论文标题
具有自噬的肿瘤生长模型：反应 - （交叉）扩散系统及其自由边界极限
A tumor growth model with autophagy: the reaction-(cross-)diffusion system and its free boundary limit
论文作者
论文摘要
在本文中，我们提出了一个肿瘤生长模型，以纳入和研究自噬的空间效应。细胞分为两个阶段：正常细胞和自噬细胞，它们的动力学也与养分相结合。首先，我们构建了一个反应 - （交叉）扩散系统，描述了细胞密度的演化，其中漂移取决于关节压的负梯度，而反应项则表现出自噬的独特机制。接下来，在不可压缩的极限中，这种细胞密度模型自然连接到自由边界系统，描述了肿瘤区域的几何运动。在特殊情况下分析自由边界模型，我们表明，单元格的两个阶段的比率成倍收敛到``固定良好''限制。在此````良好''限制的限制中，我们获得了自由边界系统的分析解决方案，该解决方案表明在不包括局限性的情况下，自动噬菌体的存在，指示了肿瘤大小的指数增长。还提供了数值模拟来说明分析属性并探索更多方案。
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients. First, we construct a reaction-(cross-)diffusion system describing the evolution of cell densities, where the drift is determined by the negative gradient of the joint pressure, and the reaction terms manifest the unique mechanism of autophagy. Next, in the incompressible limit, such a cell density model naturally connects to a free boundary system, describing the geometric motion of the tumor region. Analyzing the free boundary model in a special case, we show that the ratio of the two phases of cells exponentially converges to a ``well-mixed" limit. Within this ``well-mixed" limit, we obtain an analytical solution of the free boundary system which indicates the exponential growth of the tumor size in the presence of autophagy in contrast to the linear growth without it. Numerical simulations are also provided to illustrate the analytical properties and to explore more scenarios.
