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

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

13C Radiofrequency Amplification by Stimulated Emission of Radiation Threshold Sensing of Chemical Reactions.

Conventional nuclear magnetic resonance (NMR) enables detection of chemicals and their transformations by exciting nuclear spin ensembles with a radio-frequency pulse followed by detection of the precessing spins at their characteristic frequencies. The detected frequencies report on chemical reactions in real time and the signal amplitudes scale with concentrations of products and reactants. Here, we employ Radiofrequency Amplification by Stimulated Emission of Radiation (RASER), a quantum phenomenon producing coherent emission of 13C signals, to detect chemical transformations. The 13C signals are emitted by the negatively hyperpolarized biomolecules without external radio frequency pulses and without any background signal from other, nonhyperpolarized spins in the ensemble. Here, we studied the hydrolysis of hyperpolarized ethyl-[1-13C]acetate to hyperpolarized [1-13C]acetate, which was analyzed as a model system by conventional NMR and 13C RASER. The chemical transformation of 13C RASER-active species leads to complete and abrupt disappearance of reactant signals and delayed, abrupt reappearance of a frequency-shifted RASER signal without destroying 13C polarization. The experimentally observed "quantum" RASER threshold is supported by simulations.

To mask or not to mask? Investigating the impact of accounting for spatial frequency distributions and susceptibility sources on QSM quality.

PURPOSE: Estimating magnetic susceptibility using MRI depends on inverting a forward relationship between the susceptibility and measured Larmor frequency. However, an often-overlooked constraint in susceptibility fitting is that the Larmor frequency is only measured inside the sample, and after successful background field removal, susceptibility sources should only reside inside the same sample. Here, we test the impact of accounting for these constraints in susceptibility fitting. THEORY AND METHODS: Two different digital brain phantoms with scalar susceptibility were examined. We used the MEDI phantom, a simple phantom with no background fields, to examine the effect of the imposed constraints for various levels of SNR. Next, we considered the QSM reconstruction challenge 2.0 phantom with and without background fields. We estimated the parameter accuracy of openly-available QSM algorithms by comparing fitting results to the ground truth. Next, we implemented the mentioned constraints and compared to the standard approach. RESULTS: Including the spatial distribution of frequencies and susceptibility sources decreased the RMS-error compared to standard QSM on both brain phantoms when background fields were absent. When background field removal was unsuccessful, as is presumably the case in most in vivo conditions, it is better to allow sources outside the brain. CONCLUSION: Informing QSM algorithms about the location of susceptibility sources and where Larmor frequency was measured improves susceptibility fitting for realistic SNR levels and efficient background field removal. However, the latter remains the bottleneck of the algorithm. Allowing for external sources regularizes unsuccessful background field removal and is currently the best strategy in vivo.

On the noise in "augmented T1-weighted steady state magnetic resonance imaging".

Recently, Ye and colleagues proposed a method for "augmented T1-weighted imaging" (aT1 W). The key operation is a complex division of gradient-echo (GRE) images obtained with different flip angles. Ye and colleagues provide an equation for the standard deviation of the obtained aT1 W signal. Here, we show that this equation leads to wrong values of the standard deviation of such an aT1 W signal. This is demonstrated by Monte Carlo simulations. The derivation of the equation provided by Ye and colleagues is shown to be erroneous. The error consists of a wrong handling of random variables and their standard deviations and of the wrong assumption of correlated noise in independently acquired GRE images. Instead, the probability distribution obtained with the aT1 W-method should have been carefully analyzed, perhaps on the basis of previous literature on ratio distributions and their normal approximations.

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution.

The magnetic susceptibility of tissue can provide valuable information about its chemical composition and microstructural organization. However, the relation between the magnetic microstructure and the measurable Larmor frequency shift is understood only for a few idealized cases. Here we analyze the microstructure formed by magnetized, NMR-invisible infinite cylinders suspended in an NMR-reporting fluid. Through simulations, we scrutinize various geometries of mesoscopic Lorentz cavities and inclusions, and show that the cavity size should be approximately one order of magnitude larger than the width of the inclusions. We also analytically derive the Larmor frequency shift for a population of cylinders with arbitrary orientation dispersion and show that it is determined by the l = 2 Laplace expansion coefficients p 2 m of the cylinders' orientation distribution function. Our work underscores the need to account for microstructural organization when estimating magnetic tissue properties.

Parahydrogen-Induced Carbon-13 Radiofrequency Amplification by Stimulated Emission of Radiation.

The feasibility of Carbon-13 Radiofrequency (RF) Amplification by Stimulated Emission of Radiation (C-13 RASER) is demonstrated on a bolus of liquid hyperpolarized ethyl [1-13 C]acetate. Hyperpolarized ethyl [1-13 C]acetate was prepared via pairwise addition of parahydrogen to vinyl [1-13 C]acetate and polarization transfer from nascent parahydrogen-derived protons to the carbon-13 nucleus via magnetic field cycling yielding C-13 nuclear spin polarization of approximately 6 %. RASER signals were detected from samples with concentration ranging from 0.12 to 1 M concentration using a non-cryogenic 1.4T NMR spectrometer equipped with a radio-frequency detection coil with a quality factor (Q) of 32 without any modifications. C-13 RASER signals were observed for several minutes on a single bolus of hyperpolarized substrate to achieve 21 mHz NMR linewidths. The feasibility of creating long-lasting C-13 RASER on biomolecular carriers opens a wide range of new opportunities for the rapidly expanding field of C-13 magnetic resonance hyperpolarization.

What does FEXI measure?

Filter-exchange imaging (FEXI) has already been utilized in several biomedical studies for evaluating the permeability of cell membranes. The method relies on suppressing the extracellular signal using strong diffusion weighting (the mobility filter causing a reduction in the overall diffusivity) and monitoring the subsequent diffusivity recovery. Using Monte Carlo simulations, we demonstrate that FEXI is sensitive not uniquely to the transcytolemmal exchange but also to the geometry of involved compartments: complex geometry offers locations where spins remain unaffected by the mobility filter; moving to other locations afterwards, such spins contribute to the diffusivity recovery without actually permeating any membrane. This exchange mechanism is a warning for those who aim to use FEXI in complex media such as brain gray matter and opens wide scope for investigation towards crystallizing the genuine membrane permeation and characterizing the compartment geometry.

Three-dimensional spatially resolved phase graph framework.

PURPOSE: An open-source spatially resolved phase graph framework is proposed for simulating arbitrary pulse sequences in the presence of piece-wise constant gradients with arbitrary orientations in three dimensions. It generalizes the extended phase graph algorithm for analysis of nonperiodic sequences while preserving its efficiency, and is able to estimate the signal modulation in the 3D spatial domain. METHODS: The framework extends the recursive magnetization-evolution algorithm to account for anisotropic diffusion and exploits a novel 3D k-space grid-merging method to balance the computational effort and memory requirements against acceptable simulation errors. A new postsimulation module is proposed to track and visualize the signal evolution both in the k-space and in the image domain, which can be used for simulating image artifacts or finding frequency-response profiles. To illustrate the developed technique, three examples are presented: (1) fast off-resonance calculation for dictionary building in MR fingerprinting, (2) validation of a steady-state sequence with quasi-isotropic diffusion weighting, and (3) investigation of the magnetization evolution in PRESS-based spectroscopic imaging. RESULTS: The grid-merging algorithm of the proposed framework demonstrates high calculation efficiency exemplified by frequency-response simulation of pseudo steady-state or diffusion-weighted steady-state sequences. It further helps to visualize the signal evolution in PRESS-based sequences. CONCLUSIONS: The proposed simulation framework has been validated based on several different example applications for analyzing signal evolution in the frequency and spatial domain.

Intra-axonal diffusivity in brain white matter.

Biophysical modeling lies at the core of evaluating tissue cellular structure using diffusion-weighted MRI, albeit with shortcomings. The challenges lie not only in the complexity of the diffusion phenomenon, but also in the need to know the diffusion-specific properties of diverse cellular compartments in vivo. The likelihood function obtained from the commonly acquired Stejskal-Tanner diffusion-weighted MRI data is degenerate with different parameter constellations explaining the signal equally well, thereby hindering an unambiguous parameter estimation. The aim of this study is to measure the intra-axonal water diffusivity which is one of the central parameters of white matter models. Estimating intra-axonal diffusivity is complicated by (i) the presence of other compartments, and (ii) the orientation dispersion of axons. Our measurement involves an efficient signal suppression of water in extra-axonal space and all cellular processes oriented outside a narrow cone around the principal fiber direction. This is achieved using a planar water mobility filter that suppresses signal from all molecules that are mobile in the plane transverse to the fiber bundle. After the planar filter, the diffusivity of the remaining intra-axonal signal is measured using linear and spherical diffusion encoding. We find the average intra-axonal diffusivity D0=2.25±0.03µm2/ms for the timing of the applied gradients, which gives D0(∞)≈2.0µm2/ms when extrapolated to infinite diffusion time. The result imposes a strong limitation on the parameter selection for biophysical modeling of diffusion-weighted MRI.

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

PURPOSE: It is known that white matter modeling based on commonly used linear diffusion encoding is an ill-posed problem. We analyze the additional information gained from a double pulsed diffusion encoding. METHODS: Zeroth (spherical means) and second-order (harmonic powers) rotation invariant signal features are used to factor micro- and mesoscopic contributions. The b-value dependency up to second-order of the features form 6 nonlinear equations, which are analyzed. RESULTS: The 6 derived equations can be uniquely solved for all relevant biophysical parameters. No assumptions about the form of the mesoscopic contribution (fiber dispersion) is necessary. Under certain conditions the solution still shows a certain degeneracy which is inherent to model. It is further shown that a combination of second-order information from single and spherical diffusion encoding is not enough to solve the problem. CONCLUSIONS: A combination of single and double pulsed diffusion encodings is sufficient to solve the full 3 compartment white matter model uniquely.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation.

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

Transverse NMR relaxation in biological tissues.

Transverse NMR relaxation is a fundamental physical phenomenon underpinning a wide range of MRI-based techniques, essential for non-invasive studies in biology, physiology and neuroscience, as well as in diagnostic imaging. Biophysically, transverse relaxation originates from a number of distinct scales - molecular (nanometers), cellular (micrometers), and macroscopic (millimeter-level MRI resolution). Here we review the contributions to the observed relaxation from each of these scales, with the main focus on the cellular level of tissue organization, commensurate with the diffusion length of spin-carrying molecules. We discuss how the interplay between diffusion and spin dephasing in a spatially heterogeneous tissue environment leads to a non-monoexponential time-dependent transverse relaxation signal that contains important biophysical information about tissue microstructure.

The absence of restricted water pool in brain white matter.

Understanding diffusion-weighted MR signal in brain white matter (WM) has been a long-sought-after goal. Modern research pursues this goal by focusing on the biological compartments that contributes essentially to the signal. In this study, we experimentally address the apparent presence of a compartment in which water motion is restricted in all spatial directions. Using isotropic diffusion encoding, we establish an upper bound on the fraction of such a compartment, which is shown to be about 2% of the unweighted signal for moderate diffusion times. This helps to eliminate such a compartment that have been assumed in literature on biophysical modeling. We also used the diffusion decay curve obtained from the isotropic encoding to establish a lower limit on the mean diffusivities of either of intra- or extra-axonal compartment as a function of their relative water fraction.

Modelfree global tractography.

Tractography based on diffusion-weighted MRI investigates the large scale arrangement of the neurite fibers in brain white matter. It is usually assumed that the signal is a convolution of a fiber specific response function (FRF) with a fiber orientation distribution (FOD). The FOD is the focus of tractography. While in the past the FRF was estimated beforehand and was usually assumed to be fix, more recent approaches estimate the response function during tractography. This work proposes a novel objective function independent of the FRF, just aiming for FOD reconstruction. The objective is integrated into global tractography showing promising results.

The larmor frequency shift in magnetically heterogeneous media depends on their mesoscopic structure.

PURPOSE: Recent studies have addressed the determination of the NMR precession frequency in biological tissues containing magnetic susceptibility differences between cell types. The purpose of this study is to investigate the dependence of the precession frequency on medium microstructure using a simple physical model. THEORY: This dependence is governed by diffusion of NMR-visible molecules in magnetically heterogeneous microenvironments. In the limit of fast diffusion, the precession frequency is determined by the average susceptibility-induced magnetic field, whereas in the limit of slow diffusion it is determined by the average local phase factor of precessing spins. METHODS: The main method used is Monte Carlo simulation of isotropic suspensions of impermeable magnetized spheres. In addition, NMR spectroscopy was performed in aqueous suspensions of polystyrene microbeads. RESULTS: The precession frequency depends on the structural organization of magnetized objects in the medium. Monte Carlo simulations demonstrated a nonmonotonic transition between the regimes of fast and slow diffusion. NMR experiments confirmed the transition, but were unable to confirm its precise form. Results for a given pattern of structural organization obey a scaling law. CONCLUSION: The NMR precession frequency exhibits a complex dependence on medium structure. Our results suggest that the commonly assumed limit of fast water diffusion holds for biological tissues with small cells. Magn Reson Med 79:1101-1110, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

On modeling.

Mapping tissue microstructure with MRI holds great promise as a noninvasive window into tissue organization at the cellular level. Having originated within the realm of diffusion NMR in the late 1970s, this field is experiencing an exponential growth in the number of publications. At the same time, model-based approaches are also increasingly incorporated into advanced MRI acquisition and reconstruction techniques. However, after about two decades of intellectual and financial investment, microstructural mapping has yet to find a single commonly accepted clinical application. Here, we suggest that slow progress in clinical translation may signify unresolved fundamental problems. We outline such problems and related practical pitfalls, as well as review strategies for developing and validating tissue microstructure models, to provoke a discussion on how to bridge the gap between our scientific aspirations and the clinical reality. We argue for recalibrating the efforts of our community toward a more systematic focus on fundamental research aimed at identifying relevant degrees of freedom affecting the measured MR signal. Such a focus is essential for realizing the truly revolutionary potential of noninvasive three-dimensional in vivo microstructural mapping.

Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach.

Diffusion-sensitized magnetic resonance imaging probes the cellular structure of the human brain, but the primary microstructural information gets lost in averaging over higher-level, mesoscopic tissue organization such as different orientations of neuronal fibers. While such averaging is inevitable due to the limited imaging resolution, we propose a method for disentangling the microscopic cell properties from the effects of mesoscopic structure. We further avoid the classical fitting paradigm and use supervised machine learning in terms of a Bayesian estimator to estimate the microstructural properties. The method finds detectable parameters of a given microstructural model and calculates them within seconds, which makes it suitable for a broad range of neuroscientific applications.

Fundamentals of diffusion MRI physics.

Diffusion MRI is commonly considered the "engine" for probing the cellular structure of living biological tissues. The difficulty of this task is threefold. First, in structurally heterogeneous media, diffusion is related to structure in quite a complicated way. The challenge of finding diffusion metrics for a given structure is equivalent to other problems in physics that have been known for over a century. Second, in most cases the MRI signal is related to diffusion in an indirect way dependent on the measurement technique used. Third, finding the cellular structure given the MRI signal is an ill-posed inverse problem. This paper reviews well-established knowledge that forms the basis for responding to the first two challenges. The inverse problem is briefly discussed and the reader is warned about a number of pitfalls on the way.

Automated Infarct Core Volumetry Within the Hypoperfused Tissue: Technical Implementation and Evaluation.

OBJECTIVE: The aim of this study was to develop a rapid and fully automatic infarct core and tissue at risk volumetry approach in acute ischemic stroke. METHODS: We evaluated an algorithm in which segmentation was restricted to 1 hemisphere and the potential lesion characterized on the basis of the perfusion parameter Tmax with a region-wise comparison of local histograms to its mirrored counterpart. RESULTS: We applied the "Tmax inside" method to 30 cases of a public data set with ground-truth segmentations for diffusion-weighted and perfusion magnetic resonance imaging. Lesions were robustly identified with significantly higher dice coefficients (apparent diffusion coefficient, 0.83 ± 0.22; Tmax, 0.80 ± 0.05, compared with 0.53 ± 0.27 and 0.56 ± 0.18) than for a global thresholding approach. CONCLUSIONS: The proposed "Tmax inside" method is superior to the commonly used global thresholding approach. Furthermore, the method allows evaluating changes in cerebral blood volume and blood flow by taking the counterpart in the healthy hemisphere as a patient-individual reference.

Gibbs-ringing artifact removal based on local subvoxel-shifts.

PURPOSE: To develop a fast and stable method for correcting the gibbs-ringing artifact. METHODS: Gibbs-ringing is a well-known artifact which manifests itself as spurious oscillations in the vicinity of sharp image gradients at tissue boundaries. The origin can be seen in the truncation of k-space during MRI data-acquisition. Correction techniques like Gegenbauer reconstruction or extrapolation methods aim at recovering these missing data. Here, we present a simple and robust method which exploits a different view on the Gibbs-phenomenon: The truncation in k-space can be interpreted as a convolution of the underlying image with a sinc-function. As the image is reconstructed on a discretized grid, the severity of the ringing artifacts depends on how this grid is located with respect to the edge and the oscillation pattern of the function. We propose to reinterpolate the image based on local, subvoxel-shifts to sample the ringing pattern at the zero-crossings of the oscillating sinc-function. RESULTS: With the proposed method, the artifact can simply, effectively, and robustly be removed with a minimal amount of image smoothing. CONCLUSIONS: The robustness of the method suggests it as a suitable candidate for an implementation in the standard image processing pipeline in clinical routine. Magn Reson Med 76:1574-1581, 2016. © 2015 International Society for Magnetic Resonance in Medicine.