Introduction

Phosphorous magnetic resonance spectroscopic imaging (³¹P‑MRSI) is a valuable tool to non‑invasively investigate energy metabolism, membrane turnover, and pH in living tissues. Recent developments addressed the issue of limited sensitivity, enabling the acquisition of volumetric ³¹P‑MRSI data with reasonable spatial resolution at 7T, and demonstrated its potential value for pH and metabolic imaging in gliomas^1,2. The employed ³¹P‑MRSI protocol duration in these studies (51 minutes) is, however, prohibitively long for clinical research on larger patient cohorts. Compressed sensing (CS) techniques are well‑suited to reduce the ³¹P‑MRSI protocol measurement time via k‑space undersampling^3,4.
The purpose of this study was to develop a CS‑based data acquisition and reconstruction strategy to reduce the measurement duration of ³¹P‑MRSI of the human brain at 7T.

Methods

The proposed approach, CASSAVA, builds upon blind CS⁵ and variable‑density k‑space averaging⁶, and is applied to a pre‑existing ³¹P‑MRSI protocol¹. Adaptive undersampling patterns were generated using probability distributions created from k‑space energy distributions of reference brain data (total ³¹P signal strength), as previously proposed to avoid a priori models⁷. Repeated sampling and averaging was performed in the central k‑space region. A total undersampling factor of $$$R=3.8$$$ was chosen throughout this study.
For data reconstruction, a singular value decomposition (SVD) was applied to the spatio‑spectral Casorati matrix $$$\mathbf{\mathrm{\Gamma}}$$$ to obtain a spectral dictionary matrix, $$$\mathbf{\mathrm{V}}$$$, and a spatial weights matrix, $$$\mathbf{\mathrm{U}}$$$, with $$$\mathbf{\mathrm{\Gamma}}=\mathbf{\mathrm{U}}\mathbf{\mathrm{V}}$$$. The proposed algorithm iteratively minimizes the objective:
$$\mathbf{\mathrm{\hat{U}}} =\mathop{\arg \min}\limits_{\mathbf{\mathrm{U}}} {\Vert{W^{1/2}(F_\mathrm{u}(\mathbf{\mathrm{U}}\mathbf{\mathrm{V}})-\mathbf{\mathrm{b}})}\Vert_2^2 + \lambda\Vert{\mathbf{\mathrm{U}}}\Vert_1 + \lambda_\mathrm{w}\Vert{\Psi{}_\mathrm{w}\mathbf{\mathrm{U}}}\Vert_1}$$

with the measurements $$$\mathbf{\mathrm{b}}$$$, the variable k‑space averaging weights $$$W$$$, the undersampled Fourier transform $$$F_\mathrm{u}$$$, the wavelet transform $$$\mathrm{\Psi}_\mathrm{w}$$$, and regularization parameters $$$\lambda$$$, $$$\lambda_\mathrm{w}$$$.
For benchmarking, the reconstruction accuracy of intracellular pH (pH_i) maps was analyzed, as accurately recovering the frequency of low‑intensity resonances (i.e. inorganic phosphate P_i) poses a challenge¹. Phosphocreatine (PCr) and P_i resonances of reconstructed ³¹P‑MRSI data were fitted using AMARES⁸ and their frequencies inserted into the modified Henderson‑Hasselbach equation⁹ to determine pH_i. As quality indicators, root‑mean‑square error (RMSE) and feature similarity¹⁰ (FSIM) were calculated across the full imaging matrix. Home‑built MATLAB scripts performed all data processing.
Simulation study: A synthetic high‑resolution Ground Truth (GT) was created using 5 tissue masks (cerebrospinal fluid, white & grey brain matter, cerebellum, muscle), downsampled to a $$$24\times20\times16$$$ ³¹P‑MRSI GT, and Gaussian noise was added to replicate the signal‑to‑noise ratio (SNR) of real measurements. The noisy GT was undersampled with the adaptive pattern in Figure 1a, generated with the GT as reference.
Retrospective study: Fully‑sampled ³¹P‑MRSI data from a patient with glioblastoma was previously obtained on a 7T system (MAGNETOM, Siemens) using a 32‑channel ³¹P/¹H head coil (RAPID), coil‑combined with a whitened SVD¹¹, and undersampled with the same adaptive pattern of the simulation study (Figure 1a).
Prospective study: A healthy volunteer measurement was performed on the identical 7T system using a 1‑channel ³¹P/¹H volume coil (RAPID). The adaptive undersampling pattern in Figure 1b, generated with the patient data as reference, was implemented into the MRSI protocol with 18 averages at k‑space center (total duration: 24 minutes).
In all studies, undersampled data was reconstructed using CASSAVA.

Results

Figure 2 illustrates results from the simulation study. The representative reconstructed spectrum exhibits negligibly small differences compared to the GT. The proposed approach accurately reconstructs pH_i maps without relevant deviations (compared to local differences).
Figure 3 shows the results for the retrospectively undersampled patient data. The reconstructed spectrum is similar to the original, and their difference contains only noise‑like deviations. The reconstructed pH_i map exhibits smoothing but correctly recreates local differences, particularly for tumor tissue.
Table 1 summarizes the reconstruction quality of the proposed strategy for the simulation and retrospective studies compared to the noise‑free GT and the fully‑sampled data, respectively. CASSAVA outperforms the purely undersampled data for the simulation study, whereas no quantitative advantage is observed in the retrospective study due to higher noise variation.
Finally, Figure 4 presents the ³¹P‑MRSI volunteer data acquired prospectively. Both reconstructed spectra and pH_i maps retain important local features.

Discussion

The simulation study demonstrates the possibility of recreating ³¹P‑MRSI data with the CASSAVA approach while maintaining a close agreement with the GT. The lack of a noise‑free GT in the prospective study makes quantitative comparison difficult; qualitatively, however, there is negligible loss in data quality barring spatial smoothing. Although only pH_i evaluations were presented as a benchmark, CASSAVA performs considerably better for higher‑SNR metabolites (data not shown).
The correctness of the proposed technique was supported by the prospective measurement performed, despite using an adaptive pattern with comparatively more sampling in the k‑space periphery. Comparing the 24‑minute 1‑channel prospective measurement to the results from the 32‑channel retrospective study indicates that a 20‑minute measurement is possible: the total averages can be reduced while preserving the SNR by using a multi‑channel coil. Further development of our method will enable its use in multi‑channel acquisitions.

Conclusion

We demonstrated the feasibility of a novel CS‑based acquisition strategy to reduce the measurement time of high‑resolution ³¹P‑MRSI at 7T. Simulations and prospective acquisitions indicate that an experimental duration of 20 minutes is possible without loss in spatial resolution or data quality compared to the state‑of‑the‑art protocol. Thus, the CASSAVA method paves the way for clinical research on larger patient cohorts.

Acknowledgements

None.

References

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