Objective: Quantitative $T_1\rho$ imaging has potential for assessment of biochemical alterations of liver pathologies. Deep learning methods have been employed to accelerate quantitative $T_1\rho$ imaging. To employ artificial intelligence-based quantitative imaging methods in complicated clinical environment, it is valuable to estimate the uncertainty of the predicated $T_1\rho$ values to provide the confidence level of the quantification results. The uncertainty should also be utilized to aid the post-hoc quantitative analysis and model learning tasks. Approach: To address this need, we propose a parametric map refinement approach for learning-based $T_1\rho$ mapping and train the model in a probabilistic way to model the uncertainty. We also propose to utilize the uncertainty map to spatially weight the training of an improved $T_1\rho$ mapping network to further improve the mapping performance and to remove pixels with unreliable $T_1\rho$ values in the region of interest. The framework was tested on a dataset of 51 patients with different liver fibrosis stages. Main results: Our results indicate that the learning-based map refinement method leads to a relative mapping error of less than 3% and provides uncertainty estimation simultaneously. The estimated uncertainty reflects the actual error level, and it can be used to further reduce relative $T_1\rho$ mapping error to 2.60% as well as removing unreliable pixels in the region of interest effectively. Significance: Our studies demonstrate the proposed approach has potential to provide a learning-based quantitative MRI system for trustworthy $T_1\rho$ mapping of the liver.

翻译：目的：定量$T_1\rho$成像具有评估肝脏病理生化改变的潜力。深度学习方法已被用于加速定量$T_1\rho$成像。为在复杂的临床环境中应用基于人工智能的定量成像方法，估计预测$T_1\rho$值的不确定性以提供量化结果的置信水平具有重要价值。该不确定性还应被用于辅助后续定量分析和模型学习任务。方法：为满足这一需求，我们提出了一种用于基于学习的$T_1\rho$映射的参数图细化方法，并以概率方式训练模型以建模不确定性。我们还提出利用不确定性图对改进$T_1\rho$映射网络的训练进行空间加权，以进一步提升映射性能，并移除感兴趣区域中不可靠的$T_1\rho$值像素。该框架在包含51名不同肝纤维化分期患者的数据集上进行了测试。主要结果：我们的结果表明，基于学习的图细化方法可将相对映射误差降低至3%以下，并同时提供不确定性估计。估计的不确定性反映了实际误差水平，可被用于进一步将相对$T_1\rho$映射误差降低至2.60%，并有效移除感兴趣区域中的不可靠像素。意义：我们的研究表明，所提出的方法有潜力为肝脏提供基于学习的定量MRI系统，以实现可靠的$T_1\rho$映射。