Jarrett Angela M, Bloom Meghan J, Godfrey Wesley, Syed Anum K, Ekrut David A, Ehrlich Lauren I, Yankeelov Thomas E, Sorace Anna G
Institute for Computational Engineering and Sciences, University of Texas, Austin, TX, USA.
Livestrong Cancer Institutes, University of Texas, Austin, TX, USA.
Math Med Biol. 2019 Sep 2;36(3):381-410. doi: 10.1093/imammb/dqy014.
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.
本研究的目标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。构建了一个耦合常微分方程组，以描述肿瘤生长的时间变化，以及肿瘤内免疫反应、血管生成、坏死和缺氧的变化。该数学模型通过从HER2+乳腺癌小鼠模型的成像或组织学中获得的肿瘤体积、血管生成、坏死和缺氧的系列实验数据进行校准。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，模型模拟结果仍与实验数据一致。在给定初始条件下，数学模型预测治疗动物体内免疫浸润会随时间增加。免疫荧光染色结果表明，与对照组相比，治疗肿瘤的总组织中CD11c和F4/80（树突状细胞和/或巨噬细胞表达的蛋白质）的共染色增加，从而验证了这一预测（p<0.03）。我们认为，所提出的数学实验方法可用于阐明肿瘤中曲妥珠单抗诱导的反应与免疫系统之间的驱动相互作用，这些相互作用驱动血管系统的稳定，同时减少肿瘤生长——这是数学模型揭示的结论，仅从实验数据中无法推导得出。
