用微分方程代理模型，快速分析免疫细胞对癌细胞的抑制效果。
Learning surrogate equations for the analysis of an agent-based cancer model
- 通过耦合方程学习构建每种情景的群体反应模型。
- 发现癌细胞稳态浓度与初始免疫细胞数呈线性关系。
- 无需复杂模拟，可快速估算降低癌细胞的最优免疫条件。
本文将一个描述癌细胞与正常细胞相互作用的双物种代理模型扩展为三物种模型，引入免疫细胞参与。针对六种不同情景，研究了癌细胞与免疫细胞的竞争关系及免疫细胞初始浓度对癌细胞动态的影响。利用耦合方程学习方法，为每种情景构建了基于种群的反应模型，并将其统一为单一代理模型，其包含三个耦合的常微分方程，远比原始代理模型易于分析。以癌细胞稳态浓度为例，发现其与初始免疫细胞浓度存在线性关系，从而可在不运行昂贵的随机代理模型的前提下，快速估算出能显著减少癌细胞的最优竞争参数和初始免疫浓度。
原文摘要 · Abstract (English)
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction with a third species -- namely immune cells. We run six different scenarios to explore the competition between cancer and immune cells and the initial concentration of the immune cells on cancer dynamics. We then use coupled equation learning to construct a population-based reaction model for each scenario. We show how they can be unified into a single surrogate population-based reaction model, whose underlying three coupled ordinary differential equations are much easier to analyse than the original agent-based model. As an example, by finding the single steady state of the cancer concentration, we are able to find a linear relationship between this concentration and the initial concentration of the immune cells. This then enables us to estimate suitable values for the competition and initial concentration to reduce the cancer substantially without performing additional complex and expensive simulations from an agent-based stochastic model.
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