Modelling Tumour-Immunity Interactions With Different Stimulation Functions
Modelling Tumour-Immunity Interactions With Different Stimulation Functions
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发表时间：
2003
影响因子：
1.9
通讯作者：
P. Zhivkov;J. Waniewski
中科院分区：
文献类型：
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作者：
P. Zhivkov;J. Waniewski
肿瘤免疫疗法旨在刺激原本不活跃的免疫系统，以消除或至少限制原始肿瘤及其转移的生长。肿瘤-免疫系统相互作用涉及肿瘤抗原对免疫应答的刺激，但也涉及肿瘤诱导的淋巴细胞死亡。用两个非线性常微分方程组描述免疫系统与肿瘤相互作用的动态过程。考虑了三种不同类型的刺激功能：（a）Lotka-Volterra相互作用，（B）Michaelis-Menten形式中依赖于肿瘤大小的开关功能，以及（c）依赖于肿瘤大小与免疫能力之比的Michaelis-Menten开关功能。平衡点的线性分析产生了几种不同类型的系统的渐近行为：不受限制的肿瘤生长，消除肿瘤或稳定的肿瘤大小，如果初始的肿瘤大小是相对较小的，否则不受限制的肿瘤生长，全球稳定的肿瘤大小，和全球消除肿瘤。切换功能依赖于肿瘤的大小和肿瘤的免疫能力比的模型表现出定性相似的渐近行为。
Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different types of stimulation functions were considered: (a) Lotka-Volterra interactions, (b) switching functions dependent on the tumour size in the Michaelis-Menten form, and (c) Michaelis-Menten switching functions dependent on the ratio of the tumour size to the immune capacity. The linear analysis of equilibrium points yielded several different types of asymptotic behaviour of the system: unrestricted tumour growth, elimination of tumour or stabilization of the tumour size if the initial tumour size is relatively small, otherwise unrestricted tumour growth, global stabilization of the tumour size, and global elimination of the tumour. Models with switching functions dependent on the tumour size and the tumour to the immune capacity ratio exhibited qualitatively similar asymptotic behaviour.