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.

Mesoscopic Assessment of Microstructure in Glioblastomas and Metastases by Merging Advanced Diffusion Imaging with Immunohistopathology.

BACKGROUND AND PURPOSE: Glioblastomas and metastases are the most common malignant intra-axial brain tumors in adults and can be difficult to distinguish on conventional MR imaging due to similar imaging features. We used advanced diffusion techniques and structural histopathology to distinguish these tumor entities on the basis of microstructural axonal and fibrillar signatures in the contrast-enhancing tumor component. MATERIALS AND METHODS: Contrast-enhancing tumor components were analyzed in 22 glioblastomas and 21 brain metastases on 3T MR imaging using DTI-fractional anisotropy, neurite orientation dispersion and density imaging-orientation dispersion, and diffusion microstructural imaging-micro-fractional anisotropy. Available histopathologic specimens (10 glioblastomas and 9 metastases) were assessed for the presence of axonal structures and scored using 4-level scales for Bielschowsky staining (0: no axonal structures, 1: minimal axonal fragments preserved, 2: decreased axonal density, 3: no axonal loss) and glial fibrillary acid protein expression (0: no glial fibrillary acid protein positivity, 1: limited expression, 2: equivalent to surrounding parenchyma, 3: increased expression). RESULTS: When we compared glioblastomas and metastases, fractional anisotropy was significantly increased and orientation dispersion was decreased in glioblastomas (each P < .001), with a significant shift toward increased glial fibrillary acid protein and Bielschowsky scores. Positive associations of fractional anisotropy and negative associations of orientation dispersion with glial fibrillary acid protein and Bielschowsky scores were revealed, whereas no association between micro-fractional anisotropy with glial fibrillary acid protein and Bielschowsky scores was detected. Receiver operating characteristic curves revealed high predictive values of both fractional anisotropy (area under the curve = 0.8463) and orientation dispersion (area under the curve = 0.8398) regarding the presence of a glioblastoma. CONCLUSIONS: Diffusion imaging fractional anisotropy and orientation dispersion metrics correlated with histopathologic markers of directionality and may serve as imaging biomarkers in contrast-enhancing tumor components.

Observation of magnetic structural universality and jamming transition with NMR.

Nuclear magnetic resonance (NMR) has been instrumental in deciphering the structure of proteins. Here we show that transverse NMR relaxation, through its time-dependent relaxation rate, is distinctly sensitive to the structure of complex materials or biological tissues at the mesoscopic scale, from micrometers to tens of micrometers. Based on the ideas of universality, we show analytically and numerically that the time-dependent transverse relaxation rate approaches its long-time limit in a power-law fashion, with the dynamical exponent reflecting the universality class of mesoscopic magnetic structure. The spectral line shape acquires the corresponding non-analytic power law singularity at zero frequency. We experimentally detect the change in the dynamical exponent as a result of the transition into maximally random jammed state characterized by hyperuniform correlations. The relation between relaxational dynamics and magnetic structure opens the way for noninvasive characterization of porous media, complex materials and biological tissues.

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.

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.

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.

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.

Toward Quantification: Microstructure and Magnetic Resonance Fingerprinting.

Quantitative magnetic resonance imaging (MRI) is a long-standing challenge. We advocate that the origin of the problem is the simplification applied in commonly used models of the MRI signal relation to the target parameters of biological tissues. Two research fields are briefly reviewed as ways to respond to the challenge of quantitative MRI, both experiencing an exponential growth right now. Microstructure MRI strives to build physiology-based models from cells to signal and, given the signal, back to the cells again. Magnetic resonance fingerprinting aims at efficient simultaneous determination of multiple signal parameters. The synergy of these yet disjoined approaches promises truly quantitative MRI with specific target-oriented diagnostic tools rather than universal imaging methods.

Microstructure with diffusion MRI: what scale we are sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructure MRI (µMRI) aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal-Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

Larmor frequency dependence on structural anisotropy of magnetically heterogeneous media.

The effect of anisotropic magnetic microstructure on the measurable Larmor frequency offset is investigated in media with heterogeneous magnetic susceptibility using Monte Carlo simulations. The focus is on the transition between the regimes of fast and slow diffusion of NMR-reporting molecules. Simulations demonstrate a perfect agreement with the previously developed analytic theory for fast diffusion. Beyond this regime, the frequency offset shows a pronounced dependence on the medium microarchitecture and the diffusivity of NMR-reporting spins in relation to the magnitude of the susceptibility-induced magnetic field.

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.

Larmor frequency in heterogeneous media.

High-precision signal phase measurements ignited an ongoing discussion of the microstructural correlates of the Larmor frequency shift of water in biological tissues. In a broader context, this is the question about the averaged precession frequency in magnetically heterogenous, in particular, porous media. In this study, the Larmor frequency shift is found analytically for water filling connected pore space between NMR-invisible magnetized inclusions with a constant magnetic susceptibility tensor. The magnetic microstructure that encompasses the inclusions' shape and their spatial arrangement is arbitrary as well as the inclusions' magnetic susceptibility tensor. The result is limited to the case of effectively fast diffusion of water molecules. In this limit, the effect of magnetic microstructure on the Larmor frequency shift is represented by only five relevant parameters in the general case and by a single parameter in the case of axially symmetric microstructure. This single parameter enters the dependence of the Larmor frequency on the sample orientation relative to the main magnetic field in the previously performed experiments. The result can help interpreting known experimental data and developing realistic models of biological tissues.

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.

Discrimination of epileptogenic lesions and perilesional white matter using diffusion tensor magnetic resonance imaging.

The aim of this study was to evaluate whether ganglioglioma (GGL), dysembryoplastic neuroepithelial tumour (DNET) and FCD (focal cortical dysplasia) are distinguishable through diffusion tensor imaging. Additionally, it was investigated whether the diffusion measures differed in the perilesional (pNAWM) and in the contralateral normal appearing white matter (cNAWM). Six GGLs, eight DNETs and seven FCDs were included in this study. Quantitative diffusion measures, that is, axial, radial and mean diffusivity and fractional anisotropy, were determined in the lesion identified on isotropic T2 or FLAIR-weighted images and in pNAWM and cNAWM, respectively. DNET differed from FCD in mean diffusivity, and GGL from FCD in radial diffusivity. Both types of glioneuronal tumours were different from pNAWM in fractional anisotropy and radial diffusivity. For identifying the tumour edges, threshold values for tumour-free tissue were investigated with receiver operating characteristic analyses: tumour could be separated from pNAWM at a threshold ≤ 0.32 (fractional anisotropy) or ≥ 0.56 (radial diffusivity) *10-3 mm2/s (area under the curve 0.995 and 0.990 respectively). While diffusion parameters of FCDs differed from cNAWM (radial diffusivity (*10-3 mm/s2): 0.74 ± 0.19 vs. 0.43 ± 0.05; corrected p-value < 0.001), the pNAWM could not be differentiated from the FCD.

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.

Effects of mesoscopic susceptibility and transverse relaxation on diffusion NMR.

Measuring molecular diffusion is based on the spatial encoding of spin-carrying molecules using external Larmor frequency gradients. Intrinsic variations of the Larmor frequency and of the local relaxation rate, commonly present in structurally complex samples, interfere with the external gradients, confounding the NMR-measured diffusion propagator. Here we consider, analytically and numerically, the effects of the mesoscopic magnetic structure (local susceptibility and transverse relaxation rate) on the NMR-measured "apparent" diffusion coefficient (ADC). We show that in the fast diffusion regime, when molecules spread past the correlation length of the magnetic structure, the deviation of ADC from the genuine diffusion coefficient increases as a power law of diffusion time. The effect of mesoscopically varying transverse relaxation rate is sequence-independent and always leads to the decrease of ADC with time, whereas the effect sign for the mesoscopic Larmor frequency variations depends on the presence of refocussing pulses in the diffusion sequence. We connect this unexpectedly diverging with time ADC discrepancy to the spatial statistics of the mesocopic magnetic structure. Our results establish a novel kind of NMR contrast tied to the microstructural complexity, and can be applied to discern the mesoscopic effects of hindrances to molecular diffusion, susceptibility variations, and varying local relaxation rate, on the measured diffusion propagator. In particular, we numerically show that the susceptibility effect of a microvascular network is sufficient to explain the observed ADC decrease due to superparamagnetic iron-oxide contrast injection in monkeys.