HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint

Non-linear least squares (NLS) methods are commonly used for quantitative magnetic resonance imaging (MRI), especially for multi-exponential T1ρ mapping, which provides precise parameter estimation for different relaxation models in tissues, such as mono-exponential (ME), bi-exponential (BE), and stretched-exponential (SE) models. However, NLS may suffer from problems like sensitivity to initial guesses, slow convergence speed, and high computational cost. While deep learning (DL)-based T1ρ fitting methods offer faster alternatives, they often face challenges such as noise sensitivity and reliance on NLS-generated reference data for training. To address these limitations of both approaches, we propose the HDNLS, a hybrid model for fast multi-component parameter mapping, particularly targeted for T1ρ mapping in the knee joint. HDNLS combines voxel-wise DL, trained with synthetic data, with a few iterations of NLS to accelerate the fitting process, thus eliminating the need for reference MRI data for training. Due to the inverse-problem nature of the parameter mapping, certain parameters in a specific model may be more sensitive to noise, such as the short component in the BE model. To address this, the number of NLS iterations in HDNLS can act as a regularization, stabilizing the estimation to obtain meaningful solutions. Thus, in this work, we conducted a comprehensive analysis of the impact of NLS iterations on HDNLS performance and proposed four variants that balance estimation accuracy and computational speed. These variants are Ultrafast-NLS, Superfast-HDNLS, HDNLS, and Relaxed-HDNLS. These methods allow users to select a suitable configuration based on their specific speed and performance requirements. Among these, HDNLS emerges as the optimal trade-off between performance and fitting time. Extensive experiments on synthetic data demonstrate that HDNLS achieves comparable performance to NLS and regularized-NLS (RNLS) with a minimum of a 13-fold improvement in speed. HDNLS is just a little slower than DL-based methods; however, it significantly improves estimation quality, offering a solution for T1ρ fitting that is fast and reliable.