Singh Dilbag, Regatte Ravinder R, Zibetti Marcelo V W
Center of Biomedical Imaging, Department of Radiology, New York University Grossman School of Medicine, New York, NY 10016, USA.
Bioengineering (Basel). 2024 Dec 25;12(1):8. doi: 10.3390/bioengineering12010008.
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.
非线性最小二乘法（NLS）常用于定量磁共振成像（MRI），特别是在多指数T1ρ映射中，该方法可为组织中的不同弛豫模型提供精确的参数估计，如单指数（ME）、双指数（BE）和拉伸指数（SE）模型。然而，NLS可能存在对初始猜测敏感、收敛速度慢和计算成本高等问题。虽然基于深度学习（DL）的T1ρ拟合方法提供了更快的替代方案，但它们通常面临诸如对噪声敏感以及依赖NLS生成的参考数据进行训练等挑战。为了解决这两种方法的这些局限性，我们提出了HDNLS，一种用于快速多分量参数映射的混合模型，特别针对膝关节的T1ρ映射。HDNLS将基于合成数据训练的逐体素DL与几次NLS迭代相结合，以加速拟合过程，从而消除了训练所需的参考MRI数据。由于参数映射的逆问题性质，特定模型中的某些参数可能对噪声更敏感，例如BE模型中的短分量。为了解决这个问题，HDNLS中的NLS迭代次数可以起到正则化的作用，稳定估计以获得有意义的解。因此，在这项工作中，我们对NLS迭代对HDNLS性能的影响进行了全面分析，并提出了四种平衡估计精度和计算速度的变体。这些变体分别是超快-NLS、超快速-HDNLS、HDNLS和松弛-HDNLS。这些方法允许用户根据其特定的速度和性能要求选择合适的配置。其中，HDNLS在性能和拟合时间之间表现为最佳权衡。对合成数据的大量实验表明，HDNLS实现了与NLS和正则化NLS（RNLS）相当的性能，速度至少提高了13倍。HDNLS仅比基于DL的方法稍慢；然而，它显著提高了估计质量，为T1ρ拟合提供了一种快速且可靠的解决方案。
