Multiscale mathematical treatise of the invasion-metastasis cascade: from the solitary cancer cell migration to the holistic representation of the org

癌症是全球死亡的首要原因之一，也是人类面临的最大健康问题之一。它也是现代科学在众多科学学科的贡献下所解决的最复杂的问题之一。特别是数学，凭借其预测能力和结果的准确性，有助于更深入地了解癌症。此外，数学使新的治疗方法和早期检测策略的发展和优化成为最终治愈癌症的一个组成部分。目前的博士项目是这一整体努力的一部分，通过采用单尺度和多尺度数学方法的合并，目的是在统一的数学保护伞下，将侵袭-转移级联的几个生物医学过程结合起来。更详细地说，我们将建模和模拟癌细胞在上皮-间质转化（EMT）过程中经历的形态和迁移变化；一种细胞分化过程，在此过程中细胞获得间充质特性，打破细胞间的黏附，增强其运动性。我们还研究了短期和长期的细胞间相互作用，并研究了癌细胞的集体迁移和新的癌细胞簇的形成。在更高的尺度上，在组织水平上，我们将解决连续癌细胞簇的上皮运动，同时允许EMT发生并产生孤立的间充质样癌细胞。当这些癌细胞侵入局部组织并到达附近的血管时，它们进入体内并进入血流。在当前的博士项目中，特别重要的是对血液中癌细胞循环（称为循环肿瘤细胞）的建模，以及随后向生物体新部位的外渗。这些癌细胞经历相反的间质-上皮转化（MET）并有条件地产生新的肿瘤；在这个阶段已经发生了转移。这个博士项目发展的最终规模将是循环网络和各种身体器官在有机体的整体数学和计算表示中的全面结合。

Cancer is one of the primer causes of death globally and one of the biggest health problems humanity faces. It is also one of the most complex questions that modern science addresses with the contribution of a multitude of scientific disciplines. Mathematics, in particular contributes, with its predictive competences and the precision of its results, in gaining a deeper understanding of cancer. Moreover, Mathematics enables the development and optimisation of new treatments and early detection strategies becoming thusly an integral part of the eventual cure of cancer. The current PhD project is a part of this overall effort by employing an amalgamation of single- and multiscale mathematical methods with the aim to combine under a unified mathematical umbrella, several of the biomedical processes of the invasion-metastasis cascade. In more detail, we will model and simulate morphological and migratory changes that the cancer cells undergo during the Epithelial-to-Mesenchymal Transition (EMT); a cellular differentiation procedure after which the cells obtain mesenchymal character, break their cell-cell adhesions, and enhance their motility properties. We also study short- and long-range cell-cell interactions and investigate the collective migration of cancer cells and the formation of new cancer cell-clusters. At higher scale, at the level of the tissue, we will address the epithelial movement of a contiguous cluster of cancer cells while allowing for the EMT to take place and give rise to solitary mesenchymal-like cancer cells. When these cancer cells invade the local tissue and reach a nearby blood vessel, they intravasate and enter the blood stream. Of particular importance in the current PhD project will be the modelling of the circulation of cancer cells (termed Circulatory Tumour Cells) in the blood stream and of the subsequent extravasation to new locations in the organism. These cancer cells undergo the opposite Mesenchymal-to-Epithelial Transition (MET) and conditionally engender new tumours; at this stage the metastasis has occurred. The final scale in the development of this PhD project will be the comprehensive combination of the circulatory network and various body organs in a holistic mathematical and computational representation of the organism.