用物理约束的神经表示建模呼吸运动，提升放疗精准度。

A precise spatial delivery of the radiation dose is crucial for the treatment success in radiotherapy. In the lung and upper abdominal region, respiratory motion introduces significant treatment uncertainties, requiring special motion management techniques. To address this, respiratory motion models are commonly used to infer the patient-specific respiratory motion and target the dose more efficiently. In this work, we investigate the possibility of using implicit neural representations (INR) for surrogate-based motion modeling. Therefore, we propose physics-regularized implicit surrogate-based modeling for respiratory motion (PRISM-RM). Our new integrated respiratory motion model is free of a fixed reference breathing state. Unlike conventional pairwise registration techniques, our approach provides a trajectory-aware spatio-temporally continuous and diffeomorphic motion representation, improving generalization to extrapolation scenarios. We introduce biophysical constraints, ensuring physiologically plausible motion estimation across time beyond the training data. Our results show that our trajectory-aware approach performs on par in interpolation and improves the extrapolation ability compared to our initially proposed INR-based approach. Compared to sequential registration-based approaches both our approaches perform equally well in interpolation, but underperform in extrapolation scenarios. However, the methodical features of INRs make them particularly effective for respiratory motion modeling, and with their performance steadily improving, they demonstrate strong potential for advancing this field.