Synopsis
Many recent studies have found out that macroscopic
magnetic susceptibility at the scale of a MR imaging voxel is anisotropic in
tissues with ordered microstructure such as white matter fibers. This lecture
reviews some of such experimental evidences and introduces methods to map such
tissue anisotropy. First, we go over the theory, acquisition and processing methods
of susceptibility tensor imaging (STI) which uses MR phase measurements collected at different sample orientations with respect to
the main field. We then review some other mapping methods using susceptibility
related MR measures that are orientation dependent such as R2* and frequency
difference.Highlights
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
Target Audience
MR researchers and clinicians interested in learning the principles and methods for measuring tissue magnetic susceptibility anisotropy and susceptibility tensor imaging
Objectives
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
Methods
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).
Discussion
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.
Acknowledgements
NIH P41 EB015909References
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