Byrne H M
Department of Mathematics, UMIST, Manchester, UK.
IMA J Math Appl Med Biol. 1997 Dec;14(4):305-23.
When grading and classifying tumours several criteria are taken into consideration. These include the type of cell from which the tumour has arisen, whether it is benign or malignant and its ability to invade the surrounding tissue. In this paper we suggest that the ability with which a tumour invades its host environment can be related to the intercellular adhesion forces which maintain the tumour's structure. We develop a mathematical model to describe the growth of an avascular tumour in response to an externally supplied nutrient. Its development depends on the balance between expansive forces caused by cell proliferation and intercellular adhesion forces which maintain the tumour's compactness. We focus attention on the existence, uniqueness, and stability of steady, radially symmetric solutions to the model. Our analysis shows that as the importance of cell-cell adhesion increases the size of the radially symmetric steady tumour radius diminishes and the number of asymmetric modes to which it is stable increases. Thus we conclude that cell-cell adhesion may provide clinicians with a useful index of the invasive potential of a tumour.
在对肿瘤进行分级和分类时，会考虑几个标准。这些标准包括肿瘤起源的细胞类型、它是良性还是恶性以及其侵袭周围组织的能力。在本文中，我们认为肿瘤侵袭其宿主环境的能力可能与维持肿瘤结构的细胞间粘附力有关。我们开发了一个数学模型来描述无血管肿瘤在外部供应营养物质时的生长情况。其发展取决于细胞增殖引起的扩张力与维持肿瘤紧密性的细胞间粘附力之间的平衡。我们将注意力集中在该模型的稳定、径向对称解的存在性、唯一性和稳定性上。我们的分析表明，随着细胞间粘附的重要性增加，径向对称稳定肿瘤半径的大小减小，且其稳定的不对称模式数量增加。因此，我们得出结论，细胞间粘附可能为临床医生提供一个有用的肿瘤侵袭潜力指标。
