用物理信息神经网络模拟细菌治癌的复杂动态，预测疗效并揭示关键控制机制。
Mathematical Modeling of Cancer-Bacterial Therapy: Analysis and Numerical Simulation via Physics-Informed Neural Networks
- 构建五维非线性反应-扩散模型，刻画肿瘤、细菌、氧气等多因素交互。
- PINN方法在无网格、少数据下求解，误差率可达O(n^-2 ln^4(n) + N^-1/2)。
- 发现维持肿瘤缺氧或使用耐氧菌是长期控制肿瘤的关键策略。
细菌癌症治疗利用厌氧菌对缺氧肿瘤区域的靶向能力，但肿瘤生长、细菌定植、氧水平、免疫抑制因子及细菌通信之间的相互作用仍缺乏量化分析。本文提出一个二维组织域中的五耦合非线性反应-扩散方程数学模型，证明了其全局适定性并识别稳态以分析稳定性。进一步采用物理信息神经网络（PINN）求解该系统，无需网格且不依赖大量数据。通过残差稳定性和Sobolev逼近误差界，提供收敛性保证，整体误差率为O(n^-2 ln^4(n) + N^-1/2)，其中n为网络宽度，N为采样点数。进行了多项数值实验，包括预测肿瘤对治疗的响应，并开展参数敏感性分析。结果表明，长期治疗效果可能需要维持肿瘤内的缺氧区域，或使用耐氧性更强的细菌，以实现持续的肿瘤控制。
原文摘要 · Abstract (English)
Bacterial cancer therapy exploits anaerobic bacteria's ability to target hypoxia tumor regions, yet the interactions among tumor growth, bacterial colonization, oxygen levels, immunosuppressive cytokines, and bacterial communication remain poorly quantified. We present a mathematical model of five coupled nonlinear reaction-diffusion equations in a two-dimensional tissue domain. We proved the global well-posedness of the model and identified its steady states to analyze stability. Furthermore, a physics-informed neural network (PINN) solves the system without a mesh and without requiring extensive data. It provides convergence guarantees by combining residual stability and Sobolev approximation error bounds. This results in an overall error rate of O(n^-2 ln^4(n) + N^-1/2), which depends on the network width n and the number of collocation points N. We conducted several numerical experiments, including predicting the tumor's response to therapy. We also performed a sensitivity analysis of certain parameters. The results suggest that long-term therapeutic efficacy may require the maintenance of hypoxia regions in the tumor, or using bacteria that tolerate oxygen better, may be necessary for long-lasting tumor control.
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