Physical models in the form of partial differential equations represent an important prior for many under-constrained problems. One example is tumor treatment planning, which heavily depends on accurate estimates of the spatial distribution of tumor cells in a patient's anatomy. Medical imaging scans can identify the bulk of the tumor, but they cannot reveal its full spatial distribution. Tumor cells at low concentrations remain undetectable, for example, in the most frequent type of primary brain tumors, glioblastoma. Deep-learning-based approaches fail to estimate the complete tumor cell distribution due to a lack of reliable training data. Most existing works therefore rely on physics-based simulations to match observed tumors, providing anatomically and physiologically plausible estimations. However, these approaches struggle with complex and unknown initial conditions and are limited by overly rigid physical models. In this work, we present a novel method that balances data-driven and physics-based cost functions. In particular, we propose a unique discretization scheme that quantifies the adherence of our learned spatiotemporal tumor and brain tissue distributions to their corresponding growth and elasticity equations. This quantification, serving as a regularization term rather than a hard constraint, enables greater flexibility and proficiency in assimilating patient data than existing models. We demonstrate improved coverage of tumor recurrence areas compared to existing techniques on real-world data from a cohort of patients. The method holds the potential to enhance clinical adoption of model-driven treatment planning for glioblastoma.

本研究解决了肿瘤细胞空间分布估计的不准确问题，尤其是在属于低浓度的胶质母细胞瘤等类型的脑肿瘤中。论文提出了一种新的方法，通过平衡数据驱动和基于物理的代价函数，采用独特的离散化方案来量化肿瘤和脑组织的时空分布，显著提升了对患者数据的适应能力，展示了在现实患者数据上的肿瘤复发区域覆盖率的改进。此方法有望增强胶质母细胞瘤的模型驱动治疗规划的临床应用。 

物理正则化的多模态图像融合用于脑肿瘤定位