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Improved Visualization of the Medial Medullary Lamina with Phase Prior Reconstruction in Quantitative Susceptibility Mapping
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

No acknowledgement found.

References

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Figures

Figure 1. Location of the medial medullary lamina (MML) relative to the implant target, putamen, globus pallidus internus (GPi), and globus pallidus externus (GPe). Figure adapted from [5].

Figure 2. ROI segmentation for CNR calculation: Left GPe (red), left MML (green), left GPi (blue), right GPi (pink), right MML (teal), right GPe (yellow), noise reference (tan).

Figure 3. Improved delineation of the MML in the phase prior QSM (left, Equation 2) versus the magnitude prior QSM (right, Equation 1).

Figure 4. Statistically significant ($$$p=9.77\times10^{-4}$$$) CNR improvements in MML susceptibility.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)
1391
DOI: https://doi.org/10.58530/2023/1391