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

Background: Neurite orientation dispersion and density imaging (NODDI) and the spherical mean technique (SMT) are diffusion MRI methods providing metrics with sensitivity to similar characteristics of white matter microstructure. There has been limited comparison of changes in NODDI and SMT parameters due to multiple sclerosis (MS) pathology in clinical settings. Purpose: To compare group-wise differences between healthy controls and MS patients in NODDI and SMT metrics, investigating associations with disability and correlations with diffusion tensor imaging (DTI) metrics. Methods: Sixty three relapsing-remitting MS patients were compared to 28 healthy controls. NODDI and SMT metrics corresponding to intracellular volume fraction (vin), orientation dispersion (ODI and ODE), diffusivity (D) (SMT only) and isotropic volume fraction (viso) (NODDI only) were calculated from diffusion MRI data, alongside DTI metrics (fractional anisotropy, FA; axial/mean/radial diffusivity, AD/MD/RD). Correlations between all pairs of MRI metrics were calculated in normal-appearing white matter (NAWM). Associations with expanded disability status scale (EDSS), controlling for age and gender, were evaluated. Patient-control differences were assessed voxel-by-voxel in MNI space controlling for age and gender at the 5% significance level, correcting for multiple comparisons. Spatial overlap of areas showing significant differences were compared using Dice coefficients. Results: NODDI and SMT show significant associations with EDSS (standardised beta coefficient -0.34 in NAWM and -0.37 in lesions for NODDI vin; 0.38 and -0.31 for SMT ODE and vin in lesions; p < 0.05). Significant correlations in NAWM are observed between DTI and NODDI/SMT metrics. NODDI vin and SMT vin strongly correlated (r = 0.72, p < 0.05), likewise NODDI ODI and SMT ODE (r = -0.80, p < 0.05). All DTI, NODDI and SMT metrics detect widespread differences between patients and controls in NAWM (12.57% and 11.90% of MNI brain mask for SMT and NODDI vin, Dice overlap of 0.42). Data Conclusion: SMT and NODDI detect significant differences in white matter microstructure between MS patients and controls, concurring on the direction of these changes, providing consistent descriptors of tissue microstructure that correlate with disability and show alterations beyond focal damage. Our study suggests that NODDI and SMT may play a role in monitoring MS in clinical trials and practice.

On the potential for mapping apparent neural soma density via a clinically viable diffusion MRI protocol.

Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advances in measurement technology and modelling efforts, a clinically viable technique that reveals salient features of grey matter microstructure, such as the density of quasi-spherical cell bodies and quasi-cylindrical cell projections, is an exciting prospect. As a step towards capturing the microscopic architecture of grey matter in clinically feasible settings, this work uses a biophysical model that is designed to disentangle the diffusion signatures of spherical and cylindrical structures in the presence of orientation heterogeneity, and takes advantage of B-tensor encoding measurements, which provide additional sensitivity compared to standard single diffusion encoding sequences. For the fast and robust estimation of microstructural parameters, we leverage recent advances in machine learning and replace conventional fitting techniques with an artificial neural network that fits complex biophysical models within seconds. Our results demonstrate apparent markers of spherical and cylindrical geometries in healthy human subjects, and in particular an increased volume fraction of spherical compartments in grey matter compared to white matter. We evaluate the extent to which spherical and cylindrical geometries may be interpreted as correlates of neural soma and neural projections, respectively, and quantify parameter estimation errors in the presence of various departures from the modelling assumptions. While further work is necessary to translate the ideas presented in this work to the clinic, we suggest that biomarkers focussing on quasi-spherical cellular geometries may be valuable for the enhanced assessment of neurodevelopmental disorders and neurodegenerative diseases.

Tractographic and Microstructural Analysis of the Dentato-Rubro-Thalamo-Cortical Tracts in Children Using Diffusion MRI.

The dentato-rubro-thalamo-cortical tract (DRTC) is the main outflow pathway of the cerebellum, contributing to a finely balanced corticocerebellar loop involved in cognitive and sensorimotor functions. Damage to the DRTC has been implicated in cerebellar mutism syndrome seen in up to 25% of children after cerebellar tumor resection. Multi-shell diffusion MRI (dMRI) combined with quantitative constrained spherical deconvolution tractography and multi-compartment spherical mean technique modeling was used to explore the frontocerebellar connections and microstructural signature of the DRTC in 30 healthy children. The highest density of DRTC connections were to the precentral (M1) and superior frontal gyri (F1), and from cerebellar lobules I-IV and IX. The first evidence of a topographic organization of anterograde projections to the frontal cortex at the level of the superior cerebellar peduncle (SCP) is demonstrated, with streamlines terminating in F1 lying dorsomedially in the SCP compared to those terminating in M1. The orientation dispersion entropy of DRTC regions appears to exhibit greater contrast than that shown by fractional anisotropy. Analysis of a separate reproducibility cohort demonstrates good consistency in the dMRI metrics described. These novel anatomical insights into this well-studied pathway may prove to be of clinical relevance in the surgical resection of cerebellar tumors.

Uncertainty modelling in deep learning for safer neuroimage enhancement: Demonstration in diffusion MRI.

Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, most existing approaches are based on deterministic models, neglecting the presence of different sources of uncertainty in such problems. Here we introduce methods to characterise different components of uncertainty, and demonstrate the ideas using diffusion MRI super-resolution. Specifically, we propose to account for intrinsic uncertainty through a heteroscedastic noise model and for parameter uncertainty through approximate Bayesian inference, and integrate the two to quantify predictive uncertainty over the output image. Moreover, we introduce a method to propagate the predictive uncertainty on a multi-channelled image to derived scalar parameters, and separately quantify the effects of intrinsic and parameter uncertainty therein. The methods are evaluated for super-resolution of two different signal representations of diffusion MR images-Diffusion Tensor images and Mean Apparent Propagator MRI-and their derived quantities such as mean diffusivity and fractional anisotropy, on multiple datasets of both healthy and pathological human brains. Results highlight three key potential benefits of modelling uncertainty for improving the safety of DL-based image enhancement systems. Firstly, modelling uncertainty improves the predictive performance even when test data departs from training data ("out-of-distribution" datasets). Secondly, the predictive uncertainty highly correlates with reconstruction errors, and is therefore capable of detecting predictive "failures". Results on both healthy subjects and patients with brain glioma or multiple sclerosis demonstrate that such an uncertainty measure enables subject-specific and voxel-wise risk assessment of the super-resolved images that can be accounted for in subsequent analysis. Thirdly, we show that the method for decomposing predictive uncertainty into its independent sources provides high-level "explanations" for the model performance by separately quantifying how much uncertainty arises from the inherent difficulty of the task or the limited training examples. The introduced concepts of uncertainty modelling extend naturally to many other imaging modalities and data enhancement applications.

Cross-scanner and cross-protocol multi-shell diffusion MRI data harmonization: Algorithms and results.

Cross-scanner and cross-protocol variability of diffusion magnetic resonance imaging (dMRI) data are known to be major obstacles in multi-site clinical studies since they limit the ability to aggregate dMRI data and derived measures. Computational algorithms that harmonize the data and minimize such variability are critical to reliably combine datasets acquired from different scanners and/or protocols, thus improving the statistical power and sensitivity of multi-site studies. Different computational approaches have been proposed to harmonize diffusion MRI data or remove scanner-specific differences. To date, these methods have mostly been developed for or evaluated on single b-value diffusion MRI data. In this work, we present the evaluation results of 19 algorithms that are developed to harmonize the cross-scanner and cross-protocol variability of multi-shell diffusion MRI using a benchmark database. The proposed algorithms rely on various signal representation approaches and computational tools, such as rotational invariant spherical harmonics, deep neural networks and hybrid biophysical and statistical approaches. The benchmark database consists of data acquired from the same subjects on two scanners with different maximum gradient strength (80 and 300 â€‹mT/m) and with two protocols. We evaluated the performance of these algorithms for mapping multi-shell diffusion MRI data across scanners and across protocols using several state-of-the-art imaging measures. The results show that data harmonization algorithms can reduce the cross-scanner and cross-protocol variabilities to a similar level as scan-rescan variability using the same scanner and protocol. In particular, the LinearRISH algorithm based on adaptive linear mapping of rotational invariant spherical harmonics features yields the lowest variability for our data in predicting the fractional anisotropy (FA), mean diffusivity (MD), mean kurtosis (MK) and the rotationally invariant spherical harmonic (RISH) features. But other algorithms, such as DIAMOND, SHResNet, DIQT, CMResNet show further improvement in harmonizing the return-to-origin probability (RTOP). The performance of different approaches provides useful guidelines on data harmonization in future multi-site studies.

Microscopic susceptibility anisotropy imaging.

PURPOSE: The gradient-echo MR signal in brain white matter depends on the orientation of the fibers with respect to the external magnetic field. To map microstructure-specific magnetic susceptibility in orientationally heterogeneous material, it is thus imperative to regress out unwanted orientation effects. METHODS: This work introduces a novel framework, referred to as microscopic susceptibility anisotropy imaging, that disentangles the 2 principal effects conflated in gradient-echo measurements, (a) the susceptibility properties of tissue microenvironments, especially the myelin microstructure, and (b) the axon orientation distribution relative to the magnetic field. Specifically, we utilize information about the orientational tissue structure inferred from diffusion MRI data to factor out the B0 -direction dependence of the frequency difference signal. RESULTS: A human pilot study at 3 T demonstrates proxy maps of microscopic susceptibility anisotropy unconfounded by fiber crossings and orientation dispersion as well as magnetic field direction. The developed technique requires only a dual-echo gradient-echo scan acquired at 1 or 2 head orientations with respect to the magnetic field and a 2-shell diffusion protocol achievable on standard scanners within practical scan times. CONCLUSIONS: The quantitative recovery of microscopic susceptibility features in the presence of orientational heterogeneity potentially improves the assessment of microstructural tissue integrity.

Microstructural Investigations of the Visual Pathways in Pediatric Epilepsy Neurosurgery: Insights From Multi-Shell Diffusion Magnetic Resonance Imaging.

BACKGROUND: Surgery is a key approach for achieving seizure freedom in children with focal onset epilepsy. However, the resection can affect or be in the vicinity of the optic radiations. Multi-shell diffusion MRI and tractography can better characterize tissue structure and provide guidance to help minimize surgical related deficits. Whilst in adults tractography has been used to demonstrate that damage to the optic radiations leads to postoperative visual field deficits, this approach has yet to be properly explored in children. OBJECTIVE: To demonstrate the capabilities of multi-shell diffusion MRI and tractography in characterizing microstructural changes in children with epilepsy pre- and post-surgery affecting the occipital, parietal or temporal lobes. METHODS: Diffusion Tensor Imaging and the Spherical Mean Technique were used to investigate the microstructure of the optic radiations. Furthermore, tractography was used to evaluate whether pre-surgical reconstructions of the optic radiations overlap with the resection margin as measured using anatomical post-surgical T1-weighted MRI. RESULTS: Increased diffusivity in patients compared to controls at baseline was observed with evidence of decreased diffusivity, anisotropy, and neurite orientation distribution in contralateral hemisphere after surgery. Pre-surgical optic radiation tractography overlapped with post-surgical resection margins in 20/43 (46%) children, and where visual data was available before and after surgery, the presence of overlap indicated a visual field deficit. CONCLUSION: This is the first report in a pediatric series which highlights the relevance of tractography for future pre-surgical evaluation in children undergoing epilepsy surgery and the usefulness of multi-shell diffusion MRI to characterize brain microstructure in these patients.

MRI profiling of focal cortical dysplasia using multi-compartment diffusion models.

OBJECTIVE: Focal cortical dysplasia (FCD) lesion detection and subtyping remain challenging on conventional MRI. New diffusion models such as the spherical mean technique (SMT) and neurite orientation dispersion and density imaging (NODDI) provide measurements that potentially produce more specific maps of abnormal tissue microstructure. This study aims to assess the SMT and NODDI maps for computational and radiological lesion characterization compared to standard fractional anisotropy (FA) and mean diffusivity (MD). METHODS: SMT, NODDI, FA, and MD maps were calculated for 33 pediatric patients with suspected FCD (18 histologically confirmed). Two neuroradiologists scored lesion visibility on clinical images and diffusion maps. Signal profile changes within lesions and homologous regions were quantified using a surface-based approach. Diffusion parameter changes at multiple cortical depths were statistically compared between FCD type IIa and type IIb. RESULTS: Compared to fluid-attenuated inversion recovery (FLAIR) or T1-weighted imaging, lesions conspicuity on NODDI intracellular volume fraction (ICVF) maps was better/equal/worse in 5/14/14 patients, respectively, while on SMT intra-neurite volume fraction (INVF) in 3/3/27. Compared to FA or MD, lesion conspicuity on the ICVF was better/equal/worse in 27/4/2, while on the INVF in 20/7/6. Quantitative signal profiling demonstrated significant ICVF and INVF reductions in the lesions, whereas SMT microscopic mean, radial, and axial diffusivities were significantly increased. FCD type IIb exhibited greater changes than FCD type IIa. No changes were detected on FA or MD profiles. SIGNIFICANCE: FCD lesion-specific signal changes were found in ICVF and INVF but not in FA and MD maps. ICVF and INVF showed greater contrast than FLAIR in some cases and had consistent signal changes specific to FCD, suggesting that they could improve current presurgical pediatric epilepsy imaging protocols and can provide features useful for automated lesion detection.

Tractography reproducibility challenge with empirical data (TraCED): The 2017 ISMRM diffusion study group challenge.

BACKGROUND: Fiber tracking with diffusion-weighted MRI has become an essential tool for estimating in vivo brain white matter architecture. Fiber tracking results are sensitive to the choice of processing method and tracking criteria. PURPOSE: To assess the variability for an algorithm in group studies reproducibility is of critical context. However, reproducibility does not assess the validity of the brain connections. Phantom studies provide concrete quantitative comparisons of methods relative to absolute ground truths, yet do no capture variabilities because of in vivo physiological factors. The ISMRM 2017 TraCED challenge was created to fulfill the gap. STUDY TYPE: A systematic review of algorithms and tract reproducibility studies. SUBJECTS: Single healthy volunteers. FIELD STRENGTH/SEQUENCE: 3.0T, two different scanners by the same manufacturer. The multishell acquisition included b-values of 1000, 2000, and 3000 s/mm2 with 20, 45, and 64 diffusion gradient directions per shell, respectively. ASSESSMENT: Nine international groups submitted 46 tractography algorithm entries each consisting 16 tracts per scan. The algorithms were assessed using intraclass correlation (ICC) and the Dice similarity measure. STATISTICAL TESTS: Containment analysis was performed to assess if the submitted algorithms had containment within tracts of larger volume submissions. This also serves the purpose to detect if spurious submissions had been made. RESULTS: The top five submissions had high ICC and Dice >0.88. Reproducibility was high within the top five submissions when assessed across sessions or across scanners: 0.87-0.97. Containment analysis shows that the top five submissions are contained within larger volume submissions. From the total of 16 tracts as an outcome relatively the number of tracts with high, moderate, and low reproducibility were 8, 4, and 4. DATA CONCLUSION: The different methods clearly result in fundamentally different tract structures at the more conservative specificity choices. Data and challenge infrastructure remain available for continued analysis and provide a platform for comparison. LEVEL OF EVIDENCE: 5 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2020;51:234-249.

White matter microstructural abnormalities in children with severe congenital hypothyroidism.

This study assessed white matter microstructural integrity and behavioral correlates for children with severe congenital hypothyroidism (CH) who were identified and treated early following newborn screening. Eighteen children with severe CH and 21 healthy controls underwent a battery of behavioral measures of hearing, language and communication, along with diffusion MR imaging. Tract-based spatial statistics were performed on standard diffusion parameters of fractional anisotropy and diffusivity metrics. Microscopic diffusion anisotropy mapping based on the Spherical Mean Technique was also used to evaluate biologically specific metrics. Compared with age-matched controls, children with severe CH had poorer hearing and communication skills, albeit generally within normal limits. Children with severe CH had fractional anisotropy that was significantly lower in the cerebellum, bilateral thalami and right temporal lobe, and radial diffusivity that was significantly higher in the cerebellum and bilateral thalami. Microscopic fractional anisotropy and intra-neurite volume fraction were also significantly decreased, and transverse microscopic diffusivity was significantly increased, in the CH group in areas including the cerebellum, thalamus, occipital lobe, and corpus callosum, and in the white matter adjacent to sensorimotor cortex, particularly in the left hemisphere. Significant and widespread correlations were observed between behavioral measures and measures of white matter microstructural integrity in children with CH. The results indicate that children with severe CH who are identified through newborn screening may have significant brain white matter microstructural abnormalities despite early treatment.

Probing axons using multi-compartmental diffusion in multiple sclerosis.

OBJECTS: The diffusion-based spherical mean technique (SMT) provides a novel model to relate multi-b-value diffusion magnetic resonance imaging (MRI) data to features of tissue microstructure. We propose the first clinical application of SMT to image the brain of patients with multiple sclerosis (MS) and investigate clinical feasibility and translation. METHODS: Eighteen MS patients and nine age- and sex-matched healthy controls (HCs) underwent a 3.0 Tesla scan inclusive of clinical sequences and SMT images (isotropic resolution of 2 mm). Axial diffusivity (AD), apparent axonal volume fraction (Vax ), and effective neural diffusivity (Dax ) parametric maps were fitted. Differences in AD, Vax , and Dax between anatomically matched regions reflecting different tissues types were estimated using generalized linear mixed models for binary outcomes. RESULTS: Differences were seen in all SMT-derived parameters between chronic black holes (cBHs) and T2-lesions (P ≤ 0.0016), in Vax and AD between T2-lesions and normal appearing white matter (NAWM) (P < 0.0001), but not between the NAWM and normal WM in HCs. Inverse correlations were seen between Vax and AD in cBHs (r = -0.750, P = 0.02); in T2-lesions Dax values were associated with Vax (r = 0.824, P < 0.0001) and AD (r = 0.570, P = 0.014). INTERPRETATIONS: SMT-derived metrics are sensitive to pathological changes and hold potential for clinical application in MS patients.

In vivo demonstration of microscopic anisotropy in the human kidney using multidimensional diffusion MRI.

PURPOSE: To demonstrate the feasibility of multidimensional diffusion MRI to probe and quantify microscopic fractional anisotropy (µFA) in human kidneys in vivo. METHODS: Linear tensor encoded (LTE) and spherical tensor encoded (STE) renal diffusion MRI scans were performed in 10 healthy volunteers. Respiratory triggering and image registration were used to minimize motion artefacts during the acquisition. Kidney cortex-medulla were semi-automatically segmented based on fractional anisotropy (FA) values. A model-free analysis of LTE and STE signal dependence on b-value in the renal cortex and medulla was performed. Subsequently, µFA was estimated using a single-shell approach. Finally, a comparison of conventional FA and µFA is shown. RESULTS: The hallmark effect of µFA (divergence of LTE and STE signal with increasing b-value) was observed in all subjects. A statistically significant difference between LTE and STE signal was found in the cortex and medulla, starting from b = 750 s/mm2 and b = 500 s/mm2 , respectively. This difference was maximal at the highest b-value sampled (b = 1000 s/mm2 ) which suggests that relatively high b-values are required for µFA mapping in the kidney compared to conventional FA. Cortical and medullary µFA were, respectively, 0.53 ± 0.09 and 0.65 ± 0.05, both respectively higher than conventional FA (0.19 ± 0.02 and 0.40 ± 0.02). CONCLUSION: The feasibility of combining LTE and STE diffusion MRI to probe and quantify µFA in human kidneys is demonstrated for the first time. By doing so, we show that novel microstructure information-not accessible by conventional diffusion encoding-can be probed by multidimensional diffusion MRI. We also identify relevant technical limitations that warrant further development of the technique for body MRI.

Cross-scanner and cross-protocol diffusion MRI data harmonisation: A benchmark database and evaluation of algorithms.

Diffusion MRI is being used increasingly in studies of the brain and other parts of the body for its ability to provide quantitative measures that are sensitive to changes in tissue microstructure. However, inter-scanner and inter-protocol differences are known to induce significant measurement variability, which in turn jeopardises the ability to obtain 'truly quantitative measures' and challenges the reliable combination of different datasets. Combining datasets from different scanners and/or acquired at different time points could dramatically increase the statistical power of clinical studies, and facilitate multi-centre research. Even though careful harmonisation of acquisition parameters can reduce variability, inter-protocol differences become almost inevitable with improvements in hardware and sequence design over time, even within a site. In this work, we present a benchmark diffusion MRI database of the same subjects acquired on three distinct scanners with different maximum gradient strength (40, 80, and 300 mT/m), and with 'standard' and 'state-of-the-art' protocols, where the latter have higher spatial and angular resolution. The dataset serves as a useful testbed for method development in cross-scanner/cross-protocol diffusion MRI harmonisation and quality enhancement. Using the database, we compare the performance of five different methods for estimating mappings between the scanners and protocols. The results show that cross-scanner harmonisation of single-shell diffusion data sets can reduce the variability between scanners, and highlight the promises and shortcomings of today's data harmonisation techniques.

Relevance of time-dependence for clinically viable diffusion imaging of the spinal cord.

PURPOSE: Time-dependence is a key feature of the diffusion-weighted (DW) signal, knowledge of which informs biophysical modelling. Here, we study time-dependence in the human spinal cord, as its axonal structure is specific and different from the brain. METHODS: We run Monte Carlo simulations using a synthetic model of spinal cord white matter (WM) (large axons), and of brain WM (smaller axons). Furthermore, we study clinically feasible multi-shell DW scans of the cervical spinal cord (b = 0; b = 711 s mm-2 ; b = 2855 s mm-2 ), obtained using three diffusion times (Δ of 29, 52 and 76 ms) from three volunteers. RESULTS: Both intra-/extra-axonal perpendicular diffusivities and kurtosis excess show time-dependence in our synthetic spinal cord model. This time-dependence is reflected mostly in the intra-axonal perpendicular DW signal, which also exhibits strong decay, unlike our brain model. Time-dependence of the total DW signal appears detectable in the presence of noise in our synthetic spinal cord model, but not in the brain. In WM in vivo, we observe time-dependent macroscopic and microscopic diffusivities and diffusion kurtosis, NODDI and two-compartment SMT metrics. Accounting for large axon calibers improves fitting of multi-compartment models to a minor extent. CONCLUSIONS: Time-dependence of clinically viable DW MRI metrics can be detected in vivo in spinal cord WM, thus providing new opportunities for the non-invasive estimation of microstructural properties. The time-dependence of the perpendicular DW signal may feature strong intra-axonal contributions due to large spinal axon caliber. Hence, a popular model known as "stick" (zero-radius cylinder) may be sub-optimal to describe signals from the largest spinal axons.

Image quality transfer and applications in diffusion MRI.

This paper introduces a new computational imaging technique called image quality transfer (IQT). IQT uses machine learning to transfer the rich information available from one-off experimental medical imaging devices to the abundant but lower-quality data from routine acquisitions. The procedure uses matched pairs to learn mappings from low-quality to corresponding high-quality images. Once learned, these mappings then augment unseen low quality images, for example by enhancing image resolution or information content. Here, we demonstrate IQT using a simple patch-regression implementation and the uniquely rich diffusion MRI data set from the human connectome project (HCP). Results highlight potential benefits of IQT in both brain connectivity mapping and microstructure imaging. In brain connectivity mapping, IQT reveals, from standard data sets, thin connection pathways that tractography normally requires specialised data to reconstruct. In microstructure imaging, IQT shows potential in estimating, from standard "single-shell" data (one non-zero b-value), maps of microstructural parameters that normally require specialised multi-shell data. Further experiments show strong generalisability, highlighting IQT's benefits even when the training set does not directly represent the application domain. The concept extends naturally to many other imaging modalities and reconstruction problems.

Multi-compartment microscopic diffusion imaging.

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study.

PURPOSE: To identify optimal pulsed gradient spin-echo (PGSE) and oscillating gradient spin-echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions. METHODS: Simulations on a simple two-compartment white matter model (with nonpermeable cylinders) are used to investigate a wide space of clinically plausible PGSE and OGSE sequence parameters with trapezoidal diffusion gradient waveforms. Signal sensitivity is measured as a derivative of the signal with respect to axon diameter. Models of parallel and dispersed fibers are investigated separately to represent idealized and practical conditions. RESULTS: Simulations show that, for the simple case of gradients perfectly perpendicular to straight parallel fibers, PGSE always gives maximum sensitivity. However, in real-world scenarios where fibers have unknown and dispersed orientation, low-frequency OGSE provides higher sensitivity. Maximum sensitivity results show that on current clinical scanners (Gmax = 60 mT/m, signal to noise ratio (SNR) = 20) axon diameters below 6 µm are indistinguishable from zero. Scanners with stronger gradient systems such as the Massachusetts General Hospital (MGH) Connectom scanner (Gmax = 300 mT/m) can extend this sensitivity limit down to 2-3 µm, probing a much greater proportion of the underlying axon diameter distribution. CONCLUSION: Low-frequency OGSE provides additional sensitivity to PGSE in practical situations. OGSE is particularly advantageous for systems with high performance gradients.

Quantitative mapping of the per-axon diffusion coefficients in brain white matter.

PURPOSE: This article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per-axon or microscopic diffusion coefficients. THEORY AND METHODS: Diffusion MR imaging is used to probe the underlying tissue material. The key observation is that for a fixed b-value the spherical mean of the diffusion signal over the gradient directions does not depend on the axon orientation distribution. By exploiting this invariance property, we propose a simple, fast, and robust estimator of the per-axon diffusion coefficients, which we refer to as the spherical mean technique. RESULTS: We demonstrate quantitative maps of the axon-scale diffusion process, which has factored out the effects due to fiber dispersion and crossing, in human brain white matter. These microscopic diffusion coefficients are estimated in vivo using a widely available off-the-shelf pulse sequence featuring multiple b-shells and high-angular gradient resolution. CONCLUSION: The estimation of the per-axon diffusion coefficients is essential for the accurate recovery of the fiber orientation distribution. In addition, the spherical mean technique enables us to discriminate microscopic tissue features from fiber dispersion, which potentially improves the sensitivity and/or specificity to various neurological conditions. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

Can T2-spectroscopy resolve submicrometer axon diameters?

The microscopic geometry of white matter carries rich information about brain function in health and disease. A key challenge for medical imaging is to estimate microstructural features noninvasively. One important parameter is the axon diameter, which correlates with the conduction time delay of action potentials and is affected by various neurological disorders. Diffusion magnetic resonance (MR) experiments are the method of choice today when we aim to recover the axon diameter distribution, although the technique requires very high gradient strengths in order to assess nerve fibers with one micrometer or less in diameter. In practice in-vivo brain imaging is only sensitive to the largest axons, not least due to limitations in the human physiology which tolerates only moderate gradient strengths. This work studies, from a theoretical perspective, the feasibility of T2-spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T2-weighted signal, which is based on a surface-to-volume ratio approximation of the Bloch-Torrey equation. Under a certain regime of bulk and surface relaxation coefficients, our simulation results suggest that it might be possible to reveal axons smaller than one micrometer in diameter.

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images.

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.