GROWTH OF NONNECROTIC TUMORS IN THE PRESENCE AND ABSENCE OF INHIBITORS
GROWTH OF NONNECROTIC TUMORS IN THE PRESENCE AND ABSENCE OF INHIBITORS
复制标题
DOI：
10.1016/0025-5564(94)00117-3
复制
发表时间：
1995-12-01
影响因子：
4.3
通讯作者：
CHAPLAIN, MAJ
中科院分区：
文献类型：
--
作者：
BYRNE, HM;CHAPLAIN, MAJ
在本文中，提出了一个球对称的非坏死性肿瘤的演化模型。研究了营养物和抑制剂对时间无关解的存在性和稳定性的影响。在单一营养素和不存在抑制剂的情况下，对应于没有肿瘤存在的状态的平凡解对于所有参数值都是持续的，而对应于有限大小的肿瘤的非平凡解只存在于指定的参数范围内，这对应于细胞增殖和细胞死亡之间的平衡。基于两次计时方法的稳定性分析表明，如果存在非平凡解，则非平凡解是稳定的，而平凡解是不稳定的。否则，平凡解是稳定的。对不同类型的抑制剂对这些特征态的修饰也进行了研究，并显示出显著的效果。本文还讨论了该模型对癌症治疗的意义。
In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for all parameter values, whereas the nontrivial solution, which corresponds to a tumor of finite size, exists for only a prescribed range of parameters, which corresponds to a balance between cell proliferation and cell death. Stability analysis, based on a two-timing method, suggests that, where it exists, the nontrivial solution is stable and the trivial solution unstable. Otherwise, the trivial solution is stable. Modification to these characteristic states brought about by the presence of different types of inhibitors are also investigated and shown to have significant effect. Implications of the model for the treatment of cancer are also discussed.