Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

Susceptibility-induced internal gradients reveal axon morphology and cause anisotropic effects in the diffusion-weighted MRI signal

Diffusion-weighted MRI is our most promising method for estimating microscopic tissue morphology in vivo. The signal acquisition is based on scanner-generated external magnetic gradients. However, it will also be affected by susceptibility-induced internal magnetic gradients caused by interactions between the tissue and the static magnetic field of the scanner. With 3D in silico experiments, we show how internal gradients cause morphology-, compartment-, and orientation-dependence of spin-echo and pulsed-gradient spin-echo experiments in myelinated axons. These effects surpass those observed with previous 2D modelling corresponding to straight cylinders. For an ex vivo monkey brain, we observe the orientation-dependence generated only when including non-circular cross-sections in the in silico morphological configurations, and find orientation-dependent deviation of up to 17% for diffusion tensor metrics. Interestingly, we find that the orientation-dependence not only biases the signal across different brain regions, but also carries a sensitivity to the morphology of axonal cross-sections which is not attainable by the idealised theoretical diffusion-weighted MRI signal.

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.

High angular resolution susceptibility imaging and estimation of fiber orientation distribution functions in primate brain

Uncovering brain-tissue microstructure including axonal characteristics is a major neuroimaging research focus. Within this scope, anisotropic properties of magnetic susceptibility in white matter have been successfully employed to estimate primary axonal trajectories using mono-tensorial models. However, anisotropic susceptibility has not yet been considered for modeling more complex fiber structures within a voxel, such as intersecting bundles, or an estimation of orientation distribution functions (ODFs). This information is routinely obtained by high angular resolution diffusion imaging (HARDI) techniques. In applications to fixed tissue, however, diffusion-weighted imaging suffers from an inherently low signal-to-noise ratio and limited spatial resolution, leading to high demands on the performance of the gradient system in order to mitigate these limitations. In the current work, high angular resolution susceptibility imaging (HARSI) is proposed as a novel, phase-based methodology to estimate ODFs. A multiple gradient-echo dataset was acquired in an entire fixed chimpanzee brain at 61 orientations by reorienting the specimen in the magnetic field. The constant solid angle method was adapted for estimating phase-based ODFs. HARDI data were also acquired for comparison. HARSI yielded information on whole-brain fiber architecture, including identification of peaks of multiple bundles that resembled features of the HARDI results. Distinct differences between both methods suggest that susceptibility properties may offer complementary microstructural information. These proof-of-concept results indicate a potential to study the axonal organization in post-mortem primate and human brain at high resolution.