Fiber ball imaging

Epileptic brain network mechanisms and neuroimaging techniques for the brain network

Epilepsy can be defined as a dysfunction of the brain network, and each type of epilepsy involves different brain-network changes that are implicated differently in the control and propagation of interictal or ictal discharges. Gaining more detailed information on brain network alterations can help us to further understand the mechanisms of epilepsy and pave the way for brain network-based precise therapeutic approaches in clinical practice. An increasing number of advanced neuroimaging techniques and electrophysiological techniques such as diffusion tensor imaging-based fiber tractography, diffusion kurtosis imaging-based fiber tractography, fiber ball imaging-based tractography, electroencephalography, functional magnetic resonance imaging, magnetoencephalography, positron emission tomography, molecular imaging, and functional ultrasound imaging have been extensively used to delineate epileptic networks. In this review, we summarize the relevant neuroimaging and neuroelectrophysiological techniques for assessing structural and functional brain networks in patients with epilepsy, and extensively analyze the imaging mechanisms, advantages, limitations, and clinical application ranges of each technique. A greater focus on emerging advanced technologies, new data analysis software, a combination of multiple techniques, and the construction of personalized virtual epilepsy models can provide a theoretical basis to better understand the brain network mechanisms of epilepsy and make surgical decisions.

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to the macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense medium of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here, we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron, and so forth. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI measurements of an ex vivo mouse brain at ultra-high field.

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

PURPOSE

This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique.

THEORY AND METHODS

A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from scanning electron microscope images.

RESULTS

Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, although some discrepancies were observed. The spherical mean power-law method overestimated fiber radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fiber radii, but faced limitations in accurately estimating the radius in one particular phantom, possibly because of material-specific relaxation changes.

CONCLUSION

The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibers. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients, but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fiber radius estimation, highlights the advantages and limitations of both methods, and provides datasets for reproducible research.

PyDesigner v1.0: A Pythonic Implementation of the DESIGNER Pipeline for Diffusion Magnetic Resonance Imaging

PyDesigner is a Python-based software package based on the original Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) pipeline (Dv1) for dMRI preprocessing and tensor estimation. This software is openly provided for non-commercial research and may not be used for clinical care. PyDesigner combines tools from FSL and MRtrix3 to perform denoising, Gibbs ringing correction, eddy current motion correction, brain masking, image smoothing, and Rician bias correction to optimize the estimation of multiple diffusion measures. It can be used across platforms on Windows, Mac, and Linux to accurately derive commonly used metrics from DKI, DTI, WMTI, FBI, and FBWM datasets as well as tractography ODFs and .fib files. It is also file-format agnostic, accepting inputs in the form of .nii, .nii.gz, .mif, and dicom format. User-friendly and easy to install, this software also outputs quality control metrics illustrating signal-to-noise ratio graphs, outlier voxels, and head motion to evaluate data integrity. Additionally, this dMRI processing pipeline supports multiple echo-time dataset processing and features pipeline customization, allowing the user to specify which processes are employed and which outputs are produced to meet a variety of user needs.

Developing an AI-empowered head-only ultra-high-performance gradient MRI system for high spatiotemporal neuroimaging

Recent advances in neuroscience requires high-resolution MRI to decipher the structural and functional details of the brain. Developing a high-performance gradient system is an ongoing effort in the field to facilitate high spatial and temporal encoding. Here, we proposed a head-only gradient system NeuroFrontier, dedicated for neuroimaging with an ultra-high gradient strength of 650 mT/m and 600 T/m/s. The proposed system features in 1) ultra-high power of 7MW achieved by running two gradient power amplifiers using a novel paralleling method; 2) a force/torque balanced gradient coil design with a two-step mechanical structure that allows high-efficiency and flexible optimization of the peripheral nerve stimulation; 3) a high-density integrated RF system that is miniaturized and customized for the head-only system; 4) an AI-empowered compressed sensing technique that enables ultra-fast acquisition of high-resolution images and AI-based acceleration in q-t space for diffusion MRI (dMRI); and 5) a prospective head motion correction technique that effectively corrects motion artifacts in real-time with 3D optical tracking. We demonstrated the potential advantages of the proposed system in imaging resolution, speed, and signal-to-noise ratio for 3D structural MRI (sMRI), functional MRI (fMRI) and dMRI in neuroscience applications of submillimeter layer-specific fMRI and dMRI. We also illustrated the unique strength of this system for dMRI-based microstructural mapping, e.g., enhanced lesion contrast at short diffusion-times or high b-values, and improved estimation accuracy for cellular microstructures using diffusion-time-dependent dMRI or for neurite microstructures using q-space approaches.

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo mouse brain

PURPOSE

To extend quantitative susceptibility mapping to account for microstructure of white matter (WM) and demonstrate its effect on ex vivo mouse brain at 16.4T.

THEORY AND METHODS

Previous studies have shown that the MRI measured Larmor frequency also depends on local magnetic microstructure at the mesoscopic scale. Here, we include effects from WM microstructure using our previous results for the mesoscopic Larmor frequencyΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ of cylinders with arbitrary orientations. We scrutinize the validity of our model and QSM in a digital brain phantom includingΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from a WM susceptibility tensor and biologically stored iron with scalar susceptibility. We also apply susceptibility tensor imaging to the phantom and investigate how the fitted tensors are biased fromΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ . Last, we demonstrate how to combine multi-gradient echo and diffusion MRI images of ex vivo mouse brains acquired at 16.4T to estimate an apparent scalar susceptibility without sample rotations.

RESULTS

Our new model improves susceptibility estimation compared to QSM for the brain phantom. Applying susceptibility tensor imaging to the phantom withΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from WM axons with scalar susceptibility produces a highly anisotropic susceptibility tensor that mimics results from previous susceptibility tensor imaging studies. For the ex vivo mouse brain we find theΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ due to WM microstructure to be substantial, changing susceptibility in WM up to 25% root-mean-squared-difference.

CONCLUSION

Ω ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ impacts susceptibility estimates and biases susceptibility tensor imaging fitting substantially. Hence, it should not be neglected when imaging structurally anisotropic tissue such as brain WM.

A translational MRI approach to validate acute axonal damage detection as an early event in multiple sclerosis

Axonal degeneration is a central pathological feature of multiple sclerosis and is closely associated with irreversible clinical disability. Current noninvasive methods to detect axonal damage in vivo are limited in their specificity and clinical applicability, and by the lack of proper validation. We aimed to validate an MRI framework based on multicompartment modeling of the diffusion signal (AxCaliber) in rats in the presence of axonal pathology, achieved through injection of a neurotoxin damaging the neuronal terminal of axons. We then applied the same MRI protocol to map axonal integrity in the brain of multiple sclerosis relapsing-remitting patients and age-matched healthy controls. AxCaliber is sensitive to acute axonal damage in rats, as demonstrated by a significant increase in the mean axonal caliber along the targeted tract, which correlated with neurofilament staining. Electron microscopy confirmed that increased mean axonal diameter is associated with acute axonal pathology. In humans with multiple sclerosis, we uncovered a diffuse increase in mean axonal caliber in most areas of the normal-appearing white matter, preferentially affecting patients with short disease duration. Our results demonstrate that MRI-based axonal diameter mapping is a sensitive and specific imaging biomarker that links noninvasive imaging contrasts with the underlying biological substrate, uncovering generalized axonal damage in multiple sclerosis as an early event.

Research Progress in Diffusion Spectrum Imaging

Studies have demonstrated that many regions in the human brain include multidirectional fiber tracts, in which the diffusion of water molecules within image voxels does not follow a Gaussian distribution. Therefore, the conventional diffusion tensor imaging (DTI) that hypothesizes a single fiber orientation within a voxel is intrinsically incapable of revealing the complex microstructures of brain tissues. Diffusion spectrum imaging (DSI) employs a pulse sequence with different b-values along multiple gradient directions to sample the diffusion information of water molecules in the entire q-space and then quantitatively estimates the diffusion profile using a probability density function with a high angular resolution. Studies have suggested that DSI can reliably observe the multidirectional fibers within each voxel and allow fiber tracking along different directions, which can improve fiber reconstruction reflecting the true but complicated brain structures that were not observed in the previous DTI studies. Moreover, with increasing angular resolution, DSI is able to reveal new neuroimaging biomarkers used for disease diagnosis and the prediction of disorder progression. However, so far, this method has not been used widely in clinical studies, due to its overly long scanning time and difficult post-processing. Within this context, the current paper aims to conduct a comprehensive review of DSI research, including the fundamental principles, methodology, and application progress of DSI tractography. By summarizing the DSI studies in recent years, we propose potential solutions towards the existing problem in the methodology and applications of DSI technology as follows: (1) using compressed sensing to undersample data and to reconstruct the diffusion signal may be an efficient and promising method for reducing scanning time; (2) the probability density function includes more information than the orientation distribution function, and it should be extended in application studies; and (3) large-sample study is encouraged to confirm the reliability and reproducibility of findings in clinical diseases. These findings may help deepen the understanding of the DSI method and promote its development in clinical applications.

Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm2) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement.

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.

Optimized rectification of fiber orientation density function with background threshold

PURPOSE

To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background.

THEORY AND METHODS

The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging.

RESULTS

Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives.

CONCLUSION

Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.

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.

Advanced Diffusion MRI of Stroke Recovery

There is an urgent need for ways to improve our understanding of poststroke recovery to inform the development of novel rehabilitative interventions, and improve the clinical management of stroke patients. Supported by the notion that predictive information on poststroke recovery is embedded not only in the individual brain regions, but also the connections throughout the brain, majority of previous investigations have focused on the relationship between brain functional connections and post-stroke deficit and recovery. However, considering the fact that it is the static anatomical brain connections that constrain and facilitate the dynamic functional brain connections, the microstructures and structural connections of the brain may potentially be better alternatives to the functional MRI-based biomarkers of stroke recovery. This review, therefore, seeks to provide an overview of the basic concept and applications of two recently proposed advanced diffusion MRI techniques, namely lesion network mapping and fixel-based morphometry, that may be useful for the investigation of stroke recovery at the local and global levels of the brain. This review will also highlight the application of some of other emerging advanced diffusion MRI techniques that warrant further investigation in the context of stroke recovery research.

Impact of intra-axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging

PURPOSE

To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI).

THEORY AND METHODS

Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm2 or higher. However, recent work based on numeric simulations shows that diffusion inside axons is non-Gaussian with an intra-axonal kurtosis of ∼ 0.4. Here, the theory underlying FBI is extended to incorporate an intra-axonal kurtosis. This is done to first order in the intra-axonal kurtosis without making assumptions about the details of the diffusion dynamics and to all orders for a specific model based on a gamma distribution of diffusivities. The first order approximation is used to assess the effect of an intra-axonal kurtosis on FBI estimates for the fODF and axonal water fraction. The gamma distribution model is used to test the validity of the approximation.

RESULTS

The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent.

CONCLUSION

The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.

Reproducibility of the Standard Model of diffusion in white matter on clinical MRI systems

Estimating intra- and extra-axonal microstructure parameters, such as volume fractions and diffusivities, has been one of the major efforts in brain microstructure imaging with MRI. The Standard Model (SM) of diffusion in white matter has unified various modeling approaches based on impermeable narrow cylinders embedded in locally anisotropic extra-axonal space. However, estimating the SM parameters from a set of conventional diffusion MRI (dMRI) measurements is ill-conditioned. Multidimensional dMRI helps resolve the estimation degeneracies, but there remains a need for clinically feasible acquisitions that yield robust parameter maps. Here we find optimal multidimensional protocols by minimizing the mean-squared error of machine learning-based SM parameter estimates for two 3T scanners with corresponding gradient strengths of 40and80mT/m. We assess intra-scanner and inter-scanner repeatability for 15-minute optimal protocols by scanning 20 healthy volunteers twice on both scanners. The coefficients of variation all SM parameters except free water fraction are ≲10% voxelwise and 1-4% for their region-averaged values. As the achieved SM reproducibility outcomes are similar to those of conventional diffusion tensor imaging, our results enable robust in vivo mapping of white matter microstructure in neuroscience research and in the clinic.

Associations of White Matter and Basal Ganglia Microstructure to Cognitive Fatigue Rate in Multiple Sclerosis

Fatigue, including cognitive fatigue, is one of the most debilitating symptoms reported by persons with multiple sclerosis (pwMS). Cognitive fatigue has been associated with disruptions in striato-thalamo-cortical and frontal networks, but what remains unknown is how the rate at which pwMS become fatigued over time relates to microstructural properties within the brain. The current study aims to fill this gap in knowledge by investigating how cognitive fatigue rate relates to white matter and basal ganglia microstructure in a sample of 62 persons with relapsing-remitting MS. Participants rated their level of cognitive fatigue at baseline and after each block (x7) of a within-scanner cognitive fatigue inducing task. The slope of the regression line of all eight fatigue ratings was designated as “cognitive fatigue rate.” Diffusional kurtosis imaging maps were processed using tract-based spatial statistics and regional analyses (i.e., basal ganglia) and associated with cognitive fatigue rate. Results showed cognitive fatigue rate to be related to several white matter tracts, with many having been associated with basal ganglia connectivity or the previously proposed “fatigue network.” In addition, cognitive fatigue rate was associated with the microstructure within the putamen, though this did not survive multiple comparisons correction. Our approach of using cognitive fatigue rate, rather than trait fatigue, brings us closer to understanding how brain pathology may be impacting the experience of fatigue in the moment, which is crucial for developing interventions. These results hold promise for continuing to unpack the complex construct that is cognitive fatigue.

High b-value diffusion tractography: Abnormal axonal network organization associated with medication-refractory epilepsy

Diffusion magnetic resonance imaging (dMRI) tractography has played a critical role in characterizing patterns of aberrant brain network reorganization among patients with epilepsy. However, the accuracy of dMRI tractography is hampered by the complex biophysical properties of white matter tissue. High b-value diffusion imaging overcomes this limitation by better isolating axonal pathways. In this study, we introduce tractography derived from fiber ball imaging (FBI), a high b-value approach which excludes non-axonal signals, to identify atypical neuronal networks in patients with epilepsy. Specifically, we compared network properties obtained from multiple diffusion tractography approaches (diffusion tensor imaging, diffusion kurtosis imaging, FBI) in order to assess the pathophysiological relevance of network rearrangement in medication-responsive vs. medication-refractory adults with focal epilepsy. We show that drug-resistant epilepsy is associated with increased global network segregation detected by FBI-based tractography. We propose exploring FBI as a clinically feasible alternative to quantify topological changes that could be used to track disease progression and inform on clinical outcomes.

High fidelity fiber orientation density functions from fiber ball imaging

The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high fidelity fODFs, in the sense of having good angular resolution, adequate data to avoid sampling errors, and minimal noise artifacts, are described for fODFs calculated with fiber ball imaging. A criterion is formulated for the number of diffusion encoding directions needed to achieve a given angular resolution. The advantages of using large b-values (≥6000 s/mm² ) are also discussed. For the direct comparison of different fODFs, a method is developed for defining a local frame of reference tied to each voxel's individual axonal structure. The Matusita anisotropy axonal is proposed as a scalar fODF measure for quantifying angular variability. Experimental results, obtained at 3 T from human volunteers, are used as illustrations.

Fiber Ball White Matter Modeling Reveals Microstructural Alterations in Healthy Brain Aging

Age-related white matter degeneration is characterized by myelin breakdown and neuronal fiber loss that preferentially occur in regions that myelinate later in development. Conventional diffusion MRI (dMRI) has demonstrated age-related increases in diffusivity but provide limited information regarding the tissue-specific changes driving these effects. A recently developed dMRI biophysical modeling technique, Fiber Ball White Matter (FBWM) modeling, offers enhanced biological interpretability by estimating microstructural properties specific to the intra-axonal and extra-axonal spaces. We used FBWM to illustrate the biological mechanisms underlying changes throughout white matter in healthy aging using data from 63 cognitively unimpaired adults ages 45-85 with no radiological evidence of neurodegeneration or incipient Alzheimer's disease. Conventional dMRI and FBWM metrics were computed for two late-myelinating (genu of the corpus callosum and association tracts) and two early-myelinating regions (splenium of the corpus callosum and projection tracts). We examined the associations between age and these metrics in each region and tested whether age was differentially associated with these metrics in late- vs. early-myelinating regions. We found that conventional metrics replicated patterns of age-related increases in diffusivity in late-myelinating regions. FBWM additionally revealed specific intra- and extra-axonal changes suggestive of myelin breakdown and preferential loss of smaller-diameter axons, yielding in vivo corroboration of findings from histopathological studies of aged brains. These results demonstrate that advanced biophysical modeling approaches, such as FBWM, offer novel information about the microstructure-specific alterations contributing to white matter changes in healthy aging. These tools hold promise as sensitive indicators of early pathological changes related to neurodegenerative disease.

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.

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

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

Neurobiological underpinnings of rapid white matter plasticity during intensive reading instruction

Diffusion MRI is a powerful tool for imaging brain structure, but it is challenging to discern the biological underpinnings of plasticity inferred from these and other non-invasive MR measurements. Biophysical modeling of the diffusion signal aims to render a more biologically rich image of tissue microstructure, but the application of these models comes with important caveats. A separate approach for gaining biological specificity has been to seek converging evidence from multi-modal datasets. Here we use metrics derived from diffusion kurtosis imaging (DKI) and the white matter tract integrity (WMTI) model along with quantitative MRI measurements of T1 relaxation to characterize changes throughout the white matter during an 8-week, intensive reading intervention (160 total hours of instruction). Behavioral measures, multi-shell diffusion MRI data, and quantitative T1 data were collected at regular intervals during the intervention in a group of 33 children with reading difficulties (7-12 years old), and over the same period in an age-matched non-intervention control group. Throughout the white matter, mean 'extra-axonal' diffusivity was inversely related to intervention time. In contrast, model estimated axonal water fraction (AWF), overall diffusion kurtosis, and T1 relaxation time showed no significant change over the intervention period. Both diffusion and quantitative T1 based metrics were correlated with pre-intervention reading performance, albeit with distinct anatomical distributions. These results are consistent with the view that rapid changes in diffusion properties reflect phenomena other than widespread changes in myelin density. We discuss this result in light of recent work highlighting non-axonal factors in experience-dependent plasticity and learning.

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.

Fiber ball white matter modeling in focal epilepsy

Multicompartment diffusion magnetic resonance imaging (MRI) approaches are increasingly being applied to estimate intra‐axonal and extra‐axonal diffusion characteristics in the human brain. Fiber ball imaging (FBI) and its extension fiber ball white matter modeling (FBWM) are such recently described multicompartment approaches. However, these particular approaches have yet to be applied in clinical cohorts. The modeling of several diffusion parameters with interpretable biological meaning may offer the development of new, noninvasive biomarkers of pharmacoresistance in epilepsy. In the present study, we used FBI and FBWM to evaluate intra‐axonal and extra‐axonal diffusion properties of white matter tracts in patients with longstanding focal epilepsy. FBI/FBWM diffusion parameters were calculated along the length of 50 white matter tract bundles and statistically compared between patients with refractory epilepsy, nonrefractory epilepsy and controls. We report that patients with chronic epilepsy had a widespread distribution of extra‐axonal diffusivity relative to controls, particularly in circumscribed regions along white matter tracts projecting to cerebral cortex from thalamic, striatal, brainstem, and peduncular regions. Patients with refractory epilepsy had significantly greater markers of extra‐axonal diffusivity compared to those with nonrefractory epilepsy. The extra‐axonal diffusivity alterations in patients with epilepsy observed in the present study could be markers of neuroinflammatory processes or a reflection of reduced axonal density, both of which have been histologically demonstrated in focal epilepsy. FBI is a clinically feasible MRI approach that provides the basis for more interpretive conclusions about the microstructural environment of the brain and may represent a unique biomarker of pharmacoresistance in epilepsy.

Resolving bundle-specific intra-axonal T2 values within a voxel using diffusion-relaxation tract-based estimation

At the typical spatial resolution of MRI in the human brain, approximately 60-90% of voxels contain multiple fiber populations. Quantifying microstructural properties of distinct fiber populations within a voxel is therefore challenging but necessary. While progress has been made for diffusion and T1-relaxation properties, how to resolve intra-voxel T2 heterogeneity remains an open question. Here a novel framework, named COMMIT-T2, is proposed that uses tractography-based spatial regularization with diffusion-relaxometry data to estimate multiple intra-axonal T2 values within a voxel. Unlike previously-proposed voxel-based T2 estimation methods, which (when applied in white matter) implicitly assume just one fiber bundle in the voxel or the same T2 for all bundles in the voxel, COMMIT-T2 can recover specific T2 values for each unique fiber population passing through the voxel. In this approach, the number of recovered unique T2 values is not determined by a number of model parameters set a priori, but rather by the number of tractography-reconstructed streamlines passing through the voxel. Proof-of-concept is provided in silico and in vivo, including a demonstration that distinct tract-specific T2 profiles can be recovered even in the three-way crossing of the corpus callosum, arcuate fasciculus, and corticospinal tract. We demonstrate the favourable performance of COMMIT-T2 compared to that of voxelwise approaches for mapping intra-axonal T2 exploiting diffusion, including a direction-averaged method and AMICO-T2, a new extension to the previously-proposed Accelerated Microstructure Imaging via Convex Optimization (AMICO) framework.

Diffusion MRI revealed altered inter-hippocampal projections in the mouse brain after intrauterine inflammation

Diffusion MRI (dMRI) is commonly used to map large axonal pathways in the white matter. Recent technical advances have also enabled dMRI to resolve the small and complex axonal and dendritic projections in the gray matter. This study investigated whether high-resolution dMRI can resolve the hippocampal neuronal projections and detect abnormal connections due to neurological injury. We performed 3D high spatial and angular resolution dMRI of the mouse brains of the offspring survivors from a model of intrauterine (UI) inflammation, who had known functional deficiency in the hippocampus. We used a novel hippocampal connection mapping method to quantify the intra- and inter-hippocampal projections among 34 automatically segmented hippocampal sub-regions. The results demonstrated wide-spread intra-hippocampal projections, but rather specific intra-hippocampal projections that primarily connected through the CA3 region. Compared with the control group (n = 9), UI-injured mice (n = 11) exhibited significantly reduced inter-hippocampal projection strength (p < 0.01), which correlated well with the neurobehavioral assessments (R² = 0.47). Furthermore, using a whole-brain fixel-based analysis, we identified reduced fiber-density in the CA3 and the ventral hippocampal commissure of the UI-injured mice, which may explain the reduced inter-hippocampal projections. Histological findings also indicated reduced commissural fibers due to the UI-injury. Our study suggested that the dMRI-based connectivity mapping technique can potentially characterize abnormal hippocampal projections in neurological disorders.

Brain Reserve in a Case of Cognitive Resilience to Severe Leukoaraiosis

OBJECTIVE

Leukoaraiosis, or white matter rarefaction, is a common imaging finding in aging and is presumed to reflect vascular disease. When severe in presentation, potential congenital or acquired etiologies are investigated, prompting referral for neuropsychological evaluation in addition to neuroimaging. T2-weighted imaging is the most common magnetic resonance imaging (MRI) approach to identifying white matter disease. However, more advanced diffusion MRI techniques may provide additional insight into mechanisms that influence the abnormal T2 signal, especially when clinical presentations are discrepant with imaging findings.

METHOD

We present a case of a 74-year-old woman with severe leukoaraoisis. She was examined by a neurologist, neuropsychologist, and rheumatologist, and completed conventional (T1, T2-FLAIR) MRI, diffusion tensor imaging (DTI), and advanced single-shell, high b-value diffusion MRI (i.e., fiber ball imaging [FBI]).

RESULTS

The patient was found to have few neurological signs, no significant cognitive impairment, a negative workup for leukoencephalopathy, and a positive antibody for Sjogren's disease for which her degree of leukoaraiosis would be highly atypical. Tractography results indicate intact axonal architecture that was better resolved using FBI rather than DTI.

CONCLUSIONS

This case illustrates exceptional cognitive resilience in the face of severe leukoaraiosis and the potential for advanced diffusion MRI to identify brain reserve.

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.

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.

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.

Optimized rectification of fiber orientation density function

PURPOSE

To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs).

THEORY AND METHODS

In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and other factors, experimentally determined fODFs may take on unphysical negative values in some directions. Here, we show how to rectify such fODFs to eliminate all negative values while minimizing the mean square difference between the original and rectified fODFs. The method is demonstrated for a mathematical model and for fODFs estimated from experimental human data using both constrained spherical deconvolution and fiber ball imaging. Comparison with an alternative nonoptimized rectification approach is also provided.

RESULTS

For the mathematical model, it is found that the optimized rectification procedure removes negative fODF values while at the same time reducing the mean square error. Relative to the alternative rectification approach, the optimized fODFs are substantially more accurate. For the experimental data, the optimized fODFs have a lower average fractional anisotropy axonal and often fewer small peaks than the original, unrectified fODFs. The calculation of optimized fODFs is straightforward where the main step is the finding of the root to an equation in one variable, as may be efficiently accomplished with the bisection method.

CONCLUSION

Unphysical negative fODF values can be easily eliminated in a manner that minimizes the mean square difference between the original and rectified fODFs. Optimized fODF rectification may be useful in applications for which negative values are problematic.

Improved fibre dispersion estimation using b-tensor encoding

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/μm², increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.

Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes

Purpose

It has been shown, theoretically and in vivo, that using the Stejskal‐Tanner pulsed‐gradient, or linear tensor encoding (LTE), and in tissue exhibiting a “stick‐like” diffusion geometry, the direction‐averaged diffusion‐weighted MRI signal at high b‐values ( 7000<b<10000s/mm2) follows a power‐law, decaying as 1/b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction‐averaged diffusion‐weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction‐averaged signal for arbitrary b‐tensor shapes and different tissue substrates to look for other conditions under which a power‐law exists.

Methods

We considered the signal decay for high b‐values for encoding geometries ranging from 2‐dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power‐law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra‐strong (300 mT/m) gradients.

Results

Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b‐tensor a power‐law only exists under very specific conditions: (a) “stick‐like” tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake‐like" tissue geometry and a purely LTE waveform.

Conclusions

A complete analysis of the power‐law dependencies of the diffusion‐weighted signal at high b‐values has been performed. Only three specific forms of encoding result in a power‐law dependency, pure linear and pure PTE when the tissue geometry is “stick‐like” and pure LTE when the tissue geometry is "pancake‐like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.

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.

Triple diffusion encoding MRI predicts intra-axonal and extra-axonal diffusion tensors in white matter

PURPOSE

To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).

METHODS

Using a TDE pulse sequence with an axially symmetric b-matrix, diffusion MRI data were acquired at 3T for 3 healthy adults with an axial b-value of 4000 s/mm² , a radial b-value of 307 s/mm² , and 64 diffusion encoding directions. This acquisition was then repeated with the radial b-value set to 0. A previously proposed theory was applied to these data in order to estimate the intra-axonal diffusivity and axonal water fraction for each WM voxel. Conventional single diffusion encoding data were also obtained with b-values of 1000 and 2000 s/mm² , which provided additional information sufficient for determining both the intra-axonal and extra-axonal diffusion tensors.

RESULTS

From the TDE data, the average intra-axonal diffusivity in WM was found to be 2.24 ± 0.18 µm² /ms, and the average axonal water fraction was found to be 0.60 ± 0.11. From the 2 diffusion tensors, average WM values were estimated for several compartment-specific diffusion parameters. In particular, the extra-axonal mean diffusivity was 1.09 ± 0.19 µm² /ms, the intra-axonal fractional anisotropy was 0.50 ± 0.14, and the extra-axonal fractional anisotropy was 0.23 ± 0.13.

CONCLUSION

By using a simple TDE pulse sequence with an axially symmetric b-matrix, the diffusion tensors for the intra-axonal and extra-axonal spaces can be separately estimated in adult WM. This allows one to determine compartment-specific diffusion properties for these 2 water pools.

Reproducibility of axonal water fraction derived from the spherical mean diffusion weighted signal

Recent years have seen growing interest in measuring axonal water fraction (AWF) using the spherical mean diffusion weighted signal, but information about the reproducibility of this method is needed before applying it in large-scale studies. The current study aims to evaluate the reproducibility of AWF derived from the spherical mean signal method. This retrospective study analyzed the Human Connectome Project (HCP) test-retest diffusion data of ten healthy adults. The diffusion scan was performed two times for each subject. Diffusion tensor imaging-based fractional anisotropy (FA) was calculated with b = 1000 s/mm². AWF was calculated with b = 3000 s/mm² using the spherical mean signal method. Gradient nonlinearities were corrected in both methods. Reproducibility was assessed using the reproducibility error, which is the percent absolute change relative to the mean. The mean reproducibility error of fractional anisotropy (FA) is 9.7 ± 1.0% in white matter and 18.0 ± 2.0% in gray matter. The mean reproducibility error of AWF is 4.6 ± 0.6% in white matter and 7.0 ± 1.5% in gray matter. Spherical mean signal-based AWF is more reproducible than FA for the HCP high resolution, low signal-to-noise ratio diffusion data.

Optimization of data acquisition and analysis for fiber ball imaging

The inverse Funk transform of high angular resolution diffusion imaging (HARDI) data provides an estimate for the fiber orientation density function (fODF) in white matter (WM). Since the inverse Funk transform is a straightforward linear transformation, this technique, referred to as fiber ball imaging (FBI), offers a practical means of calculating the fODF that avoids the need for a response function or nonlinear numerical fitting. Nevertheless, the accuracy of FBI depends on both the choice of b-value and the number of diffusion-encoding directions used to acquire the HARDI data. To inform the design of optimal scan protocols for its implementation, FBI predictions are investigated here with in vivo data from healthy adult volunteers acquired at 3 T for b-values spanning 1000 to 10,000 s/mm², for diffusion-encoding directions varying in number from 30 to 256 and for TE ranging from 90 to 120 ms. Our results suggest b-values above 4000 s/mm² with at least 64 diffusion-encoding directions are adequate to achieve reasonable accuracy with FBI for calculating axon-specific diffusion measures and for performing WM fiber tractography (WMFT).

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.

Comparison of NODDI and spherical mean signal for measuring intra-neurite volume fraction

PURPOSE

Neurite orientation dispersion and density imaging (NODDI) is a clinically feasible approach to measure intra-neurite volume fraction (fin). However, the sophisticated fitting procedure takes several hours. And the NODDI model relied on several questionable assumptions. Recent analytical work demonstrated that fin could be simply calculated from the spherical mean signal (MEANS) averaged over all gradient directions with a more solid theoretical foundation. The current study aims to compare NODDI and MEANS for measuring fin in human brain and investigate the potential of MEANS as a fast approach in clinics.

METHODS

NODDI fin and MEANS fin were measured and compared on the same dataset. NODDI fin was obtained using the NODDI MATLAB Toolbox. MEANS fin is the product of the spherical mean signal and 2bD/π, where D is the intra-neurite intrinsic diffusivity.

RESULTS

NODDI fin and MEANS fin maps are similar. The voxel-by-voxel correlation suggests that NODDI fin and MEANS fin are approximately equivalent to each other.

CONCLUSION

MEANS may have potential to serve a fast and simple approach to estimate fin in clinics.

The Superoanterior Fasciculus (SAF): A Novel White Matter Pathway in the Human Brain?

Fiber tractography (FT) using diffusion magnetic resonance imaging (dMRI) is widely used for investigating microstructural properties of white matter (WM) fiber-bundles and for mapping structural connections of the human brain. While studying the architectural configuration of the brain's circuitry with FT is not without controversy, recent progress in acquisition, processing, modeling, analysis, and visualization of dMRI data pushes forward the reliability in reconstructing WM pathways. Despite being aware of the well-known pitfalls in analyzing dMRI data and several other limitations of FT discussed in recent literature, we present the superoanterior fasciculus (SAF), a novel bilateral fiber tract in the frontal region of the human brain that-to the best of our knowledge-has not been documented. The SAF has a similar shape to the anterior part of the cingulum bundle, but it is located more frontally. To minimize the possibility that these FT findings are based on acquisition or processing artifacts, different dMRI data sets and processing pipelines have been used to describe the SAF. Furthermore, we evaluated the configuration of the SAF with complementary methods, such as polarized light imaging (PLI) and human brain dissections. The FT results of the SAF demonstrate a long pathway, consistent across individuals, while the human dissections indicate fiber pathways connecting the postero-dorsal with the antero-dorsal cortices of the frontal lobe.

Measuring intra-axonal T2 in white matter with direction-averaged diffusion MRI

PURPOSE

To demonstrate how the T₂ relaxation time of intra-axonal water (T_2a ) in white matter can be measured with direction-averaged diffusion MRI.

METHODS

For b-values larger than about 4000 s/mm² , the direction-averaged diffusion MRI signal from white matter is dominated by the contribution from water within axons, which enables T_2a to be estimated by acquiring data for multiple TE values and fitting a mono-exponential decay curve. If given a value of the intra-axonal diffusivity, an extension of the method allows the extra-axonal relaxation time (T_2e ) to be calculated also. This approach was applied to estimate T_2a in white matter for 3 healthy subjects at 3 T, as well as T_2e for a selected set of assumed intra-axonal diffusivities.

RESULTS

The estimated T_2a values ranged from about 50 ms to 110 ms, with considerable variation among white matter regions. For white matter tracts with primarily collinear fibers, T_2a was found to depend on the angle of the tract relative to the main magnetic field, which is consistent with T_2a being affected by magnetic field inhomogeneities arising from spatial differences in magnetic susceptibility. The T_2e values were significantly smaller than the T_2a values across white matter regions for several plausible choices of the intra-axonal diffusivity.

CONCLUSION

The relaxation time for intra-axonal water in white matter can be determined in a straightforward manner by measuring the direction-averaged diffusion MRI signal with a large b-value for multiple TEs. In healthy brain, T_2a is greater than T_2e and varies considerably with anatomical region.

Diffusion time dependence of microstructural parameters in fixed spinal cord

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

TE dependent Diffusion Imaging (TEdDI) distinguishes between compartmental T2 relaxation times

Biophysical modeling of macroscopic diffusion-weighted MRI signal in terms of microscopic cellular parameters holds the promise of quantifying the integrity of white matter. Unfortunately, even fairly simple multi-compartment models of proton diffusion in the white matter do not provide a unique, biophysically plausible solution. Here we report a nontrivial diffusion MRI signal dependence on echo time (TE) in human white matter in vivo. We demonstrate that such TE dependence originates from compartment-specific T2 values and that it is a promising "orthogonal measure" able to break the degeneracy in parameter estimation, and to yield important relaxation metrics robustly. We thereby enable the precise estimation of the intra- and extra-axonal water T2 relaxation times, which is precluded by a limited signal-to-noise ratio when using multi-echo relaxometry alone.

Linking spherical mean diffusion weighted signal with intra-axonal volume fraction

Diffusion MRI has been widely used to assess brain tissue microstructure. However, the conventional diffusion tensor imaging (DTI) is inadequate for characterizing fiber direction or fiber density in voxels with crossing fibers in brain white matter. The constrained spherical deconvolution (CSD) technique has been proposed to measure the complex fiber orientation distribution (FOD) using a single high b-value (b ≥ 3000 s/mm²) to derive the intra-axonal volume fraction (V_in) from the calculated FOD. Recently, the spherical mean technique (SMT) was developed to fit V_in directly from a multi-compartment model with multi-shell b-values. Although different numbers of b-values are needed in the two techniques, both methods have been suggested to be related to the spherical mean diffusion weighted signal (S¯). The current study compared the two techniques on the same high-quality Human Connectome Project diffusion data and investigated the relation between S¯ and V_in systematically. At high b-values (b ≥ 3000 s/mm²), S¯ is linearly related to V_in, and S¯ provides similar contrast with V_in in white matter. At low b-values (b ~ 1000 s/mm²), the linear relation between S¯ and V_in is sensitive to the variations of intrinsic diffusivity. These results demonstrate that S¯ measured with the typical b-value of 1000 s/mm² is not an indicator of V_in, and previous DTI studies acquired with b = 1000 s/mm² cannot be re-analyzed to provide V_in-weighted contrast.

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.

Minimal number of gradient directions for robust measurement of spherical mean diffusion weighted signal

PURPOSE

Determination of the minimum number of gradient directions (N_min) for robust measurement of spherical mean diffusion weighted signal (S¯).

METHODS

Computer simulations were employed to characterize the relative standard deviation (RSD) of the measured spherical mean signal as a function of the number of gradient directions (N). The effects of diffusion weighting b-value and signal-to-noise ratio (SNR) were investigated. Multi-shell high angular resolution Human Connectome Project diffusion data were analyzed to support the simulation results.

RESULTS

RSD decreases with increasing N, and the minimum number of N needed for RSD ≤ 5% is referred to as N_min. At high SNRs, N_min increases with increasing b-value to achieve sufficient sampling. Simulations showed that N_min is linearly dependent on the b-value. At low SNRs, N_min increases with increasing b-value to reduce the noise. RSD can be estimated as σS¯N, where σ = 1/SNR is the noise level. The experimental results were in good agreement with the simulation results. The spherical mean signal can be measured accurately with a subset of gradient directions.

CONCLUSION

As N_min is affected by b-value and SNR, we recommend using 10 × b / b₁ (b₁ = 1 ms/μm²) uniformly distributed gradient directions for typical human diffusion studies with SNR ~ 20 for robust spherical mean signal measurement.

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.

Characterizing intra-axonal water diffusion with direction-averaged triple diffusion encoding MRI

For large diffusion weightings, the direction-averaged diffusion MRI (dMRI) signal from white matter is typically dominated by the contribution of water confined to axons. This fact can be exploited to characterize intra-axonal diffusion properties, which may be valuable for interpreting the biophysical meaning of diffusion changes associated with pathology. However, using just the classic Stejskal-Tanner pulse sequence, it has proven challenging to obtain reliable estimates for both the intrinsic intra-axonal diffusivity and the intra-axonal water fraction. Here we propose to apply a modification of the Stejskal-Tanner sequence designed for achieving such estimates. The key feature of the sequence is the addition of a set of extra diffusion encoding gradients that are orthogonal to the direction of the primary gradients, which corresponds to a specific type of triple diffusion encoding (TDE) MRI sequence. Given direction-averaged dMRI data for this TDE sequence, it is shown how the intra-axonal diffusivity and the intra-axonal water fraction can be determined by applying simple, analytic formulae. The method is illustrated with numerical simulations, which suggest that it should be accurate for b-values of about 4000 s/mm² or higher.

Estimating fiber orientation distribution from diffusion MRI with spherical needlets

We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted magnetic resonance imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through spherical deconvolution and a sparse representation of the FOD by a spherical needlets basis that forms a multi-resolution tight frame for spherical functions. This sparse representation allows us to estimate the FOD by ℓ1-penalized regression under a non-negativity constraint on the estimated FOD. The resulting convex optimization problem is solved by an alternating direction method of multipliers (ADMM) algorithm. The proposed method leads to a reconstruction of the FOD that is accurate, has low variability and preserves sharp features. Through extensive experiments, we demonstrate the effectiveness and favorable performance of the proposed method compared to three existing methods. Specifically, we demonstrate that the proposed method is able to successfully resolve fiber crossings at small angles and automatically identify isotropic diffusion. We also apply the proposed method to real 3T D-MRI data sets of healthy individuals. The results show realistic depictions of crossing fibers that are more accurate, less noisy, and lead to superior tractography results compared to competing methods.