Hyperpolarized imaging of 13C pyruvate is a promising tool to study cardiac metabolism. To investigate local changes in cardiac metabolism, high spatiotemporal resolution is required. Acceleration techniques exploiting spatiotemporal correlations¹ and signal sparsity² have been proposed to speed up data acquisition. The present work aims at comparing reconstruction algorithms using k–t principal component analysis (k-t PCA) and compressed sensing (k-t SPARSE) and using these techniques to acquire in-vivo metabolic maps at one millimeter in-plane resolution in rats.

Simulation: Fully sampled dynamic multi-echo single-shot EPI data (image matrix=48x32, #dynamics=20) were acquired in a rat heart after injection of hyperpolarized [1-13C] pyruvate. Dynamic metabolite maps for pyruvate, lactate and bicarbonate were reconstructed using the IDEAL approach³. This data served as reference and was used as input for a multi-echo signal model, which was then retrospectively undersampled as shown in Figure 1 with varying undersampling factors R. Reconstruction of undersampled data was performed with IDEAL and either k-t PCA⁴ or k-t SPARSE⁵, respectively. In k-t PCA the unaliased data $$$i$$$ is obtained by $$$i=WB$$$, where $$$B$$$ are spatially invariant temporal basis functions obtained using principal component analysis (PCA) of the fully sampled k-space center upon Fourier transform along time and $$$W$$$ are temporally invariant weights calculated by

$$W=M^2E^H(EM^2E^H+\Psi)^\dagger\rho_{alias}$$

where $$$M^2$$$ denotes the signal variance derived from the fully sampled k-space center, $$$E$$$ is the encoding matrix, $$$\Psi$$$ the noise variance and $$$\rho_{alias}$$$ the acquired undersampled data. In k-t SPARSE the image is obtained as the solution $$$i$$$ to the following minimization problem:

$$argmin_i\Vert FT_t\vec{i}\Vert _1 s.t. \vec{d}=E\vec{i}$$

where $$$\vec{d}$$$ is the undersampled k-t space data and $$$FT_t$$$ the Fourier transform along time. The solution to the minimization problem was found using nonlinear shrinkage. Reconstructed signal-time curves of pyruvate in the left-ventricular blood pool and lactate and bicarbonate in four myocardial segments (Figure 2) were compared to the reference signal and the root-mean-square error (RMSE) was assessed. The effective undersampling factor R was defined as the size of the image matrix divided by the total number of sampled profiles (including the fully sampled k-t space center).

In-vivo: Five healthy female Sprague-Dawley rats (250-350g) were anaesthetized using 2% isoflurane in an air/oxygen (4:1) mixture and placed in 9.4T Bruker Biospec small animal MR system. A birdcage 1H/13C coil was used for transmission, and a 13C surface coil was used for signal reception. Three samples containing 50.8µL [1-13C]-pyruvic acid with 13.5mM trityl radical and 1mM Dotarem were simultaneously polarized in a home-built DNP polarizer⁶. 1ml of 80mM solution of pyruvate was injected into the tail vein of the animal at three time points separated by 20 minutes. Metabolic maps were acquired with fully sampled EPI (reference), regular undersampling with fully sampled k-t space center (R=4) and with random undersampling (R=4), respectively. The following parameters were used: echo time 3.79ms (5.04 for fully sampled scan), number of echoes 7, echo time increment 383us, field of view 60x40mm², 69% partial Fourier acquisition, in-plane resolution 1.0x1.0mm² (1.25x1.25mm² for fully sampled scan), slice thickness 3.5mm. Images were reconstructed with IDEAL and either k-t PCA or k-t SPARSE in the undersampled cases. All animal experiments were performed in adherence to the Swiss law of Animal Protection and approved by the Zurich cantonal veterinary office.

Simulations: Figure 2 shows reconstructed images and signal-time curves for pyruvate in the left-ventricular blood pool and lactate and bicarbonate in four myocardial segments for R=3. Good agreement with the reference signal is found for both k-t PCA and k-t SPARSE. In simulations, k-t SPARSE was found to perform better at lower undersampling factors R, but is outperformed by k-t PCA for R≥3 (Figure 3). The difference in RMSE between the two methods at higher R becomes larger when partial Fourier sampling is employed.

In-vivo: Metabolic maps at a resolution of 1x1x3.5mm³ of pyruvate, lactate and bicarbonate were successfully reconstructed using prospective undersampling in conjunction with both k-t PCA and k-t SPARSE (Figure 4). Comparing the area under the curve (AUC) of lactate-to-pyruvate and bicarbonate-to-pyruvate ratios to the fully sampled reference, k-t PCA resulted in an error of 16.4±3.6% and k-t SPARSE 23.4±2.8% over the four myocardial segments for R=4 (Figure 5).

Both k-t PCA and k-t SPARSE allow to acquire in-vivo metabolic maps of the rat heart at one millimeter in-plane resolution. While k-t SPARSE performs favorably at lower undersampling factors, k-t PCA outperforms at undersampling factors ≥3. Both methods are valuable to improve spatial resolution without significant noise amplification thereby addressing the limited spatial specificity of current cardiac hyperpolarized metabolic imaging protocols.