Larmor frequency in heterogeneous media

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.

Recommended implementation of quantitative susceptibility mapping for clinical research in the brain: A consensus of the ISMRM electro-magnetic tissue properties study group

This article provides recommendations for implementing QSM for clinical brain research. It is a consensus of the International Society of Magnetic Resonance in Medicine, Electro-Magnetic Tissue Properties Study Group. While QSM technical development continues to advance rapidly, the current QSM methods have been demonstrated to be repeatable and reproducible for generating quantitative tissue magnetic susceptibility maps in the brain. However, the many QSM approaches available have generated a need in the neuroimaging community for guidelines on implementation. This article outlines considerations and implementation recommendations for QSM data acquisition, processing, analysis, and publication. We recommend that data be acquired using a monopolar 3D multi-echo gradient echo (GRE) sequence and that phase images be saved and exported in Digital Imaging and Communications in Medicine (DICOM) format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background field removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields within the brain mask should be removed using a technique based on SHARP or PDF, and the optimization approach to dipole inversion should be employed with a sparsity-based regularization. Susceptibility values should be measured relative to a specified reference, including the common reference region of the whole brain as a region of interest in the analysis. The minimum acquisition and processing details required when reporting QSM results are also provided. These recommendations should facilitate clinical QSM research and promote harmonized data acquisition, analysis, and reporting.

Exploiting gradient-echo frequency evolution: Probing white matter microstructure and extracting bulk susceptibility-induced frequency for quantitative susceptibility mapping

PURPOSE

This work is to investigate the microstructure-induced frequency shift in white matter (WM) with crossing fibers and to separate the microstructure-related frequency shift from the bulk susceptibility-induced frequency shift by model fitting the gradient-echo (GRE) frequency evolution for potentially more accurate quantitative susceptibility mapping (QSM).

METHODS

A hollow-cylinder fiber model (HCFM) with two fiber populations was developed to investigate GRE frequency evolutions in WM voxels with microstructural orientation dispersion. The simulated and experimentally measured TE-dependent local frequency shift was then fitted to a simplified frequency evolution model to obtain a microstructure-related frequency difference parameter (∆ f $$ \Delta f $$ ) and a TE-independent bulk susceptibility-induced frequency shift (C f $$ {C}_f $$ ). The obtainedC f $$ {C}_f $$ was then used for QSM reconstruction. Reconstruction performances were evaluated using a numerical head phantom and in vivo data and then compared to other multi-echo combination methods.

RESULTS

GRE frequency evolutions and∆ f $$ \Delta f $$ -based tissue parameters in both parallel and crossing fibers determined from our simulations were comparable to those observed in vivo. The TE-dependent frequency fitting method outperformed other multi-echo combination methods in estimatingC f $$ {C}_f $$ in simulations. The fitted∆ f $$ \Delta f $$ ,C f $$ {C}_f $$ , and QSM could be improved further by navigator-based B0 fluctuation correction.

CONCLUSION

A HCFM with two fiber populations can be used to characterize microstructure-induced frequency shifts in WM regions with crossing fibers. HCFM-based TE-dependent frequency fitting provides tissue contrast related to microstructure (∆ f $$ \Delta f $$ ) and in addition may help improve the quantification accuracy ofC f $$ {C}_f $$ and the corresponding QSM.

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.

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.

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.

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.

Susceptibility Perturbation MRI Maps Tumor Infiltration into Mesorectal Lymph Nodes

Noninvasive characterization of lymph node involvement in cancer is an enduring onerous challenge. In rectal cancer, pathologic lymph node status constitutes the most important determinant of local recurrence and overall survival, and patients with involved lymph nodes may benefit from preoperative chemo and/or radiotherapy. However, knowledge of lymph node status before surgery is currently hampered by limited imaging accuracy. Here, we introduce Susceptibility-Perturbation MRI (SPI) as a novel source of contrast to map malignant infiltration into mesorectal lymph nodes. SPI involves multigradient echo (MGE) signal decays presenting a nonmonoexponential nature, which we show is sensitive to the underlying microstructure via susceptibility perturbations. Using numerical simulations, we predicted that the large cell morphology and the high cellularity of tumor within affected mesorectal lymph nodes would induce signature SPI decays. We validated this prediction in mesorectal lymph nodes excised from total mesorectal excision specimens of patients with rectal cancer using ultrahigh field (16.4 T) MRI. SPI signals distinguished benign from malignant nodal tissue, both qualitatively and quantitatively, and our histologic analyses confirmed cellularity and cell size were the likely underlying sources for the differences observed. SPI was then adapted to a clinical 1.5 T scanner, added to patients' staging protocol, and compared with conventional assessment by two expert radiologists. Nonmonoexponential decays, similar to those observed in the ex vivo study, were demonstrated, and SPI classified lymph nodes more accurately than standard high-resolution T₂-weighted imaging assessment. These findings suggest this simple, yet highly informative, method can improve rectal cancer patient selection for neoadjuvant therapy. SIGNIFICANCE: These findings introduce an MRI methodology tailored to detect magnetic susceptibility perturbations induced by subtle alterations in tissue microstructure.