Biophysical modeling of brain tumors has emerged as a promising strategy for personalizing radiotherapy planning by estimating the otherwise hidden distribution of tumor cells within the brain. However, many existing state-of-the-art methods are computationally intensive, limiting their widespread translation into clinical practice. In this work, we propose an efficient and direct method that utilizes soft physical constraints to estimate the tumor cell concentration from preoperative MRI of brain tumor patients. Our approach optimizes a 3D tumor concentration field by simultaneously minimizing the difference between the observed MRI and a physically informed loss function. Compared to existing state-of-the-art techniques, our method significantly improves predicting tumor recurrence on two public datasets with a total of 192 patients while maintaining a clinically viable runtime of under one minute - a substantial reduction from the 30 minutes required by the current best approach. Furthermore, we showcase the generalizability of our framework by incorporating additional imaging information and physical constraints, highlighting its potential to translate to various medical diffusion phenomena with imperfect data.

翻译：脑肿瘤的生物物理建模已成为一种有前景的策略，通过估计大脑内原本隐藏的肿瘤细胞分布，实现放疗规划的个体化。然而，许多现有的先进方法计算密集，限制了其在临床实践中的广泛转化。在本研究中，我们提出了一种高效直接的方法，利用软物理约束从脑肿瘤患者的术前MRI图像中估计肿瘤细胞浓度。我们的方法通过同时最小化观测MRI与基于物理信息的损失函数之间的差异，来优化三维肿瘤浓度场。与现有的先进技术相比，我们的方法在两个共计包含192名患者的公共数据集上显著提高了肿瘤复发预测的准确性，同时将运行时间保持在临床可行的1分钟以内——这相较于当前最佳方法所需的30分钟有了大幅减少。此外，我们通过整合额外的影像信息和物理约束，展示了我们框架的泛化能力，凸显了其在处理数据不完美的多种医学扩散现象中的转化潜力。