论文标题
实体瘤生长的两相模型的渐近分析
Asymptotic Analysis of a Two-Phase Model of Solid Tumour Growth
论文作者
论文摘要
我们研究了血管肿瘤的生长作为由细胞和液体组成的两相过程。基于由一维连续性移动模型（由Byrne，King，McElwain，Preziosi，Applied Mathematics Letters，2003，16，567-573），我们为二维中肿瘤生长的类似模型定义了边界条件。我们研究了极限情况的移动配方中（具有可忽略的营养消耗和细胞阻力）中一个维度依赖性溶液曲线的线性稳定性。为此，我们通过使用匹配的渐近近似方法来获得二维扰动的渐近极限（在肿瘤正在生长的情况下）。在表征了扰动的渐近极限之后，我们将其与时间相关的解决方案曲线进行了比较，以便从分析上获得不稳定性的条件。提到了数值模拟。
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003, 16, 567-573), we defined boundary conditions for the analogous model of tumour growth in two dimensions. We investigate linear stability of one dimensional time-dependent solution profiles in the moving-boundary formulation of a limit case (with negligible nutrient consumption and cell drag). For this, we obtain an asymptotic limit of the two-dimensional perturbations for large time (in the case where the tumour is growing) by using the method of matched asymptotic approximations. Having characterised an asymptotic limit of the perturbations, we compare it to the time-dependent solution profile in order to analytically obtain a condition for instability. Numerical simulations are mentioned.
