Sparse and optimal acquisition design for diffusion MRI and beyond

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

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

The Subcortical Atlas of the Marmoset ("SAM") monkey based on high-resolution MRI and histology

A comprehensive three-dimensional digital brain atlas of cortical and subcortical regions based on MRI and histology has a broad array of applications in anatomical, functional, and clinical studies. We first generated a Subcortical Atlas of the Marmoset, called the "SAM," from 251 delineated subcortical regions (e.g. thalamic subregions, etc.) derived from high-resolution Mean Apparent Propagator-MRI, T2W, and magnetization transfer ratio images ex vivo. We then confirmed the location and borders of these segmented regions in the MRI data using matched histological sections with multiple stains obtained from the same specimen. Finally, we estimated and confirmed the atlas-based areal boundaries of subcortical regions by registering this ex vivo atlas template to in vivo T1- or T2W MRI datasets of different age groups (single vs. multisubject population-based marmoset control adults) using a novel pipeline developed within Analysis of Functional NeuroImages software. Tracing and validating these important deep brain structures in 3D will improve neurosurgical planning, anatomical tract tracer injections, navigation of deep brain stimulation probes, functional MRI and brain connectivity studies, and our understanding of brain structure-function relationships. This new ex vivo template and atlas are available as volumes in standard NIFTI and GIFTI file formats and are intended for use as a reference standard for marmoset brain research.

Down-sampling in diffusion MRI: a bundle-specific DTI and NODDI study

Introduction

Multi-shell diffusion Magnetic Resonance Imaging (dMRI) data has been widely used to characterise white matter microstructure in several neurodegenerative diseases. The lack of standardised dMRI protocols often implies the acquisition of redundant measurements, resulting in prolonged acquisition times. In this study, we investigate the impact of the number of gradient directions on Diffusion Tensor Imaging (DTI) and on Neurite Orientation Dispersion and Density Imaging (NODDI) metrics.

Methods

Data from 124 healthy controls collected in three different longitudinal studies were included. Using an in-house algorithm, we reduced the number of gradient directions in each data shell. We estimated DTI and NODDI measures on six white matter bundles clinically relevant for neurodegenerative diseases.

Results

Fractional Anisotropy (FA) measures on bundles where data were sampled at the 30% rate, showed a median L1 distance of up to 3.92% and a 95% CI of (1.74, 8.97)% when compared to those obtained at reference sampling. Mean Diffusivity (MD) reached up to 4.31% and a 95% CI of (1.60, 16.98)% on the same premises. At a sampling rate of 50%, we obtained a median of 3.90% and a 95% CI of (1.99, 16.65)% in FA, and 5.49% with a 95% CI of (2.14, 21.68)% in MD. The Intra-Cellular volume fraction (ICvf) median L1 distance was up to 2.83% with a 95% CI of (1.98, 4.82)% at a 30% sampling rate and 3.95% with a 95% CI of (2.39, 7.81)% at a 50% sampling rate. The volume difference of the reconstructed white matter at reference and 50% sampling reached a maximum of (2.09 ± 0.81)%.

Discussion

In conclusion, DTI and NODDI measures reported at reference sampling were comparable to those obtained when the number of dMRI volumes was reduced by up to 30%. Close to reference DTI and NODDI metrics were estimated with a significant reduction in acquisition time using three shells, respectively with: 4 directions at a b value of 700 s/mm2, 14 at 1000 s/mm2, and 32 at 2000 s/mm2. The study revealed aspects that can be important for large-scale clinical studies on bundle-specific diffusion MRI.

The Subcortical Atlas of the Marmoset ("SAM") monkey based on high-resolution MRI and histology

A comprehensive three-dimensional digital brain atlas of cortical and subcortical regions based on MRI and histology has a broad array of applications for anatomical, functional, and clinical studies. We first generated a Subcortical Atlas of the Marmoset, called the "SAM," from 251 delineated subcortical regions (e.g., thalamic subregions, etc.) derived from the high-resolution MAP-MRI, T2W, and MTR images ex vivo. We then confirmed the location and borders of these segmented regions in MRI data using matched histological sections with multiple stains obtained from the same specimen. Finally, we estimated and confirmed the atlas-based areal boundaries of subcortical regions by registering this ex vivo atlas template to in vivo T1- or T2W MRI datasets of different age groups (single vs. multisubject population-based marmoset control adults) using a novel pipeline developed within AFNI. Tracing and validating these important deep brain structures in 3D improves neurosurgical planning, anatomical tract tracer injections, navigation of deep brain stimulation probes, fMRI and brain connectivity studies, and our understanding of brain structure-function relationships. This new ex vivo template and atlas are available as volumes in standard NIFTI and GIFTI file formats and are intended for use as a reference standard for marmoset brain research.

Multimodal anatomical mapping of subcortical regions in marmoset monkeys using high-resolution MRI and matched histology with multiple stains

Subcortical nuclei and other deep brain structures play essential roles in regulating the central and peripheral nervous systems. However, many of these nuclei and their subregions are challenging to identify and delineate in conventional MRI due to their small size, hidden location, and often subtle contrasts compared to neighboring regions. To address these limitations, we scanned the whole brain of the marmoset monkeys in ex vivo using a clinically feasible diffusion MRI method, called the mean apparent propagator (MAP)-MRI, along with T2W and MTR (T1-like contrast) images acquired at 7 Tesla. Additionally, we registered these multimodal MRI volumes to the high-resolution images of matched whole-brain histology sections with seven different stains obtained from the same brain specimens. At high spatial resolution, the microstructural parameters and fiber orientation distribution functions derived with MAP-MRI can distinguish the subregions of many subcortical and deep brain structures, including fiber tracts of different sizes and orientations. The good correlation with multiple but distinct histological stains from the same brain serves as a thorough validation of the structures identified with MAP-MRI and other MRI parameters. Moreover, the anatomical details of deep brain structures found in the volumes of MAP-MRI parameters are not visible in conventional T1W or T2W images. The high-resolution mapping using novel MRI contrasts, combined and correlated with histology, can elucidate structures that were previously invisible radiologically. Thus, this multimodal approach offers a roadmap toward identifying salient brain areas in vivo in future neuroradiological studies. It also provides a useful anatomical standard reference for the region definition of subcortical targets and the generation of a 3D digital template atlas for the marmoset brain research (Saleem et al., 2023). Additionally, we conducted a cross-species comparison between marmoset and macaque monkeys using results from our previous studies (Saleem et al., 2021). We found that the two species had distinct patterns of iron distribution in subregions of the basal ganglia, red nucleus, and deep cerebellar nuclei, confirmed with T2W MRI and histology.

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

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

Multimodal anatomical mapping of subcortical regions in Marmoset monkeys using high-resolution MRI and matched histology with multiple stains

Subcortical nuclei and other deep brain structures play essential roles in regulating the central and peripheral nervous systems. However, many of these nuclei and their subregions are challenging to identify and delineate in conventional MRI due to their small size, hidden location, and often subtle contrasts compared to neighboring regions. To address these limitations, we scanned the whole brain of the marmoset monkeys in ex vivo using a clinically feasible diffusion MRI method, called the mean apparent propagator (MAP)-MRI, along with T2W and MTR (T1-like contrast) images acquired at 7 Tesla. Additionally, we registered these multimodal MRI volumes to the high-resolution images of matched whole-brain histology sections with seven different stains obtained from the same brain specimens. At high spatial resolution, the microstructural parameters and fiber orientation distribution functions derived with MAP-MRI can distinguish the subregions of many subcortical and deep brain structures, including fiber tracts of different sizes and orientations. The good correlation with multiple but distinct histological stains from the same brain serves as a thorough validation of the structures identified with MAP-MRI and other MRI parameters. Moreover, the anatomical details of deep brain structures found in the volumes of MAP-MRI parameters are not visible in conventional T1W or T2W images. The high-resolution mapping using novel MRI contrasts, combined and correlated with histology, can elucidate structures that were previously invisible radiologically. Thus, this multimodal approach offers a roadmap toward identifying salient brain areas in vivo in future neuroradiological studies. It also provides a useful anatomical standard reference for the region definition of subcortical targets and the generation of a 3D digital template atlas for the marmoset brain research (Saleem et al., 2023). Additionally, we conducted a cross-species comparison between marmoset and macaque monkeys using results from our previous studies (Saleem et al., 2021). We found that the two species had distinct patterns of iron distribution in subregions of the basal ganglia, red nucleus, and deep cerebellar nuclei, confirmed with T2W MRI and histology.

The distortions of the free water model for diffusion MRI data when assuming single compartment relaxometry and proton density

Objective.To document the bias of thesimplifiedfree water model of diffusion MRI (dMRI) signal vis-à-vis aspecificmodel which, in addition to diffusion, incorporates compartment-specific proton density (PD), T1 recovery during repetition time (TR), and T2 decay during echo time (TE).Approach.Both models assume that volume fractionfof the total signal in any voxel arises from the free water compartment (fw) such as cerebrospinal fluid or edema, and the remainder (1-f) from hindered water (hw) which is constrained by cellular structures such as white matter (WM). Thespecificandsimplifiedmodels are compared on a synthetic dataset, using a range of PD, T1 and T2 values. We then fit the models to anin vivohealthy brain dMRI dataset. For bothsyntheticandin vivodata we use experimentally feasible TR, TE, signal-to-noise ratio (SNR) and physiologically plausible diffusion profiles.Main results.From the simulations we see that the difference between the estimatedsimplified fandspecific fis largest for mid-range ground-truthf, and it increases as SNR increases. The estimation of volume fractionfis sensitive to the choice of model,simplifiedorspecific, but the estimated diffusion parameters are robust to small perturbations in the simulation.Specific fis more accurate and precise thansimplified f. In the white matter (WM) regions of thein vivoimages,specific fis lower thansimplified f.Significance.In dMRI models for free water, accounting for compartment specific PD, T1 and T2, in addition to diffusion, improves the estimation of model parameters. This extra model specification attenuates the estimation bias of compartmental volume fraction without affecting the estimation of other diffusion parameters.

COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

High-resolution imaging studies have consistently shown that in cortical tissue water diffuses preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across experiments that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for imaging non-parametric diffusion tensor distributions (DTDs) by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently using Inverse Laplace Transform methods. Moreover, the cDTD reconstruction can be performed using only data acquired efficiently with single diffusion encoding, although it also supports datasets with multiple diffusion encoding. In tissues with a well-defined architecture, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of principal diffusivities along the radial and tangential orientation with respect to the cortical surface. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data from a fixed macaque monkey brain. We estimate 2D cDTDs in the cortex and derive, in each voxel, the marginal distributions of the microscopic principal diffusivities, the corresponding distributions of the microscopic fractional anisotropies and mean diffusivities along with their 2D correlation spectra to quantify the cDTD shape-size characteristics. Signal components corresponding to specific bands in these cDTD-derived spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs in high-resolution datasets with mesoscopic voxel sizes much smaller than the radius of curvature of the underlying anatomy, e.g., cortical surface, and can be applied retrospectively to analyze existing diffusion MRI data from fixed cortical tissues.

High-resolution cortical MAP-MRI reveals areal borders and laminar substructures observed with histological staining

The variations in cellular composition and tissue architecture measured with histology provide the biological basis for partitioning the brain into distinct cytoarchitectonic areas and for characterizing neuropathological tissue alterations. Clearly, there is an urgent need to develop whole-brain neuroradiological methods that can assess cortical cyto- and myeloarchitectonic features non-invasively. Mean apparent propagator (MAP) MRI is a clinically feasible diffusion MRI method that quantifies efficiently and comprehensively the net microscopic displacements of water molecules diffusing in tissues. We investigate the sensitivity of high-resolution MAP-MRI to detecting areal and laminar variations in cortical cytoarchitecture and compare our results with observations from corresponding histological sections in the entire brain of a rhesus macaque monkey. High-resolution images of MAP-derived parameters, in particular the propagator anisotropy (PA), non-gaussianity (NG), and the return-to-axis probability (RTAP) reveal cortical area-specific lamination patterns in good agreement with the corresponding histological stained sections. In a few regions, the MAP parameters provide superior contrast to the five histological stains used in this study, delineating more clearly boundaries and transition regions between cortical areas and laminar substructures. Throughout the cortex, various MAP parameters can be used to delineate transition regions between specific cortical areas observed with histology and to refine areal boundaries estimated using atlas registration-based cortical parcellation. Using surface-based analysis of MAP parameters we quantify the cortical depth dependence of diffusion propagators in multiple regions-of-interest in a consistent and rigorous manner that is largely independent of the cortical folding geometry. The ability to assess cortical cytoarchitectonic features efficiently and non-invasively, its clinical feasibility, and translatability make high-resolution MAP-MRI a promising 3D imaging tool for studying whole-brain cortical organization, characterizing abnormal cortical development, improving early diagnosis of neurodegenerative diseases, identifying targets for biopsies, and complementing neuropathological investigations.

Cumulant expansion with localization: A new representation of the diffusion MRI signal

Diffusion MR is sensitive to the microstructural features of a sample. Fine-scale characteristics can be probed by employing strong diffusion gradients while the low b-value regime is determined by the cumulants of the distribution of particle displacements. A signal representation based on the cumulants, however, suffers from a finite convergence radius and cannot represent the 'localization regime' characterized by a stretched exponential decay that emerges at large gradient strengths. Here, we propose a new representation for the diffusion MR signal. Our method provides not only a robust estimate of the first three cumulants but also a meaningful extrapolation of the entire signal decay.

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

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

High-resolution mapping and digital atlas of subcortical regions in the macaque monkey based on matched MAP-MRI and histology

Subcortical nuclei and other deep brain structures are known to play an important role in the regulation of the central and peripheral nervous systems. It can be difficult to identify and delineate many of these nuclei and their finer subdivisions in conventional MRI due to their small size, buried location, and often subtle contrast compared to neighboring tissue. To address this problem, we applied a multi-modal approach in ex vivo non-human primate (NHP) brain that includes high-resolution mean apparent propagator (MAP)-MRI and five different histological stains imaged with high-resolution microscopy in the brain of the same subject. By registering these high-dimensional MRI data to high-resolution histology data, we can map the location, boundaries, subdivisions, and micro-architectural features of subcortical gray matter regions in the macaque monkey brain. At high spatial resolution, diffusion MRI in general, and MAP-MRI in particular, can distinguish a large number of deep brain structures, including the larger and smaller white matter fiber tracts as well as architectonic features within various nuclei. Correlation with histology from the same brain enables a thorough validation of the structures identified with MAP-MRI. Moreover, anatomical details that are evident in images of MAP-MRI parameters are not visible in conventional T₁-weighted images. We also derived subcortical template "SC21" from segmented MRI slices in three-dimensions and registered this volume to a previously published anatomical template with cortical parcellation (Reveley et al., 2017; Saleem and Logothetis, 2012), thereby integrating the 3D segmentation of both cortical and subcortical regions into the same volume. This newly updated three-dimensional D99 digital brain atlas (V2.0) is intended for use as a reference standard for macaque neuroanatomical, functional, and connectional imaging studies, involving both cortical and subcortical targets. The SC21 and D99 digital templates are available as volumes and surfaces in standard NIFTI and GIFTI formats.

Computing the orientational-average of diffusion-weighted MRI signals: a comparison of different techniques

Numerous applications in diffusion MRI involve computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or ‘shell’), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres. To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its ‘isotropic part’. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

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

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Optimization of q-space sampling for mean apparent propagator MRI metrics using a genetic algorithm

Mean Apparent Propagator (MAP) MRI is a recently introduced technique to estimate the diffusion probability density function (PDF) robustly. Using the estimated PDF, MAP MRI then calculates zero-displacement and non-Gaussianity metrics, which might better characterize tissue microstructure compared to diffusion tensor imaging or diffusion kurtosis imaging. However, intensive q-space sampling required for MAP MRI limits its widespread adoption. A reduced q-space sampling scheme that maintains the accuracy of the derived metrics would make it more practical. A heuristic approach for acquiring MAP MRI with fewer q-space samples has been introduced earlier with scan duration of less than 10 minutes. However, the sampling scheme was not optimized systematically to preserve the accuracy of the model metrics. In this work, a genetic algorithm is implemented to determine optimal q-space subsampling schemes for MAP MRI that will keep total scan time under 10 min. Results show that the metrics derived from the optimized schemes more closely match those computed from the full set, especially in dense fiber tracts such as the corpus callosum.

Neurite orientation dispersion and density imaging of mouse brain microstructure

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

Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.

A time-efficient acquisition protocol for multipurpose diffusion-weighted microstructural imaging at 7 Tesla

PURPOSE

Several diffusion-weighted MRI techniques have been developed and validated during the past 2 decades. While offering various neuroanatomical inferences, these techniques differ in their proposed optimal acquisition design, preventing clinicians and researchers benefiting from all potential inference methods, particularly when limited time is available. This study reports an optimal design that enables for a time-efficient diffusion-weighted MRI acquisition scheme at 7 Tesla. The primary audience of this article is the typical end user, interested in diffusion-weighted microstructural imaging at 7 Tesla.

METHODS

We tested b-values in the range of 700 to 3000 s/mm² with different number of angular diffusion-encoding samples, against a data-driven "gold standard."

RESULTS

The suggested design is a protocol with b-values of 1000 and 2500 s/mm² , with 25 and 50 samples, uniformly distributed over two shells. We also report a range of protocols in which the results of fitting microstructural models to the diffusion-weighted data had high correlation with the gold standard.

CONCLUSION

We estimated minimum acquisition requirements that enable diffusion tensor imaging, higher angular resolution diffusion-weighted imaging, neurite orientation dispersion, and density imaging and white matter tract integrity across whole brain with isotropic resolution of 1.8 mm in less than 11 min. Magn Reson Med 78:2170-2184, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI): A framework for single-subject analysis in diffusion tensor imaging

The purpose of this work is to develop a framework for single-subject analysis of diffusion tensor imaging (DTI) data. This framework is termed Tract Orientation and Angular Dispersion Deviation Indicator (TOADDI) because it is capable of testing whether an individual tract as represented by the major eigenvector of the diffusion tensor and its corresponding angular dispersion are significantly different from a group of tracts on a voxel-by-voxel basis. This work develops two complementary statistical tests based on the elliptical cone of uncertainty, which is a model of uncertainty or dispersion of the major eigenvector of the diffusion tensor. The orientation deviation test examines whether the major eigenvector from a single subject is within the average elliptical cone of uncertainty formed by a collection of elliptical cones of uncertainty. The shape deviation test is based on the two-tailed Wilcoxon-Mann-Whitney two-sample test between the normalized shape measures (area and circumference) of the elliptical cones of uncertainty of the single subject against a group of controls. The False Discovery Rate (FDR) and False Non-discovery Rate (FNR) were incorporated in the orientation deviation test. The shape deviation test uses FDR only. TOADDI was found to be numerically accurate and statistically effective. Clinical data from two Traumatic Brain Injury (TBI) patients and one non-TBI subject were tested against the data obtained from a group of 45 non-TBI controls to illustrate the application of the proposed framework in single-subject analysis. The frontal portion of the superior longitudinal fasciculus seemed to be implicated in both tests (orientation and shape) as significantly different from that of the control group. The TBI patients and the single non-TBI subject were well separated under the shape deviation test at the chosen FDR level of 0.0005. TOADDI is a simple but novel geometrically based statistical framework for analyzing DTI data. TOADDI may be found useful in single-subject, graph-theoretic and group analyses of DTI data or DTI-based tractography techniques.

Clinical feasibility of using mean apparent propagator (MAP) MRI to characterize brain tissue microstructure

Diffusion tensor imaging (DTI) is the most widely used method for characterizing noninvasively structural and architectural features of brain tissues. However, the assumption of a Gaussian spin displacement distribution intrinsic to DTI weakens its ability to describe intricate tissue microanatomy. Consequently, the biological interpretation of microstructural parameters, such as fractional anisotropy or mean diffusivity, is often equivocal. We evaluate the clinical feasibility of assessing brain tissue microstructure with mean apparent propagator (MAP) MRI, a powerful analytical framework that efficiently measures the probability density function (PDF) of spin displacements and quantifies useful metrics of this PDF indicative of diffusion in complex microstructure (e.g., restrictions, multiple compartments). Rotation invariant and scalar parameters computed from the MAP show consistent variation across neuroanatomical brain regions and increased ability to differentiate tissues with distinct structural and architectural features compared with DTI-derived parameters. The return-to-origin probability (RTOP) appears to reflect cellularity and restrictions better than MD, while the non-Gaussianity (NG) measures diffusion heterogeneity by comprehensively quantifying the deviation between the spin displacement PDF and its Gaussian approximation. Both RTOP and NG can be decomposed in the local anatomical frame for reference determined by the orientation of the diffusion tensor and reveal additional information complementary to DTI. The propagator anisotropy (PA) shows high tissue contrast even in deep brain nuclei and cortical gray matter and is more uniform in white matter than the FA, which drops significantly in regions containing crossing fibers. Orientational profiles of the propagator computed analytically from the MAP MRI series coefficients allow separation of different fiber populations in regions of crossing white matter pathways, which in turn improves our ability to perform whole-brain fiber tractography. Reconstructions from subsampled data sets suggest that MAP MRI parameters can be computed from a relatively small number of DWIs acquired with high b-value and good signal-to-noise ratio in clinically achievable scan durations of less than 10min. The neuroanatomical consistency across healthy subjects and reproducibility in test-retest experiments of MAP MRI microstructural parameters further substantiate the robustness and clinical feasibility of this technique. The MAP MRI metrics could potentially provide more sensitive clinical biomarkers with increased pathophysiological specificity compared to microstructural measures derived using conventional diffusion MRI techniques.

Pseudometrically constrained centroidal voronoi tessellations: Generating uniform antipodally symmetric points on the unit sphere with a novel acceleration strategy and its applications to diffusion and three-dimensional radial MRI

PURPOSE

The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role in image quality when the raw data and image data are related through the Fourier relationship. Currently, it is extremely challenging to generate large and uniform antipodally symmetric point sets suitable for three-dimensional radial MRI. A novel approach is proposed to solve this long-standing problem in a unique and optimal way.

METHODS

The proposed method is based on constrained centroidal Voronoi tessellations of the upper hemisphere with a novel pseudometric.

RESULTS

The time complexity of the proposed tessellations was shown to be effectively linear, i.e., on the order of the number of sampling measurements. For small sample size, the proposed method was comparable with the state-of-the-art method (a direct iterative minimization of the electrostatic potential energy of a collection of electrons antipodal-symmetrically distributed on the unit sphere) in terms of the sampling uniformity. For large sample size, in which the state-of-the-art method is infeasible, the reconstructed images from the proposed method has less streak and ringing artifacts, when compared with those of the commonly used methods.

CONCLUSION

This work proposed a unique and optimal approach to solving a long-standing problem in generating uniform sampling points for three-dimensional radial MRI.

A 4D hyperspherical interpretation of q-space

3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we derive several well-established q-space indices and numerically estimate the diffusion orientation distribution function (dODF). We also derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. Most importantly, we will demonstrate that for hybrid diffusion imaging (HYDI) acquisitions low order linear expansion of the HSH basis is sufficient to characterize diffusion in neural tissue. In fact, the HSH basis achieves comparable signal and better dODF reconstructions than other well-established methods, such as Bessel Fourier orientation reconstruction (BFOR), using fewer fitting parameters. All in all, this work provides a new way of looking at q-space.

Optimization of a free water elimination two-compartment model for diffusion tensor imaging

Diffusion tensor imaging is used to measure the diffusion of water in tissue. The diffusion properties carry information about the relative organization and structure of the underlying tissue. In the case of a single voxel containing both tissue and a fast diffusing component such as free water, a single diffusion tensor is no longer appropriate. A two-tensor free water elimination model has previously been proposed to correct for the case of volume mixing. Here, this model was implemented in a straightforward but novel manner without the use of spatial constraints. The optimal acquisition parameters were investigated through Monte Carlo simulations and human brain imaging studies. At a signal-to-noise ratio of 40 with 64 diffusion-weighted encoding images, the most accurate estimates of fast diffusion signal were obtained with two diffusion-weighted shells (b-value in s/mm(2)×number of directions) of 500×32 and 1500×32. The potential bias in fractional anisotropy induced by this two-compartment model was more than an order of magnitude less than the error of using the single diffusion tensor model in the presence of partial volume effects with free water. This strategy may be useful for characterizing the diffusion of tissues adjacent to cerebral spinal fluid (CSF), tissues affected by edema, and removing artifacts from blurring and ghosting of the CSF signal.

Conceptual Foundations of Diffusion in Magnetic Resonance

A thorough review of the q-space technique is presented starting from a discussion of Fick's laws. The work presented here is primarily conceptual, theoretical and hopefully pedagogical. We offered the notion of molecular concentration to unify Fick's laws and diffusion MRI within a coherent conceptual framework. The fundamental relationship between diffusion MRI and the Fick's laws are carefully established. The conceptual and theoretical basis of the q-space technique is investigated from first principles.

Design of multishell sampling schemes with uniform coverage in diffusion MRI

PURPOSE

In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques.

METHODS

The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell.

RESULTS

We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination.

DISCUSSION

We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI.

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in "q-space," and the corresponding "mean apparent propagator (MAP)" describing molecular displacements in "r-space." We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit "displacement" sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions-the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.