The transient nature of hyperpolarized (HP) C-13 signals requires fast data acquisitions to mitigate signal loss due to relaxation and to measure rapid in vivo substrate uptake and metabolic conversion. This is especially true for clinical trials, which demand much larger FOVs and concomitantly larger matrix sizes to maintain the spatial resolution currently used for preclinical studies. Parallel imaging schemes with multi-channel coils offer the potential for improved spatial coverage and high acceleration while maintaining high SNR. Conventional parallel imaging schemes such as SENSE1, SMASH2 and GRAPPA3 all require a priori knowledge of coil sensitivity through explicit calibration scans prior to image acquisition. This is difficult for HP C-13 studies due to the fact that C-13 signal is unavailable before injection of hyperpolarized substrate and incorporation of auto-calibration scans into the small matrix size used for C-13 imaging significantly limits k-space coverage. Recently a new class of calibrationless parallel imaging techniques have been developed, such as the Simultaneous Auto-calibrating and K-space Estimation (SAKE)4, that does not require explicit calibration of coil sensitivity. The purpose of this study was to investigate the efficacy of the SAKE method for HP C-13 imaging in both 2D and 3D applications.

2D studies

All MR images were acquired using a GE 3T scanner equipped with multi-nuclear capability. Proton anatomical images were acquired with the built-in body coil. A custom-designed transmitter and an 8-channel array coil (Figure 1(a)) were used for C-13 RF excitation and receive. All images were acquired with a 2D ramp-sampled symmetric EPI sequence5 (Figure 2) using a FOV of 16x16 cm (phantom) or 20x20 cm (in vivo) and a reconstructed matrix size of 64x64. Under-sampling was achieved along the Gy-blip dimension with at least 2-fold acceleration. The SAKE reconstruction scheme was first tested on a retrospectively under-sampled data acquired with a phantom of natural abundance ethylene glycol (Figure 1(b)). Its performance was compared with GRAPPA using comparable acceleration rates (Figure 3) with reconstruction coefficients estimated using a 4-by-3 kernel. Then SAKE was applied to a prospectively under-sampled in vivo imaging data. HP 13C-t-butanol was chosen in this study as it can freely diffuse across the blood brain barrier and was hyperpolarized in a Hypersense DNP polarizer (Oxford instruments). Approximately 3.0 ml of the final solution containing 100 mM 13C-t-butanol was injected into normal Sprague-Dawley rats for in vivo imaging (Figure 1(c)). The polarization level was around 20%.

3D simulation

To evaluate efficacy of SAKE reconstruction on 3D acquisition with acceleration on both phase encode directions, a 3D digital phantom of 64 x 64 x 64 matrix size was generated (Figure 5(a)) using simulated sensitivity profile of the aforementioned receive coil (Figure 1(a)). The 3D data was under-sampled with two 2D variable density Poisson disk patterns (Figure 5(b-c)).

In the ethylene glycol phantom study, the performances of SAKE and GRAPPA against 2-fold under-sampled data are comparable with RMSE of 0.0164 compared to the fully sampled image. However, at a higher acceleration factor (R = 2.6) GRAPPA failed (with 12 ACS lines) due to aggressive under-sampling of the outer k-space. In contrast, even with 3-fold acceleration, SAKE largely suppressed aliasing artifact across the phase encode direction (Figure 3). In the hyperpolarized t-butanol study, the SAKE reconstruction showed no aliasing artifacts in the phase encode direction compared to the aliased zero-filled images (Figure 4(a) versus (b)). These images show high signal intensity in the rat kidneys and brain. Notably, the SAKE reconstruction (Figure 4(e)) demonstrated better differentiation between the renal cortex and inner medulla compared to the data acquired with partial Fourier coverage with 25% oversampling (Figure 4(f)). In the simulated 3D phantom study, one axial slice (Figure 5(a), with the kz readout direction fully sampled) was chosen to test the SAKE reconstruction scheme against 2D accelerated image. Two variable density patterns with overall acceleration rates of 3 and 4.5 were used to generate the under-sampled data. Reconstructed images had RMSE of 0.0331 (3-fold) and 0.0405 (4.5-fold). In this proof-of-concept demonstration, we applied the self-calibrating SAKE parallel imaging method to hyperpolarized 13C 2D EPI studies and demonstrated its robustness against aliasing in both in silico and in vivo experiments. SAKE showed a unique advantage over conventional parallel imaging schemes that require separate calibration scans. This approach is being extended to 3D imaging of HP 13C study. Greater acceleration can be achieved with sequences such as 3D multi-shot EPI since incoherent undersampling can be performed on both phase-encode dimensions, reducing RF requirements and improving volumetric coverage and/or temporal resolution.