Inria Centre de l'Université de Bordeaux, Institut de Mathématiques de Bordeaux, CNRS UMR 5251, 351 cours de la Libération, 33405, Talence Cedex, France.
Sorbonne Université Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint- Antoine Research Center (CRSA), 75012, Paris, France.
Bull Math Biol. 2024 Feb 12;86(3):30. doi: 10.1007/s11538-024-01260-w.
One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal membrane separating the epithelial tissue from the connective one. In this work, we employ a synergistic experimental and mathematical modelling approach to explore the invasion process of tumor cells. A mathematical model composed of reaction-diffusion equations describing the evolution of the tumor cells density on a gelatin substrate, MMPs enzymes concentration and the degradation of the gelatin is proposed. This is completed with a calibration strategy. We perform a sensitivity analysis and explore a parameter estimation technique both on synthetic and experimental data in order to find the optimal parameters that describe the in vitro experiments. A comparison between numerical and experimental solutions ends the work.
固体肿瘤最关键和致命的特征之一是癌细胞在所谓的转移扩散过程中迁移和侵袭其他器官的能力增强。这要归功于基质金属蛋白酶 (MMPs) 的产生，这种酶能够降解基底膜中丰富的一种胶原蛋白，基底膜将上皮组织与结缔组织分开。在这项工作中，我们采用协同的实验和数学建模方法来探索肿瘤细胞的侵袭过程。提出了一个由反应-扩散方程组成的数学模型，这些方程描述了在明胶基质上肿瘤细胞密度、MMPs 酶浓度和明胶降解的演变。这与校准策略相结合。我们对合成数据和实验数据进行了敏感性分析和参数估计技术的探索，以便找到描述体外实验的最佳参数。数值解和实验解的比较结束了这项工作。
