Frequency shifts in the myelin water compartment

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.

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.

Fiber-orientation independent component of R2* obtained from single-orientation MRI measurements in simulations and a post-mortem human optic chiasm

The effective transverse relaxation rate (R2*) is sensitive to the microstructure of the human brain like the g-ratio which characterises the relative myelination of axons. However, the fibre-orientation dependence of R2* degrades its reproducibility and any microstructural derivative measure. To estimate its orientation-independent part (R2,iso*) from single multi-echo gradient-recalled-echo (meGRE) measurements at arbitrary orientations, a second-order polynomial in time model (hereafter M2) can be used. Its linear time-dependent parameter, β1, can be biophysically related to R2,iso* when neglecting the myelin water (MW) signal in the hollow cylinder fibre model (HCFM). Here, we examined the performance of M2 using experimental and simulated data with variable g-ratio and fibre dispersion. We found that the fitted β1 can estimate R2,iso* using meGRE with long maximum-echo time (TEmax ≈ 54 ms), but not accurately captures its microscopic dependence on the g-ratio (error 84%). We proposed a new heuristic expression for β1 that reduced the error to 12% for ex vivo compartmental R2 values. Using the new expression, we could estimate an MW fraction of 0.14 for fibres with negligible dispersion in a fixed human optic chiasm for the ex vivo compartmental R2 values but not for the in vivo values. M2 and the HCFM-based simulations failed to explain the measured R2*-orientation-dependence around the magic angle for a typical in vivo meGRE protocol (with TEmax ≈ 18 ms). In conclusion, further validation and the development of movement-robust in vivo meGRE protocols with TEmax ≈ 54 ms are required before M2 can be used to estimate R2,iso* in subjects.

Quantitative Study of the Changes in Cerebral Blood Flow and Iron Deposition During Progression of Alzheimer's Disease

BACKGROUND

Advanced Alzheimer's disease (AD) has no effective treatment, and identifying early diagnosis markers can provide a time window for treatment.

OBJECTIVE

To quantify the changes in cerebral blood flow (CBF) and iron deposition during progression of AD.

METHODS

94 subjects underwent brain imaging on a 3.0-T MRI scanner with techniques of three-dimensional arterial spin labeling (3D-ASL) and quantitative susceptibility mapping (QSM). The subjects included 22 patients with probable AD, 22 patients with mild cognitive impairment (MCI), 25 patients with subjective cognitive decline (SCD), and 25 normal controls (NC). The CBF and QSM values were obtained using a standardized brain region method based on the Brainnetome Atlas. The differences in CBF and QSM values were analyzed between and within groups using variance analysis and correlation analysis.

RESULTS

CBF and QSM identified several abnormal brain regions of interest (ROIs) at different stages of AD (p < 0.05). Regionally, the CBF values in several ROIs of the AD and MCI subjects were lower than for NC subjects (p < 0.001). Higher QSM values were observed in the globus pallidus. The CBF and QSM values in multiple ROI were negatively correlated, while the putamen was the common ROI of the three study groups (p < 0.05). The CBF and QSM values in hippocampus were cross-correlated with scale scores during the progression of AD (p < 0.05).

CONCLUSION

Iron deposition in the basal ganglia and reduction in blood perfusion in multiple regions existed during the progression of AD. The QSM values in putamen can be used as an imaging biomarker for early diagnosis of AD.

On the separation of susceptibility sources in quantitative susceptibility mapping: Theory and phantom validation with an in vivo application to multiple sclerosis lesions of different age

PURPOSE

In biological tissue, phase contrast is determined by multiple substances such as iron, myelin or calcifications. Often, these substances occur co-located within the same measurement volume. However, quantitative susceptibility mapping can solely measure the average susceptibility per voxel. To provide new insight in disease progression and mechanisms in neurological diseases, where multiple processes such as demyelination and iron accumulation occur simultaneously in the same location, a separation of susceptibility sources is desirable to disentangle the underlying susceptibility proportions.

METHODS

The basic concept of separating the susceptibility effects from sources with different sign within one voxel is to include information on relaxation rate ΔR₂^∗ in the quantitative susceptibility mapping reconstruction pipeline. The presented reconstruction algorithm is implemented as a constrained minimization problem and solved using conjugate gradients. The algorithm is evaluated using a software phantom and validated in MRI measurements with a phantom containing mixtures of microscopic positive and negative susceptibility sources. Data from three multiple sclerosis patients are used to show in vivo feasibility.

RESULTS

In numerical simulations, the feasibility of disentangling susceptibility sources within the same voxel was confirmed provided the critera of the static dephasing regime were fulfilled. In phantom experiments, the magnitude decay kernel, which is an essential reconstruction parameter of the algorithm, was determined to be D_m=194.5T^-1s^-1ppm^-1, and susceptibility sources could be separated in MRI measurement data.

CONCLUSIONS

In conclusion, in this study a detailed description of the implementation of an algorithm for the separation of positive and negative susceptibility sources within the same volume element as well as its limitations is presented and validated quantitatively in both simulation and phantom experiments for the first time. An application to multiple sclerosis lesions shows promising results for in vivo usability.

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.

Diffusion effects in myelin sheath free induction decay

Myelin sheath microstructure and composition produce MR signal decay characteristics that can be used to evaluate status and outcome of demyelinating disease. We extend a recently proposed model of neuronal magnetic susceptibility, that accounts for both the structural and inherent anisotropy of the myelin sheath, by including the whole dynamic range of diffusion effects. The respective Bloch-Torrey equation for local spin dephasing is solved with a uniformly convergent perturbation expansion method, and the resulting magnetization decay is validated with a numerical solution based on a finite difference method. We show that a variation of diffusion strengths can lead to substantially different MR signal decay curves. Our results may be used to adjust or control simulations for water diffusion in neuronal structures.

Quantitative Susceptibility MRI to Detect Brain Iron in Amyotrophic Lateral Sclerosis

Purpose To investigate the whole-brain landscape of iron-related abnormalities in amyotrophic lateral sclerosis (ALS) by using the in vivo MRI technique of quantitative susceptibility mapping (QSM). Materials and Methods For this prospective study, 28 patients with ALS (mean age, 61 years; age range, 43-77 years; 18 men [mean age, 61 years; range, 43-77 years] and 10 women [mean age, 61 years; range, 47-74 years]) recruited between January 17, 2014, and September 4, 2015, and 39 matched control subjects (mean age, 61 years; age range, 39-77 years; 24 men [mean age, 62 years; range, 39-77 years] and 15 women [mean age, 59 years; range, 39-73 years]) were examined by using structural and susceptibility 3.0-T MRI techniques. Group data were cross sectionally compared with family-wise error (FWE) corrections by using voxel-based morphometry (random-field theory), cortical thickness analysis (Monte Carlo simulated), subcortical volumetry (Bonferroni-corrected Wilcoxon rank-sum testing), and QSM analysis (cluster-enhanced whole-brain permutation testing and Bonferroni-corrected rank-sum testing in regions of interest). In patients with ALS, a potential relationship between diffusion and susceptibility measurements in the corticospinal tracts (CSTs) was also examined by using Spearman rank-correlation tests. Results Conventional structural measures failed to identify atrophy in the present cohort (FWE P > .05). However, QSM identified several whole-brain abnormalities (FWE P < .05) in ALS. Regionally, higher susceptibility (expressed as means in parts per million ± standard errors of the mean) was confirmed in the motor cortex (ALS = 0.0188 ± 0.0003, control = 0.0173 ± 0.0003; P < .001), the left substantia nigra (ALS = 0.127 ± 0.004, control = 0.113 ± 0.003; P = .008), the right substantia nigra (ALS = 0.141 ± 0.005, control = 0.120 ± 0.003; P < .001), the globus pallidus (ALS = 0.086 ± 0.003, control = 0.075 ± 0.002; P = .003), and the red nucleus (ALS = 0.115 ± 0.004, control = 0.098 ± 0.003; P < .001). Lower susceptibility was found in CST white matter (ALS = -0.047 ± 0.001, control = -0.043 ± 0.001; P = .01). Nigral and pallidal QSM values were cross correlated in ALS (ρ² = 0.42, P < .001), a phenomenon visually traceable in many individual patients. QSM in the CST in ALS also correlated with diffusion-tensor metrics in this tract (ρ² = 0.25, P = .007). Conclusion Whole-brain MRI quantitative susceptibility mapping analysis is sensitive to tissue alterations in amyotrophic lateral sclerosis that may be relevant to pathologic changes. © RSNA, 2018.

Lorentzian effects in magnetic susceptibility mapping of anisotropic biological tissues

The ultimate goal of MRI is to provide information on biological tissue microstructure and function. Quantitative Susceptibility Mapping (QSM) is one of the newer approaches for studying tissue microstructure by means of measuring phase of Gradient Recalled Echo (GRE) MRI signal. The fundamental question in the heart of this approach is: what is the relationship between the net phase/frequency of the GRE signal from an imaging voxel and the underlying tissue microstructure at the cellular and sub-cellular levels? In the presence of external magnetic field, biological media (e.g. cells, cellular components, blood) become magnetized leading to the MR signal frequency shift that is affected not only by bulk magnetic susceptibility but by the local cellular environment as well. The latter effect is often termed the Lorentzian contribution to the frequency shift. Evaluating the Lorentzian contribution - one of the most intriguing and challenging problems in this field - is the main focus of this review. While the traditional approach to this problem is based on introduction of an imaginary Lorentzian cavity, a more rigorous treatment was proposed recently based on a statistical approach and a direct solution of the Maxwell equations. This approach, termed the Generalized Lorentzian Tensor Approach (GLTA), is especially fruitful for describing anisotropic biological media. The GLTA adequately accounts for two types of anisotropy: anisotropy of magnetic susceptibility and tissue structural anisotropy (e.g., cylindrical axonal bundles in white matter). In the framework of the GLTA the frequency shift due to the local environment is described in terms of the Lorentzian tensor L̂ which can have a substantially different structure than the susceptibility tensor χ̂. While the components of χ̂ are compartmental susceptibilities "weighted" by their volume fractions, the components of L̂ are additionally weighted by specific numerical factors depending on cellular geometrical symmetry. In addition to describing the GLTA that is a phenomenological approach largely based on considering the system symmetry, we also briefly discuss a microscopic approaches to the problem that are based on modeling of the MR signal in different regimes (i.e. static dephasing vs. motion narrowing) and in different cellular environments (e.g., accounting for WM microstructure).

Extended phase graph formalism for systems with magnetization transfer and exchange

Purpose

An extended phase graph framework (EPG‐X) for modeling systems with exchange or magnetization transfer (MT) is proposed.

Theory

EPG‐X models coupled two‐compartment systems by describing each compartment with separate phase graphs that exchange during evolution periods. There are two variants: EPG‐X(BM) for systems governed by the Bloch‐McConnell equations, and EPG‐X(MT) for the pulsed MT formalism. For the MT case, the “bound” protons have no transverse components, so their phase graph consists of only longitudinal states.

Methods

The EPG‐X model was validated against steady‐state solutions and isochromat‐based simulation of gradient‐echo sequences. Three additional test cases were investigated: (i) MT effects in multislice turbo spin‐echo; (ii) variable flip angle gradient‐echo imaging of the type used for MR fingerprinting; and (iii) water exchange in multi‐echo spin‐echo T₂ relaxometry.

Results

EPG‐X was validated successfully against isochromat based transient simulations and known steady‐state solutions. EPG‐X(MT) simulations matched in‐vivo measurements of signal attenuation in white matter in multislice turbo spin‐echo images. Magnetic resonance fingerprinting–style experiments with a bovine serum albumin (MT) phantom showed that the data were not consistent with a single‐pool model, but EPG‐X(MT) could be used to fit the data well. The EPG‐X(BM) simulations of multi‐echo spin‐echo T₂ relaxometry suggest that exchange could lead to an underestimation of the myelin‐water fraction.

Conclusions

The EPG‐X framework can be used for modeling both steady‐state and transient signal response of systems exhibiting exchange or MT. This may be particularly beneficial for relaxometry approaches that rely on characterizing transient rather than steady‐state sequences. Magn Reson Med 80:767–779, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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.

Contributions to magnetic susceptibility of brain tissue

This review discusses the major contributors to the subtle magnetic properties of brain tissue and how they affect MRI contrast. With the increased availability of high-field scanners, the use of magnetic susceptibility contrast for the study of human brain anatomy and function has increased dramatically. This has not only led to novel applications, but has also improved our understanding of the complex relationship between MRI contrast and magnetic susceptibility. Chief contributors to the magnetic susceptibility of brain tissue have been found to include myelin as well as iron. In the brain, iron exists in various forms with diverse biological roles, many of which are now only starting to be uncovered. An interesting aspect of magnetic susceptibility contrast is its sensitivity to the microscopic distribution of iron and myelin, which provides opportunities to extract information at spatial scales well below MRI resolution. For example, in white matter, the myelin sheath that surrounds the axons can provide tissue contrast that is dependent on the axonal orientation and reflects the relative size of intra- and extra-axonal water compartments. The extraction of such ultrastructural information, together with quantitative information about iron and myelin concentrations, is an active area of research geared towards the characterization of brain structure and function, and their alteration in disease. Copyright © 2016 John Wiley & Sons, Ltd.

Contributions to magnetic susceptibility of brain tissue

This review discusses the major contributors to the subtle magnetic properties of brain tissue and how they affect MRI contrast. With the increased availability of high-field scanners, the use of magnetic susceptibility contrast for the study of human brain anatomy and function has increased dramatically. This has not only led to novel applications, but has also improved our understanding of the complex relationship between MRI contrast and magnetic susceptibility. Chief contributors to the magnetic susceptibility of brain tissue have been found to include myelin as well as iron. In the brain, iron exists in various forms with diverse biological roles, many of which are now only starting to be uncovered. An interesting aspect of magnetic susceptibility contrast is its sensitivity to the microscopic distribution of iron and myelin, which provides opportunities to extract information at spatial scales well below MRI resolution. For example, in white matter, the myelin sheath that surrounds the axons can provide tissue contrast that is dependent on the axonal orientation and reflects the relative size of intra- and extra-axonal water compartments. The extraction of such ultrastructural information, together with quantitative information about iron and myelin concentrations, is an active area of research geared towards the characterization of brain structure and function, and their alteration in disease. Copyright © 2016 John Wiley & Sons, Ltd.

Effects of biological tissue structural anisotropy and anisotropy of magnetic susceptibility on the gradient echo MRI signal phase: theoretical background

Quantitative susceptibility mapping is a potentially powerful technique for mapping tissue magnetic susceptibility from gradient recalled echo (GRE) MRI signal phase. In this review, we present up-to-date theoretical developments in analyzing the relationships between GRE signal phase and the underlying tissue microstructure and magnetic susceptibility at the cellular level. Two important phenomena contributing to the GRE signal phase are at the focus of this review - tissue structural anisotropy (e.g. cylindrical axonal bundles in white matter) and magnetic susceptibility anisotropy. One of the most intriguing and challenging problems in this field is calculating the so-called Lorentzian contribution to the phase shift induced by the local environment - magnetized tissue structures that have dimensions smaller than the imaging voxel (e.g. cells, cellular components, blood capillaries). In this review, we briefly discuss a "standard" approach to this problem, based on introduction of an imaginary Lorentzian cavity, as well as a more recent method - the generalized Lorentzian tensor approach (GLTA) - that is based on a statistical approach and a direct solution of the magnetostatic Maxwell equations. The latter adequately accounts for both types of anisotropy: the anisotropy of magnetic susceptibility and the structural tissue anisotropy. In the GLTA the frequency shift due to the local environment is characterized by the Lorentzian tensor L^, which has a substantially different structure than the susceptibility tensor χ^. While the components of χ^ are compartmental susceptibilities "weighted" by their volume fractions, the components of L^ are weighted by specific numerical factors depending on tissue geometrical microsymmetry. In multi-compartment structures, the components of the Lorentzian tensor also depend on the compartmental relaxation properties, hence the MR pulse sequence settings. Copyright © 2016 John Wiley & Sons, Ltd.

Heterogeneous anisotropic magnetic susceptibility of the myelin-water layers causes local magnetic field perturbations in axons

One goal of MRI is to determine the myelin water fraction in neural tissue. One approach is to measure the reduction in T₂ * arising from microscopic perturbations in the magnetic field caused by heterogeneities in the magnetic susceptibility of myelin. In this paper, analytic expressions for the induced magnetic field distribution are derived within and around an axon, assuming that the myelin susceptibility is anisotropic. Previous models considered the susceptibility to be piecewise continuous, whereas this model considers a sinusoidally varying susceptibility. Many conclusions are common in both models. When the magnetic field is applied perpendicular to the axon, the magnetic field in the intraaxonal space is uniformly perturbed, the magnetic field in the myelin sheath oscillates between the lipid and water layers, and the magnetic field in the extracellular space just outside the myelin sheath is heterogeneous. These field heterogeneities cause the spins to dephase, shortening T₂ *. When the magnetic field is applied along the axon, the field is homogeneous within water-filled regions, including between lipid layers. Therefore the spins do not dephase and the magnetic susceptibility has no effect on T₂ *. Generally, the response of an axon is given as the superposition of these two contributions. The sinusoidal model uses a different set of approximations compared with the piecewise model, so their common predictions indicate that the models are not too sensitive to the details of the myelin-water distribution. Other predictions, such as the sensitivity to water diffusion between myelin and water layers, may highlight differences between the two approaches. Copyright © 2016 John Wiley & Sons, Ltd.

Mechanisms of T2 * anisotropy and gradient echo myelin water imaging

In MRI, structurally aligned molecular or micro-organization (e.g. axonal fibers) can be a source of substantial signal variations that depend on the structural orientation and the applied magnetic field. This signal anisotropy gives us a unique opportunity to explore information that exists at a resolution several orders of magnitude smaller than that of typical MRI. In this review, one of the signal anisotropies, T₂ * anisotropy in white matter, and a related imaging method, gradient echo myelin water imaging (GRE-MWI), are explored. The T₂ * anisotropy has been attributed to isotropic and anisotropic magnetic susceptibility of myelin and compartmentalized microstructure of white matter fibers (i.e. axonal, myelin, and extracellular space). The susceptibility and microstructure create magnetic frequency shifts that change with the relative orientation of the fiber and the main magnetic field, generating the T₂ * anisotropy. The resulting multi-component magnitude decay and nonlinear phase evolution have been utilized for GRE-MWI, assisting in resolving the signal fraction of the multiple compartments in white matter. The GRE-MWI method has been further improved by signal compensation techniques including physiological noise compensation schemes. The T₂ * anisotropy and GRE-MWI provide microstructural information on a voxel (e.g. fiber orientation and tissue composition), and may serve as sensitive biomarkers for microstructural changes in the brain. Copyright © 2016 John Wiley & Sons, Ltd.

Mapping axonal density and average diameter using non-monotonic time-dependent gradient-echo MRI

White Matter (WM) microstructures, such as axonal density and average diameter, are crucial to the normal function of the Central Nervous System (CNS) as they are closely related with axonal conduction velocities. Conversely, disruptions of these microstructural features may result in severe neurological deficits, suggesting that their noninvasive mapping could be an important step towards diagnosing and following pathophysiology. Whereas diffusion based MRI methods have been proposed to map these features, they typically entail the application of powerful gradients, which are rarely available in the clinic, or extremely long acquisition schemes to extract information from parameter-intensive models. In this study, we suggest that simple and time-efficient multi-gradient-echo (MGE) MRI can be used to extract the axon density from susceptibility-driven non-monotonic decay in the time-dependent signal. We show, both theoretically and with simulations, that a non-monotonic signal decay will occur for multi-compartmental microstructures - such as axons and extra-axonal spaces, which were here used as a simple model for the microstructure - and that, for axons parallel to the main magnetic field, the axonal density can be extracted. We then experimentally demonstrate in ex-vivo rat spinal cords that its different tracts - characterized by different microstructures - can be clearly contrasted using the MGE-derived maps. When the quantitative results are compared against ground-truth histology, they reflect the axonal fraction (though with a bias, as evident from Bland-Altman analysis). As well, the extra-axonal fraction can be estimated. The results suggest that our model is oversimplified, yet at the same time evidencing a potential and usefulness of the approach to map underlying microstructures using a simple and time-efficient MRI sequence. We further show that a simple general-linear-model can predict the average axonal diameters from the four model parameters, and map these average axonal diameters in the spinal cords. While clearly further modelling and theoretical developments are necessary, we conclude that salient WM microstructural features can be extracted from simple, SNR-efficient multi-gradient echo MRI, and that this paves the way towards easier estimation of WM microstructure in vivo.

White matter shifts in MRI: Rehabilitating the Lorentz sphere in magnetic resonance

A thorough exposition and analysis of the role of the Lorentz sphere in magnetic resonance is presented from the fundamental standpoint of macroscopic magnetostatics. The analysis will be useful to those interested in understanding susceptibility and chemical shift contributions to frequency shifts in magnetic resonance. Though the topic is mature, recent research on white matter shifts in the brain promotes the notion of replacing the Lorentz sphere with a generalized Lorentzian cylinder, and has put into question the long standing spherical approach when elongated structures are present. The cavity shape issue can be resolved by applying Helmholtz's theorem, which can be expressed in a differential and an integral formulation. The general validity of the Lorentz sphere for any situation is confirmed. Furthermore, a clear exposition of the "generalized approach" is offered, using the language of Lorentz's theory. With the rehabilitation of the Lorentz sphere settled, one must consider alternative contributions to white matter shifts and a likely candidate is the effect of molecular environment on chemical shifts.

Advances in MRI-based computational neuroanatomy: from morphometry to in-vivo histology

PURPOSE OF REVIEW

Current computational neuroanatomy based on MRI focuses on morphological measures of the brain. We present recent methodological developments in quantitative MRI (qMRI) that provide standardized measures of the brain, which go beyond morphology. We show how biophysical modelling of qMRI data can provide quantitative histological measures of brain tissue, leading to the emerging field of in-vivo histology using MRI (hMRI).

RECENT FINDINGS

qMRI has greatly improved the sensitivity and specificity of computational neuroanatomy studies. qMRI metrics can also be used as direct indicators of the mechanisms driving observed morphological findings. For hMRI, biophysical models of the MRI signal are being developed to directly access histological information such as cortical myelination, axonal diameters or axonal g-ratio in white matter. Emerging results indicate promising prospects for the combined study of brain microstructure and function.

SUMMARY

Non-invasive brain tissue characterization using qMRI or hMRI has significant implications for both research and clinics. Both approaches improve comparability across sites and time points, facilitating multicentre/longitudinal studies and standardized diagnostics. hMRI is expected to shed new light on the relationship between brain microstructure, function and behaviour, both in health and disease, and become an indispensable addition to computational neuroanatomy.

Detection of demyelination in multiple sclerosis by analysis of [Formula: see text] relaxation at 7 T

Multiple sclerosis (MS) is a relatively common cause of inflammatory demyelinating lesions of the central nervous system. In an attempt to detect and characterize ongoing demyelination in MS patient brains, we used a novel magnetic resonance imaging (MRI) technique, involving the fitting of a three-component model to the [Formula: see text] relaxation behavior at high-field (7 T). This model allowed estimation of the amount of myelin water (and thus indirectly myelin content), axonal water, and interstitial water. In this study, 25 relapsing-remitting MS patients underwent a 7 T MRI from which 12 gadolinium-enhancing lesions, 61 non-enhancing lesions, and their corresponding contralateral normal appearing white matter (NAWM) regions were analyzed. In both enhancing and non-enhancing lesions, the amplitude of myelin water was significantly decreased, and interstitial and axonal water were increased relative to the contralateral NAWM. Longer relaxation time [Formula: see text] of interstitial and axonal water, and lower frequency shift of axonal water, were also observed in both enhancing and non-enhancing lesions when compared to the contralateral NAWM. No significant difference was found between enhancing lesions and non-enhancing lesions. These findings suggest that the fitting of a three-component model to the [Formula: see text] decay curve in MS lesions may help to quantify myelin loss.

Generalized Lorentzian Tensor Approach (GLTA) as a biophysical background for quantitative susceptibility mapping

PURPOSE

Quantitative susceptibility mapping (QSM) is a potentially powerful technique for mapping tissue magnetic susceptibility from gradient recalled echo (GRE) MRI. Herein we aim to derive the relationships between GRE signal phase and the underlying tissue microstructure and magnetic susceptibility at the cellular level.

METHODS

We use Maxwell's equations and a statistical approach to derive the expression for the magnetic-susceptibility-induced MR signal frequency shift of the GRE signal in single- and multicompartment systems, in which inhomogeneous magnetic field is induced by the cellular constituents (proteins, lipids, iron, etc.) distributed in intra- and extracellular spaces.

RESULTS

We introduce the Generalized Lorentzian Tensor Approach (GLTA) that accounts for both types of anisotropy: the anisotropy of magnetic susceptibility and the structural tissue anisotropy. In the GLTA the frequency shift due to the local environment is characterized by the Lorentzian tensor L⁁ which has a substantially different structure than the susceptibility tensor χ⁁. While components of χ⁁ are simply compartmental susceptibilities "weighted" by their relative volumes, the components of L⁁ are weighted by specific numerical factors depending on tissue micro-symmetry and parameters related to the MR pulse sequence. We also provide equations bridging phenomenological and microscopic considerations.

CONCLUSION

The GLTA provides a consistent background for deciphering phase data.