{"doi":"10.1002/mrm.70154","title":"Balancing Bias and Variance in Deep Learning‐Based Tumor Microstructural Parameter Mapping","abstract":"PURPOSE: Time-dependent diffusion MRI enables quantification of tumor microstructural parameters useful for diagnosis and prognosis. Nevertheless, current model fitting approaches exhibit suboptimal bias-variance trade-offs; specifically, nonlinear least squares fitting (NLLS) demonstrated low bias but high variance, whereas supervised deep learning methods trained with mean squared error loss (MSE-Net) yielded low variance but elevated bias. This study investigates these bias-variance characteristics and proposes a method to control fitting bias and variance. METHODS: Random walk with barrier model was used as a representative biophysical model. NLLS and MSE-Net were reformulated within the Bayesian framework to elucidate their bias-variance behaviors. We introduced B2V-Net, a supervised learning approach using a loss function with adjustable bias-variance weighting, to control bias-variance trade-off. B2V-Net was evaluated and compared against NLLS and MSE-Net numerically across a wide range of parameters and noise levels, as well as in vivo in patients with head and neck cancer. RESULTS: Flat posterior distributions that were not centered at ground truth parameters explained the bias-variance behaviors of NLLS and MSE-Net. B2V-Net controlled the bias-variance trade-off, achieving a 56% reduction in standard deviation relative to NLLS and an 18% reduction in bias compared to MSE-Net. In vivo parameter maps from B2V-Net demonstrated a balance between smoothness and accuracy. CONCLUSION: We demonstrated and explained the low bias-high variance of NLLS and the low variance-high bias of MSE-Net. The proposed B2V-Net can balance bias and variance. Our work provided insights and methods to guide the design of customized loss functions tailored to specific clinical imaging needs.","journal":"Magnetic Resonance in Medicine","year":2025,"id":578837,"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":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9506,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2025-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":334256,"name":"Yue Cao","orcid":"0000-0003-3910-3261","position":1,"is_corresponding":false},{"id":334254,"name":"Jiaren Zou","orcid":"0000-0002-8356-1967","position":0,"is_corresponding":true}],"reference_count":35,"raw_metadata":null,"created_at":"2026-07-19T02:58:24.957414Z","pmid":"41126537","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":[]}