The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical-experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth-conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

中文翻译：

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曲妥珠单抗诱导的HER2 +乳腺癌体内小鼠模型中免疫应答的数学模型。

这项研究的目的是开发一种综合的数学实验方法，以了解免疫系统与曲妥珠单抗对过度表达人表皮生长因子受体2（HER2 +）的乳腺癌的影响之间的相互作用。构建了一个耦合的常微分方程系统，以描述肿瘤生长的时间变化，以及免疫应答，血管，坏死和缺氧时肿瘤内的变化。使用从HER2 +乳腺癌鼠模型的成像或组织学获得的肿瘤体积，血管，坏死和缺氧的连续采集实验数据对数学模型进行校准。敏感性分析表明，模型组件对13个参数中的12个敏感，但考虑到参数值的不确定性，模型仿真仍然与实验数据一致。在给定初始条件的情况下，数学模型预测了治疗动物中免疫浸润随时间的增加。免疫荧光染色结果证实了这一预测，方法是与对照组相比，治疗后肿瘤的总组织中CD11c和F4 / 80（树突状细胞和/或巨噬细胞表达的蛋白）的共染色增加（$ p <0.03） $）。我们认为，所提出的数学实验方法可用于阐明曲妥珠单抗诱导的肿瘤反应与免疫系统之间的驱动相互作用，该免疫系统驱动脉管系统的稳定，同时减少数学模型所揭示的肿瘤生长结论，但并未减少仅从实验数据就可以推论得出。