The absence of restricted water pool in brain white matter

Considerations and recommendations from the ISMRM Diffusion Study Group for preclinical diffusion MRI: Part 3-Ex vivo imaging: Data processing, comparisons with microscopy, and tractography

Preclinical diffusion MRI (dMRI) has proven value in methods development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. While dMRI enables in vivo non-invasive characterization of tissue, ex vivo dMRI is increasingly being used to probe tissue microstructure and brain connectivity. Ex vivo dMRI has several experimental advantages that facilitate high spatial resolution and high SNR images, cutting-edge diffusion contrasts, and direct comparison with histological data as a methodological validation. However, there are a number of considerations that must be made when performing ex vivo experiments. The steps from tissue preparation, image acquisition and processing, and interpretation of results are complex, with many decisions that not only differ dramatically from in vivo imaging of small animals, but ultimately affect what questions can be answered using the data. This work concludes a three-part series of recommendations and considerations for preclinical dMRI. Herein, we describe best practices for dMRI of ex vivo tissue, with a focus on image pre-processing, data processing, and comparisons with microscopy. In each section, we attempt to provide guidelines and recommendations but also highlight areas for which no guidelines exist (and why), and where future work should lie. We end by providing guidelines on code sharing and data sharing and point toward open-source software and databases specific to small animal and ex vivo imaging.

Comparative utility of MRI and EEG for early detection of cortical dysmaturation after postnatal systemic inflammation in the neonatal rat

BACKGROUND

Exposure to postnatal systemic inflammation is associated with increased risk of brain injury in preterm infants, leading to impaired maturation of the cerebral cortex and adverse neurodevelopmental outcomes. However, the optimal method for identifying cortical dysmaturation is unclear. Herein, we compared the utility of electroencephalography (EEG), diffusion tensor imaging (DTI), and neurite orientation dispersion and density imaging (NODDI) at different recovery times after systemic inflammation in newborn rats.

METHODS

Sprague Dawley rat pups of both sexes received single-daily lipopolysaccharide (LPS; 0.3 mg/kg i.p.; n = 51) or saline (n = 55) injections on postnatal days (P)1, 2, and 3. A subset of these animals were implanted with EEG electrodes. Cortical EEG was recorded for 30 min from unanesthetized, unrestrained pups at P7, P14, and P21, and in separate groups, brain tissues were collected at these ages for ex-vivo MRI analysis (9.4 T) and Golgi-Cox staining (to assess neuronal morphology) in the motor cortex.

RESULTS

Postnatal inflammation was associated with reduced cortical pyramidal neuron arborization from P7, P14, and P21. These changes were associated with dysmature EEG features (e.g., persistence of delta waveforms, higher EEG amplitude, reduced spectral edge frequency) at P7 and P14, and higher EEG power in the theta and alpha ranges at P21. By contrast, there were no changes in cortical DTI or NODDI in LPS rats at P7 or P14, while there was an increase in cortical fractional anisotropy (FA) and decrease in orientation dispersion index (ODI) at P21.

CONCLUSIONS

EEG may be useful for identifying the early evolution of impaired cortical development after early life postnatal systemic inflammation, while DTI and NODDI seem to be more suited to assessing established cortical changes.

High-resolution diffusion magnetic resonance imaging and spatial-transcriptomic in developing mouse brain

Brain development is a highly complex process regulated by numerous genes at the molecular and cellular levels. Brain tissue exhibits serial microstructural changes during the development process. High-resolution diffusion magnetic resonance imaging (dMRI) affords a unique opportunity to probe these changes in the developing brain non-destructively. In this study, we acquired multi-shell dMRI datasets at 32 µm isotropic resolution to investigate the tissue microstructure alterations, which we believe to be the highest spatial resolution dMRI datasets obtained for postnatal mouse brains. We adapted the Allen Developing Mouse Brain Atlas (ADMBA) to integrate quantitative MRI metrics and spatial transcriptomics. Diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), and neurite orientation dispersion and density imaging (NODDI) metrics were used to quantify brain development at different postnatal days. We demonstrated that the differential evolutions of fiber orientation distributions contribute to the distinct development patterns in white matter (WM) and gray matter (GM). Furthermore, the genes enriched in the nervous system that regulate brain structure and function were expressed in spatial correlation with age-matched dMRI. This study is the first one providing high-resolution dMRI, including DTI, DKI, and NODDI models, to trace mouse brain microstructural changes in WM and GM during postnatal development. This study also highlighted the genotype-phenotype correlation of spatial transcriptomics and dMRI, which may improve our understanding of brain microstructure changes at the molecular level.

Insights and improvements in correspondence between axonal volume fraction measured with diffusion-weighted MRI and electron microscopy

Biophysical diffusion-weighted imaging (DWI) models are increasingly used in neuroscience to estimate the axonal water fraction (f AW ), which in turn is key for noninvasive estimation of the axonal volume fraction (f A ). These models require thorough validation by comparison with a reference method, for example, electron microscopy (EM). While EM studies often neglect the unmyelinated axons and solely report the fraction of myelinated axons, in DWI both myelinated and unmyelinated axons contribute to the DWI signal. However, DWI models often include simplifications, for example, the neglect of differences in the compartmental relaxation times or fixed diffusivities, which in turn might affect the estimation off AW . We investigate whether linear calibration parameters (scaling and offset) can improve the comparability between EM- and DWI-based metrics off A . To this end, we (a) used six DWI models based on the so-called standard model of white matter (WM), including two models with fixed compartmental diffusivities (e.g., neurite orientation dispersion and density imaging, NODDI) and four models that fitted the compartmental diffusivities (e.g., white matter tract integrity, WMTI), and (b) used a multimodal data set including ex vivo diffusion DWI and EM data in mice with a broad dynamic range of fibre volume metrics. We demonstrated that the offset is associated with the volume fraction of unmyelinated axons and the scaling factor is associated with different compartmentalT 2 and can substantially enhance the comparability between EM- and DWI-based metrics off A . We found that DWI models that fitted compartmental diffusivities provided the most accurate estimates of the EM-basedf A . Finally, we introduced a more efficient hybrid calibration approach, where only the offset is estimated but the scaling is fixed to a theoretically predicted value. Using this approach, a similar one-to-one correspondence to EM was achieved for WMTI. The method presented can pave the way for use of validated DWI-based models in clinical research and neuroscience.

Quantitative MRI reveals widespread, network-specific myelination change during generalized epilepsy progression

Activity-dependent myelination is a fundamental mode of brain plasticity which significantly influences network function. We recently discovered that absence seizures, which occur in multiple forms of generalized epilepsy, can induce activity-dependent myelination, which in turn promotes further progression of epilepsy. Structural alterations of myelin are likely to be widespread, given that absence seizures arise from an extensive thalamocortical network involving frontoparietal regions of the bilateral hemispheres. However, the temporal course and spatial extent of myelin plasticity is unknown, due to limitations of gold-standard histological methods such as electron microscopy (EM). In this study, we leveraged magnetization transfer and diffusion MRI for estimation of g-ratios across major white matter tracts in a mouse model of generalized epilepsy with progressive absence seizures. EM was performed on the same brains after MRI. After seizure progression, we found increased myelination (decreased g-ratios) throughout the anterior portion (genu-to-body) of the corpus callosum but not in the posterior portion (body-splenium) nor in the fornix or the internal capsule. Curves obtained from averaging g-ratio values at every longitudinal point of the corpus callosum were statistically different with p<0.001. Seizure-associated myelin differences found in the corpus callosum body with MRI were statistically significant (p = 0.0027) and were concordant with EM in the same region (p = 0.01). Notably, these differences were not detected by diffusion tensor imaging. This study reveals widespread myelin structural change that is specific to the absence seizure network. Furthermore, our findings demonstrate the potential utility and importance of MRI-based g-ratio estimation to non-invasively detect myelin plasticity.

Mapping the individual human cortex using multidimensional MRI and unsupervised learning

Human evolution has seen the development of higher-order cognitive and social capabilities in conjunction with the unique laminar cytoarchitecture of the human cortex. Moreover, early-life cortical maldevelopment has been associated with various neurodevelopmental diseases. Despite these connections, there is currently no noninvasive technique available for imaging the detailed cortical laminar structure. This study aims to address this scientific and clinical gap by introducing an approach for imaging human cortical lamina. This method combines diffusion-relaxation multidimensional MRI with a tailored unsupervised machine learning approach that introduces enhanced microstructural sensitivity. This new imaging method simultaneously encodes the microstructure, the local chemical composition and importantly their correlation within complex and heterogenous tissue. To validate our approach, we compared the intra-cortical layers obtained using our ex vivo MRI-based method with those derived from Nissl staining of postmortem human brain specimens. The integration of unsupervised learning with diffusion-relaxation correlation MRI generated maps that demonstrate sensitivity to areal differences in cytoarchitectonic features observed in histology. Significantly, our observations revealed layer-specific diffusion-relaxation signatures, showing reductions in both relaxation times and diffusivities at the deeper cortical levels. These findings suggest a radial decrease in myelin content and changes in cell size and anisotropy, reflecting variations in both cytoarchitecture and myeloarchitecture. Additionally, we demonstrated that 1D relaxation and high-order diffusion MRI scalar indices, even when aggregated and used jointly in a multimodal fashion, cannot disentangle the cortical layers. Looking ahead, our technique holds the potential to open new avenues of research in human neurodevelopment and the vast array of disorders caused by disruptions in neurodevelopment.

Integrating multimodality magnetic resonance imaging to the Allen Mouse Brain Common Coordinate Framework

High-resolution magnetic resonance imaging (MRI) affords unique image contrasts to nondestructively probe the tissue microstructure; validation of MRI findings with conventional histology is essential to better understand the MRI contrasts. However, the dramatic difference in the spatial resolution and image contrast of these two techniques impedes accurate comparison between MRI metrics and traditional histology. To better validate various MRI metrics, we acquired whole mouse brain multigradient recalled-echo and multishell diffusion MRI datasets at 25-μm isotropic resolution. The recently developed Allen Mouse Brain Common Coordinate Framework (CCFv3) provides opportunities to integrate multimodal and multiscale datasets of the whole mouse brain in a common three-dimensional (3D) space. The T2*, quantitative susceptibility mapping, diffusion tensor imaging, and neurite orientation dispersion and density imaging parameters were compared with both serial two-photon tomography images and 3D Nissl staining images in the CCFv3 at the same spatial resolution. The correlation between MRI and Nissl staining strongly depends on different metrics and different regions of the brain. Integrating different imaging modalities to the same space may substantially improve our understanding of the complexity of the brain at different scales.

Both noise-floor and tissue compartment difference in diffusivity contribute to FA dependence on b-value in diffusion MRI

Noninvasive diffusion magnetic resonance imaging (dMRI) has been widely employed in both clinical and research settings to investigate brain tissue microstructure. Despite the evidence that dMRI-derived fractional anisotropy (FA) correlates with white matter properties, the metric is not specific. Recent studies have reported that FA is dependent on the b-value, and its origin has primarily been attributed to either the influence of microstructure or the noise-floor effect. A systematic investigation into the inter-relationship of these two effects is however still lacking. This study aims to quantify contributions of the reported differences in intra- and extra-neurite diffusivity to the observed changes in FA, in addition to the noise in measurements. We used in-vivo and post-mortem human brain imaging, as well as numerical simulations and histological validation, for this purpose. Our investigations reveal that the percentage difference of FA between b-values (pdFA) has significant positive associations with neurite density index (NDI), which is derived from in-vivo neurite orientation dispersion and density imaging (NODDI), or Bielschowsky's silver impregnation (BIEL) staining sections of fixed post-mortem human brain samples. Furthermore, such an association is found to be varied with Signal-to-Noise Ratio (SNR) level, indicating a nonlinear interaction effect between tissue microstructure and noise. Finally, a multicompartment model simulation revealed that these findings can be driven by differing diffusivities of intra- and extra-neurite compartments in tissue, with the noise-floor further amplifying the effect. In conclusion, both the differences in intra- and extra-neurite diffusivity and noise-floor effects significantly contribute to the FA difference associated with the b-value.

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Estimating axial diffusivity in the NODDI model

To estimate microstructure-related parameters from diffusion MRI data, biophysical models make strong, simplifying assumptions about the underlying tissue. The extent to which many of these assumptions are valid remains an open research question. This study was inspired by the disparity between the estimated intra-axonal axial diffusivity from literature and that typically assumed by the Neurite Orientation Dispersion and Density Imaging (NODDI) model (d_∥=1.7μm²/ms). We first demonstrate how changing the assumed axial diffusivity results in considerably different NODDI parameter estimates. Second, we illustrate the ability to estimate axial diffusivity as a free parameter of the model using high b-value data and an adapted NODDI framework. Using both simulated and in vivo data we investigate the impact of fitting to either real-valued or magnitude data, with Gaussian and Rician noise characteristics respectively, and what happens if we get the noise assumptions wrong in this high b-value and thus low SNR regime. Our results from real-valued human data estimate intra-axonal axial diffusivities of ∼2-2.5μm²/ms, in line with current literature. Crucially, our results demonstrate the importance of accounting for both a rectified noise floor and/or a signal offset to avoid biased parameter estimates when dealing with low SNR data.

Performance of orientation distribution function-fingerprinting with a biophysical multicompartment diffusion model

PURPOSE

Orientation Distribution Function (ODF) peak finding methods typically fail to reconstruct fibers crossing at shallow angles below 40°, leading to errors in tractography. ODF-Fingerprinting (ODF-FP) with the biophysical multicompartment diffusion model allows for breaking this barrier.

METHODS

A randomized mechanism to generate a multidimensional ODF-dictionary that covers biologically plausible ranges of intra- and extra-axonal diffusivities and fraction volumes is introduced. This enables ODF-FP to address the high variability of brain tissue. The performance of the proposed approach is evaluated on both numerical simulations and a reconstruction of major fascicles from high- and low-resolution in vivo diffusion images.

RESULTS

ODF-FP with the suggested modifications correctly identifies fibers crossing at angles as shallow as 10 degrees in the simulated data. In vivo, our approach reaches 56% of true positives in determining fiber directions, resulting in visibly more accurate reconstruction of pyramidal tracts, arcuate fasciculus, and optic radiations than the state-of-the-art techniques. Moreover, the estimated diffusivity values and fraction volumes in corpus callosum conform with the values reported in the literature.

CONCLUSION

The modified ODF-FP outperforms commonly used fiber reconstruction methods at shallow angles, which improves deterministic tractography outcomes of major fascicles. In addition, the proposed approach allows for linearization of the microstructure parameters fitting problem.

Mapping the human connectome using diffusion MRI at 300 mT/m gradient strength: Methodological advances and scientific impact

Tremendous efforts have been made in the last decade to advance cutting-edge MRI technology in pursuit of mapping structural connectivity in the living human brain with unprecedented sensitivity and speed. The first Connectom 3T MRI scanner equipped with a 300 mT/m whole-body gradient system was installed at the Massachusetts General Hospital in 2011 and was specifically constructed as part of the Human Connectome Project. Since that time, numerous technological advances have been made to enable the broader use of the Connectom high gradient system for diffusion tractography and tissue microstructure studies and leverage its unique advantages and sensitivity to resolving macroscopic and microscopic structural information in neural tissue for clinical and neuroscientific studies. The goal of this review article is to summarize the technical developments that have emerged in the last decade to support and promote large-scale and scientific studies of the human brain using the Connectom scanner. We provide a brief historical perspective on the development of Connectom gradient technology and the efforts that led to the installation of three other Connectom 3T MRI scanners worldwide - one in the United Kingdom in Cardiff, Wales, another in continental Europe in Leipzig, Germany, and the latest in Asia in Shanghai, China. We summarize the key developments in gradient hardware and image acquisition technology that have formed the backbone of Connectom-related research efforts, including the rich array of high-sensitivity receiver coils, pulse sequences, image artifact correction strategies and data preprocessing methods needed to optimize the quality of high-gradient strength diffusion MRI data for subsequent analyses. Finally, we review the scientific impact of the Connectom MRI scanner, including advances in diffusion tractography, tissue microstructural imaging, ex vivo validation, and clinical investigations that have been enabled by Connectom technology. We conclude with brief insights into the unique value of strong gradients for diffusion MRI and where the field is headed in the coming years.

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.

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.

Multi-tissue spherical deconvolution of tensor-valued diffusion MRI

Multi-tissue constrained spherical deconvolution (MT-CSD) leverages the characteristic b-value dependency of each tissue type to estimate both the apparent tissue densities and the white matter fiber orientation distribution function from diffusion MRI data. In this work, we generalize MT-CSD to tensor-valued diffusion encoding with arbitrary b-tensor shapes. This enables the use of data encoded with mixed b-tensors, rather than being limited to the subset of linear (conventional) b-tensors. Using the complete set of data, including all b-tensor shapes, provides a categorical improvement in the estimation of apparent tissue densities, fiber ODF, and resulting tractography. Furthermore, we demonstrate that including multiple b-tensor shapes in the analysis provides improved contrast between tissue types, in particular between gray matter and white matter. We also show that our approach provides high-quality apparent tissue density maps and high-quality fiber tracking from data, even with sparse sampling across b-tensors that yield whole-brain coverage at 2 mm isotropic resolution in approximately 5:15 min.

Axonal T2 estimation using the spherical variance of the strongly diffusion-weighted MRI signal

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T₂ that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T₂, as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T₂ based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T₂ estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system.

Accuracy and precision in super-resolution MRI: Enabling spherical tensor diffusion encoding at ultra-high b-values and high resolution

Diffusion MRI (dMRI) can probe the tissue microstructure but suffers from low signal-to-noise ratio (SNR) whenever high resolution is combined with high diffusion encoding strengths. Low SNR leads to poor precision as well as poor accuracy of the diffusion-weighted signal; the latter is caused by the rectified noise floor and can be observed as a positive bias in magnitude signal. Super-resolution techniques may facilitate a beneficial tradeoff between bias and resolution by allowing acquisition at low spatial resolution and high SNR, whereafter high spatial resolution is recovered by image reconstruction. In this work, we describe a super-resolution reconstruction framework for dMRI and investigate its performance with respect to signal accuracy and precision. Using phantom experiments and numerical simulations, we show that the super-resolution approach improves accuracy by facilitating a more beneficial trade-off between spatial resolution and diffusion encoding strength before the noise floor affects the signal. By contrast, precision is shown to have a less straightforward dependency on acquisition, reconstruction, and intrinsic tissue parameters. Indeed, we find a gain in precision from super-resolution reconstruction is substantial only when some spatial resolution is sacrificed. Finally, we deployed super-resolution reconstruction in a healthy brain for the challenging combination of spherical b-tensor encoding at ultra-high b-values and high spatial resolution—a configuration that produces a unique contrast that emphasizes tissue in which diffusion is restricted in all directions. This demonstration showcased that super-resolution reconstruction enables a vastly superior image contrast compared to conventional imaging, facilitating investigations that would otherwise have prohibitively low SNR, resolution or require non-conventional MRI hardware.

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.

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.

Evaluation of early microstructural changes in the R6/1 mouse model of Huntington's disease by ultra-high field diffusion MR imaging

Diffusion MRI (dMRI) has been able to detect early structural changes related to neurological symptoms present in Huntington's disease (HD). However, there is still a knowledge gap to interpret the biological significance at early neuropathological stages. The purpose of this study is two-fold: (i) establish if the combination of Ultra-High Field Diffusion MRI (UHFD-MRI) techniques can add a more comprehensive analysis of the early microstructural changes observed in HD, and (ii) evaluate if early changes in dMRI microstructural parameters can be linked to cellular biomarkers of neuroinflammation. Ultra-high field magnet (16.7T), diffusion tensor imaging (DTI), and neurite orientation dispersion and density imaging (NODDI) techniques were applied to fixed ex-vivo brains of a preclinical model of HD (R6/1 mice). Fractional anisotropy (FA) was decreased in deep and superficial grey matter (GM) as well as white matter (WM) brain regions with well-known early HD microstructure and connectivity pathology. NODDI parameters associated with the intracellular and extracellular compartment, such as intracellular ventricular fraction (ICVF), orientation dispersion index (ODI), and isotropic volume fractions (IsoVF) were altered in R6/1 mice GM. Further, histological studies in these areas showed that glia cell markers associated with neuroinflammation (GFAP & Iba1) were consistent with the dMRI findings. dMRI can be used to extract non-invasive information of neuropathological events present in the early stages of HD. The combination of multiple imaging techniques represents a better approach to understand the neuropathological process allowing the early diagnosis and neuromonitoring of patients affected by HD.

Long-term coordinated microstructural disruptions of the developing neocortex and subcortical white matter after early postnatal systemic inflammation

Severe postnatal systemic infection is highly associated with persistent disturbances in brain development and neurobehavioral outcomes in survivors of preterm birth. However, the contribution of less severe but prolonged postnatal infection and inflammation to such disturbances is unclear. Further, the ability of modern imaging techniques to detect the underlying changes in cellular microstructure of the brain in these infants remains to be validated. We used high-field ex-vivo MRI, neurohistopathology, and behavioral tests in newborn rats to demonstrate that prolonged postnatal systemic inflammation causes subtle, persisting disturbances in brain development, with neurodevelopmental delays and mild motor impairments. Diffusion-tensor MRI and neurite orientation dispersion and density imaging (NODDI) revealed delayed maturation of neocortical and subcortical white matter microstructure. Analysis of pyramidal neurons showed that the cortical deficits involved impaired dendritic arborization and spine formation. Analysis of oligodendrocytes showed that the white matter deficits involved impaired oligodendrocyte maturation and axonal myelination. These findings indicate that prolonged postnatal inflammation, without severe infection, may critically contribute to the diffuse spectrum of brain pathology and subtle long-term disability in preterm infants, with a cellular mechanism involving oligodendrocyte and neuronal dysmaturation. NODDI may be useful for clinical detection of these microstructural deficits.

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.

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

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.

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.

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.

Direct and specific assessment of axonal injury and spinal cord microenvironments using diffusion correlation imaging

We describe a practical two-dimensional (2D) diffusion MRI framework to deliver specificity and improve sensitivity to axonal injury in the spinal cord. This approach provides intravoxel distributions of correlations of water mobilities in orthogonal directions, revealing sub-voxel diffusion components. Here we use it to investigate water diffusivities along axial and radial orientations within spinal cord specimens with confirmed, tract-specific axonal injury. First, we show using transmission electron microscopy and immunohistochemistry that tract-specific axonal beading occurs following Wallerian degeneration in the cortico-spinal tract as direct sequelae to closed head injury. We demonstrate that although some voxel-averaged diffusion tensor imaging (DTI) metrics are sensitive to this axonal injury, they are non-specific, i.e., they do not reveal an underlying biophysical mechanism of injury. Then we employ 2D diffusion correlation imaging (DCI) to improve discrimination of different water microenvironments by measuring and mapping the joint water mobility distributions perpendicular and parallel to the spinal cord axis. We determine six distinct diffusion spectral components that differ according to their microscopic anisotropy and mobility. We show that at the injury site a highly anisotropic diffusion component completely disappears and instead becomes more isotropic. Based on these findings, an injury-specific MR image of the spinal cord was generated, and a radiological-pathological correlation with histological silver staining % area was performed. The resulting strong and significant correlation (r=0.70,p < 0.0001) indicates the high specificity with which DCI detects injury-induced tissue alterations. We predict that the ability to selectively image microstructural changes following axonal injury in the spinal cord can be useful in clinical and research applications by enabling specific detection and increased sensitivity to injury-induced microstructural alterations. These results also encourage us to translate DCI to higher spatial dimensions to enable assessment of traumatic axonal injury, and possibly other diseases and disorders in the brain.

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.

Microstructure with diffusion MRI: what scale we are sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructure MRI (μMRI) aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal-Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

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.

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.

Towards unconstrained compartment modeling in white matter using diffusion-relaxation MRI with tensor-valued diffusion encoding

PURPOSE

To optimize diffusion-relaxation MRI with tensor-valued diffusion encoding for precise estimation of compartment-specific fractions, diffusivities, and T₂ values within a two-compartment model of white matter, and to explore the approach in vivo.

METHODS

Sampling protocols featuring different b-values (b), b-tensor shapes (b_Δ ), and echo times (TE) were optimized using Cramér-Rao lower bounds (CRLB). Whole-brain data were acquired in children, adults, and elderly with white matter lesions. Compartment fractions, diffusivities, and T₂ values were estimated in a model featuring two microstructural compartments represented by a "stick" and a "zeppelin."

RESULTS

Precise parameter estimates were enabled by sampling protocols featuring seven or more "shells" with unique b/b_Δ /TE-combinations. Acquisition times were approximately 15 minutes. In white matter of adults, the "stick" compartment had a fraction of approximately 0.5 and, compared with the "zeppelin" compartment, featured lower isotropic diffusivities (0.6 vs. 1.3 μm² /ms) but higher T₂ values (85 vs. 65 ms). Children featured lower "stick" fractions (0.4). White matter lesions exhibited high "zeppelin" isotropic diffusivities (1.7 μm² /ms) and T₂ values (150 ms).

CONCLUSIONS

Diffusion-relaxation MRI with tensor-valued diffusion encoding expands the set of microstructure parameters that can be precisely estimated and therefore increases their specificity to biological quantities.

Nonivasive quantification of axon radii using diffusion MRI

Axon caliber plays a crucial role in determining conduction velocity and, consequently, in the timing and synchronization of neural activation. Noninvasive measurement of axon radii could have significant impact on the understanding of healthy and diseased neural processes. Until now, accurate axon radius mapping has eluded in vivo neuroimaging, mainly due to a lack of sensitivity of the MRI signal to micron-sized axons. Here, we show how - when confounding factors such as extra-axonal water and axonal orientation dispersion are eliminated - heavily diffusion-weighted MRI signals become sensitive to axon radii. However, diffusion MRI is only capable of estimating a single metric, the effective radius, representing the entire axon radius distribution within a voxel that emphasizes the larger axons. Our findings, both in rodents and humans, enable noninvasive mapping of critical information on axon radii, as well as resolve the long-standing debate on whether axon radii can be quantified.

The dot-compartment revealed? Diffusion MRI with ultra-strong gradients and spherical tensor encoding in the living human brain

The so-called “dot-compartment” is conjectured in diffusion MRI to represent small spherical spaces, such as cell bodies, in which the diffusion is restricted in all directions. Previous investigations inferred its existence from data acquired with directional diffusion encoding which does not permit a straightforward separation of signals from ‘sticks’ (axons) and signals from ‘dots’. Here we combine isotropic diffusion encoding with ultra-strong diffusion gradients (240 ​mT/m) to achieve high diffusion-weightings with high signal to noise ratio, while suppressing signal arising from anisotropic water compartments with significant mobility along at least one axis (e.g., axons). A dot-compartment, defined to have apparent diffusion coefficient equal to zero and no exchange, would result in a non-decaying signal at very high b-values (b≳7000s/mm2). With this unique experimental setup, a residual yet slowly decaying signal above the noise floor for b-values as high as 15000s/mm2 was seen clearly in the cerebellar grey matter (GM), and in several white matter (WM) regions to some extent. Upper limits of the dot-signal-fraction were estimated to be 1.8% in cerebellar GM and 0.5% in WM. By relaxing the assumption of zero diffusivity, the signal at high b-values in cerebellar GM could be represented more accurately by an isotropic water pool with a low apparent diffusivity of 0.12 μm2/ms and a substantial signal fraction of 9.7%. The T2 of this component was estimated to be around 61ms. This remaining signal at high b-values has potential to serve as a novel and simple marker for isotropically-restricted water compartments in cerebellar GM.

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The “dot-compartment” is conjectured in diffusion MRI to represent e.g. cell bodies.

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We combine isotropic encoding with ultra-strong gradients to study the dot-compartment.

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A slowly decaying signal for high b-values was seen in cerebellar GM.

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An apparent diffusivity of 0.12 and signal fraction of 9.7% were estimated.

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The signal could serve as a novel and simple marker for spherical compartments.

On the need for bundle-specific microstructure kernels in diffusion MRI

Probing microstructure with diffusion magnetic resonance imaging (dMRI) on a scale orders of magnitude below the imaging resolution relies on biophysical modelling of the signal response in the tissue. The vast majority of these biophysical models of diffusion in white matter assume that the measured dMRI signal is the sum of the signals emanating from each of the constituent compartments, each of which exhibits a distinct behaviour in the b-value and/or orientation domain. Many of these models further assume that the dMRI behaviour of the oriented compartments (e.g. the intra-axonal space) is identical between distinct fibre populations, at least at the level of a single voxel. This implicitly assumes that any potential biological differences between fibre populations are negligible, at least as far as is measurable using dMRI. Here, we validate this assumption by means of a voxel-wise, model-free signal decomposition that, under the assumption above and in the absence of noise, is shown to be rank-1. We evaluate the effect size of signal components beyond this rank-1 representation and use permutation testing to assess their significance. We conclude that in the healthy adult brain, the dMRI signal is adequately represented by a rank-1 model, implying that biologically more realistic, but mathematically more complex fascicle-specific microstructure models do not capture statistically significant or anatomically meaningful structure, even in extended high-b diffusion MRI scans.

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

PURPOSE

Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, it has been shown recently that, in the general Standard Model, parameter estimation from dMRI data is ill-conditioned even when very high b-values are applied. We analyze this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from single diffusion encoding (SDE) to double diffusion encoding (DDE) resolves the ill-posedness for intermediate diffusion weightings, producing an increase in accuracy and precision of the parameter estimation.

METHODS

We analyze theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions.

RESULTS

We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space.

CONCLUSIONS

DDE adds additional information for estimating the model parameters, unexplored by SDE. We show, as an example, that this is sufficient to solve the previously reported degeneracies in the NODDIDA model parameter estimation.

Neurite orientation dispersion and density imaging of mouse brain microstructure

Advanced biophysical models like neurite orientation dispersion and density imaging (NODDI) have been developed to estimate the microstructural complexity of voxels enriched in dendrites and axons for both in vivo and ex vivo studies. NODDI metrics derived from high spatial and angular resolution diffusion MRI using the fixed mouse brain as a reference template have not yet been reported due in part to the extremely long scan time required. In this study, we modified the three-dimensional diffusion-weighted spin-echo pulse sequence for multi-shell and undersampling acquisition to reduce the scan time. This allowed us to acquire several exhaustive datasets that would otherwise not be attainable. NODDI metrics were derived from a complex 8-shell diffusion (1000-8000 s/mm²) dataset with 384 diffusion gradient-encoding directions at 50 µm isotropic resolution. These provided a foundation for exploration of tradeoffs among acquisition parameters. A three-shell acquisition strategy covering low, medium, and high b values with at least angular resolution of 64 is essential for ex vivo NODDI experiments. The good agreement between neurite density index (NDI) and the orientation dispersion index (ODI) with the subsequent histochemical analysis of myelin and neuronal density highlights that NODDI could provide new insight into the microstructure of the brain. Furthermore, we found that NDI is sensitive to microstructural variations in the corpus callosum using a well-established demyelination cuprizone model. The study lays the ground work for developing protocols for routine use of high-resolution NODDI method in characterizing brain microstructure in mouse models.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

Effects of nongaussian diffusion on "isotropic diffusion" measurements: An ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.

A unique analytical solution of the white matter standard model using linear and planar encodings

PURPOSE

It is known that white matter modeling based on commonly used linear diffusion encoding is an ill-posed problem. We analyze the additional information gained from a double pulsed diffusion encoding.

METHODS

Zeroth (spherical means) and second-order (harmonic powers) rotation invariant signal features are used to factor micro- and mesoscopic contributions. The b-value dependency up to second-order of the features form 6 nonlinear equations, which are analyzed.

RESULTS

The 6 derived equations can be uniquely solved for all relevant biophysical parameters. No assumptions about the form of the mesoscopic contribution (fiber dispersion) is necessary. Under certain conditions the solution still shows a certain degeneracy which is inherent to model. It is further shown that a combination of second-order information from single and spherical diffusion encoding is not enough to solve the problem.

CONCLUSIONS

A combination of single and double pulsed diffusion encodings is sufficient to solve the full 3 compartment white matter model uniquely.

Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI

The key component of a microstructural diffusion MRI 'super-scanner' is a dedicated high-strength gradient system that enables stronger diffusion weightings per unit time compared to conventional gradient designs. This can, in turn, drastically shorten the time needed for diffusion encoding, increase the signal-to-noise ratio, and facilitate measurements at shorter diffusion times. This review, written from the perspective of the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure, an initiative to establish a shared 300 mT/m-gradient facility amongst the microstructural imaging community, describes ten advantages of ultra-strong gradients for microstructural imaging. Specifically, we will discuss how the increase of the accessible measurement space compared to a lower-gradient systems (in terms of Δ, b-value, and TE) can accelerate developments in the areas of 1) axon diameter distribution mapping; 2) microstructural parameter estimation; 3) mapping micro-vs macroscopic anisotropy features with gradient waveforms beyond a single pair of pulsed-gradients; 4) multi-contrast experiments, e.g. diffusion-relaxometry; 5) tractography and high-resolution imaging in vivo and 6) post mortem; 7) diffusion-weighted spectroscopy of metabolites other than water; 8) tumour characterisation; 9) functional diffusion MRI; and 10) quality enhancement of images acquired on lower-gradient systems. We finally discuss practical barriers in the use of ultra-strong gradients, and provide an outlook on the next generation of 'super-scanners'.

Measuring non-parametric distributions of intravoxel mean diffusivities using a clinical MRI scanner

We measure spectra of water mobilities (i.e., mean diffusivities) from intravoxel pools in brain tissues of healthy subjects with a non-parametric approach. Using a single-shot isotropic diffusion encoding (IDE) preparation, we eliminate signal confounds caused by anisotropic diffusion, including microscopic anisotropy, and acquire in vivo diffusion-weighted images (DWIs) over a wide range of diffusion sensitizations. We analyze the measured IDE signal decays using a regularized inverse laplace transform (ILT) to derive a probability distribution of mean diffusivities of tissue water in each voxel. Based on numerical simulations we assess the sensitivity and accuracy of our ILT analysis and optimize an experimental protocol for use with clinical MRI scanners. In vivo spectra of intravoxel mean diffusivities measured in healthy subjects generally show single-peak distributions throughout the brain parenchyma, with small differences in peak location and shape among white matter, cortical and subcortical gray matter, and cerebrospinal fluid. Mean diffusivity distributions (MDDs) with multiple peaks are observed primarily in voxels at tissue interfaces and are likely due to partial volume contributions. To quantify tissue-specific MDDs with improved statistical power, we average voxel-wise normalized MDDs in corresponding regions-of-interest (ROIs). This non-parametric, rotation-invariant assessment of isotropic diffusivities of tissue water may reflect important microstructural information, such as cell packing and cell size, and active physiological processes, such as water transport and exchange, which may enhance biological specificity in the clinical diagnosis and characterization of ischemic stroke, cancer, neuroinflammation, and neurodegenerative disorders and diseases.

On the scaling behavior of water diffusion in human brain white matter

Development of therapies for neurological disorders depends on our ability to non-invasively diagnose and monitor the progression of underlying pathologies at the cellular level. Physics and physiology limit the resolution of human MRI to be orders of magnitude coarser than cell dimensions. Here we identify and quantify the MRI signal coming from within micrometer-thin axons in human white matter tracts in vivo, by utilizing the sensitivity of diffusion MRI to Brownian motion of water molecules restricted by cell walls. We study a specific power-law scaling of the diffusion MRI signal with the diffusion weighting, predicted for water confined to narrow axons, and quantify axonal water fraction and orientation dispersion.

Modeling white matter microstructure with fiber ball imaging

Fiber ball imaging (FBI) provides a means of calculating the fiber orientation density function (fODF) in white matter from diffusion MRI (dMRI) data obtained over a spherical shell with a b-value of about 4000 s/mm2 or higher. By supplementing this FBI-derived fODF with dMRI data acquired for two lower b-value shells, it is shown that several microstructural parameters may be estimated, including the axonal water fraction (AWF) and the intrinsic intra-axonal diffusivity. This fiber ball white matter (FBWM) modeling method is demonstrated for dMRI data acquired from healthy volunteers, and the results are compared with those of the white matter tract integrity (WMTI) method. Both the AWF and the intra-axonal diffusivity obtained with FBWM are found to be significantly larger than for WMTI, with the FBWM values for the intra-axonal diffusivity being more consistent with recent results obtained using isotropic diffusion weighting. An important practical advantage of FBWM is that the only nonlinear fitting required is the minimization of a cost function with just a single free parameter, which facilitates the implementation of efficient and robust numerical routines.

Diffusional kurtosis imaging and white matter microstructure modeling in a clinical study of major depressive disorder

Major depressive disorder (MDD) is a globally prevalent psychiatric disorder that results from disruption of multiple neural circuits involved in emotional regulation. Although previous studies using diffusion tensor imaging (DTI) found smaller values of fractional anisotropy (FA) in the white matter, predominantly in the frontal lobe, of patients with MDD, studies using diffusion kurtosis imaging (DKI) are scarce. Here, we used DKI whole-brain analysis with tract-based spatial statistics (TBSS) to investigate the brain microstructural abnormalities in MDD. Twenty-six patients with MDD and 42 age- and sex-matched control subjects were enrolled. To investigate the microstructural pathology underlying the observations in DKI, a compartment model analysis was conducted focusing on the corpus callosum. In TBSS, the patients with MDD showed significantly smaller values of FA in the genu and frontal portion of the body of the corpus callosum. The patients also had smaller values of mean kurtosis (MK) and radial kurtosis (RK), but MK and RK abnormalities were distributed more widely compared with FA, predominantly in the frontal lobe but also in the parietal, occipital, and temporal lobes. Within the callosum, the regions with smaller MK and RK were located more posteriorly than the region with smaller FA. Model analysis suggested significantly smaller values of intra-neurite signal fraction in the body of the callosum and greater fiber dispersion in the genu, which were compatible with the existing literature of white matter pathology in MDD. Our results show that DKI is capable of demonstrating microstructural alterations in the brains of patients with MDD that cannot be fully depicted by conventional DTI. Though the issues of model validation and parameter estimation still remain, it is suggested that diffusion MRI combined with a biophysical model is a promising approach for investigation of the pathophysiology of MDD.