Title: Hypoxia-resistance heterogeneity in tumours: the impact of geometrical characterization of environmental niches and evolutionary trade-offs. A mathematical approach Show Chinese title

Title: 肿瘤中缺氧抗性异质性：环境生态位几何表征和进化权衡的影响 一种数学方法

Abstract: In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the phenotypic heterogeneity of cancer cell populations, whose qualitative and geometric characteristics are predominant factors in the occurrence of relapses and failure of eradication. We propose a mathematical model able to describe the eco-evolutionary spatial dynamics of tumour cells in their adaptation to hypoxic microenvironments. As a main novelty with respect to the existing literature, we combine a phenotypic indicator reflecting the experimentally-observed metabolic trade-off between the hypoxia-resistance ability and the proliferative potential with a 2d geometric domain, without the constraint of radial symmetry. The model is settled in the mathematical framework of phenotype-structured population dynamics and it is formulated in terms of systems of coupled non-linear integro-differential equations. The computational outcomes demonstrate that hypoxia-induced selection results in a geometric characterization of phenotypic-defined tumour niches that impact on tumour aggressiveness and invasive ability. Furthermore, results show how the knowledge of environmental characteristics provides a predictive advantage on tumour mass development in terms of size, shape, and composition. Show Chinese abstract

Abstract: 在癌症进化和治疗策略的研究中，科学证据表明，关键的动态在于肿瘤与环境的相互作用。 特别是，氧气浓度在决定癌细胞群体表型异质性中起着核心作用，其定性和几何特征是复发和根除失败的主要因素。 我们提出一个数学模型，能够描述肿瘤细胞在其适应低氧微环境时的生态进化空间动态。 作为相对于现有文献的主要创新，我们将一个反映实验观察到的低氧抗性能力和增殖潜力之间代谢权衡的表型指标与二维几何域相结合，而不受径向对称性的限制。 该模型建立在表型结构化种群动力学的数学框架内，并以耦合的非线性积分微分方程组的形式进行表述。 计算结果表明，低氧诱导的选择导致了表型定义的肿瘤生态位的几何表征，这影响了肿瘤的侵略性和侵袭能力。 此外，结果表明，对环境特征的了解在肿瘤质量发展方面提供了预测优势，包括大小、形状和组成。