Error Bound Analysis of Physics-Informed Neural Networks-Driven T2 Quantification in Cardiac Magnetic Resonance Imaging

2025-12-16

AI Summary

T₂ quantification in cardiac MRI lacks a gold standard, theoretical guarantees, and relies heavily on large annotated datasets. Method: This paper proposes the first physics-informed neural network (PINN) framework constrained by the Bloch equations for T₂ mapping, requiring only a single target scan—eliminating dependence on training databases. Contribution/Results: We establish, for the first time, theoretical upper bounds on both estimation error and generalization error for PINN-driven T₂ estimation, enabling verifiable, ground-truth-free quantitative accuracy assessment. Validation across a numerical cardiac phantom, a water phantom experiment, and clinical data from 94 patients with acute myocardial infarction demonstrates high T₂ quantification accuracy; empirical errors strictly adhere to the derived theoretical bounds, confirming robustness and clinical feasibility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Physics-Informed Neural Networks (PINN) are emerging as a promising approach for quantitative parameter estimation of Magnetic Resonance Imaging (MRI). While existing deep learning methods can provide an accurate quantitative estimation of the T2 parameter, they still require large amounts of training data and lack theoretical support and a recognized gold standard. Thus, given the absence of PINN-based approaches for T2 estimation, we propose embedding the fundamental physics of MRI, the Bloch equation, in the loss of PINN, which is solely based on target scan data and does not require a pre-defined training database. Furthermore, by deriving rigorous upper bounds for both the T2 estimation error and the generalization error of the Bloch equation solution, we establish a theoretical foundation for evaluating the PINN's quantitative accuracy. Even without access to the ground truth or a gold standard, this theory enables us to estimate the error with respect to the real quantitative parameter T2. The accuracy of T2 mapping and the validity of the theoretical analysis are demonstrated on a numerical cardiac model and a water phantom, where our method exhibits excellent quantitative precision in the myocardial T2 range. Clinical applicability is confirmed in 94 acute myocardial infarction (AMI) patients, achieving low-error quantitative T2 estimation under the theoretical error bound, highlighting the robustness and potential of PINN.

Problem

• Develops a PINN-based method for T2 quantification in cardiac MRI without requiring large training datasets.
• Establishes theoretical error bounds for T2 estimation and generalization to evaluate quantitative accuracy.
• Validates the approach on numerical models, phantoms, and clinical AMI patients for robustness and precision.

Innovation

• Embedding Bloch equation in PINN loss for T2 estimation
• Deriving theoretical error bounds for T2 estimation accuracy
• Validating method on cardiac model and clinical AMI patients