算法渐近分析：扩展癌症免疫学建模的工具库
Algorithmic asymptotic analysis: extending the arsenal of cancer immunology modeling
AI总结：
本研究利用算法渐近分析考察肿瘤-免疫系统多尺度模型，通过Computational Singular Perturbation方法识别肿瘤爆发阶段的慢动态机制，构建了参数减半且准确预测的降阶模型，为简化复杂模型和开发更有效靶向治疗提供了新途径。
摘要：
癌症免疫疗法的最新进展推动了肿瘤-免疫系统模型的发展，旨在提供机制理解并指示更有效的治疗方案。然而，此类模型的复杂性、多尺度动态及其过度参数化的特性使其难以被广泛使用。在本研究中，考察了一个构建肿瘤细胞与自然杀伤细胞、CD8$^+$ T细胞和循环淋巴细胞相互作用的基础模型的动态。首先表明，系统向高肿瘤或无肿瘤平衡态的长期演化是由肿瘤进展的初始“爆发阶段”的动态决定的。聚焦于该阶段，采用算法化的Computational Singular Perturbation方法来识别限制系统向平衡态演化的底层机制以及沿其主导的慢动态。结果表明，这些见解在不同的肿瘤-免疫系统和依赖患者的实现中均得以保留。利用所获得的机制理解，以算法方式构建了一个新的降阶模型，该模型能准确预测系统在爆发阶段的动态，且仅包含详细模型一半的参数。本分析展示了算法渐近分析在简化癌症免疫学模型复杂、过度参数化和多尺度特性方面的潜力，并指出了为开发更有效治疗而需靶向的相互作用和细胞类型。
英文摘要：
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their multi-scale dynamics and their overparameterized character renders them inaccessible for wide utilization. In this work, the dynamics of a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8$^+$ T cells and circulating lymphocytes is examined. It is first shown that the long-term evolution of the system towards high-tumor or tumor-free equilibria is determined by the dynamics of an initial \emph{explosive stage} of tumor progression. Focusing on this stage, the algorithmic Computational Singular Perturbation methodology is employed to identify the underlying mechanisms confining the system's evolution towards the equilibrium and the governing slow dynamics along them. It is shown that these insights are preserved along different tumor-immune system and patient-dependent realizations. Utilizing the obtained mechanistic understanding, a novel reduced model is constructed in an algorithmic fashion, which accurately predicts the dynamics of the system during the explosive stage and includes half of the parameters of the detailed model. This present analysis demonstrates the potential of algorithmic asymptotic analysis to simplify the complex, overeparameterized and multi-scale nature of cancer immunology models and to indicate the interactions and cell types to target for more effective treatment development.
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