Structural information in neuronal tissue as revealed by q-space diffusion NMR spectroscopy of metabolites in bovine optic nerve

Diffusion-weighted MR spectroscopy: Consensus, recommendations, and resources from acquisition to modeling

Brain cell structure and function reflect neurodevelopment, plasticity, and aging; and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to noninvasively disentangle cellular structural features are needed and are a substantial focus of brain research. Diffusion-weighted MRS (dMRS) gives access to diffusion properties of endogenous intracellular brain metabolites that are preferentially located inside specific brain cell populations. Despite its great potential, dMRS remains a challenging technique on all levels: from the data acquisition to the analysis, quantification, modeling, and interpretation of results. These challenges were the motivation behind the organization of the Lorentz Center workshop on "Best Practices & Tools for Diffusion MR Spectroscopy" held in Leiden, the Netherlands, in September 2021. During the workshop, the dMRS community established a set of recommendations to execute robust dMRS studies. This paper provides a description of the steps needed for acquiring, processing, fitting, and modeling dMRS data, and provides links to useful resources.

Rapid acquisition diffusion MR spectroscopy of metabolites in human brain

Few studies have focused on metabolite diffusion in the human brain using ¹ H-MRS due to significant technical challenges. Moreover, such studies have required lengthy acquisition times and are therefore impractical to implement clinically. By first characterizing and then minimizing the effects of linear and oscillating eddy currents, which arise from the diffusion gradients, and by implementing phase-cycle and slice-order strategies, as well as introducing a new phase-alignment methodology, we report a method that allows data acquisition requiring 20 seconds per spectrum. This remained feasible, even for b-values >8000 s/mm² , with a rapid acquisition diffusion MRS methodology. It has allowed the nonlinear characterization of signal intensity with multiple b-values, and has improved the measurement of rotationally invariant diffusion parameters via six-direction, six b-value diffusion tensor spectroscopy (DTS) in 12 minutes at 4.7 T. The shorter DTS acquisition will enable its application to white matter regions not aligned with the gradients and permit clinical studies in a feasible time.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

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.

From micro- to macro-structures in multiple sclerosis: what is the added value of diffusion imaging

Diffusion imaging has been instrumental in understanding damage to the central nervous system as a result of its sensitivity to microstructural changes. Clinical applications of diffusion imaging have grown exponentially over the past couple of decades in many neurological and neurodegenerative diseases, such as multiple sclerosis (MS). For several reasons, MS has been extensively researched using advanced neuroimaging techniques, which makes it an 'example disease' to illustrate the potential of diffusion imaging for clinical applications. In addition, MS pathology is characterized by several key processes competing with each other, such as inflammation, demyelination, remyelination, gliosis and axonal loss, enabling the specificity of diffusion to be challenged. In this review, we describe how diffusion imaging can be exploited to investigate micro-, meso- and macro-scale properties of the brain structure and discuss how they are affected by different pathological substrates. Conclusions from the literature are that larger studies are needed to confirm the exciting results from initial investigations before current trends in diffusion imaging can be translated to the neurology clinic. Also, for a comprehensive understanding of pathological processes, it is essential to take a multiple-level approach, in which information at the micro-, meso- and macroscopic scales is fully integrated.

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

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

Generalized diffusion spectrum magnetic resonance imaging (GDSI) for model-free reconstruction of the ensemble average propagator

Diffusion spectrum MRI (DSI) provides model-free estimation of the diffusion ensemble average propagator (EAP) and orientation distribution function (ODF) but requires the diffusion data to be acquired on a Cartesian q-space grid. Multi-shell diffusion acquisitions are more flexible and more commonly acquired but have, thus far, only been compatible with model-based analysis methods. Here, we propose a generalized DSI (GDSI) framework to recover the EAP from multi-shell diffusion MRI data. The proposed GDSI approach corrects for q-space sampling density non-uniformity using a fast geometrical approach. The EAP is directly calculated in a preferable coordinate system by multiplying the sampling density corrected q-space signals by a discrete Fourier transform matrix, without any need for gridding. The EAP is demonstrated as a way to map diffusion patterns in brain regions such as the thalamus, cortex and brainstem where the tissue microstructure is not as well characterized as in white matter. Scalar metrics such as the zero displacement probability and displacement distances at different fractions of the zero displacement probability were computed from the recovered EAP to characterize the diffusion pattern within each voxel. The probability averaged across directions at a specific displacement distance provides a diffusion property based image contrast that clearly differentiates tissue types. The displacement distance at the first zero crossing of the EAP averaged across directions orthogonal to the primary fiber orientation in the corpus callosum is found to be larger in the body (5.65 ± 0.09 μm) than in the genu (5.55 ± 0.15 μm) and splenium (5.4 ± 0.15 μm) of the corpus callosum, which corresponds well to prior histological studies. The EAP also provides model-free representations of angular structure such as the diffusion ODF, which allows estimation and comparison of fiber orientations from both the model-free and model-based methods on the same multi-shell data. For the model-free methods, detection of crossing fibers is found to be strongly dependent on the maximum b-value and less sensitive compared to the model-based methods. In conclusion, our study provides a generalized DSI approach that allows flexible reconstruction of the diffusion EAP and ODF from multi-shell diffusion data and data acquired with other sampling patterns.

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

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

Can we detect the effect of spines and leaflets on the diffusion of brain intracellular metabolites?

Prior models used to clarify which aspects of tissue microstructure mostly affect intracellular diffusion and corresponding diffusion-weighted magnetic resonance (DW-MR) signal have focused on relatively simple geometrical descriptions of the cellular microenvironment (spheres, randomly oriented cylinders, etc…), neglecting finer morphological details which may have an important role. Some types of neurons present high density of spines; and astrocytes and macroglial cells processes present leaflets, which may all impact the diffusion process. Here, we use Monte-Carlo simulations of many particles diffusing in cylindrical compartments with secondary structures mimicking spines and leaflets of neuronal and glial cell fibers, to investigate to what extent the diffusion-weighted signal of intracellular molecules is sensitive to spines/leaflets density and length. In order to study the specificity of DW-MR signal to these kinds of secondary structures, beading-like geometry is simulated as "control" deviation from smooth cylinder too. Results suggest that: a) the estimated intracellular tortuosity increases as spines/leaflets density or length (beading amplitude) increase; b) the tortuosity limit is reached for diffusion time t_d>200 ms for metabolites and t_d>70 ms for water molecules, suggesting that the effects of these finer morphological details are negligible at t_d longer than these threshold values; c) fiber diameter is overestimated, while intracellular diffusivity is underestimated, when simple geometrical models based on hollow smooth cylinders are used; d) apparent surface-to-volume, S/V, ratio estimated by linear fit of high frequency OG data appears to be an excellent estimation of the actual S/V ratio, even in the presence of secondary structures, and it increases as spines and leaflets density or length increase (while decreasing as beadings amplitude increases). Comparison between numerical simulations and multimodal metabolites DW-MRS experiments in vivo in mouse brain shows that these fine structures may affect the DW-MRS signal and the derived diffusion metrics consistently with their expected density and geometrical features. This work suggests that finer structures of cell morphology have non-negligible effects on intracellular molecules' diffusion that may be measured by using multimodal DW-MRS approaches, stimulating future developments and applications.

Modeling diffusion of intracellular metabolites in the mouse brain up to very high diffusion-weighting: Diffusion in long fibers (almost) accounts for non-monoexponential attenuation

PURPOSE

To investigate how intracellular metabolites diffusion measured in vivo up to very high q/b in the mouse brain can be explained in terms of simple geometries.

METHODS

10 mice were scanned using our new STE-LASER sequence, at 11.7 Tesla (T), up to qmax = 1 μm-1 at diffusion time td = 63.2 ms, corresponding to bmax = 60 ms/µm². We model cell fibers as randomly oriented cylinders, with radius a and intracellular diffusivity Dintracyl, and fit experimental data as a function of q to estimate Dintracyl and a.

RESULTS

Randomly oriented cylinders account well for measured attenuation, giving fiber radii and Dintracyl in the expected ranges (0.5-1.5 µm and 0.30-0.45 µm2/ms, respectively). The only exception is N-acetyl-aspartate (NAA) (extracted a∼0), which we show to be compatible with a small fraction of the NAA pool being confined in highly restricted compartments (with short T2).

CONCLUSION

The non-monoexponential signal attenuation of intracellular metabolites in the mouse brain can be described by diffusion in long and thin cylinders, yielding realistic Dintra and fiber diameters. However, this simple model may require small "corrections" for NAA, in the form of a small fraction of the NAA signal originating from a highly restricted compartment. Magn Reson Med, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Q-space truncation and sampling in diffusion spectrum imaging

PURPOSE

To characterize the q-space truncation and sampling on the spin-displacement probability density function (PDF) in diffusion spectrum imaging (DSI).

METHODS

DSI data were acquired using the MGH-USC connectome scanner (Gmax  = 300 mT/m) with bmax  = 30,000 s/mm2 , 17 × 17 × 17, 15 × 15 × 15 and 11 × 11 × 11 grids in ex vivo human brains and bmax  = 10,000 s/mm2 , 11 × 11 × 11 grid in vivo. An additional in vivo scan using bmax =7,000 s/mm2 , 11 × 11 × 11 grid was performed with a derated gradient strength of 40 mT/m. PDFs and orientation distribution functions (ODFs) were reconstructed with different q-space filtering and PDF integration lengths, and from down-sampled data by factors of two and three.

RESULTS

Both ex vivo and in vivo data showed Gibbs ringing in PDFs, which becomes the main source of artifact in the subsequently reconstructed ODFs. For down-sampled data, PDFs interfere with the first replicas or their ringing, leading to obscured orientations in ODFs.

CONCLUSION

The minimum required q-space sampling density corresponds to a field-of-view approximately equal to twice the mean displacement distance (MDD) of the tissue. The 11 × 11 × 11 grid is suitable for both ex vivo and in vivo DSI experiments. To minimize the effects of Gibbs ringing, ODFs should be reconstructed from unfiltered q-space data with the integration length over the PDF constrained to around the MDD. Magn Reson Med 76:1750-1763, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Metabolite diffusion up to very high b in the mouse brain in vivo: Revisiting the potential correlation between relaxation and diffusion properties

PURPOSE

To assess the potential correlation between metabolites diffusion and relaxation in the mouse brain, which is of importance for interpreting and modeling metabolite diffusion based on pure geometry, irrespective of relaxation properties (multicompartmental relaxation or surface relaxivity).

METHODS

A new diffusion-weighted magnetic resonance spectroscopy sequence is introduced, dubbed "STE-LASER," which presents several nice properties, in particular the absence of cross-terms with selection gradients and a very clean localization. Metabolite diffusion is then measured in a large voxel in the mouse brain at 11.7 Tesla using a cryoprobe, resulting in excellent signal-to-noise ratio, up to very high b-values under different echo time, mixing time, and diffusion time combinations.

RESULTS

Our results suggest that the correlation between relaxation and diffusion properties is extremely small or even nonexistent for metabolites in the mouse brain.

CONCLUSION

The present work strongly supports the interpretation and modeling of metabolite diffusion primarily based on geometry, irrespective of relaxation properties, at least under current experimental conditions. Magn Reson Med 77:1390-1398, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Real-time measurement and correction of both B0 changes and subject motion in diffusion tensor imaging using a double volumetric navigated (DvNav) sequence

Diffusion tensor imaging (DTI) requires a set of diffusion weighted measurements in order to acquire enough information to characterize local structure. The MRI scanner automatically performs a shimming process by acquiring a field map before the start of a DTI scan. Changes in B0, which can occur throughout the DTI acquisition due to several factors (including heating of the iron shim coils or subject motion), cause significant signal distortions that result in warped diffusion tensor (DT) parameter estimates. In this work we introduce a novel technique to simultaneously measure, report and correct in real time subject motion and changes in B0 field homogeneity, both in and through the imaging plane. This is achieved using double volumetric navigators (DvNav), i.e. a pair of 3D EPI acquisitions, interleaved with the DTI pulse sequence. Changes in the B0 field are evaluated in terms of zero-order (frequency) and first-order (linear gradients) shim. The ability of the DvNav to accurately estimate the shim parameters was first validated in a water phantom. Two healthy subjects were scanned both in the presence and absence of motion using standard, motion corrected (single navigator, vNav), and DvNav DTI sequences. The difference in performance between the proposed 3D EPI field maps and the standard 3D gradient echo field maps of the MRI scanner was also evaluated in a phantom and two healthy subjects. The DvNav sequence was shown to accurately measure and correct changes in B0 following manual adjustments of the scanner's central frequency and the linear shim gradients. Compared to other methods, the DvNav produced DTI results that showed greater spatial overlap with anatomical references, particularly in scans with subject motion. This is largely due to the ability of the DvNav system to correct shim changes and subject motion between each volume acquisition, thus reducing shear distortion.

Motion artifact reduction in pediatric diffusion tensor imaging using fast prospective correction

PURPOSE

To evaluate the patterns of head motion in scans of young children and to examine the influence of corrective techniques, both qualitatively and quantitatively. We investigate changes that both retrospective (with and without diffusion table reorientation) and prospective (implemented with a short navigator sequence) motion correction induce in the resulting diffusion tensor measures.

MATERIALS AND METHODS

Eighteen pediatric subjects (aged 5-6 years) were scanned using 1) a twice-refocused, 2D diffusion pulse sequence, 2) a prospectively motion-corrected, navigated diffusion sequence with reacquisition of a maximum of five corrupted diffusion volumes, and 3) a T1 -weighted structural image. Mean fractional anisotropy (FA) values in white and gray matter regions, as well as tractography in the brainstem and projection fibers, were evaluated to assess differences arising from retrospective (via FLIRT in FSL) and prospective motion correction. In addition to human scans, a stationary phantom was also used for further evaluation.

RESULTS

In several white and gray matter regions retrospective correction led to significantly (P < 0.05) reduced FA means and altered distributions compared to the navigated sequence. Spurious tractographic changes in the retrospectively corrected data were also observed in subject data, as well as in phantom and simulated data.

CONCLUSION

Due to the heterogeneity of brain structures and the comparatively low resolution (∼2 mm) of diffusion data using 2D single shot sequencing, retrospective motion correction is susceptible to distortion from partial voluming. These changes often negatively bias diffusion tensor imaging parameters. Prospective motion correction was shown to produce smaller changes.

The interaction between apparent diffusion coefficients and transverse relaxation rates of human brain metabolites and water studied by diffusion-weighted spectroscopy at 7 T

The dependence of apparent diffusion coefficients (ADCs) of molecules in biological tissues on an acquisition-specific timescale is a powerful mechanism for studying tissue microstructure. Unlike water, metabolites are confined mainly to intracellular compartments, thus providing higher specificity to tissue microstructure. Compartment-specific structural and chemical properties may also affect molecule transverse relaxation times (T₂). Here, we investigated the correlation between diffusion and relaxation for N-acetylaspartate, creatine and choline compounds in human brain white matter in vivo at 7 T, and compared them with those of water under the same experimental conditions. Data were acquired in a volume of interest in parietal white matter at two different diffusion times, Δ = 44 and 246 ms, using a matrix of three echo times (T(E)) and five diffusion weighting values (up to 4575 s/mm²). Significant differences in the dependence of the ADCs on T(E) were found between water and metabolites, as well as among the different metabolites. A significant decrease in water ADC as a function of TE was observed only at the longest diffusion time (p < 0.001), supporting the hypothesis that at least part of the restricted water pool can be associated with longer T₂, as suggested by previous studies in vitro. Metabolite data showed an increase of creatine (p < 0.05) and N-acetylaspartate (p < 0.05) ADCs with TE at Δ = 44 ms, and a decrease of creatine (p < 0.05) and N-acetylaspartate (p = 0.1) ADCs with TE at Δ = 246 ms. No dependence of choline ADC on TE was observed. The metabolite results suggest that diffusion and relaxation properties are dictated not only by metabolite distribution in different cell types, but also by other mechanisms, such as interactions with membranes, exchange between "free" and "bound" states or interactions with microsusceptibility gradients.

Modeling of the diffusion MR signal in calibrated model systems and nerves

Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.

Advanced MRI strategies for assessing spinal cord injury

Advanced magnetic resonance (MR) approaches permit the noninvasive quantification of macromolecular, functional, and physiological properties of biological tissues. In this chapter, we review the application of advanced MR techniques to the spinal cord. Macromolecular properties of the spinal cord can be studied using magnetization transfer (MT) MR, diffusion tensor imaging (DTI), Q-space diffusion spectroscopy, and selective detection of myelin water. The functional and metabolic status of the spinal cord can be studied using functional MRI (fMRI), perfusion imaging, and magnetic resonance spectroscopy (MRS). Finally, we consider the outlook for advanced MR studies in persons in whom metal hardware has been implanted to stabilize the cord. In spite of the spinal cord's diminutive size, its location deep within the body, and constant motion, recent work shows that the spinal cord can be studied using these advanced MR approaches.

WITHDRAWN: First observation of diffusion-diffraction pattern in neuronal tissue by double-pulsed-field-gradient NMR

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The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study

Many axons follow wave-like undulating courses. This is a general feature of extracranial nerve segments, but is also found in some intracranial nervous tissue. The importance of axonal undulation has previously been considered, for example, in the context of biomechanics, where it has been shown that posture affects undulation properties. However, the importance of axonal undulation in the context of diffusion MR measurements has not been investigated. Using an analytical model and Monte Carlo simulations of water diffusion, this study compared undulating and straight axons in terms of diffusion propagators, diffusion-weighted signal intensities and parameters derived from diffusion tensor imaging, such as the mean diffusivity (MD), the eigenvalues and the fractional anisotropy (FA). All parameters were strongly affected by the presence of undulation. The diffusivity perpendicular to the undulating axons increased with the undulation amplitude, thus resembling that of straight axons with larger diameters. Consequently, models assuming straight axons for the estimation of the axon diameter from diffusion MR measurements might overestimate the diameter if undulation is present. FA decreased from approximately 0.7 to 0.5 when axonal undulation was introduced into the simulation model structure. Our results indicate that axonal undulation may play a role in diffusion measurements when investigating, for example, the optic and sciatic nerves and the spinal cord. The simulations also demonstrate that the stretching or compression of neuronal tissue comprising undulating axons alters the observed water diffusivity, suggesting that posture may be of importance for the outcome of diffusion MRI measurements.

The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g.

Volumetric navigators for real-time motion correction in diffusion tensor imaging

Prospective motion correction methods using an optical system, diffusion-weighted prospective acquisition correction, or a free induction decay navigator have recently been applied to correct for motion in diffusion tensor imaging. These methods have some limitations and drawbacks. This article describes a novel technique using a three-dimensional-echo planar imaging navigator, of which the contrast is independent of the b-value, to perform prospective motion correction in diffusion weighted images, without having to reacquire volumes during which motion occurred, unless motion exceeded some preset thresholds. Water phantom and human brain data were acquired using the standard and navigated diffusion sequences, and the mean and whole brain histogram of the fractional anisotropy and mean diffusivity were analyzed. Our results show that adding the navigator does not influence the diffusion sequence. With head motion, the whole brain histogram-fractional anisotropy shows a shift toward lower anisotropy with a significant decrease in both the mean fractional anisotropy and the fractional anisotropy histogram peak location (P<0.01), whereas the whole brain histogram-mean diffusivity shows a shift toward higher diffusivity with a significant increase in the mean diffusivity (P<0.01), even after retrospective motion correction. These changes in the mean and the shape of the histograms are recovered substantially in the prospective motion corrected data acquired using the navigated sequence.

Advanced MRI strategies for assessing spinal cord injury

Advanced magnetic resonance (MR) approaches permit the noninvasive quantification of macromolecular, functional, and physiological properties of biological tissues. In this chapter, we review the application of advanced MR techniques to the spinal cord. Macromolecular properties of the spinal cord can be studied using magnetization transfer (MT) MR, diffusion tensor imaging (DTI), Q-space diffusion spectroscopy, and selective detection of myelin water. The functional and metabolic status of the spinal cord can be studied using functional MRI (fMRI), perfusion imaging, and magnetic resonance spectroscopy (MRS). Finally, we consider the outlook for advanced MR studies in persons in whom metal hardware has been implanted to stabilize the cord. In spite of the spinal cord's diminutive size, its location deep within the body, and constant motion, recent work shows that the spinal cord can be studied using these advanced MR approaches.

Mean displacement map of spine and spinal cord disorders using high b-value q-space imaging-feasibility study

BACKGROUND

Q-space analysis is a new metric that uses multiple, high b-value, diffusion-weighted magnetic resonance (MR) data. This technique shows promising results as a tool to provide information complementary to that of other imaging techniques used on biological tissue in vivo.

PURPOSE

To investigate the use of a mean displacement (MDP) map of high b-value, q-space imaging (QSI) to characterize spinal and spinal cord lesions in vivo.

MATERIAL AND METHODS

Eight patients with spine or spinal cord disorders (two neurinomas, one myeloma, three cases of syringohydromyelia, and two cases of cervical spondylosis) were included. The MR imaging protocol consisted of conventional MR sequences, conventional diffusion-weighted imaging (DWI; b = 1000), and high b-value QSI with a maximum q value of 836.9 cm(-1). Apparent diffusion coefficient (ADC) maps of conventional DWI and MDP maps of QSI data were obtained and region-of-interest analyses for the lesions were performed.

RESULTS

MDP values of normal spinal cord, cerebrospinal fluid (CSF), and tumor parenchyma were 6.57 ± 0.52, 17.6 ± 2.75, and 8.49 ± 2.09, respectively (µm, mean ± standard deviation). In general, MDP maps were not well correlated with the corresponding ADC maps at the pathologic lesions. Spondylotic lesions tended to have higher MDP values than normal spinal cord, whereas syringohydromyelia produced MDP values slightly lower than those of CSF.

CONCLUSION

The heterogeneous MDP values were probably due to differences in tissues and pathologic structures. This technique has potential to provide additional clinical information to that obtained with conventional MR imaging.

Diffusion MR imaging: basic principles

From their origin as simple techniques primarily used for detecting acute cerebral ischemia, diffusion MR imaging techniques have rapidly evolved into a versatile set of tools that provide the only noninvasive means of characterizing brain microstructure and connectivity, becoming a mainstay of both clinical and investigational brain MR imaging. In this article, the basic principles required for understanding diffusion MR imaging techniques are reviewed with clinical neuroradiologists in mind.

Diffusion tensor imaging of cerebral white matter integrity in cognitive aging

In this article we review recent research on diffusion tensor imaging (DTI) of white matter (WM) integrity and the implications for age-related differences in cognition. Neurobiological mechanisms defined from DTI analyses suggest that a primary dimension of age-related decline in WM is a decline in the structural integrity of myelin, particularly in brain regions that myelinate later developmentally. Research integrating behavioral measures with DTI indicates that WM integrity supports the communication among cortical networks, particularly those involving executive function, perceptual speed, and memory (i.e., fluid cognition). In the absence of significant disease, age shares a substantial portion of the variance associated with the relation between WM integrity and fluid cognition. Current data are consistent with one model in which age-related decline in WM integrity contributes to a decreased efficiency of communication among networks for fluid cognitive abilities. Neurocognitive disorders for which older adults are at risk, such as depression, further modulate the relation between WM and cognition, in ways that are not as yet entirely clear. Developments in DTI technology are providing a new insight into both the neurobiological mechanisms of aging WM and the potential contribution of DTI to understanding functional measures of brain activity. This article is part of a Special Issue entitled: Imaging Brain Aging and Neurodegenerative disease.

A comparison of mean displacement values using high b-value Q-space diffusion-weighted MRI with conventional apparent diffusion coefficients in patients with stroke

RATIONALE AND OBJECTIVES

Q-space analysis using high b-value diffusion-weighted magnetic resonance (MR) data provides information on tissue microstructure in contrast to conventional MR imaging (MRI) based on low b-value diffusion-weighted imaging (DWI). The purpose of this study was to evaluate the use of mean displacement (MDP) map in stroke patients using q-space diffusion-weighted MRI (QSI).

MATERIALS AND METHODS

Twenty-one patients presenting with a total of 22 acute or subacute cerebral infarctions were included. MR protocol consisted of conventional MR sequences, DWI (b-value; 1000 s/mm(2)) and QSI (b-value; maximum 12,000 s/mm(2)). Apparent diffusion coefficient (ADC) maps of conventional DWI and MDP maps of QSI data were obtained and compared in the ischemic lesions and corresponding normal tissues.

RESULTS

Decreased ADC values were present in all lesions. There was no correlation between ADC and MDP values in the lesions (r = 0.21). MDP values of the lesions were 8.60 ± 1.26 μm (mean ± SD). Most of the lesions (16/22) had higher MDP values than normal brain tissue. Three lesions showed lower MDP values and three showed mixed MDP values.

CONCLUSIONS

The MDP maps using QSI data provides additional information for stroke patients compared to conventional DWI.

Diffusion imaging with prospective motion correction and reacquisition

A major source of artifacts in diffusion-weighted imaging is subject motion. Slow bulk subject motion causes misalignment of data when more than one average or diffusion gradient direction is acquired. Fast bulk subject motion can cause signal dropout artifacts in diffusion-weighted images and results in erroneous derived maps, e.g., fractional anisotropy maps. To address both types of artifacts, a fully automatic method is presented that combines prospective motion correction with a reacquisition scheme. Motion correction is based on the prospective acquisition correction method modified to work with diffusion-weighted data. The images to reacquire are determined automatically during the acquisition from the imaging data, i.e., no extra reference scan, navigators, or external devices are necessary. The number of reacquired images, i.e., the additional scan duration can be adjusted freely. Diffusion-weighted prospective acquisition correction corrects slow bulk motion well and reduces misalignment artifacts like image blurring. Mean absolute residual values for translation and rotation were <0.6 mm and 0.5°. Reacquisition of images affected by signal dropout artifacts results in diffusion maps and fiber tracking free of artifacts. The presented method allows the reduction of two types of common motion related artifacts at the cost of slightly increased acquisition time.

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

Considerations for measuring the fractional anisotropy of metabolites with diffusion tensor spectroscopy

Diffusion tensor spectroscopy of metabolites in brain is challenging because of their lower diffusivity (i.e. less signal attenuation for a given b value) and much poorer signal-to-noise ratio relative to water. Although diffusion tensor acquisition protocols have been studied in detail for water, they have not been evaluated systematically for the measurement of the fractional anisotropy of metabolites such as N-acetylaspartate, creatine and choline in the white and gray matter of human brain. Diffusion tensor spectroscopy was performed in vivo with variable maximal b values (1815 or 5018  s/mm(2)). Experiments were also performed on simulated spectra and isotropic alcohol phantoms of various diffusivities, ranging from approximately 0.54 × 10(-3) to 0.13 × 10(-3) mm(2)/s, to assess the sensitivity of diffusion tensor spectroscopic parameters to low diffusivity, noise and b value. The low maximum b value of 1815  s/mm(2) yielded elevated fractional anisotropy (0.53-0.60) of N-acetylaspartate in cortical gray matter relative to the more isotropic value (0.25-0.30) obtained with a higher b value of 5018  s/mm(2); in contrast, the fractional anisotropy of white matter was consistently anisotropic with the different maximal b values (i.e. 0.43-0.54 for b = 1815  s/mm(2) and 0.47-0.51 for b = 5018  s/mm(2)). Simulations, phantoms and in vivo data indicate that greater signal attenuation, to a degree, is desirable for the accurate quantification of diffusion-weighted spectra for slowly diffusing metabolites.

High b-value q-space analyzed diffusion-weighted MRI using 1.5 tesla clinical scanner; determination of displacement parameters in the brains of normal versus multiple sclerosis and low-grade glioma subjects

PURPOSE

We aimed to determine the displacement parameters in the brains of normal individuals relative to brain parenchymal abnormalities, such as multiple sclerosis (MS) and low-grade glioma, by q-space imaging (QSI) using 1.5-T magnetic resonance (MR) scanner.

MATERIALS AND METHODS

Thirty-five normal, three pathologically proven low-grade glioma, and five MS subjects were imaged by a 1.5-T MR unit for QSI (b-values, 0-12,000 s/mm(2)). Mean displacement (MD) values in white matter (WM), gray matter (GM), and lateral ventricle (cerebrospinal fluid [CSF]) of normal subjects, plaques, and normal appearing WM (NAWM) of MS subjects and glioma lesions were calculated. Mann-Whitney U test was used for comparison.

RESULTS

In normal subjects, MD values were 6.6 ± 0.2, 8.44 ± 0.41, and 17.08 ± 0.80 μm for WM, GM, and CSF, respectively, while those for NAWM and WM plaques in MS, and glioma lesions were significantly higher at 7.0 ± 0.17, 9.3 ± 2.3, and 9.6 ± 0.40 μm, respectively, compared to WM in normal subjects.

CONCLUSION

We propose that the relative values of MD obtained by QSI in control and diseased tissues can be useful for diagnosing various WM abnormalities.

Theoretical models of the diffusion weighted MR signal

Diffusion MRI plays a very important role in studying biological tissue structure and functioning both in health and disease. Proper interpretation of experimental data requires development of theoretical models that connect the diffusion MRI signal to salient features of tissue microstructure at the cellular level. In this review, we present some models (mostly, relevant to the brain) for describing diffusion attenuated MR signals. These range from the simplest approach, where the signal is described in terms of an apparent diffusion coefficient, to rather complicated models, where consideration is given to signals originating from extra- and intracellular spaces and where account is taken of the specific geometry and orientation distribution of cells. To better understand the characteristics of the diffusion attenuated MR signal arising from the complex structure of whole tissue, it is instructive to appreciate first the characteristics of the signal arising from simple single-cell-like structures. For this purpose, we also present here a theoretical analysis of models allowing exact analytical calculation of the MR signal, specifically, a single-compartment model with impermeable boundaries and a periodic structure of identical cells separated by permeable membranes. Such pure theoretical models give important insights into mechanisms contributing to the MR signal formation in the presence of diffusion. In this review we targeted both scientists just entering the MR field and more experienced MR researchers interested in applying diffusion methods to study biological tissues.

In vivo generalized diffusion tensor imaging (GDTI) using higher-order tensors (HOT)

Generalized diffusion tensor imaging (GDTI) using higher-order tensor (HOT) statistics generalizes the technique of diffusion tensor imaging by including the effect of nongaussian diffusion on the signal of MRI. In GDTI-HOT, the effect of nongaussian diffusion is characterized by higher-order tensor statistics (i.e., the cumulant tensors or the moment tensors), such as the covariance matrix (the second-order cumulant tensor), the skewness tensor (the third-order cumulant tensor), and the kurtosis tensor (the fourth-order cumulant tensor). Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI-HOT has been reported. The primary goal of this study is to establish GDTI-HOT as a feasible in vivo technique for imaging nongaussian diffusion. We show that probability distribution function of the molecular diffusion process can be measured in vivo with GDTI-HOT and be visualized with three-dimensional glyphs. By comparing GDTI-HOT to fiber structures that are revealed by the highest resolution diffusion-weighted imaging (DWI) possible in vivo, we show that the GDTI-HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible, with a small statistical variation that is similar to that of diffusion tensor imaging.

New methods in diffusion-weighted and diffusion tensor imaging

Considerable strides have been made by countless individual researchers in diffusion-weighted imaging (DWI) to push DWI from an experimental tool, limited to a few institutions with specialized instrumentation, to a powerful tool used routinely for diagnostic imaging. The field of DWI constantly evolves, and progress has been made on several fronts. These developments are primarily composed of improved robustness against patient and physiologic motion, increased spatial resolution, new biophysical and tissue models, and new clinical applications for DWI. This article aims to provide a succinct overview of some of these new developments and a description of some of the major challenges associated with DWI.

New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models

We present new diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models. The phantom design permits the application of imaging parameters that are typically employed in studies of the human brain. The phantoms were made of small-diameter acrylic fibers, chosen for their high hydrophobicity and flexibility that ensured good control of the phantom geometry. The polyurethane medium was filled under vacuum with an aqueous solution that was previously degassed, doped with gadolinium-tetraazacyclododecanetetraacetic acid (Gd-DOTA), and treated by ultrasonic waves. Two versions of such phantoms were manufactured and tested. The phantom's applicability was demonstrated on an analytical Q-ball model. Numerical simulations were performed to assess the accuracy of the phantom. The phantom data will be made accessible to the community with the objective of analyzing various HARDI models.

Erythrocyte-shape evolution recorded with fast-measurement NMR diffusion-diffraction

PURPOSE

To monitor red blood cell (RBC) shape evolution by (1)H(2)O diffusion-diffraction NMR in time steps comparable to those required for the acquisition of a (31)P NMR spectrum; thus, to correlate RBC mean diameter with ATP concentration after poisoning with NaF.

MATERIALS AND METHODS

Pulsed-field gradient-stimulated echo (PFGSTE) diffusion experiments were recorded on (1)H(2)O in RBC suspensions. Under conditions of restricted diffusion, q-space experiments report on mean RBC diameter. To decrease experiment time, the phase cycling of radiofrequency (RF) pulses was cut to two transients by using unbalanced pairs of gradient pulses. Data processing used a recent digital filter. Differential interference contrast (DIC) light microscopy also recorded shape changes. (31)P NMR spectroscopy gave estimates of mean ATP concentration.

RESULTS

NaF caused RBC-shape evolution from discocytes, through various forms of echinocytes, to spherocytes, over approximately 6 h and approximately 10 h at 37 degrees C and 25 degrees C, respectively. ATP declined to approximately 0.5 its normal concentration before the first stage of discocyte transformation; the concentration was 0.0 after approximately 1.5 h and 3.0 h, respectively, at the two temperatures.

CONCLUSION

RBC shape was readily monitored by NMR with a temporal resolution that was useful for correlations with both DIC microscopy and (31)P NMR spectra.

The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, delta, is comparable to the diffusion time, Delta. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Delta/delta, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Delta/delta approximately 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long delta the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Delta/delta approximately 1 the diffraction peaks are shifted to even higher q-values, even when delta is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Delta/delta approximately 1.

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.

Evaluation of the accuracy and angular resolution of q-ball imaging

Q-ball imaging (QBI) has been proposed for the mapping of multiple intravoxel fiber structures using the Funk-Radon transform on high angular resolution diffusion images (HARDI). However, the accuracy and the angular resolution of QBI to define fiber orientations and its dependence on diffusion imaging parameters remain unclear. The phantom models, made up of sheets of parallel capillaries filled with water, were designed to evaluate the accuracy and the angular resolution of QBI at different |q| values. With an inner diameter of 20 mum and an outer diameter of 90 mum, the capillaries afforded a restrictive environment compared with the diffusion measurement scale. Further, the angular resolutions of QBI at various |q| value were also quantified on the corpus callosum in the human brain. The full width at half maximum (FWHM) of the main lobe of normalized orientation distribution function (nODF) was calculated and adopted to quantify the angular resolution of QBI. With the phantom model, a higher |q| value resulted in worse accuracy but better angular resolution for QBI. The same trend where a higher |q| value yielded a better angular resolution was also observed in the human study. Upon comparison of QBI with T2WI, QBI with |q|=277 cm(-1) (b=3000 s/mm(2)) was found to be insufficient to differentiate capillaries crossing at 45 degrees . However, when encoding with |q|=320, 358, and 392 cm(-1) (b=4000, 5000, and 6000 s/mm(2)), the deviation angles between the primary ODF and the 45 degrees phantoms were -4.91 degrees +/-2.72 degrees , -1.37 degrees +/-2.32 degrees , and -0.69 degrees +/-1.54 degrees with adequate signal-to-noise ratio (SNR). These results were consistent with the FWHM-nODF, which showed that a |q| value of 320 cm(-1) was the threshold to resolve capillaries intersecting at 45 degrees . Additionally, it was demonstrated in both the phantom model and the human brain that QBI encoding with lower |q| values may result in underestimation of the orientations of the crossing fibers. In conclusion, QBI was found to accurately resolve crossing fiber orientations and was highly dependent on the selected |q| value.