基于 chemo-fluid 耦合的癌症生长多物理场连续介质建模的物理信息神经网络方法
A Physics-Informed Neural Network Approach to Multiphysics Continuum Modeling of Cancer Growth via Chemo-fluid Coupling
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中文总结 AI 辅助
该研究提出 PINN 框架，构建 chemo-fluid 耦合的肿瘤生长多物理连续介质模型，正问题求解精度高，逆问题可从含噪稀疏观测中精准恢复参数，为多物理肿瘤建模提供高效计算途径。
中文摘要 AI 辅助
肿瘤进展是一种固有多物理现象，其中间质流体动力学、生化输运和细胞力学在多个时空尺度上相互作用。经典的基于网格的求解器虽然精确，但对于逆参数识别和未来个性化患者预测管道所需的重复评估而言，会产生过高的计算成本。在这项工作中，我们引入了一种 Physics-Informed Neural Network（PINN，物理信息神经网络）框架，用于可处理的肿瘤生长 chemo-fluidic（化学流体）连续介质模型，该模型将肿瘤体积分数的平流-扩散-反应（ADR）方程与间质流体压力的准静态 Darcy（达西）压力方程耦合。通过有意解耦固体力学平衡，我们得到了一个三方程系统，其梯度结构在自动微分下稳定，支持鲁棒的深度学习优化。该网络仅通过物理约束同时学习状态变量（正问题），并从稀疏、含噪声的合成测量中恢复隐藏的输运参数（Data-Assimilation PINN，DA-PINN，数据同化 PINN，逆问题）。我们针对高分辨率有限差分（FD）参考验证了正求解器，实现了低于 0.002 的平均绝对误差。对于逆问题，从初始渗透率估计值 0.08（比真实值 0.02 高出 4 倍）开始，仅使用受 5% 高斯噪声污染的 5% 空间稀疏观测，DA-PINN 恢复渗透率的相对误差低于 5%。这些结果表明，物理信息深度学习为多物理肿瘤建模提供了一种可行、计算高效的途径，并为未来集成到临床数据同化管道奠定了数学基础。
英文摘要
Tumor progression is an inherently multiphysical phenomenon in which interstitial fluid dynamics, biochemical transport, and cellular mechanics interact across multiple spatiotemporal scales. Classical mesh-based solvers, although accurate, impose prohibitive computational costs for the repeated evaluations demanded by inverse parameter identification and future patient-specific predictive pipelines. In this work we introduce a Physics-Informed Neural Network (PINN) framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure. By intentionally decoupling the solid-mechanical equilibrium, we obtain a three-equation system whose gradient structure is stable under automatic differentiation, enabling robust deep-learning optimization. The network simultaneously learns both state variables from physics constraints alone (forward problem) and recovers hidden transport parameters from sparse, noisy synthetic measurements (Data-Assimilation PINN, DA-PINN, inverse problem). We verify the forward solver against a high-resolution finite-difference (FD) reference, achieving a mean absolute error below 0.002. For the inverse problem, starting from an initial permeability estimate of 0.08 (a factor of 4x above the true value of 0.02) with only 5% spatially sparse observations corrupted by 5% Gaussian noise, the DA-PINN recovers the permeability with a relative error below 5%. These results demonstrate that physics-informed deep learning constitutes a viable, computationally efficient route to multiphysics oncology modeling and lays the mathematical groundwork for future integration into clinical data assimilation pipelines.
