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 st...
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2024-12-01
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| author | Dilbag Singh Ravinder R. Regatte Marcelo V. W. Zibetti |
| author_facet | Dilbag Singh Ravinder R. Regatte Marcelo V. W. Zibetti |
| author_sort | Dilbag Singh |
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| description | 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. |
| format | Article |
| id | doaj-art-be7646c68da740899f7bf2bf016afd9d |
| institution | Kabale University |
| issn | 2306-5354 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Bioengineering |
| spelling | doaj-art-be7646c68da740899f7bf2bf016afd9d2025-01-24T13:22:56ZengMDPI AGBioengineering2306-53542024-12-01121810.3390/bioengineering12010008HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee JointDilbag Singh0Ravinder R. Regatte1Marcelo V. W. Zibetti2Center of Biomedical Imaging, Department of Radiology, New York University Grossman School of Medicine, New York, NY 10016, USACenter of Biomedical Imaging, Department of Radiology, New York University Grossman School of Medicine, New York, NY 10016, USACenter of Biomedical Imaging, Department of Radiology, New York University Grossman School of Medicine, New York, NY 10016, USANon-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.https://www.mdpi.com/2306-5354/12/1/8multi-component MRI fittingnon-linear least squares (NLS)T1ρ mappingdeep learningknee joint |
| spellingShingle | Dilbag Singh Ravinder R. Regatte Marcelo V. W. Zibetti HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint Bioengineering multi-component MRI fitting non-linear least squares (NLS) T1ρ mapping deep learning knee joint |
| title | HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint |
| title_full | HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint |
| title_fullStr | HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint |
| title_full_unstemmed | HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint |
| title_short | HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint |
| title_sort | hdnls hybrid deep learning and non linear least squares based method for fast multi component t1ρ mapping in the knee joint |
| topic | multi-component MRI fitting non-linear least squares (NLS) T1ρ mapping deep learning knee joint |
| url | https://www.mdpi.com/2306-5354/12/1/8 |
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