Spatially constrained hyperpolarized 13C MRI pharmacokinetic rate constant map estimation using a digital brain phantom and a U-Net

Fitting rate constants to Hyperpolarized [1-¹³C]Pyruvate (HP C13) MRI data is a promising approach for quantifying metabolism in vivo. Current methods typically fit each voxel of the dataset using a least-squares objective. With these methods, each voxel is considered independently, and the spatial relationships are not considered during fitting. In this work, we use a convolutional neural network, a U-Net, with convolutions across the 2D spatial dimensions to estimate pyruvate-to-lactate conversion rate, k_PL, maps from dynamic HP C13 datasets. We designed a framework for creating simulated anatomically accurate brain data that matches typical HP C13 characteristics to provide large amounts of data for training with ground truth results. The U-Net is initially trained with the digital phantom data and then further trained with in vivo datasets for regularization. In simulation where ground-truth k_PL maps are available, the U-Net outperforms voxel-wise fitting with and without spatiotemporal denoising, particularly for low SNR data. In vivo data was evaluated qualitatively, as no ground truth is available, and before regularization the U-Net predicted k_PL maps appear oversmoothed. After further training with in vivo data, the resulting k_PL maps appear more realistic. This study demonstrates how to use a U-Net to estimate rate constant maps for HP C13 data, including a comprehensive framework for generating a large amount of anatomically realistic simulated data and an approach for regularization. This simulation and architecture provide a foundation that can be built upon in the future for improved performance.