The Shortley-Weller scheme for variable coefficient two-point boundary value problems and its application to tumor growth problem with heterogeneous microenvironment
The Shortley-Weller scheme for variable coefficient two-point boundary value problems and its application to tumor growth problem with heterogeneous microenvironment
复制标题
变系数两点边值问题的Shortley-Weller格式及其在异质微环境肿瘤生长问题中的应用
DOI：
10.1016/j.cam.2020.112874
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发表时间：
2020-10-01
影响因子：
2.4
通讯作者：
Zheng, Xiaoming
中科院分区：
文献类型：
--
作者：
Sweidan, Mohyeedden;Chen, Xiaojun;Zheng, Xiaoming
本文的前半部分发展和分析了Shortley-Weller格式（或带二次外推的Ghost-Fluid方法）求解变系数两点边值问题，其中边界点不在均匀网格上。我们证明了局部截断误差在边界附近是一阶收敛的，而解在边界附近是三阶精度的，离开边界是二阶精度的。本文的后半部分将该数值格式应用于研究异质微环境中的肿瘤生长问题。我们发现经典的达西定律肿瘤模型可以通过可变的营养扩散速率捕获趋化特性，并通过可变的细胞外基质（ECM）渗透性捕获趋触机制。具体而言，肿瘤倾向于移动到具有较高扩散速率或较低ECM渗透性的区域。(C)2020爱思唯尔B. V.保留所有权利。
The first half of this work develops and analyzes the Shortley-Weller scheme (or Ghost-Fluid method with quadratic extrapolation) for a two-point boundary value problem with variable coefficients, where the boundary points are not on the uniform mesh. We prove that the local truncation error is first order convergent near the boundary, but the solution is third order accurate near the boundary and second order accurate away from the boundary. The second half of this work applies this numerical scheme to investigate the tumor growth problems in heterogeneous microenvironment. We discover that the classic Darcy's law tumor model can capture the chemotaxis property using variable nutrient diffusion rate and the haptotaxis mechanism through the variable extracellular matrix (ECM) permeability. Specifically, the tumor tends to move to the regions with higher diffusion rate or lower ECM permeability. (C) 2020 Elsevier B.V. All rights reserved.