我们关于肿瘤生长相场混合理论的论文发表在JMPS上。连续介质模型模拟了不同微环境下无血管肿瘤生长的重要机械-化学-生物学特征，即营养浓度和机械应力。
Faghihi, Feng, Lima, Oden, and yankee(2020)。多组分肿瘤生长的耦合质量传递和变形理论。固体力学与物理学报，2009,39(3):391 - 391。
https://www.sciencedirect.com/science/article/pii/S0022509620301721
< span>摘要:
< span>我们开发了一类一般的，基于相效应混合理论的连续体模型，描述了大量相互作用的组分的行为。这些成分由经历大弹性变形的固体和不可压缩的粘性流体组成。混合物理论的基本组成部分包括扩散物质的质量平衡定律、微观(细胞尺度)和宏观(组织尺度)的力平衡、能量平衡以及由热力学第一定律和第二定律导出的熵产不等式。通过假设本构方程(即自由能的特定形式和耗散势的速率)关闭系统来描述微环境中肿瘤的生长，从而开发出一般的相场框架。 A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.
