Joint spatial-spectral reconstruction and k-t spirals for accelerated 2D spatial/1D spectral imaging of 13C dynamics

Magnetic resonance imaging (MRI) of 13C holds the potential to probe pathology at a molecular level. Unfortunately, signal from endogenous 13C is indistinguishable from noise due to low receptivity, sub millimolar in vivo concentrations, and scan time limitations. Recent advances in hyperpolarization (1,2) now allow for 100,000 fold increases in polarization, enabling the use of 13C-labeled molecules as tracers. With modern dynamic nuclear polarization, almost any endogenous, organic molecule can be polarized and subsequently imaged. For example, hyperpolarized (HP) [1-13C]pyruvate shows great potential as a molecular biomarker of cellular metabolism. In such experiments, a small sample of [1-13C]pyruvate is hyper-polarized and intravenously injected. In vivo it is transported into the cell and undergoes rapid conversion into its primary metabolic byproducts, [1-13C]lactate, [1-13C]alanine, and 13C bicarbonate (3). Preferential conversion of pyruvate to lactate is an indicator of increased glycolysis, a common feature of cancerous lesions associated with the Warburg Effect (4). Quantification of pyruvate metabolism promises to dramatically improve evaluation of prostate cancer and glioblastomas, where fluorodeoxyglucose positron emission tomography (5) shows limited prognostic value. Other promising HP compounds include 13C bicarbonate to measure extracellular pH (6) and [1,4-13C2]fumarate to measure cellular necrosis (7). Imaging of HP 13C compounds is more challenging than other contrast agents. Immediately after the sample is removed from the polarizer, HP molecules undergo chemical and spin exchange with the endogenous environment. Polarization also decays at a rate governed by the nuclear spin–lattice relaxation time, T1. In vivo, chemical species with unique resonant frequencies are often produced, especially with injection of metabolically active molecules. As with pyruvate to lactate conversion, there is often great value in measuring the relative signal from each species, which can be achieved with spectral imaging techniques (8). Spectral imaging with HP species presents substantially different challenges than endogenous, thermally polarized nuclei. While the signal-to-noise ratio (SNR) is quite high for a single radio frequency (RF) excitation, each excitation consumes a portion of the finite hyperpolarization (9). Due to perfusion and washout, 13C molecules are imaged in a nonequilibrium state and thus dynamic imaging is essential for potential quantification of apparent conversion rates (10). Conventional spectroscopic imaging techniques, such as chemical shift imaging (CSI) (3,11), provide excellent spectral resolution, but the long imaging time ( ~10s) and the need to phase encode both spatial dimensions limits the ability to measure dynamics. Rapid spectroscopic imaging techniques, such as echo planar spectroscopic imaging (EPSI) (12,13) and spiral CSI (14,15), greatly reduce the scan time and RF deposition but are often limited by a narrow spectral bandwidth, a consequence of gradient slew rate limitations and the reduced 13C gyromagnetic ratio (~4× lower than 1H). However, the sparse [1-13C]pyruvate spectrum is well suited to these techniques, as off-resonance peaks can be aliased without spectral overlap and corrected in the reconstruction (16). A priori knowledge of the expected chemical species presents opportunities for model-based spectral reconstructions such as least squares estimation algorithms (e.g., iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL)) (17–19) and compressed sensing approaches (20). Unlike conventional Fourier-based spectroscopic imaging, optimally chosen echo times will prevent spectral aliasing without the need to fully sample the spectral dimension (21). Combined with efficient sampling strategies, such as centric phase encoding, variable flip-angle schemes (22), and spiral sampling (14,15,19), these techniques can further reduce RF decay while still providing high SNR data. Nevertheless, these sequences still require spatial or spectral interleaves to sufficiently sample kx-ky-kf space. This limits the acquisition efficiency and necessitates multiple RF excitations. In this work, we propose a novel technique, hereafter referred to as k-t spiral, to generate spatially and spectrally resolved images with a single RF excitation. This technique oversamples spatial k-space to provide temporal sampling suitable for reconstruction of images with sparse spectra. We employ a reconstruction that jointly solves for both spatial frequency and spectral frequency dimensions (i.e., k-t sampling) utilizing a model-based approach. Using the phase evolution over the full k-t trajectory allows reconstruction from a single spiral shot. Digital simulations and phantom experiments were performed to verify theory and evaluate performance. Initial experiments are performed to show in-vivo feasibility. It is anticipated that this method can minimize RF excitations, increase acquisition speed, and mitigate polarization decay for HP 13C MRI applications.