Lee Hyun Geun, Kim Yangjin, Kim Junseok
Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, South Korea. email:
Math Biosci Eng. 2015 Dec;12(6):1173-87. doi: 10.3934/mbe.2015.12.1173.
In this paper, we reformulate the diffuse interface model of the tumor growth (S.M. Wise et al., Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524--543). In the new proposed model, we use the conservative second-order Allen--Cahn equation with a space--time dependent Lagrange multiplier instead of using the fourth-order Cahn--Hilliard equation in the original model. To numerically solve the new model, we apply a recently developed hybrid numerical method. We perform various numerical experiments. The computational results demonstrate that the new model is not only fast but also has a good feature such as distributing excess mass from the inside of tumor to its boundary regions.
在本文中，我们重新阐述了肿瘤生长的扩散界面模型（S.M. 怀斯等人，《三维多物种非线性肿瘤生长 - I：模型与数值方法》，《理论生物学杂志》253卷（2008年）524 - 543页）。在新提出的模型中，我们使用带有时空依赖拉格朗日乘子的守恒二阶艾伦 - 卡恩方程，而非原始模型中使用的四阶卡恩 - 希利尔方程。为了数值求解新模型，我们应用了一种最近开发的混合数值方法。我们进行了各种数值实验。计算结果表明，新模型不仅速度快，而且具有将多余质量从肿瘤内部扩散到其边界区域等良好特性。
