Alexandra Grace Roberts1,2, Ilhami Kovanlikaya2, Brian Koppel3, Pascal Spincemaille2, Thanh Nguyen2, and Yi Wang1,2
1Electrical Engineering, Cornell University, Ithaca, NY, United States, 2Radiology, Weill Cornell Medicine, New York, NY, United States, 3Radiology, Mount Sinai Hospital, New York, NY, United States
Synopsis
Keywords: Parkinson's Disease, Brain
Morphology Enabled Dipole Inversion (MEDI) is an iterative reconstruction
algorithm for Quantitative Susceptibility Mapping (QSM) that is effective in
suppressing artifacts by exploiting the magnitude image as a morphological
prior. Use of a phase prior such as the local field to determine the
$$$L_1$$$ regularization term results in improved
visualization of the medial medullary lamina as measured by the
contrast-to-noise ratio and was preferred by a radiologist over the magnitude
prior in each case.
Introduction
Quantitative Susceptibility Mapping
(QSM) is an MRI contrast mapping the magnetic susceptibility of tissue in vivo
from gradient echo measurements. The inverse problem in QSM is ill-posed
requiring the use of regularization. Bayesian
inference approaches such as Morphology Enabled Dipole Inversion (MEDI) use an
edge-weighted gradient under an
norm to penalize the streaking and shadowing artifacts
arising from dipole-incompatible sources (such as noise) in the phase of the
gradient echo data [1], [2], [3]. This is achieved by computing the gradient of the morphological prior
and penalizing edges in the reconstruction outside of this gradient. Reduced
contrast in the magnitude image can lead to smoothing of fine structures [4]
such as the medial medullary lamina (MML), portions of which derive from nerve fibers
of the striatum [5]. MLL can be used to define the globus pallidus internus
(GPi) which is targeted for deep brain stimulation in the treatment of
Parkinson’s disease [6]. The use of a phase-based prior (the local field) is
compared to the conventional magnitude prior for the visualization of the
medial medullary lamina using the metrics of contrast-to-noise ratio (CNR) and radiologist preference.Theory
The cost function in MEDI+0 [7] is: $$\chi^*(r)=\mathrm{argmin}_{\chi}(‖w(e^{ib}-e^{id*\chi} )‖_2^2+λ_1‖M_M \nabla\chi‖_1+λ_2‖M_{CSF} (χ-\bar{\chi}_{CSF})‖_2^2) \tag{1}$$
where
$$$b$$$ is the
relative difference field, $$$d$$$ the dipole
kernel,
$$$\chi$$$ the susceptibility,
$$$w$$$ the noise weighting matrix,
$$$M_M$$$ morphological weighting matrix,
$$$\nabla$$$ the gradient,
$$$M_{CSF}$$$ is
the CSF mask and $$$\bar{\chi}$$$ the
mean susceptibility within such mask. The morphological weighting matrix
$$$M_M$$$, or edge mask, is typically acquired by
thresholding ($$$T$$$)
the gradient of the magnitude image, $$$M_M=T(\nabla|S_0|)$$$
. The relative difference field, or local
field
$$$b$$$, here called a “phase prior” is defined
as
$$$M_P=T(\nabla|b|)$$$
and replaces
$$$M_M$$$ (the magnitude prior) in the cost function to give $$\chi^*(r)=\mathrm{argmin}_{\chi}(‖w(e^{ib}-e^{id*\chi} )‖_2^2+λ_1‖M_P
\nabla\chi‖_1+λ_2‖M_{CSF} (χ-\bar{\chi}_{CSF})‖_2^2) \tag{2}$$Methods
Ten patients were
scanned at 3T (GE Healthcare) using a 3D multi-echo spoiled gradient echo
sequence. Acquisition parameters were FOV = 25.6 cm, partial FOV factor = 0.8,
acquisition matrix size = 320 × 320 × 180, flip angle = 15°, slice thickness = 1
mm, TR = 49 ms, number of echoes = 10, first TE = 4.2 ms, echo spacing = 4.9
ms, parallel imaging factor 2, scan time of ~15 minutes. Each QSM was
reconstructed using Equation 1 after nonlinear fitting and region-growing phase
unwrapping, [8] projection onto dipole fields (PDF) background field removal [9],
and a spherical mean value (SMV) [10] kernel of 5 mm. Regularization
parameters were
$$$\lambda_1=1000$$$, $$$\lambda_2=100$$$
. For each
patient, separate QSMs were reconstructed using the gradient of magnitude and
phase prior to generate the edge mask
. The QSMs were presented to an experienced (more than 20 years)
neuroradiologist, who selected the map with superior MML visualization. The QSM
with superior MML visualization was then segmented as shown in Figure 2. The
CNR at each boundary was calculated using the standard deviation of
susceptibility within the head of the caudate nucleus as a noise reference. The
boundaries assessed were the external MML boundary (MML-GPe) and the internal
MML boundary (MML-GPi) on the left and right side of the brain. Improvements in
the CNR were assessed with a Wilcoxon signed rank test.Results
The phase prior QSM reconstructions provided superior MML
visualization according to the radiologist. An example comparison is shown in
Figure 3. This qualitative finding is consistent with the increased
CNR shown in Figure 4. All CNR improvements were found to
be significant at
$$$\alpha=0.01$$$.Discussion
As noted in [11], QSM and the
magnitude
image will generate different contrasts due to differences in the underlying
signal generation. Spatial variation in coil sensitivity may reduce the local
effectiveness of the magnitude prior due to global thresholding. It is
speculated that the phase image does not suffer from this effect at adequate
signal-to-noise ratio (SNR). In the magnitude image, the signal is generated by the precession of
protons in water molecules following radio-frequency (RF) excitation. Additionally,
variations in myelin content were identified as the source of phase contrast
between cortical gray and white matter [12] and contrast on the MML QSM is
thought to be due to the presence of myelin in the nerve fibers [13], which
provides diamagnetic susceptibility contributions. Since the phase image
reflects the field generated by tissue susceptibility, it is sensitive to iron
deposition and myelin content in the components of the globus pallidus and an
alternative prior for QSM reconstruction when the MML is of interest.Acknowledgements
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