Random under-sampling and spectra reconstruction for in vivo 13C magnetic resonance spectroscopy
Ningzhi Li1, Shizhe Steve Li1, and Jun Shen1

1National Institute of Mental Health, Bethesda, MD, United States

Synopsis

The present study proposes and evaluates a novel under-sampled decoupling strategy in which no decoupling was applied during randomly selected segments of data acquisition. By taking advantage of the sparse spectral pattern of carboxylic/amide region of in vivo 13C spectra of brain, an iterative algorithm was developed to reconstruct spectra from under-sampled data. Simulations and in vivo experiments show that this novel decoupling and data processing strategy can effectively reduce decoupling power deposition by >30%.

Purpose

In in vivo 13C experiments, the specific absorption rate (SAR) accumulates linearly with the duration of decoupling and increases quadratically with field strength. The purpose of the present study is to demonstrate a novel decoupling and data processing strategy to significantly reduce decoupling power deposition. This new strategy uses a windowed decoupling scheme in the time domain in which no decoupling was applied during randomly selected segments of data sampling. The spectra are iteratively reconstructed only using data points when decoupling is present. Because the decoupling is not present over a significant portion of data acquisition, this novel approach effectively reduces the required decoupling power and thus the SAR.

Methods

An iterative algorithm was developed to reconstruct spectra from under-sampled datasets. This algorithm takes advantage of the sparse spectral pattern of carboxylic/amide region of 13C spectra. It iteratively reconstructs the 13C spectra from under-sampled data until the calculated data are consistent with the under-sampled experimental data. Reconstruction of the fully sampled data was also performed to validate the proposed approach. Signals including GABA1, Glu5, NAA1, NAA4, Gln5, Asp4, Glu1, Asp1, Gln1 and NAA5 were simulated using a global linewidth and individual intensities. Two undersampling strategies were compared: a total random sampling pattern (A) and a gradually decreasing sampling pattern (B). Both strategies begin with a fully sampled core. Spectra were iteratively reconstructed using the under-sampled datasets. Different core sizes and under-sampling rates were evaluated by the residuals and signal intensity errors between the reconstructed spectra from under- and fully sampled datasets. Four sets of in vivo 13C data acquired at 7 Tesla were used.1,2 Since the spectral baseline in the carboxylic/amide region remains fairly constant, a baseline model was determined experimentally by averaging all in vivo baselines using an in-house developed fitting software.3

Results

Figures 1-3 displays numerical simulation examples. Figure 1 shows the effects of the two different under-sampling strategies. Spectra from fully sampled datasets are also displayed for comparison. Strategy A resulted in very small fitting residuals. In comparison, strategy B shows relatively large residuals for the same under-sampling rate. Only results from under-sampling strategy A are shown below. Figure 2 compares the spectra with different size of the fully sampled core. The mean signal intensity errors (between the under- and fully sampled spectra) from 10 simulated chemicals are 1.16%, 0.49% and 1.29% for 10%, 20% and 30% of the fully sampled core, respectively. The size of fully sampled core has relatively small influence on the final results as the mean signal intensity errors did not change sizably when the core size varies. Figure 3 shows two examples of the reconstructed spectra with different under-sampling rates. The first 20% of the FID was fully sampled. The reconstructed spectrum associated with lower under-sampling rate has smaller residuals and signal intensity errors compared to the reconstructed spectrum with larger under-sampling rate. Figure 4 shows the four in vivo reconstructed spectra with under-sampling rate of 30%. Because the in vivo data decayed rapidly at the beginning, a 5% fully sampled core was used. With a 30% under-sampling rate, excellent reconstructed spectra were obtained from all four in vivo datasets. Figure 4E shows the changes of the mean signal intensity error of Glu5 averaged over 4 subjects when the under-sampling rate varies.

Discussion

This study aims to propose and evaluate a novel approach to acquire 13C data with decreased decoupling power deposition and reconstruct spectra using under-sampled data. Since the decoupling power has been turned off for a significant period of time through the data sampling, the accumulated SAR could be significantly reduced, and thus benefits the in vivo 13C experiments at high field and for frontal lobe studies. Because the carboxylic/amide region of 13C spectra has a relatively sparse distribution, random sampling allows cancellation of reconstruction errors in a manner bearing certain similarity to compressed sensing.

Conclusion

A novel approach for decreasing decoupling power and thus SAR for the in vivo 13C experiments is developed. A total random sampling pattern works much better than a gradually decreased sampling pattern. The size of the fully sample core has relatively small influence on the final results. Both simulations and in vivo experiments show that excellent spectra reconstruction could be achieved with a ~30% under-sampling rate. Further optimization of the under-sampling pattern may further reduce decoupling power deposition.

Acknowledgements

This work was supported by the Intramural Research Program of the National Institute of Mental Health, National Institutes of Health.

References

1. Li S, et al., J Magn Reson 2012;218:16-21. 2. Li S, et al., Magn Reson Med 2015 [Epub ahead of print]. 3. Li N, et al., NMR Biomed 2015 [Epub ahead of print].

Figures

Figure 1. Examples of data reconstruction using the total random sampling pattern(A) and gradually decrease sampling pattern (B). Both methods began with a 20% fully sampled core and 20% under-sampling rate. The corresponding reconstructed spectra are displayed below.

Figure 2. Under-sampled spectra reconstructed using 10%(A), 20%(B) and 30%(C) fully sampled core at beginning. Spectra from fully sampled data are displayed for comparison. Fairly small residuals and small chemical mean errors from all three cases indicate that the core size has relatively small influence on the final results.

Figure 3. Examples of reconstructed spectra from FID with 25% under-sampled rate (A) and 35% under-sampled rate (B).

Figure 4. Reconstructed spectra from four different under-sampled in vivo data. Spectra from fully sampled data are displayed for comparison and used for signal intensity error calculation. E shows the absolute mean signal intensity error (averaged over 4 subjects) of Glu5 verses different under-sampling rate.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
3967