Transverse NMR relaxation in biological tissues

Signatures of microstructure in gradient-echo and spin-echo signals

PURPOSE

To determine whether the spatial scale and magnetic susceptibility of microstructure can be evaluated robustly from the decay of gradient-echo and spin-echo signals.

THEORY AND METHODS

Gradient-echo and spin-echo images were acquired from suspensions of spherical polystyrene microbeads of 10, 20, and 40 μm nominal diameter. The sizes of the beads and their magnetic susceptibility relative to the medium were estimated from the signal decay curves, using a lookup table generated from Monte Carlo simulations and an analytic model based on the Gaussian phase approximation.

RESULTS

Fitting Monte Carlo predictions to spin-echo data yielded acceptable estimates of microstructural parameters for the 20 and 40 μm microbeads. Using gradient-echo data, the Monte Carlo lookup table provided satisfactory parameter estimates for the 20 μm beads but unstable results for the diameter of the largest beads. Neither spin-echo nor gradient-echo data allowed accurate parameter estimation for the smallest beads. The analytic model performed poorly over all bead sizes.

CONCLUSIONS

Microstructural sources of magnetic susceptibility produce distinctive non-exponential signatures in the decay of gradient-echo and spin-echo signals. However, inverting the problem to extract microstructural parameters from the signals is nontrivial and, in certain regimes, ill-conditioned. For microstructure with small characteristic length scales, parameter estimation is hampered by the difficulty of acquiring accurate data at very short echo times. For microstructure with large characteristic lengths, the gradient-echo signal approaches the static-dephasing regime, where it becomes insensitive to size. Applicability of the analytic model was further limited by failure of the Gaussian phase approximation for all but the smallest beads.

Distinguishing microgliosis and tau deposition in the mouse brain using paramagnetic and diamagnetic susceptibility source separation

Tauopathies, including Alzheimer's disease (AD), are neurodegenerative disorders characterized by hyperphosphorylated tau protein aggregates in the brain. In addition to protein aggregates, microglia-mediated inflammation and iron dyshomeostasis are other pathological features observed in AD and other tauopathies. It is known that these alterations at the subcellular level occur much before the onset of macroscopic tissue atrophy or cognitive deficits. The ability to detect these microstructural changes with MRI therefore has substantive importance for improved characterization of disease pathogenesis. In this study, we demonstrate that quantitative susceptibility mapping (QSM) with paramagnetic and diamagnetic susceptibility source separation has the potential to distinguish neuropathological alterations in a transgenic mouse model of tauopathy. 3D multi-echo gradient echo data were acquired from fixed brains of PS19 (Tau) transgenic mice and age-matched wild-type (WT) mice (n = 5 each) at 11.7 T. The multi-echo data were fit to a 3-pool complex signal model to derive maps of paramagnetic component susceptibility (PCS) and diamagnetic component susceptibility (DCS). Group-averaged signal fraction and composite susceptibility maps showed significant region-specific differences between the WT and Tau mouse brains. Significant bilateral increases in PCS and |DCS| were observed in specific hippocampal and cortical sub-regions of the Tau mice relative to WT controls. Comparison with immunohistological staining for microglia (Iba1) and phosphorylated-tau (AT8) further indicated that the PCS and DCS differences corresponded to regional microgliosis and tau deposition in the PS19 mouse brains, respectively. The results demonstrate that quantitative susceptibility source separation may provide sensitive imaging markers to detect distinct pathological alterations in tauopathies.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model

PURPOSE

To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters.

THEORY AND METHODS

We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency.

RESULTS

We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports.

CONCLUSION

The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Comparison of three magnetic resonance imaging measures of brain iron in healthy and cocaine use disorder participants

Several magnetic resonance imaging (MRI) measures for quantifying endogenous nonheme brain iron have been proposed. These correspond to distinct physical properties with varying sensitivities and specificities to iron. Moreover, they may depend not only on tissue iron concentration, but also on the intravoxel spatial pattern of iron deposition, which is complex in many brain regions. Here, the three MRI brain iron measures of R 2 * , magnetic field correlation (MFC), and magnetic susceptibility are compared in several deep gray matter regions for both healthy participants (HPs) and individuals with cocaine use disorder (CUD). Their concordance is assessed from their correlations with each other and their relative dependencies on age. In addition, associations between the iron measures and microstructure in adjacent white matter regions are investigated by calculating their correlations with diffusion MRI measures from the internal capsule, and associations with cognition are determined by using results from a battery of standardized tests relevant to CUD. It is found that all three iron measures are strongly correlated with each other for the considered gray matter regions, but with correlation coefficients substantially less than one indicating important differences. The age dependencies of all three measures are qualitatively similar in most regions, except for the red nucleus, where the susceptibility has a significantly stronger correlation with age than R 2 * . Weak to moderate correlations are seen for the iron measures with several of the diffusion and cognitive measures, with the strongest correlations being obtained for R 2 * . The iron measures differ little between the HP and CUD groups, although susceptibility is significantly lower in the red nucleus for the CUD group. For the comparisons made, the iron measures behave similarly in most respects, but with notable quantitative differences. It is suggested that these differences may be, in part, attributable to a higher sensitivity to the spatial pattern of iron deposition for R 2 * and MFC than for susceptibility. This is supported most strongly by a sharp contrast between the values of the iron measures in the globus pallidus relative to those in the red nucleus. The observed correlations of the iron measures with diffusion and cognitive scores point to possible connections between gray matter iron, white matter microstructure, and cognition.

Myelin water imaging at 0.55 T using a multigradient-echo sequence

PURPOSE

To investigate the prospects of a multigradient-echo (mGRE) acquisition for in vivo myelin water imaging at 0.55 T.

METHODS

Scans were performed on the brain of four healthy volunteers at 0.55 and 3 T, using a 3D mGRE sequence. The myelin water fraction (MWF) was calculated for both field strengths using a nonnegative least squares (NNLS) algorithm, implemented in the qMRLab suite. The quality of these maps as well as single-voxel fits were compared visually for 0.55 and 3 T.

RESULTS

The obtained MWF values at 0.55 T are consistent with previously reported ones at higher field strengths. The MWF maps are a considerable improvement over the ones at 3 T. Example fits show that 0.55 T data is better described by an exponential model than 3 T data, making the assumed multi-exponential model of the NNLS algorithm more accurate.

CONCLUSION

This first assessment shows that mGRE myelin water imaging at 0.55 T is feasible and has the potential to yield better results than at higher fields.

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo mouse brain

PURPOSE

To extend quantitative susceptibility mapping to account for microstructure of white matter (WM) and demonstrate its effect on ex vivo mouse brain at 16.4T.

THEORY AND METHODS

Previous studies have shown that the MRI measured Larmor frequency also depends on local magnetic microstructure at the mesoscopic scale. Here, we include effects from WM microstructure using our previous results for the mesoscopic Larmor frequencyΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ of cylinders with arbitrary orientations. We scrutinize the validity of our model and QSM in a digital brain phantom includingΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from a WM susceptibility tensor and biologically stored iron with scalar susceptibility. We also apply susceptibility tensor imaging to the phantom and investigate how the fitted tensors are biased fromΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ . Last, we demonstrate how to combine multi-gradient echo and diffusion MRI images of ex vivo mouse brains acquired at 16.4T to estimate an apparent scalar susceptibility without sample rotations.

RESULTS

Our new model improves susceptibility estimation compared to QSM for the brain phantom. Applying susceptibility tensor imaging to the phantom withΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from WM axons with scalar susceptibility produces a highly anisotropic susceptibility tensor that mimics results from previous susceptibility tensor imaging studies. For the ex vivo mouse brain we find theΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ due to WM microstructure to be substantial, changing susceptibility in WM up to 25% root-mean-squared-difference.

CONCLUSION

Ω ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ impacts susceptibility estimates and biases susceptibility tensor imaging fitting substantially. Hence, it should not be neglected when imaging structurally anisotropic tissue such as brain WM.

Non-invasive assessment of normal and impaired iron homeostasis in the brain

Strict iron regulation is essential for normal brain function. The iron homeostasis, determined by the milieu of available iron compounds, is impaired in aging, neurodegenerative diseases and cancer. However, non-invasive assessment of different molecular iron environments implicating brain tissue's iron homeostasis remains a challenge. We present a magnetic resonance imaging (MRI) technology sensitive to the iron homeostasis of the living brain (the r1-r2* relaxivity). In vitro, our MRI approach reveals the distinct paramagnetic properties of ferritin, transferrin and ferrous iron ions. In the in vivo human brain, we validate our approach against ex vivo iron compounds quantification and gene expression. Our approach varies with the iron mobilization capacity across brain regions and in aging. It reveals brain tumors' iron homeostasis, and enhances the distinction between tumor tissue and non-pathological tissue without contrast agents. Therefore, our approach may allow for non-invasive research and diagnosis of iron homeostasis in living human brains.

Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm2) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement.

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.

Adaptive model-based Magnetic Resonance

PURPOSE

Conventional sequences are static in nature, fixing measurement parameters in advance in anticipation of a wide range of expected tissue parameter values. We set out to design and benchmark a new, personalized approach-termed adaptive MR-in which incoming subject data is used to update and fine-tune the pulse sequence parameters in real time.

METHODS

We implemented an adaptive, real-time multi-echo (MTE) experiment for estimating T₂ s. Our approach combined a Bayesian framework with model-based reconstruction. It maintained and continuously updated a prior distribution of the desired tissue parameters, including T₂ , which was used to guide the selection of sequence parameters in real time.

RESULTS

Computer simulations predicted accelerations between 1.7- and 3.3-fold for adaptive multi-echo sequences relative to static ones. These predictions were corroborated in phantom experiments. In healthy volunteers, our adaptive framework accelerated the measurement of T₂ for n-acetyl-aspartate by a factor of 2.5.

CONCLUSION

Adaptive pulse sequences that alter their excitations in real time could provide substantial reductions in acquisition times. Given the generality of our proposed framework, our results motivate further research into other adaptive model-based approaches to MRI and MRS.

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.

High-resolution magnetization-transfer imaging of post-mortem marmoset brain: Comparisons with relaxometry and histology

Cell membranes and macromolecules or paramagnetic compounds interact with water proton spins, which modulates magnetic resonance imaging (MRI) contrast providing information on tissue composition. For a further investigation, quantitative magnetization transfer (qMT) parameters (at 3T), including the ratio of the macromolecular and water proton pools, F, and the exchange-rate constant as well as the (observed) longitudinal and the effective transverse relaxation rates (at 3T and 7T), R₁^obs and R₂^*, respectively, were measured at high spatial resolution (200 µm) in a slice of fixed marmoset brain and compared to histology results obtained with Gallyas' myelin stain and Perls' iron stain. R₁^obs and R₂^* were linearly correlated with the iron content for the entire slice, whereas distinct differences were obtained between gray and white matter for correlations of relaxometry and qMT parameters with myelin content. The combined results suggest that the macromolecular pool interacting with water consists of myelin and (less efficient) non-myelin contributions. Despite strong correlation of F and R₁^obs, none of these parameters was uniquely specific to myelination. Due to additional sensitivity to iron stores, R₁^obs and R₂^* were more sensitive for depicting microstructural differences between cortical layers than F.

Information theoretic evaluation of Lorentzian, Gaussian, Voigt, and symmetric alpha-stable models of reversible transverse relaxation in cervical cancer in vivo at 3 T

OBJECTS

To better characterize cervical cancer at 3 T. MRI transverse relaxation patterns hold valuable biophysical information about cellular scale microstructure. Lorentzian modeling is typically used to represent intravoxel frequency distributions, resulting in mono-exponential decay of reversible transverse relaxation. However, deviations from mono-exponential decay are expected theoretically and observed experimentally.

MATERIALS AND METHODS

We compared the information content of four models of signal attenuation with reversible transverse relaxation. Biological phantoms and six women with cervical squamous cell carcinoma were imaged using a gradient-echo sampling of the spin-echo (GESSE) sequence. Lorentzian, Gaussian, Voigt, and Symmetric α-Stable (SAS) models were ranked using Akaike's Information Criterion (AIC), and the model retaining the highest information content was identified at each voxel as the best model.

RESULTS

The Lorentzian model resulted in information loss in large fractions of the phantoms and cervix. Gaussian and SAS models frequently had higher information content than the Lorentzian in much of the areas of interest. The Voigt model rarely surpassed the three other models in terms of information content.

DISCUSSION

Gaussian and SAS models provide better fitting of data in much of the human cervix at 3 T. Minimizing information loss through improved tissue modeling may have important implications for identifying reliable biomarkers of tumor hypoxia and iron deposition.

Effective R2 relaxation rate, derived from dual-contrast fast-spin-echo MRI, enables detection of hemisphere differences in iron level and dopamine function in Parkinson's disease and healthy individuals

BACKGROUND

Clinical estimates of brain iron concentration are achievable with quantitative transverse relaxation rate R₂, via time-consuming multiple spin-echo (SE) sequences. The objective of this study was to investigate whether quantitative iron-sensitive information may be derived from 3.0 T dual-contrast fast-spin-echo (FSE) sequences (typically employed in anatomical non-quantitative evaluations), as a routinely-collected alternative to evaluate iron levels in healthy (HC) and Parkinson's disease (PD) brains.

NEW METHOD

MRI 3.0 T FSE data from the Parkinson's Progression Markers Initiative (PPMI) (12 PD, 12 age- and gender-matched HC subjects) were cross-sectionally and longitudinally evaluated. A new measure, 'effective R₂', was calculated for bilateral subcortical grey matter (caudate nucleus, putamen, globus pallidus, red nucleus, substantia nigra). Linear regression analysis was performed to correlate 'effective R₂' with models of age-dependent brain iron concentration and striatal dopamine transporter (DaT) receptor binding ratio.

RESULTS

Effective R₂ was strongly correlated with estimated brain iron concentration. In PD, putaminal effective R₂ difference was observed between the hemispheres contra-/ipsi-lateral to the predominantly symptomatic side at onset. This hemispheric difference was correlated with the putaminal DaT binding ratios in PD.

COMPARISON WITH EXISTING METHOD(S)

Effective R₂, derived from rapid dual-contrast FSE sequences, showed viability as an alternative to R₂ from SE sequences. Linear correlation of effective R₂ with estimated iron concentration was comparable to documented iron-dependent R₂. The effective R₂ correlation coefficient was consistent with theoretical R₂ iron-dependence at 3.0 T.

CONCLUSIONS

Effective R₂ has clinical potential as a fast quantitative method, as an alternative to R₂, to aid evaluation of brain iron levels and DaT function.

In-cell NMR: Why and how?

NMR spectroscopy has been applied to cells and tissues analysis since its beginnings, as early as 1950. We have attempted to gather here in a didactic fashion the broad diversity of data and ideas that emerged from NMR investigations on living cells. Covering a large proportion of the periodic table, NMR spectroscopy permits scrutiny of a great variety of atomic nuclei in all living organisms non-invasively. It has thus provided quantitative information on cellular atoms and their chemical environment, dynamics, or interactions. We will show that NMR studies have generated valuable knowledge on a vast array of cellular molecules and events, from water, salts, metabolites, cell walls, proteins, nucleic acids, drugs and drug targets, to pH, redox equilibria and chemical reactions. The characterization of such a multitude of objects at the atomic scale has thus shaped our mental representation of cellular life at multiple levels, together with major techniques like mass-spectrometry or microscopies. NMR studies on cells has accompanied the developments of MRI and metabolomics, and various subfields have flourished, coined with appealing names: fluxomics, foodomics, MRI and MRS (i.e. imaging and localized spectroscopy of living tissues, respectively), whole-cell NMR, on-cell ligand-based NMR, systems NMR, cellular structural biology, in-cell NMR… All these have not grown separately, but rather by reinforcing each other like a braided trunk. Hence, we try here to provide an analytical account of a large ensemble of intricately linked approaches, whose integration has been and will be key to their success. We present extensive overviews, firstly on the various types of information provided by NMR in a cellular environment (the "why", oriented towards a broad readership), and secondly on the employed NMR techniques and setups (the "how", where we discuss the past, current and future methods). Each subsection is constructed as a historical anthology, showing how the intrinsic properties of NMR spectroscopy and its developments structured the accessible knowledge on cellular phenomena. Using this systematic approach, we sought i) to make this review accessible to the broadest audience and ii) to highlight some early techniques that may find renewed interest. Finally, we present a brief discussion on what may be potential and desirable developments in the context of integrative studies in biology.

Influence of diffusion on transverse relaxation rates and phases of an ensemble of magnetic spheres

In quantitative susceptibility mapping, the tissue susceptibility is determined from the magnitude and phase of the gradient echo signal, which is influenced by the interplay of complex susceptibility and diffusion effect. Herein, we analytically analyze the influence of diffusion on magnitude and phase images generated by randomly arranged magnetic spheres as a model of intracerebral iron depositions. We demonstrate that both gradient and spin echo relaxation rate constants have a strong and nonlinear dependence on diffusion strength and give empirical formulas for magnitude and phase. This may be used in the future to improve QSM processing methods. In addition, we show that, in theory, combined acquisitions of gradient and spin echo can be used to determine the dimension of the magnetic spheres and the diffusion strength.

Assessing potential correlation between T2 relaxation and diffusion of lactate in the mouse brain

Purpose

While diffusion and T₂ relaxation are intertwined, little or no correlation exists between diffusion and T₂ relaxation of intracellular metabolites in the rodent brain, as measured by diffusion‐weighted MRS at different TEs. However, situation might be different for lactate, since it is present in both extracellular and intracellular spaces, which exhibit different diffusion properties and may also exhibit different T₂. Such a TE dependence would be crucial to account for when interpreting or modeling lactate diffusion. Here we propose to take advantage of a new diffusion sequence, where J‐modulation of lactate is canceled even at long TE, thus retaining excellent signal, to assess potential T₂ dependence on diffusion of lactate in the mouse brain.

Methods

Using a frequency‐selective diffusion‐weighted spin‐echo sequence that removes J‐modulation at 1.3 ppm, thus preserving lactate signal even at long TE, we investigate the effect of TE between 50.9 and 110.9 ms (while keeping diffusion time constant) on apparent diffusivity and kurtosis in the mouse brain.

Results

Regardless of the metabolites, no difference appears for the diffusion‐weighted signal attenuation with increasing TE. For lactate, apparent diffusivity and kurtosis remain unchanged as TE increases.

Conclusion

No significant TE dependence of diffusivity and kurtosis is measured for lactate in the 50–110 ms TE range, confirming that potential T₂ effects can be ignored when interpreting or modeling lactate diffusion.

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In vivo irreversible and reversible transverse relaxation rates in human cerebral cortex via line scans at 7 T with 250 micron resolution perpendicular to the cortical surface

Understanding how and why MR signals and their associated relaxation rates vary with cortical depth could ultimately enable the noninvasive investigation of the laminar architecture of cerebral cortex in the living human brain. However, cortical gray matter is typically only a few millimeters thick, making it challenging to sample many cortical depths with the voxel sizes commonly used in MRI studies. Line-scan techniques provide a way to overcome this challenge and here we implemented a novel line-scan GESSE pulse sequence that allowed us to measure irreversible and reversible transverse relaxation rates-R₂ and R₂´, respectively-with extremely high resolution (250 μm) in the radial direction, perpendicular to the cortical surface. Eight healthy human subjects were scanned at 7 T using this sequence, with primary visual cortex (V1) targeted in three subjects and primary motor (M1) and somatosensory cortex (S1) targeted in the other five. In all three cortical areas, a peak in R₂ values near the central depths was seen consistently across subjects-an observation that has not been made before, to our knowledge. On the other hand, no consistent pattern was apparent for R₂´ values as a function of cortical depth. The intracortical R₂ peak reported here is unlikely to be explained by myelin content or by deoxyhemoglobin in the microvasculature; however, this peak is in accord with the laminar distribution of non-heme iron in these cortical areas, known from prior histology studies. Obtaining information about tissue microstructure via measurements of transverse relaxation (and other quantitative MR contrast mechanisms) at the extremely high radial resolutions achievable through the use of line-scan techniques could therefore bring us closer to being able to perform "in vivo histology" of the cerebral cortex.

Lattice Boltzmann framework for accurate NMR simulation in porous media

Nuclear magnetic resonance (NMR) responses of fluids saturating porous media arise from complex relaxation-diffusion dynamics of polarized spins. These constitute a sensitive probe of the microstructure and are described by the Bloch-Torrey equations. An NMR simulation framework based on an augmented lattice Boltzmann method aimed at the fine-scale resolution of nuclear polarization density is presented. The approach encapsulates the time evolution of the full magnetization vector and naturally incorporates the mechanisms of diffusional transport. Spin dephasing mechanisms are fully resolved at tomogram voxel scale to account for magnetic field inhomogeneity. The approach is validated against analytical solutions of spin-echo decays for simple pore geometries. An application to a nano-computed-tomography image of chalk with inhomogeneous internal fields yields T_{2} spectral measures in good agreement with experiment and illustrates the spatial pore-scale dynamics of net magnetization. Findings establish the feasibility of the framework for pure diffusion and present an approach vector to modeling the evolution of magnetization under flow conditions.

In vivo Estimation of Axonal Morphology From Magnetic Resonance Imaging and Electroencephalography Data

Purpose

We present a novel approach that allows the estimation of morphological features of axonal fibers from data acquired in vivo in humans. This approach allows the assessment of white matter microscopic properties non-invasively with improved specificity.

Theory

The proposed approach is based on a biophysical model of Magnetic Resonance Imaging (MRI) data and of axonal conduction velocity estimates obtained with Electroencephalography (EEG). In a white matter tract of interest, these data depend on (1) the distribution of axonal radius [P(r)] and (2) the g-ratio of the individual axons that compose this tract [g(r)]. P(r) is assumed to follow a Gamma distribution with mode and scale parameters, M and θ, and g(r) is described by a power law with parameters α and β.

Methods

MRI and EEG data were recorded from 14 healthy volunteers. MRI data were collected with a 3T scanner. MRI-measured g-ratio maps were computed and sampled along the visual transcallosal tract. EEG data were recorded using a 128-lead system with a visual Poffenberg paradigm. The interhemispheric transfer time and axonal conduction velocity were computed from the EEG current density at the group level. Using the MRI and EEG measures and the proposed model, we estimated morphological properties of axons in the visual transcallosal tract.

Results

The estimated interhemispheric transfer time was 11.72 ± 2.87 ms, leading to an average conduction velocity across subjects of 13.22 ± 1.18 m/s. Out of the 4 free parameters of the proposed model, we estimated θ – the width of the right tail of the axonal radius distribution – and β – the scaling factor of the axonal g-ratio, a measure of fiber myelination. Across subjects, the parameter θ was 0.40 ± 0.07 μm and the parameter β was 0.67 ± 0.02 μm^−α.

Conclusion

The estimates of axonal radius and myelination are consistent with histological findings, illustrating the feasibility of this approach. The proposed method allows the measurement of the distribution of axonal radius and myelination within a white matter tract, opening new avenues for the combined study of brain structure and function, and for in vivo histological studies of the human brain.

Three-Dimensional Iron Oxide Nanoparticle-Based Contrast-Enhanced Magnetic Resonance Imaging for Characterization of Cerebral Arteriogenesis in the Mouse Neocortex

Purpose: Subsurface blood vessels in the cerebral cortex have been identified as a bottleneck in cerebral perfusion with the potential for collateral remodeling. However, valid techniques for non-invasive, longitudinal characterization of neocortical microvessels are still lacking. In this study, we validated contrast-enhanced magnetic resonance imaging (CE-MRI) for in vivo characterization of vascular changes in a model of spontaneous collateral outgrowth following chronic cerebral hypoperfusion. Methods: C57BL/6J mice were randomly assigned to unilateral internal carotid artery occlusion or sham surgery and after 21 days, CE-MRI based on T2*-weighted imaging was performed using ultra-small superparamagnetic iron oxide nanoparticles to obtain subtraction angiographies and steady-state cerebral blood volume (ss-CBV) maps. First pass dynamic susceptibility contrast MRI (DSC-MRI) was performed for internal validation of ss-CBV. Further validation at the histological level was provided by ex vivo serial two-photon tomography (STP). Results: Qualitatively, an increase in vessel density was observed on CE-MRI subtraction angiographies following occlusion; however, a quantitative vessel tracing analysis was prone to errors in our model. Measurements of ss-CBV reliably identified an increase in cortical vasculature, validated by DSC-MRI and STP. Conclusion: Iron oxide nanoparticle-based ss-CBV serves as a robust, non-invasive imaging surrogate marker for neocortical vessels, with the potential to reduce and refine preclinical models targeting the development and outgrowth of cerebral collateralization.

Spin echo formation in muscle tissue

Determination of the spin echo signal evolution and of transverse relaxation rates is of high importance for microstructural modeling of muscle tissue in magnetic resonance imaging. So far, numerically exact solutions for the NMR signal dynamics in muscle tissue models have been reported only for the gradient echo free induction decay, with spin echo problems usually solved by approximate methods. In this work, we modeled the spin echo signal numerically exact by discretizing the radial dimension of the Bloch-Torrey equation and expanding the angular dependency in terms of even Chebyshev polynomials. This allows us to express the time dependence of the local magnetization as a closed-form matrix expression. Using this method, we were able to accurately capture the spin echo local and total magnetization dynamics. The obtained transverse relaxation rates showed a high concordance with random walker and finite-element simulations. We could demonstrate that in cases of smaller diffusion coefficients, the commonly used strong collision approximation significantly underestimates the true value considerably. Instead, the limiting behavior in this regime is correctly described either by the full solution or by the slow diffusion approximation. Experimentally measured transverse relaxation rates of a mouse limb muscle showed an angular dependence in accordance with the theoretical prediction.

Magnetic resonance free induction decay in geological porous materials

Magnetic resonance is an important noninvasive technology across life sciences and industry. Free induction decay is the simplest [Formula: see text]H magnetic resonance measurement method and an important means of probing fast-decaying signals in porous materials such as rocks, lung, and bone. It is commonly assumed that the free induction decay in geological porous materials is single-exponential. We experimentally observed two regimes of free induction decay behavior in geological porous materials: single-exponential and non-exponential decay. Numerical simulations that match experimental data highlight the effect of mass diffusion, especially in the single-exponential behavior. These two regimes of free induction decay in porous materials are associated with a bifurcation point in the solutions of the Bloch-Torrey equation for diffusion of fluids in confined domains in the presence of internal magnetic field gradients. This finding facilitates the extraction of absolute internal magnetic field gradient intensities from simple free induction decay measurements in the laboratory and field. This work also warns against common single-exponential assumptions in surface magnetic resonance methods employed in surveying underground water aquifers.

Measuring the iron content of dopaminergic neurons in substantia nigra with MRI relaxometry

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Dopaminergic neurons dominate effective transverse relaxation in nigrosome 1.

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Ion beam microscopy reveals highest iron concentrations in dopaminergic neurons.

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Developed biophysical model links MRI parameters to cellular iron content.

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Ferritin- and neuromelanin-bound iron impact MRI parameters differently.

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Quantitative MRI provides a potential biomarker of iron in dopaminergic neurons.

In Parkinson’s disease, the depletion of iron-rich dopaminergic neurons in nigrosome 1 of the substantia nigra precedes motor symptoms by two decades. Methods capable of monitoring this neuronal depletion, at an early disease stage, are needed for early diagnosis and treatment monitoring. Magnetic resonance imaging (MRI) is particularly suitable for this task due to its sensitivity to tissue microstructure and in particular, to iron. However, the exact mechanisms of MRI contrast in the substantia nigra are not well understood, hindering the development of powerful biomarkers. In the present report, we illuminate the contrast mechanisms in gradient and spin echo MR images in human nigrosome 1 by combining quantitative 3D iron histology and biophysical modeling with quantitative MRI on post mortem human brain tissue. We show that the dominant contribution to the effective transverse relaxation rate (R2*) in nigrosome 1 originates from iron accumulated in the neuromelanin of dopaminergic neurons. This contribution is appropriately described by a static dephasing approximation of the MRI signal. We demonstrate that the R2* contribution from dopaminergic neurons reflects the product of cell density and cellular iron concentration. These results demonstrate that the in vivo monitoring of neuronal density and iron in nigrosome 1 may be feasible with MRI and provide directions for the development of biomarkers for an early detection of dopaminergic neuron depletion in Parkinson’s disease.

BOLD sensitivity and vessel size specificity along CPMG and GRASE echo trains

PURPOSE

To assess the vessel size specificity and sensitivity of rapid CPMG and GRASE for functional BOLD imaging for different echo train lengths, echo spacings, field strength, and refocusing flip angle schemes. In addition, the behavior of signals acquired before and after the refocusing time points is analyzed.

METHODS

Evolution of magnetization within a network of artificial cylinders is simulated with Monte Carlo methods for all relevant coherence pathways. In addition, measurements on microspheres were performed to confirm some of the theoretical results.

RESULTS

For reduced refocusing flip angles, the peak of the vessel size sensitivity curve is shifting toward larger radii with increasing echo time. Furthermore, the BOLD-related signal change along the echo train depends on the chosen refocusing flip angle scheme and in general does not follow corresponding echo amplitudes.

CONCLUSION

CPMG or GRASE can be used with low refocusing flip angles without significant loss of sensitivity to BOLD. The evolution of BOLD signal changes along the echo train can be used to design optimal k-space reordering schemes. Signals acquired before or after the spin echo time point show contributions from larger vessels similar to gradient echo sequences. Short echo spacing (time between refocusing pulses) suppresses gradient echo-related contributions from larger vessels, whereas the spin echo-related contribution from small vessels remains constant and is independent of the echo spacing.

Resolving bundle-specific intra-axonal T2 values within a voxel using diffusion-relaxation tract-based estimation

At the typical spatial resolution of MRI in the human brain, approximately 60-90% of voxels contain multiple fiber populations. Quantifying microstructural properties of distinct fiber populations within a voxel is therefore challenging but necessary. While progress has been made for diffusion and T1-relaxation properties, how to resolve intra-voxel T2 heterogeneity remains an open question. Here a novel framework, named COMMIT-T2, is proposed that uses tractography-based spatial regularization with diffusion-relaxometry data to estimate multiple intra-axonal T2 values within a voxel. Unlike previously-proposed voxel-based T2 estimation methods, which (when applied in white matter) implicitly assume just one fiber bundle in the voxel or the same T2 for all bundles in the voxel, COMMIT-T2 can recover specific T2 values for each unique fiber population passing through the voxel. In this approach, the number of recovered unique T2 values is not determined by a number of model parameters set a priori, but rather by the number of tractography-reconstructed streamlines passing through the voxel. Proof-of-concept is provided in silico and in vivo, including a demonstration that distinct tract-specific T2 profiles can be recovered even in the three-way crossing of the corpus callosum, arcuate fasciculus, and corticospinal tract. We demonstrate the favourable performance of COMMIT-T2 compared to that of voxelwise approaches for mapping intra-axonal T2 exploiting diffusion, including a direction-averaged method and AMICO-T2, a new extension to the previously-proposed Accelerated Microstructure Imaging via Convex Optimization (AMICO) framework.

The present and the future of microstructure MRI: From a paradigm shift to normal science

The aspiration of imaging tissue microstructure with MRI is to uncover micrometer-scale tissue features within millimeter-scale imaging voxels, in vivo. This kind of super-resolution has fueled a paradigm shift within the biomedical imaging community. However, what feels like an ongoing revolution in MRI, has been conceptually experienced in physics decades ago; from this point of view, our current developments can be seen as Thomas Kuhn's "normal science" stage of progress. While the concept of model-based quantification below the nominal imaging resolution is not new, its possibilities in neuroscience and neuroradiology are only beginning to be widely appreciated. This disconnect calls for communicating the progress of tissue microstructure MR imaging to its potential users. Here, a number of recent research developments are outlined in terms of the overarching concept of coarse-graining the tissue structure over an increasing diffusion length. A variety of diffusion models and phenomena are summarized on the phase diagram of diffusion MRI, with the unresolved problems and future directions corresponding to its unexplored domains.

Dynamic contrast-enhanced QSM for perfusion imaging: a systematic comparison of ΔR2*- and QSM-based contrast agent concentration time curves in blood and tissue

OBJECTIVE

In dynamic susceptibility contrast MRI (DSC-MRI), an arterial input function (AIF) is required to quantify perfusion. However, estimation of the concentration of contrast agent (CA) from magnitude MRI signal data is challenging. A reasonable alternative would be to quantify CA concentration using quantitative susceptibility mapping (QSM), as the CA alters the magnetic susceptibility in proportion to its concentration.

MATERIAL AND METHODS

AIFs with reasonable appearance, selected on the basis of conventional criteria related to timing, shape, and peak concentration, were registered from both ΔR2* and QSM images and mutually compared by visual inspection. Both ΔR2*- and QSM-based AIFs were used for perfusion calculations based on tissue concentration data from ΔR2*as well as QSM images.

RESULTS

AIFs based on ΔR2* and QSM data showed very similar shapes and the estimated cerebral blood flow values and mean transit times were similar. Analysis of corresponding ΔR2* versus QSM-based concentration estimates yielded a transverse relaxivity estimate of 89 s^-1 mM^-1, for voxels identified as useful AIF candidate in ΔR2* images according to the conventional criteria.

DISCUSSION

Interestingly, arterial concentration time curves based on ΔR2* versus QSM data, for a standard DSC-MRI experiment, were generally very similar in shape, and the relaxivity obtained in voxels representing blood was similar to tissue relaxivity obtained in previous studies.

Superficial white matter imaging: Contrast mechanisms and whole-brain in vivo mapping

Superficial white matter (SWM) contains the most cortico-cortical white matter connections in the human brain encompassing the short U-shaped association fibers. Despite its importance for brain connectivity, very little is known about SWM in humans, mainly due to the lack of noninvasive imaging methods. Here, we lay the groundwork for systematic in vivo SWM mapping using ultrahigh resolution 7 T magnetic resonance imaging. Using biophysical modeling informed by quantitative ion beam microscopy on postmortem brain tissue, we demonstrate that MR contrast in SWM is driven by iron and can be linked to the microscopic iron distribution. Higher SWM iron concentrations were observed in U-fiber-rich frontal, temporal, and parietal areas, potentially reflecting high fiber density or late myelination in these areas. Our SWM mapping approach provides the foundation for systematic studies of interindividual differences, plasticity, and pathologies of this crucial structure for cortico-cortical connectivity in humans.

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.

The impact of realistic axonal shape on axon diameter estimation using diffusion MRI

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D_⊥(t) and kurtosis K_⊥(t), to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D_⊥(t) is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K_⊥∣_t→∞ deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.

MRI size assessment of cerebral microvasculature using diffusion-time-dependent stimulated-echo acquisition: A feasibility study in rodent

In this study, a stimulated-echo (STE) method was employed to robustify the cerebral vessel size estimation near air-tissue, bone-tissue interfaces, and large vessels. The proposed solution is to replace the relaxation rate change from gradient-echo (GRE) with that from STE with long diffusion time after the injection of an intravascular contrast agent, superparamagnetic iron oxide nanoparticles. The corresponding diffusion length of STE is shorter than the length over which the unwanted macroscopic field inhomogeneities but is still longer than the correlation length of the fields induced by small vessels. Therefore, the unwanted field inhomogeneities are refocused, while preserving microscopic susceptibility contrast from cerebral vessels. The mean vessel diameter (dimensionless) derived from the diffusion-time-varying STE method was compared to the mean vessel diameter obtained by a conventional spin-echo (SE) and GRE combination based on Monte-Carlo proton diffusion simulations and in vivo rat experiments at 7 ​T. The in vivo mean vessel diameter from the MRI experiments was directly compared to available reference mouse brain vasculature obtained by a knife-edge scanning microscope (KESM), which is considered to be the gold standard. Monte-Carlo simulation revealed that SE and GRE-based MR relaxation rate changes (ΔR₂ and ΔR₂∗, respectively) can be enhanced using single STE-based MR relaxation rate change (ΔR_STE) by regulating diffusion time, especially for small vessels. The in vivo mean vessel diameter from the STE method demonstrated a closer agreement with that from the KESM compared to the combined SE and GRE method, especially in the olfactory bulb and cortex. This study demonstrates that STE relaxation rate changes can be used as consistent measures for assessing small cerebral microvasculature, where macroscopic field inhomogeneity is severe and signal contamination from adjacent large vessels is significant.

A time-dependent diffusion MRI signature of axon caliber variations and beading

MRI provides a unique non-invasive window into the brain, yet is limited to millimeter resolution, orders of magnitude coarser than cell dimensions. Here, we show that diffusion MRI is sensitive to the micrometer-scale variations in axon caliber or pathological beading, by identifying a signature power-law diffusion time-dependence of the along-fiber diffusion coefficient. We observe this signature in human brain white matter and identify its origins by Monte Carlo simulations in realistic substrates from 3-dimensional electron microscopy of mouse corpus callosum. Simulations reveal that the time-dependence originates from axon caliber variation, rather than from mitochondria or axonal undulations. We report a decreased amplitude of time-dependence in multiple sclerosis lesions, illustrating the potential sensitivity of our method to axonal beading in a plethora of neurodegenerative disorders. This specificity to microstructure offers an exciting possibility of bridging across scales to image cellular-level pathology with a clinically feasible MRI technique.

Quantitative theory for the transverse relaxation time of blood water

An integrative model is proposed to describe the dependence of the transverse relaxation rate of blood water protons (R_2blood = 1/T_2blood ) on hematocrit fraction and oxygenation fraction (Y). This unified model takes into account (a) the diamagnetic effects of albumin, hemoglobin and the cell membrane; (b) the paramagnetic effect of hemoglobin; (c) the effect of compartmental exchange between plasma and erythrocytes under both fast and slow exchange conditions that vary depending on field strength and compartmental relaxation rates and (d) the effect of diffusion through field gradients near the erythrocyte membrane. To validate the model, whole-blood and lysed-blood R₂ data acquired previously using Carr-Purcell-Meiboom-Gill measurements as a function of inter-echo spacing τ_cp at magnetic fields of 3.0, 7.0, 9.4 and 11.7 T were fitted to determine the lifetimes (field-independent physiological constants) for water diffusion and exchange, as well as several physical constants, some of which are field-independent (magnetic susceptibilities) and some are field-dependent (relaxation rates for water protons in solutions of albumin and oxygenated and deoxygenated hemoglobin, ie, blood plasma and erythrocytes, respectively). This combined exchange-diffusion model allowed excellent fitting of the curve of the τ_cp -dependent relaxation rate dispersion at all four fields using a single average erythrocyte water lifetime, τ_ery = 9.1 ± 1.4 ms, and an averaged diffusional correlation time, τ_D = 3.15 ± 0.43 ms. Using this model and the determined physiological time constants and relaxation parameters, blood T₂ values published by multiple groups based on measurements at magnetic field strengths of 1.5 T and higher could be predicted correctly within error. Establishment of this theory is a fundamental step for quantitative modeling of the BOLD effect underlying functional MRI.

In vivo measurements of irreversible and reversible transverse relaxation rates in human basal ganglia at 7 T: making inferences about the microscopic and mesoscopic structure of iron and calcification deposits

The goal of this study was to measure irreversible and reversible transverse relaxation rates in the globus pallidus and putamen at 7 T, and to use these rates to make inferences about the sub-voxel structure of iron and calcification deposits. Gradient Echo Sampling of a Spin Echo (GESSE) data were acquired at 7 T on eighteen volunteers spanning a large range of ages (23-85 years), with calcifications in the globus pallidus incidentally observed in one volunteer. Maps of transverse relaxation rates were derived from the GESSE data, and the mean value of these rates in globus pallidus and putamen was estimated for each volunteer. Both irreversible and reversible transverse relaxation rates increased with the expected age-dependent iron content in these structures, except for the individual with calcifications for whom extremely large reversible relaxation rates but normal irreversible relaxation rates were found in the globus pallidus. Given the sensitivity of irreversible and reversible transverse relaxation rates to microscopic and mesoscopic field variations, respectively, our findings suggest that joint consideration of these rates may yield information not only about the amount of iron and calcification deposited in the brain, but also about the sub-voxel structure of these deposits, perhaps revealing certain aspects of their geometry and cellular distribution.

Hybrid-state free precession in nuclear magnetic resonance

The dynamics of large spin-1/2 ensembles are commonly described by the Bloch equation, which is characterized by the magnetization's non-linear response to the driving magnetic field. Consequently, most magnetic field variations result in non-intuitive spin dynamics, which are sensitive to small calibration errors. Although simplistic field variations result in robust spin dynamics, they do not explore the richness of the system's phase space. Here, we identify adiabaticity conditions that span a large experiment design space with tractable dynamics. All dynamics are trapped in a one-dimensional subspace, namely in the magnetization's absolute value, which is in a transient state, while its direction adiabatically follows the steady state. In this hybrid state, the polar angle is the effective drive of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain.

Optimized quantification of spin relaxation times in the hybrid state

PURPOSE

The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state.

METHODS

Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for T 1 -encoding, T 2 -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain.

RESULTS

After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance T 1 - and T 2 -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost.

CONCLUSIONS

We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of T 1 and T 2 in the hybrid state are substantially more efficient than sequential encoding techniques.

Iron, Myelin, and the Brain: Neuroimaging Meets Neurobiology

Although iron is crucial for neuronal functioning, many aspects of cerebral iron biology await clarification. The ability to quantify specific iron forms in the living brain would open new avenues for diagnosis, therapeutic monitoring, and understanding pathogenesis of diseases. A modality that allows assessment of brain tissue composition in vivo, in particular of iron deposits or myelin content on a submillimeter spatial scale, is magnetic resonance imaging (MRI). Multimodal strategies combining MRI with complementary analytical techniques ex vivo have emerged, which may lead to improved specificity. Interdisciplinary collaborations will be key to advance beyond simple correlative analyses in the biological interpretation of MRI data and to gain deeper insights into key factors leading to iron accumulation and/or redistribution associated with neurodegeneration.

Spin echoes: full numerical solution and breakdown of approximative solutions

The spin echo signal from vessels in Krogh's capillary model as well in the random distribution vessel model are studied by numerically solving the Bloch-Torrey equation. A comparison is made with the Gaussian local phase approximation, the Gaussian phase approximation and the strong-collision approximation. Differences between the Gaussian local phase approximation and the Gaussian phase approximation are explained. In the intermediate diffusion regime, the full numerical solution shows oscillations which are absent in any of the approximate solutions. In the limit of large diffusion coefficients, where the approximations become exact, the signal shows a linear-exponential decay governed by a single parameter. The features of the exact numerical solution can be explained by an analytically solvable discrete two-level model. There is a one-to-one correspondence between the different diffusion regimes and the three cases of the damped harmonic oscillator.

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.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.

The Kärger vs bi-exponential model: Theoretical insights and experimental validations

We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the Kärger model, and a modified Kärger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The Kärger model and the modified Kärger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.