Phosphorus-31 MR spectroscopic imaging (31P-MRSI) has been recognized as a powerful tool for non-invasive studies of energy metabolism, carbohydrates, and phospholipid metabolism of the human body.¹ However, conventional Fourier based 31P-MRSI methods have been limited by spatial resolution due to the low concentrations of phosphate-contained chemical compounds in the human body and the relatively low sensitivity of 31P NMR. This work presents a subspace-based method to achieve accelerated, high-resolution 31P-MRSI.

A special data acquisition and reconstruction scheme enabled by a subspace model based on the partial separability (PS)² of MRSI signals is used to recover high-resolution spatiotemporal distributions of metabolites from sparse data. More specifically, two complementary datasets are acquired. A “training” dataset (called $$$D_1$$$) is acquired, covering limited k-space but at a high temporal sampling rate, to capture the spectral distributions of the spatiospectral function with a high spectral bandwidth. A separate "imaging" dataset (called $$$D_2$$$) is acquired, covering extended k-space but with limited temporal sampling (or spectral encodings), to recover the spatial distributions of the spatiospectral function at a high spatial resolution. The proposed acquisition schemes can be easily implemented using CSI, EPSI, or a hybrid CSI/EPSI acquisitions depending on the desired resolution and imaging time of a study.^3-5

In reconstruction, the spatiospectral function is modeled as PS functions:$$\rho(\mathbf{x},f)=\sum_{l=1}^{L}u_{l}(\mathbf{x})v_{l}(f),$$where $$$\{v_{l}(f)\}_{l=1}^{L}$$$ can be viewed as a set of spectral basis functions, $$$\{u_{l}(\mathbf{x})\}_{l=1}^{L}$$$are the corresponding spatial coefficients, and $$$L$$$ is the model order. High-resolution spatiospectral distributions of metabolites are then recovered by determining the spectral basis functions and spatial coefficients of the PS model from the sparsely sampled data described above.

More specifically, the spectral basis functions are first estimated from $$$D_1$$$, e.g., using singular value decomposition (SVD).^3-5 A practical issue at this step is correcting the $$$B_0$$$ field inhomogeneity effects on $$$D_1$$$, which only covers limited k-space. This issue is resolved by exploiting the measured $$$B_0$$$ map and any prior knowledge of the spatial distributions of metabolites for $$$B_0$$$ inhomogeneity correction.⁶ Denoting the estimated spectral basis functions as $$$\{\hat{v}_{l}(f)\}_{l=1}^{L}$$$, the corresponding spatial coefficients are determined by fitting the data in $$$D_2$$$: $$ \min \limits_{u_l (\mathbf{x})} \parallel \mathbf{s}_{2}- \mathbf{F}_{B} \{ \sum_{l=1}^{L}u_{l}(\mathbf{x})\hat{v}_{l}(f) \}\parallel_2^2 + R(\sum_{l=1}^{L}u_{l}(\mathbf{x})\hat{v}_{l}(f)),$$ where $$$\mathbf{s}_{2}$$$ contains the sparsely sampled data in $$$D_2$$$, $$$\mathbf{F}_{B}$$$ is a Fourier encoding operator taking $$$B_0$$$ field inhomogeneity into consideration, and the regularization term is used to incorporate the prior knowledge of the spatial distributions of metabolites.³

The proposed method has been validated using both phantom and in vivo 3D 31P-MRSI experiments (approved by our local IRB), which were carried out on a 3T Siemens Trio scanner equipped with a dual-channel 31P surface coil (PulseTeq, UK). Short-TE, Short-TR FID sequences with CSI or EPSI acquisitions were developed to collect 31P-MRSI data with high SNR and acquisition efficiencies.

Figure 1 shows the results from an equivalent-acquisition-time experiment on a phantom containing three vials filled with sodium phosphate solution at 100 mM concentration. Compared to the conventional CSI and EPSI results, the proposed method was able to recover the spatiospectral distribution of the chemical compound with both high resolution and high SNR. Most notably, the three vials can be clearly seen in the reconstructed Pi map and the spectrum has a SNR comparable to the CSI result.

In vivo 31P-MRSI results of the calf muscle obtained from healthy volunteers are shown in Figs. 2 and 3. Figure 2 shows the results obtained by the proposed method with 6.9 mm x 6.9 mm x 10 mm nominal resolution using CSI acquisitions in a 15 min scan. Compared to the conventional Fourier construction, the proposed method significantly improved the SNR. Besides the strong PCr peak, the peaks of Pi and ATP are clearly seen in the reconstructed spectrum and the bone areas with expected low 31P signals in the reconstructed PCr map matched well with the 1H structure image. Figure 3 shows a set of reconstructed spectra and PCr maps at an even higher resolution (4.8 mm isotropic) obtained by the proposed method using hybrid CSI/EPSI acquisitions. Although very noisy, the preliminary results show the potential of proposed method in achieving very high-resolution 31P-MRSI. We expect the SNR can be further improved by using more advanced hardware and/or image reconstruction methods.

This paper presents a new method to achieve high-resolution 31P-MRSI using a subspace-based approach. The feasibility of the proposed method is demonstrated using both phantom and in vivo experimental studies on a 3T scanner, which have yielded very promising results. The proposed method can be used in a range of 31P-MRSI applications.