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Regularized CG-SENSE for 30-channel 23Na head MRI at 7T1Medical Physics in Radiology, German Cancer Research Center, Heidelberg, Germany, 2Institute of Radiology, University Hospital Erlangen, Erlangen, Germany
Synopsis
23Na MRI provides important information for many pathologies. However, its low SNR entails low spatial resolutions and long acquisition times. The proposed work reconstructs 3D radially undersampled in vivo 30-channel 23Na head data at B0=7T with a sensitivity encoding using a nonlinear conjugate gradient method (CG-SENSE) including a total variation and a discrete cosine transform. With CG-SENSE using iteratively generated Lagrangian coil sensitivities, image quality and contrast within the object are improved compared to sum of squares (SOS) and adaptive combination (ADC) reconstructions.
Introduction
MRI of Sodium (23Na) possesses high diagnostic potential for a variety of physiological processes1. The inherently low signal-to-noise ratio (SNR) and the fast transverse relaxation lead to low spatial resolutions and long acquisition times in 23Na MRI; these challenges can only partly be alleviated using ultra-high field MR systems and ultra-short echo time sequences2,3. Parallel Imaging and Compressed Sensing4 shorten acquisition times and enable image reconstructions with reduced artifacts5. The combination of both, as in the case of nonlinear conjugate gradient sensitivity encoding (CG-SENSE), enables further shortening of the acquisition times and an increased SNR, making this technique highly attractive for 23Na MRI applications. This work investigates the reconstruction of undersampled in vivo 30-channel 23Na head data of a healthy volunteer using CG-SENSE with nonhomogeneous coil sensitivities.Methods
CG-SENSE iteratively minimizes the following cost function using a nonlinear conjugate gradient algorithm6:
$$\bf{ \arg\min_m||FCm -
y||_2^2 +\sum_{i=1}^N{\lambda_i || \Psi_i m ||_1},}$$
where $$$\bf{F}$$$ is a non-uniform fast Fourier transform operator (NUFFT)7, $$$\bf{C}$$$ are the coil sensitivities, $$$\bf{m}$$$ is the reconstructed image, $$$\bf{y}$$$ are the k-space data, and $$$\bf{\Psi_i}$$$ is one of $$$\bf{N}$$$ sparsifying transform operators with $$$\bf{\lambda_i}$$$ as its corresponding regularization tuning constant. In this work, three differently generated coil sensitivities $$$\bf{C}$$$ are used. The conventional sum of squares (SOS) and birdcage (BC) coil sensitivities are created by dividing each gaussian filtered and phase-corrected individual coil image by the SOS or BC image, respectively. The Lagrangian coil sensitivities $$$\bf{C_{opt}}$$$ are generated by minimizing another cost function using an iterative Augmented Lagrangian Method8:
$$\bf{C_{opt}\stackrel{\wedge}{=} \arg\min_C \frac{1}{2} ||Z-DC||_W^2 + \frac{\lambda}{2}||RC||_2^2 ,}$$
where $$$\bf{Z}$$$ are the single-coil images, $$$\bf{D}$$$ is the BC image, $$$\bf{C}$$$ are the coil sensitivities, $$$\bf{W}$$$ is a weighting matrix, $$$\bf{\lambda}$$$ is a regularization tuning constant, and $$$\bf{R}$$$ is a finite difference matrix. The weighting matrix acts as a threshold and is subjectively adjusted to the noise level of the BC image. The 23Na data were acquired using a density-adapted 3D radial projection pulse sequence2 on a 7T whole body MR system (MAGNETOM 7T, Siemens Healthcare GmbH, Erlangen, Germany) and a double-resonant 1H/23Na Tx/Rx quadrature volume head coil integrating a 30-channel 23Na Rx phased array (Rapid Biomedical GmbH, Rimpar, Germany). The data were acquired with the following parameters: (Δx)3=(3mm)3, 15000 projections, TE/TR=0.35ms/30ms, α=53°, TA=30min, USF= 1, and Navg=4. The CG-SENSE was regularized with a 3D total variaton3 (TV) and discrete cosine transform (DCT)9. The regularization tuning constants were empirically determined by visual inspection. The reconstruction was initialized with a (72x72x72) matrix of zeros. Convergence was assumed after a maximum of 50 iterations (Figure 1). The performance of CG-SENSE using Lagrangian coil sensitivities is compared to SOS and adaptive combination (ADC) reconstructions. Blurring artifacts in the outer parts of the CG-SENSE images are suppressed by applying a binary mask obtained with the BC data. Furthermore, the influence of the differently generated coil sensitivities on CG-SENSE is analysed.
Results
The reconstruction times of SOS and ADC are ~2min. The times for CG-SENSE are between 2 and 5h for undersampled and between 5 and 10h for fully sampled data on a standalone PC (CPU: IntelXeonE5-1620v4, RAM: 64GB). The generation of the conventional and Lagrangian coil sensitivities requires ~2min and ~2h, respectively. Figure 2 shows the reconstructed 23Na in vivo data using SOS, ADC, and CG-SENSE with Lagrangian coil sensitivities at USF=1/2/3/5. The CG-SENSE images show the best image quality and contrast within the object compared to the SOS and ADC images. For acquisition times TA≥4.5min and USF≤5, fine structures are well resolved and incoherent undersampling artifacts as well as Gaussian noise of the raw data are markedly reduced. The performance of CG-SENSE depends on the coil sensitivities (Figure 3). CG-SENSE with conventional coil sensitivities results in artifacts within the object for USF≥2. CG-SENSE with Lagrangian coil sensitivities does not show these artifacts; while blurry artifacts outside the object are induced, the object itself is reconstructed in detail.Discussion & Conclusion
Parallel Imaging and Compressed Sensing of 23Na reduces acquisition times while increasing image quality. CG-SENSE with Lagrangian coil sensitivities improves the image quality and contrast within the object compared to the SOS and ADC images. For USF≤5, fine structures are resolvable and incoherent undersampling artifacts as well as Gaussian noise of the raw data are reduced. The analysis of CG-SENSE with differently generated coil sensitivities supports the superiority of Lagrangian coil sensitivities, which are iteratively generated including a regularization. Outside the object, CG-SENSE images show blurry artifacts that strongly depend on the SNR of the coil sensitivities. The correction of the receive coil sensitivities might allow more exact quantification of 23Na content in the brain.Acknowledgements
No acknowledgement found.References
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9. Myronenko A, NVIDIA, Santa Clara, California, https://sites.google.com/site/myronenko/.
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