1. Macroscopic magnetic susceptibility at the scale of a MR imaging voxel is anisotropic in certain types of tissue with highly ordered microstructure such as white matter fibers

2. Susceptibility anisotropy may be mapped by susceptibility tensor imaging (STI) using MR phase measurements collected at different sample orientations with respect to the main field

3. Susceptibility related MR measures that are orientation dependent such as R2* and frequency difference may also be used to image tissue anisotropy

MR researchers and clinicians interested in learning the principles and methods for measuring tissue magnetic susceptibility anisotropy and susceptibility tensor imaging

After this lecture, the participants would be able to

1. Understand the basic evidence for anisotropy of the magnetic susceptibility in tissue and the need to use a susceptibility tensor model

2. Understand the basic theory of susceptibility tensor imaging (STI) and how to generate susceptibility tensor maps using MRI phase measurements

3. Better understand and interpret the orientation dependent susceptibility related contrast in anisotropic tissue

1. Overview:

Magnetic susceptibility is a physical property defined as the degree of magnetization of a material in response to an applied magnetic field. Magnetic susceptibility may be isotropic or anisotropic in different materials. For example, asymmetric macromolecules such as lipids, proteins and DNAs are known to have a large anisotropic magnetic susceptibility (1-3), but even small molecules have such anisotropy (4). If magnetic susceptibility is anisotropic the induced magnetization in response to an applied field will depend upon the orientation of the sample material with respect to the field and magnetization is induced in directions other than that of the applied field.

Measuring tissue magnetic susceptibility is possible using MRI. Spatial variations of tissue magnetic susceptibility lead to local magnetic field variations and corresponding MR resonance frequency variations. These can be sensitively detected and mapped using MR phase imaging with gradient echo (GRE) sequences (5). However, the calculation of magnetic susceptibilities from such images is complex because an ill-posed phase-to-susceptibility inverse problem has to be solved. Fortunately quantitative susceptibility mapping (QSM) techniques have been designed to address this and allow calculation of the voxel-based magnetic susceptibility (6-12).

In contrast to the isotropic magnetic susceptibility in gray matter, which is believed to be determined mainly by tissue iron concentration (13-16), many studies have shown that macroscopic susceptibility in white matter is in fact anisotropic due to the cumulative molecular susceptibility anisotropy of well-aligned myelin lipids (17-23). Such anisotropic susceptibility at macroscopic level may be modeled as a second order tensor and mapped with MR phase measurements collected at different sample orientations with respect to the main field using susceptibility tensor imaging (STI) (19). STI has been applied to image susceptibility anisotropies ex vivo in mouse brain (24) and in vivo in human brain (20,25,26). In addition, using similar GRE sequences, other orientation dependent MR measures that are determined by the underlying anisotropic susceptibility or microstructure such as R2* and frequency differences may also be used to map tissue anisotropy (27-29).

2. Evidence of macroscopic susceptibility anisotropy in brain white matter

It is known that MR phase or resonance frequency (phase scaled by echo time) is non-local and depends on head orientation (30-32). However, besides such orientation dependence, some pilot studies found that MR phase in white matter also depends on the orientation of white matter fibers with respect to the main magnetic field in a manner that cannot be explained solely by its isotropic volume susceptibility (17,18,33). Such orientation dependence of MR phase in white matter has been attributed to the elongated axonal and cylindrically shaped cellular structures and compartments in white matter fiber (17). In another study, Lee et al. confirmed the dependence of MR phase or frequency on the white matter microstructure orientation using postmortem tissue samples by an experimental design that allowed separation of microstructural contributions and possible confounding macrostructural effects (18). The data showed that white matter fibers were more diamagnetic when perpendicular to the main field than when parallel to the field. In addition, nonlocal phase variations were observed outside the tissue sample caused by changing only the microstructural orientations of some tissue segments, which may be explained more appropriately by macroscopic anisotropic susceptibility in those white matter fibers (18). At about the same time, Liu also observed anisotropic frequency and susceptibility in mouse brains ex vivo and further proposed to use a symmetric second-order tensor to model this effect (19). With further developed QSM techniques, many later studies using single-orientation QSM have also reported consistently that magnetic susceptibility in brain white matter, both ex vivo in mouse brain and in vivo in human brain, is anisotropic and depends on the orientation of the fibers relative to the magnetic field (12,20,25,34).

3. Susceptibility tensor imaging

Similar to the relationship between isotropic magnetic susceptibility and MR frequency shift in k space used in QSM (6), a relationship between the susceptibility tensor $$$\bf\chi$$$ and MR frequency shift in k space was also derived as in the following equation (19)

$$\frac{f(\bf k)}{\gamma B_{0}}=\frac{1}{3}\hat {\bf H}^{T}FT(\bf\chi)\hat{\bf H}-{\bf k}^{\it T}\hat{\bf H}\frac{{\bf k}^{\it T}{\it FT}(\bf\chi)\hat{\bf H}}{k^{2}} $$

Here the susceptibility tensor $$$\bf\chi$$$ represents a real and symmetric 3x3 second order tensor; $$$\hat{\bf H}$$$ is the unit vector of the applied field (commonly defined as the z direction in the laboratory frame of reference); $$$\bf k$$$ is the spatial frequency vector; FT represents the Fourier Transform and the term 1/3 corresponds to a correction using the sphere of Lorentz. $$$f(\bf k)$$$ is the MR frequency shift in k space, and $$$\gamma $$$ is the gyromagnetic ratio.

Based on this relationship, susceptibility tensor imaging (STI) aims at mapping the susceptibility tensor with 6 unknown tensor components for each voxel with measurements of MR phase or frequency shift collected at 6 or more head orientations with respect to the main magnetic field. Experimentally STI data acquisition is typically achieved by physically rotating the brain inside the MRI scanner multiple times and collecting the GRE phase data at each brain position (20,24). After image acquisition, STI requires image coregistration and similar phase preprocessing as used in QSM, which includes, 3D phase unwrapping (34-36) and background phase removal (15,37-39). After phase preprocessing, with the coregistered phase from multiple head orientations, susceptibility tensors can then be estimated using either k-space based methods (19,20,24) or image-space based methods (29,40) with appropriate inverse regularization. The estimated susceptibility tensor can be further decomposed into three eigenvalues and the corresponding eigenvectors and tractography can be obtained similar as using DTI (24,41). In addition, using priori information such as fiber directions as estimated from DTI and assuming cylindrical symmetry of the susceptibility tensor, GRE phase data acquired at fewer than 6 head orientations may be used to estimate some orientation independent tensor components such as the mean magnetic susceptibility and the susceptibility anisotropy (25,26). Besides its applications in the brain, STI has also been explored to study tissue anisotropy of other organs such as the heart (42) and kidney (43).

4. Mapping tissue anisotropy with other susceptibility related measures

Besides MR phase or frequency shift, other susceptibility related MR measures such as R2* have also been found to depend on the fiber microstructure orientations with respect to the main field (27,28,33,44,45). In addition, studies have shown that the molecular susceptibility anisotropy of myelin lipids and the multi-compartment effect, i.e. the water protons in axon, myelin and extracellular space having different relaxation rates and susceptibility induced frequency shifts, are the main mechanisms underlying the nonlinear phase evolution in white matter (21,46). Based on that, frequency difference mapping (FDM) based on comparing MR frequency shifts at short and long TE ranges was recently proposed to be a sensitive measure of local microstructure without the confounding nonlocal effects as in frequency shift measurements (21). With multiple echo GRE data collected at different sample orientations, a general model linking R2* or frequency difference and the fiber angle can be fitted to image the corresponding tissue anisotropy and fiber directions (27,28).

A spectrum analysis based on a multi-pole magnetic response or p-space MRI has also been proposed to map tissue anisotropy in white matter without rotating the brain (47). By applying a gradient field before the normal GRE sequence or by shifting the k-space reconstruction window, the p-space method aims at detecting sub-voxel field variations in white matter fibers at different angles relative to the main field. However, the practical utility of this approach for human brain imaging in vivo is still a subject of debate (48).

One big challenge of mapping tissue anisotropy using STI, R2* or FDM is the requirement of rotating the sample inside the magnet. This is not a significant concern for ex vivo experiments using fixed specimens, as the rotation of the tissue sample inside the magnet is only constrained by the coil size. However, it is the major challenge for in vivo studies due to the physical constraints on head or body rotation and long scan time. Currently, the quality of STI is still not as good as that of DTI (41). However, STI offers powerful advantages in terms of higher spatial resolution, reduced gradient strength requirements and lower SAR compared to diffusion weighted MRI. Better modeling such as the consideration of multi-compartment effects and the generalized Lorentzian correction (49,50) may need to be incorporated in STI in the future.