The growth and progression of brain tumors is governed by patient-specific dynamics. Even when the tumor appears well-delineated in medical imaging scans, tumor cells typically already have infiltrated the surrounding brain tissue beyond the visible lesion boundaries. Quantifying and understanding these growth dynamics promises to reveal this otherwise hidden spread and is key to individualized therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a standard uniform margin around the visible tumor on imaging scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. Here, we present the framework GliODIL which infers the full spatial distribution of tumor cell concentration from available imaging data based on PDE-constrained optimization. The framework builds on the newly introduced method of Optimizing the Discrete Loss (ODIL), data are assimilated in the solution of the Partial Differential Equations (PDEs) by optimizing a cost function that combines the discrete form of the equations and data as penalty terms. By utilizing consistent and stable discrete approximations of the PDEs, employing a multigrid method, and leveraging automatic differentiation, we achieve computation times suitable for clinical application such as radiotherapy planning. Our method performs parameter estimation in a manner that is consistent with the PDEs. Through a harmonious blend of physics-based constraints and data-driven approaches, GliODIL improves the accuracy of estimating tumor cell distribution and, clinically highly relevant, also predicting tumor recurrences, outperforming all other studied benchmarks.

翻译：脑肿瘤的生长与进展受患者特异性动力学支配。即便肿瘤在医学影像扫描中呈现边界清晰形态，肿瘤细胞通常已浸润至可见病变边界之外的周围脑组织。量化并理解这些生长动力学有望揭示这种隐匿扩散，这是实现个体化治疗的关键。目前针对脑肿瘤的治疗方案（如放射治疗）通常采用在影像可见肿瘤周围划定标准统一边界的方法来覆盖不可见肿瘤生长。这种"一刀切"方法源自群体研究，往往无法反映个体患者病情的细微差别。本文提出GliODIL框架，该框架基于偏微分方程约束优化，从可用影像数据推断肿瘤细胞浓度的完整空间分布。该框架建立在最新提出的离散损失优化方法之上，通过结合方程离散形式与数据作为惩罚项的代价函数优化，将数据同化到偏微分方程求解过程中。通过采用一致稳定的偏微分方程离散近似、运用多重网格方法并利用自动微分技术，我们实现了适用于放射治疗计划等临床场景的计算时间。我们的方法以与偏微分方程一致的方式进行参数估计。通过物理约束与数据驱动方法的和谐融合，GliODIL在估算肿瘤细胞分布精度及临床高度关注的肿瘤复发预测方面均优于所有其他基准方法。