Mallet D G, De Pillis L G
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
J Theor Biol. 2006 Apr 7;239(3):334-50. doi: 10.1016/j.jtbi.2005.08.002. Epub 2005 Sep 15.
We present a hybrid cellular automata-partial differential equation model of moderate complexity to describe the interactions between a growing tumor next to a nutrient source and the immune system of the host organism. The model allows both temporal and two-dimensional spatial evolution of the system under investigation and is comprised of biological cell metabolism rules derived from both the experimental and mathematical modeling literature. We present numerical simulations that display behaviors which are qualitatively similar to those exhibited in tumor-immune system interaction experiments. These include spherical tumor growth, stable and unstable oscillatory tumor growth, satellitosis and tumor infiltration by immune cells. Finally, the relationship between these different growth regimes and key system parameters is discussed.
我们提出了一个中等复杂度的混合细胞自动机-偏微分方程模型，以描述靠近营养源生长的肿瘤与宿主生物体免疫系统之间的相互作用。该模型允许对所研究系统进行时间和二维空间演化，并且由源自实验和数学建模文献的生物细胞代谢规则组成。我们给出了数值模拟，其显示出的行为在定性上与肿瘤-免疫系统相互作用实验中表现出的行为相似。这些行为包括球形肿瘤生长、稳定和不稳定的振荡肿瘤生长、卫星瘤形成以及免疫细胞对肿瘤的浸润。最后，讨论了这些不同生长模式与关键系统参数之间的关系。
