Osojnik Ana, Gaffney Eamonn A, Davies Michael, Yates James W T, Byrne Helen M
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK.
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK.
J Theor Biol. 2020 Sep 21;501:110250. doi: 10.1016/j.jtbi.2020.110250. Epub 2020 Mar 19.
We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters.
我们研究了一个最初由库兹涅佐夫等人（1994年）提出的五室数学模型，以研究肿瘤微环境中肿瘤细胞与免疫细胞之间非线性相互作用的影响，其中免疫细胞可能诱导肿瘤细胞死亡，而肿瘤细胞可能使免疫细胞失活。利用模型中的时间尺度分离，我们使用匹配渐近法推导出全模型的一个新的二维、长时间尺度近似，它不同于库兹涅佐夫等人（1994年）引入的准稳态近似，但已针对全模型的数值解进行了验证。通过相平面分析，我们表明我们的简化模型是可激发的，这是一个传统上与肿瘤免疫动力学无关的特征。通过系统的参数敏感性分析，我们证明可激发性在模型中产生复杂的分岔动力学。这些与各种临床观察到的现象一致，并表明可激发性可能是肿瘤免疫相互作用的基础。该模型通过具有不同肿瘤细胞浓度的稳定稳态展现了免疫编辑的三个阶段——清除、平衡和逃逸。肿瘤细胞数量的这种异质性可能源于初始条件的变异性和/或控制免疫系统特性及其对肿瘤反应的模型参数。我们确定了可以通过免疫疗法操纵以控制肿瘤大小的不同生物物理参数靶点，并且我们发现根据相关模型参数的患者特异性值所确定的免疫系统强度不同，患者之间的首选策略可能会有所不同。
