A new mathematical model for avascular tumour growth
A new mathematical model for avascular tumour growth
复制标题
DOI：
10.1007/s002850100088
复制
发表时间：
2001-10-01
影响因子：
1.9
通讯作者：
Chaplain, MAJ
中科院分区：
文献类型：
--
作者：
Sherratt, JA;Chaplain, MAJ
实体瘤的早期发展已被广泛研究，无论是通过多细胞球体测定实验，并在理论上使用数学建模。绝大多数以前的模型专门适用于多细胞球体，其具有增殖边缘和坏死核心的特征结构，由一条静止细胞带隔开。许多以前的模型将这些表示为离散层，由移动边界分隔。在这里，作者开发了一个新模型，根据增殖、静止和坏死细胞的连续密度以及通用营养/生长因子来制定。该模型面向体内而不是体外环境，并且关键地允许来自下层组织的营养供应，这将在上皮内生长的肿瘤的二维环境中出现。此外，该模型涉及到一个新的代表性的细胞运动，这反映了接触抑制迁移。模型的解决方案能够重现经典的三层结构熟悉的多细胞球体，但也表明，新的行为可以发生的结果，从底层组织的营养供应。作者分析了这些不同的解决方案类型的近似解的行波方程，使波前解决方案的详细分类。
The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models represent these as discrete layers, separated by moving boundaries. Here, the authors develop a new model, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor. The model is oriented towards an in vivo rather than in vitro setting, and crucially allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium. In addition, the model involves a new representation of cell movement, which reflects contact inhibition of migration. Model solutions are able to reproduce the classic three layer structure familiar from multicellular spheroids, but also show that new behaviour can occur as a result of the nutrient supply from underlying tissue. The authors analyse these different solution types by approximate solution of the travelling wave equations, enabling a detailed classification of wave front solutions.