{"doi":"10.3390/bioengineering12010008","title":"HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint","abstract":"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.","journal":"Bioengineering","year":2024,"id":478212,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":2,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.955,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":371096,"name":"Ravinder R. Regatte","orcid":"0000-0002-4607-7682","position":1,"is_corresponding":false},{"id":371093,"name":"Marcelo V. W. Zibetti","orcid":"0000-0003-2856-3625","position":2,"is_corresponding":false},{"id":1030817,"name":"Dilbag Singh","orcid":"0000-0001-6475-4491","position":0,"is_corresponding":true}],"reference_count":48,"raw_metadata":null,"created_at":"2026-07-19T02:06:42.155024Z","pmid":"39851282","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}