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

癌症是全球主要的死亡原因之一，也是人类面临的最大健康问题之一。这也是现代科学通过众多科学学科的贡献来解决的最复杂的问题之一。尤其是数学，凭借其预测能力和结果的精确度，有助于加深对癌症的理解。此外，数学能够开发和优化新的治疗方法和早期发现策略，从而成为癌症最终治愈的不可或缺的一部分。目前的博士项目是这一整体努力的一部分，它采用了单尺度和多尺度数学方法的融合，目的是在一个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，我们将模拟和模拟癌细胞在上皮向间充质转变(EMT)过程中所经历的形态和迁移变化；EMT是一种细胞分化过程，在此过程中，细胞获得间质特征，打破细胞与细胞之间的粘连，并增强其运动特性。我们还研究了短期和远程的细胞-细胞相互作用，并研究了癌细胞的集体迁移和新的癌细胞群的形成。在更高的尺度上，在组织水平上，我们将解决连续的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，它们进入血管内并进入血流。在目前的PHD项目中，特别重要的将是对血液中癌细胞(称为循环肿瘤细胞)的循环以及随后的渗出到生物体中新位置的建模。这些癌细胞经历了相反的间质到上皮的转变(MET)，并有条件地产生新的肿瘤；在这个阶段，转移已经发生。这个博士项目开发的最终规模将是循环系统和各种身体器官的全面结合，以整体的、数学的和计算的方式表示有机体。

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.