Synopsis

The clinical application of Sodium MRI is hampered due to relatively low image quality and associated long acquisition times (TA). Compressed Sensing (CS) aims at a reduction of TA, but has been found to encompass quantitative estimation bias when used in low SNR x-Nuclei imaging. This work analyses CS in human brain Sodium MRI from both angles, acquisition speed-up and quantification, and presents an optimized setup allowing an up to four-fold TA reduction with recommendations for quantitative assessments. The demonstrated global optima of CS weighting parameters and achievable reduction in TA greatly support the transition of Sodium MRI into clinical routine.

Introduction

Methods

Imaging was performed on a research 7T MRI scanner (Siemens Healthcare, Erlangen, Germany) with a transmit/receive dual-tuned ¹H-²³Na head coil (QED, USA). Data was collected with a custom-built 3D-radial sequence. Five healthy volunteers were imaged with the following parameters: TR=160ms, TE=0.4ms, FA=90°, 10,000 projections, FOV=(20cm)³, TA=26min40s.

Image reconstruction was performed offline in Matlab onto an isotropic 3.1mm-grid. A standard NUFFT⁵-reconstruction of the full raw-data (I_ref) was compared with randomly undersampled reconstructions (I_u) from NUFFT and CS. The employed CS optimization was

$$\hat{x}=\arg\min_x\|\mathcal{F}_u(x)-y\|_2^2+\lambda_1\|\Psi x\|_1+\lambda_2 \text{TV}(x)$$

where $$$\|\cdot\|_1$$$ and $$$\|\cdot\|_2$$$ denote the l₁ and l₂-norm, respectively, $$$\mathcal{F}_u$$$ is the undersampled NUFFT-operator, x is the reconstructed image, y the undersampled raw-data, Ψ the applied sparsity transform and λ₁ and λ₂ the weights on the transform sparsity and total variation (TV), respectively. Reconstructions were investigated for undersampling factors (USF) ranging from 2 to 10 with increments of 1 and across regularization weights, λ₁ (sparsity domain) = [0,1.0] step size 0.1; λ₂ (TV) = [0,0.0001,0.0005,0.001,0.005,0.01,0.05,0.1,0.5]. The employed sparsity domains Ψ were identity, i.e. the inherent image sparsity, Discrete CosineTransform (DCT) and Wavelet transform (WT).

Image reconstruction performance of each I_u was assessed by calculating the MSE, pSNR and sSim with respect to I_ref.

Results

Figure 1 illustrates reconstruction performance of CS for all investigated regularization weights and USF; red line surrounds area where CS reconstruction achieves higher scores than NUFFT-based reconstruction at the same USF. DCT and WT clearly outperform image-sparsity based and standard NUFFT-reconstructions in all investigated quality measures. WT shows a robust performance over a wide range of parameters (moderate to high λ₁, low to moderate λ₂).

Figure 2 shows mean and standard errors of quality scores with regards to λ₁ (Figure 2a) and λ₂ (Figure 2b) across subjects for all USF. The curves re-emphasize the overall better performance of WT reconstructions. Vertical red lines indicate the joint optimum across all image quality measures at λ₁=0.2 and λ₂=0.01. sSim scores were found to show good agreement with visual assessments; MSE and pSNR show a bias towards higher TV weights where images were visually smoothed.

Figure 3 illustrates cross sections of I_ref and I_u. CS reconstructions with highest sSim score are displayed. Up to an USF of 4, WT reconstructions show good structural detail.

Figure 4 plots the correlation between I_ref and I_u for all USF. Point clouds show some non-linear behavior, particularly for DCT and Identity-based CS reconstructions. Linear fits through point clouds (Figure 4b) show a decreasing slope manifested in an overall increase in noise and decrease in high image intensities. WT reconstruction fit residuals are distributed around zero highlighting the good linear correlation (Figure 4c).

In Figure 5 mean intensities of 200 evenly spaced intensity intervals in I_ref and I_u are plotted for all undersampled reconstruction schemes. The non-linear intensity reconstruction behavior is re-accentuated, dynamic ranges decrease with higher USF. Iterative CS reconstruction show better noise suppression. Wavelet-based reconstructions follow a more linear trend and lead to smaller drop in high intensities.

Discussion & Conclusion

This work investigated the optimization of sparsity and TV-regularized CS reconstructions with regards to TA reduction, image quality and intensity accuracy. A clear advantage towards Wavelet-based CS results was found, enabling USF=4 with great image quality and structural detail while maintaining good signal intensity reconstruction performance (mean linear bias slope: 0.96±0.02, Figure 4). Nevertheless, the use of a range of Sodium concentration phantoms across the whole spectrum of brain Sodium concentrations (20-150mM) is advised if quantitative information of Sodium content are to be extracted from CS reconstructed images; the use of background signal as a 0mM reference should be avoided due to the non-linear denoising properties of iterative reconstructions.

Apart from TA reduction, CS reconstructions can be further exploited for SNR enhancements. Additional regularization terms, e.g. ¹H-constraints⁶ or learned dictionaries⁷, have shown great SNR results and could be included in Eq[1]. The radial acquisition scheme can furthermore be used for flexible time-resolved imaging^8,9,10.

In summary, the demonstrated global optima of CS weighting parameters and achievable reduction in TA greatly support the transition of Sodium MRI into clinical routine.

Acknowledgements

References

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