High-Resolution Dynamic $^{31}$P-MR Spectroscopic Imaging for Mapping Mitochondrial Function

Objective: To enable non-invasive dynamic metabolic mapping in rodent model studies of mitochondrial function using $^{31}$ P-MR spectroscopic imaging (MRSI). Methods: We developed a novel method for high-resolution dynamic $^{31}$ P-MRSI. The method synergistically integrates physics-based models of spectral structures, biological modeling of molecular dynamics, and subspace learning to capture spatiospectral variations. Fast data acquisition was achieved using rapid spiral trajectories and sparse sampling of ( $k,\;t,\;T$ )-space; image reconstruction was accomplished using a low-rank tensor-based framework. Results: The proposed method provided high-resolution dynamic metabolic mapping in rat hindlimb at spatial and temporal resolutions of $4 \times 4 \times 2 \;\text{mm}^{3}$ and 1.28 s, respectively. This allowed for in vivo mapping of the time-constant of phosphocreatine resynthesis, a well established index of mitochondrial oxidative capacity. Multiple rounds of in vivo experiments were performed to demonstrate reproducibility, and in vitro experiments were used to validate the accuracy of the estimated metabolite maps. Conclusions: A new model-based method is proposed to achieve high-resolution dynamic $^{31}$ P-MRSI. The proposed method's ability to delineate metabolic heterogeneity was demonstrated in rat hindlimb. Significance: Abnormal mitochondrial metabolism is a key cellular dysfunction in many prevalent diseases such as diabetes and heart disease; however, current understanding of mitochondrial function is mostly gained from studies on isolated mitochondria under nonphysiological conditions. The proposed method has the potential to open new avenues of research by allowing in vivo and longitudinal studies of mitochondrial dysfunction in disease development and progression.