用物理方程约束神经网络,实现无需大量数据的精准心脏MRI T2定量。
Error Bound Analysis of Physics-Informed Neural Networks-Driven T2 Quantification in Cardiac Magnetic Resonance Imaging
- 将磁共振物理方程嵌入损失函数,仅需扫描数据即可训练。
- 理论证明误差上限,即使无真实值也能评估T2估计精度。
- 在94名心梗患者中验证,结果稳定且误差可控,适合临床应用。
物理信息神经网络(PINN)正成为磁共振成像(MRI)定量参数估计的新兴方法。现有深度学习方法虽能准确估算T2参数,但仍需大量训练数据,缺乏理论支持和公认金标准。针对此,本文提出将MRI基本物理原理——布洛赫方程嵌入PINN的损失函数,仅依赖目标扫描数据,无需预先定义训练数据库。同时,通过推导T2估计误差与布洛赫方程解泛化误差的严格上界,建立了评估PINN定量精度的理论基础。即使无法获得真实值或金标准,该理论仍可估算与真实T2参数的误差。数值心脏模型与水胶体幻影实验验证了方法在心肌T2范围内的优异定量精度;94例急性心肌梗死患者的临床数据进一步证实其鲁棒性,实现了符合理论误差边界下的低误差定量估计,凸显了PINN的应用潜力。
原文摘要 · Abstract (English)
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.
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