural Bayesian approach exhibited a stronger correlation with EDSS and sNfL than the individual measures. This work demonstrates that the proposed method might be useful to select the microstructural measures that are most discriminative of focal tissue damage and that may also be combined to a unique contrast to achieve stronger correlations to clinical disability and neuroaxonal damage.

Time-dependent diffusion MRI probes cerebellar microstructural alterations in a mouse model of Down syndrome

The cerebellum is a complex system with distinct cortical laminar organization. Alterations in cerebellar microstructure are common and associated with many factors such as genetics, cancer and ageing. Diffusion MRI (dMRI) provides a non-invasive tool to map the brain structural organization, and the recently proposed diffusion-time (td )-dependent dMRI further improves its capability to probe the cellular and axonal/dendritic microstructures by measuring water diffusion at multiple spatial scales. The td -dependent diffusion profile in the cerebellum and its utility in detecting cerebellar disorders, however, are not yet elucidated. Here, we first deciphered the spatial correspondence between dMRI contrast and cerebellar layers, based on which the cerebellar layer-specific td -dependent dMRI patterns were characterized in both euploid and Ts65Dn mice, a mouse model of Down syndrome. Using oscillating gradient dMRI, which accesses diffusion at short td 's by modulating the oscillating frequency, we detected subtle changes in the apparent diffusivity coefficient of the cerebellar internal granular layer and Purkinje cell layer of Ts65Dn mice that were not detectable by conventional pulsed gradient dMRI. The detection sensitivity of oscillating gradient dMRI increased with the oscillating frequency at both the neonatal and adult stages. The td -dependence, quantified by ΔADC map, was reduced in Ts65Dn mice, likely associated with the reduced granule cell density and abnormal dendritic arborization of Purkinje cells as revealed from histological evidence. Our study demonstrates superior sensitivity of short-td diffusion using oscillating gradient dMRI to detect cerebellar microstructural changes in Down syndrome, suggesting the potential application of this technique in cerebellar disorders.

MR cell size imaging with temporal diffusion spectroscopy

Cytological features such as cell size and intracellular morphology provide fundamental information on cell status and hence may provide specific information on changes that arise within biological tissues. Such information is usually obtained by invasive biopsy in current clinical practice, which suffers several well-known disadvantages. Recently, novel MRI methods such as IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) have been developed for direct measurements of mean cell size non-invasively. The IMPULSED protocol is based on using temporal diffusion spectroscopy (TDS) to combine measurements of water diffusion over a wide range of diffusion times to probe cellular microstructure over varying length scales. IMPULSED has been shown to provide rapid, robust, and reliable mapping of mean cell size and is suitable for clinical imaging. More recently, cell size distributions have also been derived by appropriate analyses of data acquired with IMPULSED or similar sequences, which thus provides MRI-cytometry. This review summarizes the basic principles, practical implementations, validations, and example applications of MR cell size imaging based on TDS and demonstrates how cytometric information can be used in various applications. In addition, the limitations and potential future directions of MR cytometry are identified including the diagnosis of nonalcoholic steatohepatitis of the liver and the assessment of treatment response of cancers.

Technical Basics of Diffusion-Weighted Imaging

Diffusion-weighted images provide a unique contrast that shows the ability to assess tissue structure and condition on a micrometer scale. Notably, these equations are necessary to understand diffusion MR imaging as a theory but not for real imaging, particularly in clinical practice. The diffusion phenomenon can be observed only through MR measurements. One of the emerging fields of diffusion MRI is to probe the tissue microstructure by altering the diffusion time t, the time interval over which spin displacements are sampled. However, the diffusion time is, in a sense, more important than the b-value for diffusion-weighted images and their quantitative metrics.

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.

Heterogeneity of multiple sclerosis lesions in fast diffusional kurtosis imaging

Background

Mean kurtosis (MK), one of the parameters derived from diffusion kurtosis imaging (DKI), has shown increased sensitivity to tissue microstructure damage in several neurological disorders.

Methods

Thirty-seven patients with relapsing-remitting MS and eleven healthy controls (HC) received brain imaging on a 3T MR scanner, including a fast DKI sequence. MK and mean diffusivity (MD) were measured in the white matter of HC, normal-appearing white matter (NAWM) of MS patients, contrast-enhancing lesions (CE-L), FLAIR lesions (FLAIR-L) and black holes (BH).

Results

Overall 1529 lesions were analyzed, including 30 CE-L, 832 FLAIR-L and 667 BH. Highest MK values were obtained in the white matter of HC (0.814 ± 0.129), followed by NAWM (0.724 ± 0.137), CE-L (0.619 ± 0.096), FLAIR-L (0.565 ± 0.123) and BH (0.549 ± 0.12). Lowest MD values were obtained in the white matter of HC (0.747 ± 0.068 10⁻³mm²/sec), followed by NAWM (0.808 ± 0.163 10⁻³mm²/sec), CE-L (0.853 ± 0.211 10⁻³mm²/sec), BH (0.957 ± 0.304 10⁻³mm²/sec) and FLAIR-L (0.976 ± 0.35 10⁻³mm²/sec). While MK differed significantly between CE-L and non-enhancing lesions, MD did not.

Conclusion

MK adds predictive value to differentiate between MS lesions and might provide further information about diffuse white matter injury and lesion microstructure.

The effect of gradient nonlinearities on fiber orientation estimates from spherical deconvolution of diffusion magnetic resonance imaging data

Gradient nonlinearities in magnetic resonance imaging (MRI) cause spatially varying mismatches between the imposed and the effective gradients and can cause significant biases in rotationally invariant diffusion MRI measures derived from, for example, diffusion tensor imaging. The estimation of the orientational organization of fibrous tissue, which is nowadays frequently performed with spherical deconvolution techniques ideally using higher diffusion weightings, can likewise be biased by gradient nonlinearities. We explore the sensitivity of two established spherical deconvolution approaches to gradient nonlinearities, namely constrained spherical deconvolution (CSD) and damped Richardson-Lucy (dRL). Additionally, we propose an extension of dRL to take into account gradient imperfections, without the need of data interpolation. Simulations show that using the effective b-matrix can improve dRL fiber orientation estimation and reduces angular deviations, while CSD can be more robust to gradient nonlinearity depending on the implementation. Angular errors depend on a complex interplay of many factors, including the direction and magnitude of gradient deviations, underlying microstructure, SNR, anisotropy of the effective response function, and diffusion weighting. Notably, angular deviations can also be observed at lower b-values in contrast to the perhaps common assumption that only high b-value data are affected. In in vivo Human Connectome Project data and acquisitions from an ultrastrong gradient (300 mT/m) scanner, angular differences are observed between applying and not applying the effective gradients in dRL estimation. As even small angular differences can lead to error propagation during tractography and as such impact connectivity analyses, incorporating gradient deviations into the estimation of fiber orientations should make such analyses more reliable.

Computing and visualising intra-voxel orientation-specific relaxation-diffusion features in the human brain

Diffusion MRI techniques are used widely to study the characteristics of the human brain connectome in vivo. However, to resolve and characterise white matter (WM) fibres in heterogeneous MRI voxels remains a challenging problem typically approached with signal models that rely on prior information and constraints. We have recently introduced a 5D relaxation-diffusion correlation framework wherein multidimensional diffusion encoding strategies are used to acquire data at multiple echo-times to increase the amount of information encoded into the signal and ease the constraints needed for signal inversion. Nonparametric Monte Carlo inversion of the resulting datasets yields 5D relaxation-diffusion distributions where contributions from different sub-voxel tissue environments are separated with minimal assumptions on their microscopic properties. Here, we build on the 5D correlation approach to derive fibre-specific metrics that can be mapped throughout the imaged brain volume. Distribution components ascribed to fibrous tissues are resolved, and subsequently mapped to a dense mesh of overlapping orientation bins to define a smooth orientation distribution function (ODF). Moreover, relaxation and diffusion measures are correlated to each independent ODF coordinate, thereby allowing the estimation of orientation-specific relaxation rates and diffusivities. The proposed method is tested on a healthy volunteer, where the estimated ODFs were observed to capture major WM tracts, resolve fibre crossings, and, more importantly, inform on the relaxation and diffusion features along with distinct fibre bundles. If combined with fibre-tracking algorithms, the methodology presented in this work has potential for increasing the depth of characterisation of microstructural properties along individual WM pathways.

Hierarchical Microstructure Informed Tractography

Background: Tractography uses diffusion magnetic resonance imaging to noninvasively infer the macroscopic pathways of white matter fibers and it is the only available technique to probe in vivo the structural connectivity of the brain. However, despite this unique and compelling ability and its wide range of possible neurological applications, tractography is still limited, lacks anatomical precision, and suffers from a serious sensitivity/specificity trade-off. For this reason, in the past few years, tractography postprocessing techniques have emerged and proved effective for improving the quality of the reconstructions. Among them, the Convex Optimization Modeling for Microstructure Informed Tractography formulation allows incorporating the anatomical prior that fibers are naturally organized in fascicles, and has obtained exceptional results in increasing the accuracy of the estimated tractograms. Methods: We propose an extension to this idea and introduce a multilevel grouping of the streamlines to capture the white matter arrangement in fascicles and subfascicles. We tested our proposed formulation in synthetic and in vivo data. Results: Our experiments show that using multiple levels allows considering information about the white matter organization more adequately and helps to improve further the accuracy of the resulting tractograms. Conclusion: This new formulation represents a further important step toward a more accurate structural connectivity estimation.

Longitudinal Reproducibility of Neurite Orientation Dispersion and Density Imaging (NODDI) Derived Metrics in the White Matter

Diffusion-weighted magnetic resonance imaging (DWI) is undergoing constant evolution with the ambitious goal of developing in-vivo histology of the brain. A recent methodological advancement is Neurite Orientation Dispersion and Density Imaging (NODDI), a histologically validated multi-compartment model to yield microstructural features of brain tissue such as geometric complexity and neurite packing density, which are especially useful in imaging the white matter. Since NODDI is increasingly popular in clinical research and fields such as developmental neuroscience and neuroplasticity, it is of vast importance to characterize its reproducibility (or reliability). We acquired multi-shell DWI data in 29 healthy young subjects twice over a rescan interval of 4 weeks to assess the within-subject coefficient of variation (CV_WS), between-subject coefficient of variation (CV_BS) and the intraclass correlation coefficient (ICC), respectively. Using these metrics, we compared regional and voxel-by-voxel reproducibility of the most common image analysis approaches (tract-based spatial statistics [TBSS], voxel-based analysis with different extents of smoothing ["VBM-style"], ROI-based analysis). We observed high test-retest reproducibility for the orientation dispersion index (ODI) and slightly worse results for the neurite density index (NDI). Our findings also suggest that the choice of analysis approach might have significant consequences for the results of a study. Collectively, the voxel-based approach with Gaussian smoothing kernels of ≥4 mm FWHM and ROI-averaging yielded the highest reproducibility across NDI and ODI maps (CV_WS mostly ≤3%, ICC mostly ≥0.8), respectively, whilst smaller kernels and TBSS performed consistently worse. Furthermore, we demonstrate that image quality (signal-to-noise ratio [SNR]) is an important determinant of NODDI metric reproducibility. We discuss the implications of these results for longitudinal and cross-sectional research designs commonly employed in the neuroimaging field.

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.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Toward Quantification: Microstructure and Magnetic Resonance Fingerprinting

Quantitative magnetic resonance imaging (MRI) is a long-standing challenge. We advocate that the origin of the problem is the simplification applied in commonly used models of the MRI signal relation to the target parameters of biological tissues. Two research fields are briefly reviewed as ways to respond to the challenge of quantitative MRI, both experiencing an exponential growth right now. Microstructure MRI strives to build physiology-based models from cells to signal and, given the signal, back to the cells again. Magnetic resonance fingerprinting aims at efficient simultaneous determination of multiple signal parameters. The synergy of these yet disjoined approaches promises truly quantitative MRI with specific target-oriented diagnostic tools rather than universal imaging methods.

Electrospinning for healthcare: recent advancements

This perspective explores recent developments and innovations in the electrospinning technique and their potential applications in biomedicine.

Longitudinal Structural MRI Findings in Individuals at Genetic and Clinical High Risk for Psychosis: A Systematic Review

Background: Several cross-sectional studies report brain structure differences between healthy volunteers and subjects at genetic or clinical high risk of developing schizophrenia. However, longitudinal studies are important to determine whether altered trajectories of brain development precede psychosis onset. Methods: We conducted a systematic review to determine if brain trajectories differ between (i) those with psychotic experiences (PE), genetic (GHR) or clinical high risk (CHR), compared to healthy volunteers, and (ii) those who transition to psychosis compared to those who do not. Results: Thirty-eight studies measured gray matter and 18 studies measured white matter in 2,473 high risk subjects and 990 healthy volunteers. GHR, CHR, and PE subjects show an accelerated decline in gray matter primarily in temporal, and also frontal, cingulate and parietal cortex. In those who remain symptomatic or transition to psychosis, gray matter loss is more pronounced in these brain regions. White matter volume and fractional anisotropy, which typically increase until early adulthood, did not change or reduced in high risk subjects in the cingulum, thalamic radiation, cerebellum, retrolenticular part of internal capsule, and hippocampal-thalamic tracts. In those who transitioned, white matter volume and fractional anisotropy reduced over time in the inferior and superior fronto-occipital fasciculus, corpus callosum, anterior limb of the internal capsule, superior corona radiate, and calcarine cortex. Conclusion: High risk subjects show deficits in white matter maturation and an accelerated decline in gray matter. Gray matter loss is more pronounced in those who transition to psychosis, but may normalize by early adulthood in remitters.

Microstructural changes in the brain after long-term post-concussion symptoms: A randomized trial

A recent randomized controlled trial in young patients with long-term post-concussion symptoms showed that a novel behavioral intervention "Get going After concussIoN" is superior to enhanced usual care in terms of symptom reduction. It is unknown whether these interventional effects are associated with microstructural brain changes. The aim of this study was to examine whether diffusion-weighted MRI indices, which are sensitive to the interactions between cellular structures and water molecules' Brownian motion, respond differently to the interventions of the above-mentioned trial and whether such differences correlate with the improvement of post-concussion symptoms. Twenty-three patients from the intervention group (mean age 22.8, 18 females) and 19 patients from the control group (enhanced usual care) (mean age 23.9, 14 females) were enrolled. The primary outcome measure was the mean kurtosis tensor, which is sensitive to the microscopic complexity of brain tissue. The mean kurtosis tensor was significantly increased in the intervention group (p = 0.003) in the corpus callosum but not in the thalamus (p = 0.78) and the hippocampus (p = 0.34). An increase in mean kurtosis tensor in the corpus callosum tended to be associated with a reduction in symptoms, but this association did not reach significance (p = 0.059). Changes in diffusion tensor imaging metrics did not differ between intervention groups and were not associated with symptoms. The current study found different diffusion-weighted MRI responses from the microscopic cellular structures of the corpus callosum between patients receiving a novel behavioral intervention and patients receiving enhanced usual care. Correlations with improvement of post-concussion symptoms were not evident.

Probing neural tissues at small scales: Recent progress of oscillating gradient spin echo (OGSE) neuroimaging in humans

The detection sensitivity of diffusion MRI (dMRI) is dependent on diffusion times. A shorter diffusion time can increase the sensitivity to smaller length scales. However, the conventional dMRI uses the pulse gradient spin echo (PGSE) sequence that probes relatively long diffusion times only. To overcome this, the oscillating gradient spin echo (OGSE) sequence has been developed to probe much shorter diffusion times with hardware limitations on preclinical and clinical MRI systems. The OGSE sequence has been previously used on preclinical animal MRI systems. Recently, several studies have translated the OGSE sequence to humans on clinical MRI systems and achieved new information that is invisible using conventional PGSE sequence. This paper provides an overview of the recent progress of the OGSE neuroimaging in humans, including the technical improvements in the translation of the OGSE sequence to human imaging and various applications in different neurological disorders and stroke. Some possible future directions of the OGSE sequence are also discussed.

A simple estimate of axon size with diffusion MRI

Noninvasive estimation of mean axon diameter presents a new opportunity to explore white matter plasticity, development, and pathology. Several diffusion-weighted MRI (DW-MRI) methods have been proposed to measure the average axon diameter in white matter, but they typically require many diffusion encoding measurements and complicated mathematical models to fit the signal to multiple tissue compartments, including intra- and extra-axonal spaces. Here, Monte Carlo simulations uncovered a straightforward DW-MRI metric of axon diameter: the change in radial apparent diffusion coefficient estimated at different effective diffusion times, ΔD_⊥. Simulations indicated that this metric increases monotonically within a relevant range of effective mean axon diameter while being insensitive to changes in extra-axonal volume fraction, axon diameter distribution, g-ratio, and influence of myelin water. Also, a monotonic relationship was found to exist for signals coming from both intra- and extra-axonal compartments. The slope in ΔD_⊥ with effective axon diameter increased with the difference in diffusion time of both oscillating and pulsed gradient diffusion sequences.

Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images

BACKGROUND

Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries.

NEW METHOD

Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations.

RESULTS

Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange.

COMPARISON WITH EXISTING METHODS

To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes.

CONCLUSIONS

The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T₁ and T₂ NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T₂^* effects and flow.

In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

The dependence of the diffusion MRI signal on the diffusion time t is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity D(t) and mean kurtosis K(t) in cortical gray matter and in 25 ​gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for t=21.2-100 ​ms, and is characterized by a power-law tail ∼t-ϑ with dynamical exponent ϑ. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using the effective medium theory formalism, we derive an exact relation between the power-law tails in D(t) and K(t). The estimated dynamical exponent ϑ≃1/2 in both D(t) and K(t) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the ϑ=1/2 exponent. In contrast, the Kärger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from K(t) falls below our measured t-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the t-1/2 tail in D(t) and K(t) altogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

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.

In vivo microstructural heterogeneity of white matter lesions in healthy elderly and Alzheimer's disease participants using tissue compositional analysis of diffusion MRI data

White matter hyperintensities (WMH) are regions of high signal intensity typically identified on fluid attenuated inversion recovery (FLAIR). Although commonly observed in elderly individuals, they are more prevalent in Alzheimer's disease (AD) patients. Given that WMH appear relatively homogeneous on FLAIR, they are commonly partitioned into location- or distance-based classes when investigating their relevance to disease. Since pathology indicates that such lesions are often heterogeneous, probing their microstructure in vivo may provide greater insight than relying on such arbitrary classification schemes. In this study, we investigated WMH in vivo using an advanced diffusion MRI method known as single-shell 3-tissue constrained spherical deconvolution (SS3T-CSD), which models white matter microstructure while accounting for grey matter and CSF compartments. Diffusion MRI data and FLAIR images were obtained from AD (n = 48) and healthy elderly control (n = 94) subjects. WMH were automatically segmented, and classified: (1) as either periventricular or deep; or (2) into three distance-based contours from the ventricles. The 3-tissue profile of WMH enabled their characterisation in terms of white matter-, grey matter-, and fluid-like characteristics of the diffusion signal. Our SS3T-CSD findings revealed substantial heterogeneity in the 3-tissue profile of WMH, both within lesions and across the various classes. Moreover, this heterogeneity information indicated that the use of different commonly used WMH classification schemes can result in different disease-based conclusions. We conclude that future studies of WMH in AD would benefit from inclusion of microstructural information when characterising lesions, which we demonstrate can be performed in vivo using SS3T-CSD.

Super-Resolved q-Space deep learning with uncertainty quantification

Diffusion magnetic resonance imaging (dMRI) provides a noninvasive method for measuring brain tissue microstructure. q-Space deep learning(q-DL) methods have been developed to accurately estimate tissue microstructure from dMRI scans acquired with a reduced number of diffusion gradients. In these methods, deep networks are trained to learn the mapping directly from diffusion signals to tissue microstructure. However, the quality of tissue microstructure estimation can be limited not only by the reduced number of diffusion gradients but also by the low spatial resolution of typical dMRI acquisitions. Therefore, in this work we extend q-DL to super-resolved tissue microstructure estimation and propose super-resolvedq-DL (SR-q-DL), where deep networks are designed to map low-resolution diffusion signals undersampled in the q-space to high-resolution tissue microstructure. Specifically, we use a patch-based strategy, where a deep network takes low-resolution patches of diffusion signals as input and outputs high-resolution tissue microstructure patches. The high-resolution patches are then combined to obtain the final high-resolution tissue microstructure map. Motivated by existing q-DL methods, we integrate the sparsity of diffusion signals in the network design, which comprises two functional components. The first component computes sparse representation of diffusion signals for the low-resolution input patch, and the second component maps the low-resolution sparse representation to high-resolution tissue microstructure. The weights in the two components are learned jointly and the trained network performs end-to-end tissue microstructure estimation. In addition to SR-q-DL, we further propose probabilistic SR-q-DL, which can quantify the uncertainty of the network output as well as achieve improved estimation accuracy. In probabilistic SR-q-DL, a deep ensemble strategy is used. Specifically, the deep network for SR-q-DL is revised to produce not only tissue microstructure estimates but also the uncertainty of the estimates. Then, multiple deep networks are trained and their results are fused for the final prediction of high-resolution tissue microstructure and uncertainty quantification. The proposed method was evaluated on two independent datasets of brain dMRI scans. Results indicate that our approach outperforms competing methods in terms of estimation accuracy. In addition, uncertainty measures provided by our method correlate with estimation errors, which indicates potential application of the proposed uncertainty quantification method in brain studies.

The present and the future of microstructure MRI: From a paradigm shift to normal science

The aspiration of imaging tissue microstructure with MRI is to uncover micrometer-scale tissue features within millimeter-scale imaging voxels, in vivo. This kind of super-resolution has fueled a paradigm shift within the biomedical imaging community. However, what feels like an ongoing revolution in MRI, has been conceptually experienced in physics decades ago; from this point of view, our current developments can be seen as Thomas Kuhn's "normal science" stage of progress. While the concept of model-based quantification below the nominal imaging resolution is not new, its possibilities in neuroscience and neuroradiology are only beginning to be widely appreciated. This disconnect calls for communicating the progress of tissue microstructure MR imaging to its potential users. Here, a number of recent research developments are outlined in terms of the overarching concept of coarse-graining the tissue structure over an increasing diffusion length. A variety of diffusion models and phenomena are summarized on the phase diagram of diffusion MRI, with the unresolved problems and future directions corresponding to its unexplored domains.

Low-frequency dominant electrical conductivity imaging of in vivo human brain using high-frequency conductivity at Larmor-frequency and spherical mean diffusivity without external injection current

Diffusion weighted imaging based on random Brownian motion of water molecules within a voxel provides information on the micro-structure of biological tissues through water molecule diffusivity. As the electrical conductivity is primarily determined by the concentration and mobility of ionic charge carriers, the macroscopic electrical conductivity of biological tissues is also related to the diffusion of electrical ions. This paper aims to investigate the low-frequency electrical conductivity by relying on a pre-defined biological model that separates the brain into the intracellular (restricted) and extracellular (hindered) compartments. The proposed method uses B1 mapping technique, which provides a high-frequency conductivity distribution at Larmor frequency, and the spherical mean technique, which directly estimates the microscopic tissue structure based on the water molecule diffusivity and neurite orientation distribution. The total extracellular ion concentration, which is separated from the high-frequency conductivity, is recovered using the estimated diffusivity parameters and volume fraction in each compartment. We propose a method to reconstruct the low-frequency dominant conductivity tensor by taking into consideration the extracted extracellular diffusion tensor map and the reconstructed electrical parameters. To demonstrate the reliability of the proposed method, we conducted two phantom experiments. The first one used a cylindrical acrylic cage filled with an agar in the background region and four anomalies for the effect of ion concentration on the electrical conductivity. The other experiment, in which the effect of ion mobility on the conductivity was verified, used cell-like materials with thin insulating membranes suspended in an electrolyte. Animal and human brain experiments were conducted to visualize the low-frequency dominant conductivity tensor images. The proposed method using a conventional MRI scanner can predict the internal current density map in the brain without directly injected external currents.

Mesoscale diffusion magnetic resonance imaging of the ex vivo human hippocampus

Mesoscale diffusion magnetic resonance imaging (MRI) endeavors to bridge the gap between macroscopic white matter tractography and microscopic studies investigating the cytoarchitecture of human brain tissue. To ensure a robust measurement of diffusion at the mesoscale, acquisition parameters were arrayed to investigate their effects on scalar indices (mean, radial, axial diffusivity, and fractional anisotropy) and streamlines (i.e., graphical representation of axonal tracts) in hippocampal layers. A mesoscale resolution afforded segementation of the pyramidal cell layer (CA1-4), the dentate gyrus, as well as stratum moleculare, radiatum, and oriens. Using ex vivo samples, surgically excised from patients with intractable epilepsy (n = 3), we found that shorter diffusion times (23.7 ms) with a b-value of 4,000 s/mm2 were advantageous at the mesoscale, providing a compromise between mean diffusivity and fractional anisotropy measurements. Spatial resolution and sample orientation exerted a major effect on tractography, whereas the number of diffusion gradient encoding directions minimally affected scalar indices and streamline density. A sample temperature of 15°C provided a compromise between increasing signal-to-noise ratio and increasing the diffusion properties of the tissue. Optimization of the acquisition afforded a system's view of intra- and extra-hippocampal connections. Tractography reflected histological boundaries of hippocampal layers. Individual layer connectivity was visualized, as well as streamlines emanating from individual sub-fields. The perforant path, subiculum and angular bundle demonstrated extra-hippocampal connections. Histology of the samples confirmed individual cell layers corresponding to ROIs defined on MR images. We anticipate that this ex vivo mesoscale imaging will yield novel insights into human hippocampal connectivity.

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.

Neuroanatomical underpinning of diffusion kurtosis measurements in the cerebral cortex of healthy macaque brains

PURPOSE

To investigate the neuroanatomical underpinning of healthy macaque brain cortical microstructure measured by diffusion kurtosis imaging (DKI), which characterizes non-Gaussian water diffusion.

METHODS

High-resolution DKI was acquired from 6 postmortem macaque brains. Neurofilament density (ND) was quantified based on structure tensor from neurofilament histological images of a different macaque brain sample. After alignment of DKI-derived mean kurtosis (MK) maps to the histological images, MK and histology-based ND were measured at corresponding regions of interests characterized by distinguished cortical MK values in the prefrontal/precentral-postcentral and temporal cortices. Pearson correlation was performed to test significant correlation between these cortical MK and ND measurements.

RESULTS

Heterogeneity of cortical MK across different cortical regions was revealed, with significantly and consistently higher MK measurements in the prefrontal/precentral-postcentral cortex compared to those in the temporal cortex across all six scanned macaque brains. Corresponding higher ND measurements in the prefrontal/precentral-postcentral cortex than in the temporal cortex were also found. The heterogeneity of cortical MK is associated with heterogeneity of histology-based ND measurements, with significant correlation between cortical MK and corresponding ND measurements (P < .005).

CONCLUSION

These findings suggested that DKI-derived MK can potentially be an effective noninvasive biomarker quantifying underlying neuroanatomical complexity inside the cerebral cortical mantle for clinical and neuroscientific research.

White matter microstructure across the adult lifespan: A mixed longitudinal and cross-sectional study using advanced diffusion models and brain-age prediction

The macro- and microstructural architecture of human brain white matter undergoes substantial alterations throughout development and ageing. Most of our understanding of the spatial and temporal characteristics of these lifespan adaptations come from magnetic resonance imaging (MRI), including diffusion MRI (dMRI), which enables visualisation and quantification of brain white matter with unprecedented sensitivity and detail. However, with some notable exceptions, previous studies have relied on cross-sectional designs, limited age ranges, and diffusion tensor imaging (DTI) based on conventional single-shell dMRI. In this mixed cross-sectional and longitudinal study (mean interval: 15.2 months) including 702 multi-shell dMRI datasets, we combined complementary dMRI models to investigate age trajectories in healthy individuals aged 18 to 94 years (57.12% women). Using linear mixed effect models and machine learning based brain age prediction, we assessed the age-dependence of diffusion metrics, and compared the age prediction accuracy of six different diffusion models, including diffusion tensor (DTI) and kurtosis imaging (DKI), neurite orientation dispersion and density imaging (NODDI), restriction spectrum imaging (RSI), spherical mean technique multi-compartment (SMT-mc), and white matter tract integrity (WMTI). The results showed that the age slopes for conventional DTI metrics (fractional anisotropy [FA], mean diffusivity [MD], axial diffusivity [AD], radial diffusivity [RD]) were largely consistent with previous research, and that the highest performing advanced dMRI models showed comparable age prediction accuracy to conventional DTI. Linear mixed effects models and Wilk's theorem analysis showed that the 'FA fine' metric of the RSI model and 'orientation dispersion' (OD) metric of the NODDI model showed the highest sensitivity to age. The results indicate that advanced diffusion models (DKI, NODDI, RSI, SMT mc, WMTI) provide sensitive measures of age-related microstructural changes of white matter in the brain that complement and extend the contribution of conventional DTI.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Characterization of multiple sclerosis lesions with distinct clinical correlates through quantitative diffusion MRI

Diffusion magnetic resonance imaging can reveal quantitative information about the tissue changes in multiple sclerosis. The recently developed multi-compartment spherical mean technique can map different microscopic properties based only on local diffusion signals, and it may provide specific information on the underlying microstructural modifications that arise in multiple sclerosis. Given that the lesions in multiple sclerosis may reflect different degrees of damage, we hypothesized that quantitative diffusion maps may help characterize the severity of lesions "in vivo" and correlate these to an individual's clinical profile. We evaluated this in a cohort of 59 multiple sclerosis patients (62% female, mean age 44.7 years), for whom demographic and disease information was obtained, and who underwent a comprehensive physical and cognitive evaluation. The magnetic resonance imaging protocol included conventional sequences to define focal lesions, and multi-shell diffusion imaging was used with b-values of 1000, 2000 and 3000 s/mm² in 180 encoding directions. Quantitative diffusion properties on a macro- and micro-scale were used to discriminate distinct types of lesions through a k-means clustering algorithm, and the number and volume of those lesion types were correlated with parameters of the disease. The combination of diffusion tensor imaging metrics (fractional anisotropy and radial diffusivity) and multi-compartment spherical mean technique values (microscopic fractional anisotropy and intra-neurite volume fraction) differentiated two type of lesions, with a prediction strength of 0.931. The B-type lesions had larger diffusion changes compared to the A-type lesions, irrespective of their location (P < 0.001). The number of A and B type lesions was similar, although in juxtacortical areas B-type lesions predominated (60%, P < 0.001). Also, the percentage of B-type lesion volume was higher (64%, P < 0.001), indicating that these lesions were larger. The number and volume of B-type lesions was related to the severity of disease evolution, clinical disability and cognitive decline (P = 0.004, Bonferroni correction). Specifically, more and larger B-type lesions were correlated with a worse Multiple Sclerosis Severity Score, cerebellar function and cognitive performance. Thus, by combining several microscopic and macroscopic diffusion properties, the severity of damage within focal lesions can be characterized, further contributing to our understanding of the mechanisms that drive disease evolution. Accordingly, the classification of lesion types has the potential to permit more specific and better-targeted treatment of patients with multiple sclerosis.

The impact of realistic axonal shape on axon diameter estimation using diffusion MRI

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D_⊥(t) and kurtosis K_⊥(t), to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D_⊥(t) is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K_⊥∣_t→∞ deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.

Assessment of MRI-based anomalous diffusion changes in brain ischemic stroke with a fractional motion model

The actual diffusion process in human brain has been shown to be anomalous comparing to that predicted with traditional diffusion MRI (dMRI) theory. Recently, dMRI based on fractional motion (FM) model has demonstrated the potential to accurately describe anomalous diffusion in vivo. In this work, we explored the potential value of FM model-based dMRI in quantificational identification of ischemic stroke and compared that with the traditional apparent diffusion coefficient (ADC). We included 23 acute stroke patients, 8 of whom finished a follow-up scan, and 22 matched healthy controls. The dMRI images were acquired by using a Stejskal-Tanner single-shot spin-echo echo-planar-imaging sequence (diffusion gradients were applied in three orthogonal directions with 25 non-zero b values ranging from 248 to 4474 s/mm²) at 3.0 T MRI. We calculated the coefficient of variation (CV) for FM-related parameters in stroke lesions, and compared the mean values for FM-related parameters and ADC by using two-sample t-tests. Correlation analysis was achieved using Pearson correlation coefficient test. In acute stroke lesions, CV for FM-related parameters showed significant increase compared with normal tissues (P < 0.01), while those of ADC didn't appear statistical difference. Mean values for FM-related parameters showed significant decrease in acute lesion (P < 0.01) and their changing pattern during follow-up was positively correlated with ADC (P < 0.005). Our results initially verified the utility of the FM-model in detecting ischemic stroke compared with traditional dMRI.

Diffusion-prepared 3D gradient spin-echo sequence for improved oscillating gradient diffusion MRI

PURPOSE

Oscillating gradient (OG) enables the access of short diffusion times for time-dependent diffusion MRI (dMRI); however, it poses several technical challenges for clinical use. This study proposes a 3D oscillating gradient-prepared gradient spin-echo (OGprep-GRASE) sequence to improve SNR and shorten acquisition time for OG dMRI on clinical scanners.

METHODS

The 3D OGprep-GRASE sequence consisted of global saturation, diffusion encoding, fat saturation, and GRASE readout modules. Multiplexed sensitivity-encoding reconstruction was used to correct the phase errors between multiple shots. We compared the scan time and SNR of the proposed sequence and the conventional 2D-EPI sequence for OG dMRI at 30-90-mm slice coverage. We also examined the time-dependent diffusivity changes with OG dMRI acquired at frequencies of 50 Hz and 25 Hz and pulsed-gradient dMRI at diffusion times of 30 ms and 60 ms.

RESULTS

The OGprep-GRASE sequence reduced the scan time by a factor of 1.38, and increased the SNR by 1.74-2.27 times compared with 2D EPI for relatively thick slice coverage (60-90 mm). The SNR gain led to improved diffusion-tensor reconstruction in the multishot protocols. Image distortion in 2D-EPI images was also reduced in GRASE images. Diffusivity measurements from the pulsed-gradient dMRI and OG dMRI showed clear diffusion-time dependency in the white matter and gray matter of the human brain, using both the GRASE and EPI sequences.

CONCLUSION

The 3D OGprep-GRASE sequence improved scan time and SNR and reduced image distortion compared with the 2D multislice acquisition for OG dMRI on a 3T clinical system, which may facilitate the clinical translation of time-dependent dMRI.

A time-dependent diffusion MRI signature of axon caliber variations and beading

MRI provides a unique non-invasive window into the brain, yet is limited to millimeter resolution, orders of magnitude coarser than cell dimensions. Here, we show that diffusion MRI is sensitive to the micrometer-scale variations in axon caliber or pathological beading, by identifying a signature power-law diffusion time-dependence of the along-fiber diffusion coefficient. We observe this signature in human brain white matter and identify its origins by Monte Carlo simulations in realistic substrates from 3-dimensional electron microscopy of mouse corpus callosum. Simulations reveal that the time-dependence originates from axon caliber variation, rather than from mitochondria or axonal undulations. We report a decreased amplitude of time-dependence in multiple sclerosis lesions, illustrating the potential sensitivity of our method to axonal beading in a plethora of neurodegenerative disorders. This specificity to microstructure offers an exciting possibility of bridging across scales to image cellular-level pathology with a clinically feasible MRI technique.

Time-dependent Diffusion in Transient Splenial Lesion: Comparison between Oscillating-gradient Spin-echo Measurements and Monte-Carlo Simulation

The microstructural underpinnings of reduced diffusivity in transient splenial lesion remain unclear. Here, we report findings from oscillating gradient spin-echo (OGSE) diffusion imaging in a case of transient splenial lesion. Compared with normal-appearing white matter, the splenial lesion exhibited greater differences between diffusion time t = 6.5 and 35.2 ms, indicating microstructural changes occurring within the corresponding length scale. We also conducted 2D Monte-Carlo simulation. The results suggested that emergence of small and non-exchanging compartment, as often imagined in intramyelinic edema, does not fit well with the in vivo observation. Simulations with axonal swelling and microglial infiltration yielded results closer to the in vivo observations. The present report exemplifies the importance of controlling t for more specific radiological image interpretations.

A new method for accurate in vivo mapping of human brain connections using microstructural and anatomical information

Diffusion magnetic resonance imaging is a noninvasive imaging modality that has been extensively used in the literature to study the neuronal architecture of the brain in a wide range of neurological conditions using tractography. However, recent studies highlighted that the anatomical accuracy of the reconstructions is inherently limited and challenged its appropriateness. Several solutions have been proposed to tackle this issue, but none of them proved effective to overcome this fundamental limitation. In this work, we present a novel processing framework to inject into the reconstruction problem basic prior knowledge about brain anatomy and its organization and evaluate its effectiveness using both simulated and real human brain data. Our results indicate that our proposed method dramatically increases the accuracy of the estimated brain networks and, thus, represents a major step forward for the study of connectivity.

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.

Model-Based Deep Learning for Reconstruction of Joint k-q Under-sampled High Resolution Diffusion MRI

We propose a model-based deep learning architecture for the reconstruction of highly accelerated diffusion magnetic resonance imaging (MRI) that enables high resolution imaging. The proposed reconstruction jointly recovers all the diffusion weighted images in a single step from a joint k-q under-sampled acquisition in a parallel MRI setting. We propose the novel use of a pre-trained denoiser as a regularizer in a model-based reconstruction for the recovery of highly under-sampled data. Specifically, we designed the denoiser based on a general diffusion MRI tissue microstructure model for multi-compartmental modeling. By using a wide range of biologically plausible parameter values for the multi-compartmental microstructure model, we simulated diffusion signal that spans the entire microstructure parameter space. A neural network was trained in an unsupervised manner using an autoencoder to learn the diffusion MRI signal subspace. We employed the autoencoder in a model-based reconstruction and show that the autoencoder provides a strong denoising prior to recover the q-space signal. We show reconstruction results on a simulated brain dataset that shows high acceleration capabilities of the proposed method.