Cancer invasion and metastatic spread to secondary sites in the body are facilitated by a complex interplay between cancer cells of different phenotypes and their microenvironment. A trade-off between the cancer cells’ ability to invade the tissue and to metastasize, and their ability to proliferate has been observed. This gives rise to the classification of cancer cells into those of mesenchymal and epithelial phenotype, respectively. Additionally, mixed phenotypic states between these two extremes exist. Cancer cells can transit between these states via epithelial–mesenchymal transition (EMT) and the reverse process, mesenchymal–epithelial transition (MET). These processes are crucial for both the local tissue invasion and the metastatic spread of cancer cells. To shed light on the role of these phenotypic states and the transitions between them in the invasive and metastatic process, we extend our recently published multi-grid, hybrid, individual-based mathematical metastasis framework (Franssen et al. 2019, A mathematical framework for modelling the metastatic spread of cancer. Bull. Math. Biol., 81, 1965). In addition to cancer cells of epithelial and of mesenchymal phenotype, we now also include those of an intermediate partial-EMT phenotype. Furthermore, we allow for the switching between these phenotypic states via EMT and MET at the biologically appropriate steps of the invasion-metastasis cascade. We also account for the likelihood of spread of cancer cells to the various secondary sites and differentiate between the tissues of the organs involved in our simulations. Finally, we consider the maladaptation of metastasized cancer cells to the new tumour microenvironment at secondary sites as well as the immune response at these sites by accounting for cancer cell dormancy and death. This way, we create a first mathematical multi-organ model that explicitly accounts for EMT-processes occurring at the level of individual cancer cells in the context of the invasion-metastasis cascade.

中文翻译：

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癌症转移扩散中双向上皮-间质转化的数学多器官模型

不同表型的癌细胞与其微环境之间的复杂相互作用促进了癌症的侵袭和转移扩散到体内的次要部位。已经观察到癌细胞侵袭组织和转移的能力与它们的增殖能力之间的权衡。这将癌细胞分别分为间充质和上皮表型。此外，这两个极端之间存在混合表型状态。癌细胞可以通过上皮-间充质转化（EMT）和逆过程，间充质-上皮转化（MET）在这些状态之间迁移。这些过程对于局部组织浸润和癌细胞的转移扩散都至关重要。等。2019年，一个用于模拟癌症转移扩散的数学框架。公牛。数学。生物学，81，1965）。除了上皮和间充质表型的癌细胞外，我们现在还包括中等部分EMT表型的癌细胞。此外，我们允许在侵袭转移级联的生物学上适当的步骤通过EMT和MET在这些表型状态之间切换。我们还考虑了癌细胞扩散到各个次级部位的可能性，并区分了我们的模拟所涉及的器官组织。最后，通过考虑癌细胞的休眠和死亡，我们考虑了转移癌细胞适应新肿瘤在次要部位的微环境以及这些部位的免疫反应。这条路，