  The objective of our study is to observe dynamics of multiple substances in
vivo with high temporal resolution from multi-spectral magnetic resonance
spectroscopic imaging (MRSI) data. The multi-spectral MRSI can effectively
separate spectral peaks of multiple substances and is useful to measure spatial
distributions of substances. However it is difficult to measure time-varying
substance distributions directly by ordinary full sampling because the
measurement requires a significantly long time. In this study, we propose a
novel method to reconstruct the spatio-temporal distributions of substances
from randomly undersampled multi-spectral MRSI data on the basis of compressed
sensing (CS) and the partially separable function model with base spectra of
substances. In our method, we have employed spatio-temporal sparsity and
temporal smoothness of the substance distributions as prior knowledge to
perform CS. The effectiveness of our method has been evaluated using phantom
data sets of glass tubes filled with glucose or lactate solution in increasing
amounts over time and animal data sets of a tumor-bearing mouse to observe the
metabolic dynamics involved in the Warburg effect in vivo. The reconstructed
results are consistent with the expected behaviors, showing that our method can
reconstruct the spatio-temporal distribution of substances with a temporal
resolution of four seconds which is extremely short time scale compared with
that of full sampling. Since this method utilizes only prior knowledge
naturally assumed for the spatio-temporal distributions of substances and is
independent of the number of the spectral and spatial dimensions or the
acquisition sequence of MRSI, it is expected to contribute to revealing the
underlying substance dynamics in MRSI data already acquired or to be acquired
in the future.
