Uncertainty-weighted Multi-tasking for $T_{1ρ}$ and T$_2$ Mapping in the Liver with Self-supervised Learning

Multi-parametric mapping of MRI relaxations in liver has the potential of revealing pathological information of the liver. A self-supervised learning based multi-parametric mapping method is proposed to map T$T_{1\rho}$ and T$_2$ simultaneously, by utilising the relaxation constraint in the learning process. Data noise of different mapping tasks is utilised to make the model uncertainty-aware, which adaptively weight different mapping tasks during learning. The method was examined on a dataset of 51 patients with non-alcoholic fatter liver disease. Results showed that the proposed method can produce comparable parametric maps to the traditional multi-contrast pixel wise fitting method, with a reduced number of images and less computation time. The uncertainty weighting also improves the model performance. It has the potential of accelerating MRI quantitative imaging.

Uncertainty-Aware Self-supervised Neural Network for Liver $T_{1ρ}$ Mapping with Relaxation Constraint

$T_{1\rho}$ mapping is a promising quantitative MRI technique for the non-invasive assessment of tissue properties. Learning-based approaches can map $T_{1\rho}$ from a reduced number of $T_{1\rho}$ weighted images, but requires significant amounts of high quality training data. Moreover, existing methods do not provide the confidence level of the $T_{1\rho}$ estimation. To address these problems, we proposed a self-supervised learning neural network that learns a $T_{1\rho}$ mapping using the relaxation constraint in the learning process. Epistemic uncertainty and aleatoric uncertainty are modelled for the $T_{1\rho}$ quantification network to provide a Bayesian confidence estimation of the $T_{1\rho}$ mapping. The uncertainty estimation can also regularize the model to prevent it from learning imperfect data. We conducted experiments on $T_{1\rho}$ data collected from 52 patients with non-alcoholic fatty liver disease. The results showed that our method outperformed the existing methods for $T_{1\rho}$ quantification of the liver using as few as two $T_{1\rho}$-weighted images. Our uncertainty estimation provided a feasible way of modelling the confidence of the self-supervised learning based $T_{1\rho}$ estimation, which is consistent with the reality in liver $T_{1\rho}$ imaging.