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Feasibility of a Novel Sampling/Reconstruction Method Ensuring a SNR Benefit Over the Traditional Sampling Approach
Samuel Perron1, Matthew S. Fox1,2, Hacene Serrai1, and Alexei Ouriadov1,2,3
1Physics and Astronomy, The University of Western Ontario, London, ON, Canada, 2Lawson Health Research Institute, London, ON, Canada, 3School of Biomedical Engineering, The University of Western Ontario, London, ON, Canada

Synopsis

To produce high-SNR images, MRI systems usually employ many signal averages, expensive high field-strength coils, and/or expensive contrast agents. The proposed sampling and reconstruction method, requiring no hardware modifications, would produce images with higher SNR without increasing scan times. Nine under-sampled images are averaged for every combination of images, and the resulting SNR vs. averages function is fitted according to the Stretched-Exponential Model (SEM). The resulting reconstructed image yielded higher SNR than the original image for all three imaging schemes (FGRE, x-Centric, FE-Sectoral), demonstrating the feasibility of the proposed method for the first time.

Introduction

The MRI modality is generally a low sensitivity method1 due to the nature of the MRI-signal formation governed by a very small number of the nuclear spins that contribute to the resulting signal. It is well known that the resolution of any imaging modality always depends on the signal-to-noise ratio (SNR). For MRI, this limitation is mostly solved only for high field clinical 1H MRI measurements. In this particular case, the low sensitivity can be overcome by very high concentrations of water content in body tissue and the high gyromagnetic ratio of 1H. Unfortunately, this is the only example when the image-quality and image-resolution are acceptable. In cases of other nuclei with low gyromagnetic ratios (e.g., 13C/23Na/129Xe)2-4, low isotopic natural-abundance (2Deuterium)5, low-density (1H/3He/19F thermally polarized gases)6-8, or low field MRI9, image quality remains a longstanding scientific problem which can presently be solved by using expensive MRI-hardware or expensive enriched isotopes. Alternatively, higher SNR can be achieved by performing many averages during, for example, a breath-hold as in the case of the 19F lung MRI.10 We propose a new method that does not require any extra MRI-hardware or signal averaging to significantly improve the quality of MRI images. We will use a significant k-space under-sampling acquisition method where only 10% of the k-space points will be acquired per image, resulting in an accelerated type of k-space data acquisition with acceleration factor (AF) of 10. Thus, the time necessary to acquire one fully-sampled image should be equal to the time needed to acquire ten under-sampled images. The MRI image SNR is directly proportional to the spin-density and √(signal averages), so one can average ten different under-sampled k-spaces together using a specific averaging-pattern, generating 14 under-sampled k-spaces with different SNR levels. It can be assumed that this SNR difference reflects the spin-density difference rather than the actual signal level difference. In this case, a density decay curve can be fitted and reconstructed using the Stretched-Exponential-Model (SEM) combined with Compressed Sensing (CS).11,12 We hypothesize that the SEM-equation can be adapted for fitting the SNR dependence of the MR-signal similar to fitting time/b-value dependences.13,14

Methods

1H MR was performed on a resolution-phantom at 3.0T (MR750, GEHC, WI) using a clinical gradient coil set and commercial head RF coil. The following parameters were used: FOV=10x10cm2, Matrix=128x128, TE/TR=1ms/3sec, BW=32kHz, 90°. Nine 2D single-averaged fully-sampled k-spaces were acquired. We have obtained five k-spaces using 9-averages, 8-averages, 7-averages, 6-averages, and 5-averages (1_k-space each); two k-spaces using 4-averages (2_combinations); three separate k-spaces using 3-averages (3_ combinations); and four separate k-spaces using 2-averages (4_ combinations). This resulted in 14 k-spaces total. Three Cartesian sampling schemes (FGRE, x-Centric15 and 8-sector FE_Sectoral16) were used. 14 fully-sampled k-spaces were retroactively under-sampled (AF=7/10/14) in the wash-out or SNR attenuation direction. Figure_1 shows the under-sampling patterns for three sampling schemes/AF. The signal-intensity of the under-sampled k-spaces were represented as a function of the image number (Figure_3) and then fit following Abascal method.12 Values of $$$\boldsymbol{n}$$$ =1, …,14 were used to fit the under-sampled data and generate the pseudo mean fractional-ventilation maps. For simplicity, one can assume that the SNR attenuation reflects a decrease of the fluorinated-gas in the lung after delivery of the oxygen wash-out breaths.7 Clearly, each new wash-out breath of oxygen replaces some volume of the fluorinated-gas in lung, so the signal-intensity of the resulting images were gradually attenuated. The following equation can be fitted to the wash-out data:17 $$$\boldsymbol{S(n)} = \boldsymbol{S_0(1-r)^n}$$$, where S0 is the initial signal, n is the breath number, S(n) is the signal intensity after the nth wash-out breath and r is the fractional-ventilation parameter.7,17 r can be expressed as the fraction of fresh gas entering the lung and the total volume of gas within the lung ($$$V_{total}$$$):7,17 $$$r = V_{new}/V_{total}$$$ or $$$V_{new}/(V_{new}+V_{old})$$$. To generate a pseudo r-value the traditional approach17 was utilized. The SNR of the original/averaged/reconstructed images were then calculated.

Results

Figure_2 shows 8 images generated by averaging (1-8) and one original image. The SNR of the 9 k-space averaged image was 22 and the SNR of the original image was 6.5. Figure_4 shows the reconstructed images for three sampling-schemes and three AF. SNRFGRE/SNRx-Centric/SNRSectoral=20/28/25.
Figure_5 shows pseudo-fractional-ventilation maps obtained for three sampling-schemes and three AF. The figure legend shows the MRI-based mean r; the r-value obtained for the fully-sampled case was 0.30 ± 0.01.

Discussion and Conclusion

In this proof-of-concept study, we showed that the SEM equation can be adapted for fitting the SNR attenuation dependence of the MR-signal, similar to fitting the time/b-value dependences. The reconstructed images yielded improved SNR over the original fully-sampled images (>20 vs. 6.5) for all three imaging schemes, with comparable or identical imaging times. Due to this technique not requiring extra hardware, the proposed method could be implemented in current MRI-systems and yield improved images. Further comparison of identifiable biomarkers between the reconstructed and original images would determine accuracy of the reconstruction, with the goal of possible integration into clinical-MRI-systems. One potential limitation of the method is the CS-based reconstruction leading to the artefacts clearly visible for higher AF (FGRE/x-Centric); however, this can be minimized by using a Deep Learning-based correction after the fact.18-20

Acknowledgements

No acknowledgement found.

References

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Figures

Figure 1. Depicts three different k-space under-sampling patterns corresponding to AF=10, used for each wash-out image retroactively in wash-out or SNR attenuation direction.

Figure 2. Pseudo Wash-out Images Obtained in Resolution Phantom

Depicts 8 images (1-8) generated using the proposed averaging pattern and the original image (9), acquired at the 3T GE scanner. SNR of the first image (9 k-space averages) was 22 and SNR of the last image was 6.5.


Figure 3. Bulk signal intensity dependence as a function of image number obtained from 14 pseudo wash-out images (Figure 2). The dashed lines show the best-fit of single exponentials obtained from Figure 2.

Figure 4. Representative resolution phantom images reconstructed from retroactively under-sampled k-spaces corresponding to FGRE, x-Centric and FE Sectoral. AF were 7, 10 and 14. FGRE SNR was 20, x-Centric SNR was 28 and Sectoral SNR was 25. The FE Sectoral images show much less image distortions at all three AF compared to FGRE and x-Centric.

Figure 5. Representative pseudo fractional-ventilation maps obtained from the SEM-based reconstructed images for the three sampling schemes with AF of 7, 10 and 14.

  • FGRE: r= 0.28 ± 0.08 with AF=7; r= 0.28 ± 0.07 with AF=10; r= 0.34 ± 0.08 with AF=14
  • x-Centric: r= 0.28 ± 0.05 with AF=7; r= 0.29 ± 0.07 with AF=10; r= 0.37 ± 0.08 with AF=14
  • FE Sectoral: r= 0.29 ± 0.07 with AF=7; r= 0.41 ± 0.06 with AF=10; r= 0.38 ± 0.07 with AF=14

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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