Spatio-temporal reconstruction of substance dynamics using compressed sensing in multi-spectral magnetic resonance spectroscopic imaging

TL;DR

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 is proposed.

Abstract

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.

Figures (7)

• Figure 1: A diagram of the proposed reconstruction method. The randomly undersampled MRSI signals are divided into time frames with arbitrary time width along the actual elapsed time and the spatio-temporal distributions of substances are assigned to the time frames.
• Figure 2: The root mean squares (RMSs) of $\bm{x}^k-\bm{z}^k$ and $\bm{z}^k-\bm{z}^{k-1}$ at $k$th iteration. The vertical axis is in the logarithmic scale. Around the 500th iteration, the slope of the curves became more gradual.
• Figure 3: The RMSE of the 2-fold CV for combinations of the regularization parameters in Experiment 4. (a) All combinations. (b) Combinations with $\lambda_{\mathrm{x}} = 10^0$. Note that the same color range covers different value ranges in figures (a) and (b) to provide the visualization to identify large and small values.
• Figure 4: Reconstructed spatio-temporal distributions of each substance in the phantom experiments (Experiments 1, 2, and 3). One column shows the time variation of one substance in one experiment. Each figure shows a colored map of the spatial distribution of a substance in a single time frame. In Experiment 3, images are displayed as colored maps overlaid on the $^1$H T$_2$-weighted images of mouse shown in gray scale for anatomical reference. For each substance, values of $\bm{x}$ were rescaled so that the maximum value is equal to 1. The "Frame" indicates the time frame index of the reconstruction and the "Time" indicates the elapsed time (in minute) from the beginning of the scanning. The images lined up vertically throughout all the experiments are the results of the same time frame. The rightmost column shows the T2-weighted images taken immediately after the end of each experiment.
• Figure 5: Reconstructed temporal profiles of the amount of substances at spatial pixels with the largest value for each substance in the phantom experiments. The locations of the selected pixels are indicated by square markers in the T2-weighted image in each figure. Horizontal axis represents the elapsed time in minute. Vertical axis represents values of $\bm{x}$, rescaled so that the maximum value is equal to 1 in each substance.