Chaplain M A, Giles S M, Sleeman B D, Jarvis R J
School of Mathematical Sciences, University of Bath, England.
J Math Biol. 1995;33(7):744-70. doi: 10.1007/BF00184647.
In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Neighbouring endothelial cells respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. A mathematical model is presented which takes into account two of the most important events associated with the endothelial cells as they form capillary sprouts and make their way towards the tumour i.e. cell migration and proliferation. The numerical simulations of the model compare very well with the actual experimental observations. We subsequently investigate the model analytically by making some relevant biological simplifications. The mathematical analysis helps to clarify the particular contributions to the model of the two independent processes of endothelial cell migration and proliferation.
为了实现从无血管生长到血管生成的转变，实体瘤会向周围组织分泌一种名为肿瘤血管生成因子（TAF）的可扩散物质。邻近的内皮细胞会以一系列有序的事件对这种趋化刺激做出反应，这些事件至少包括基底膜的降解、迁移和增殖。本文提出了一个数学模型，该模型考虑了内皮细胞形成毛细血管芽并向肿瘤方向生长时两个最重要的事件，即细胞迁移和增殖。该模型的数值模拟结果与实际实验观察结果非常吻合。随后，我们通过进行一些相关的生物学简化对该模型进行了分析研究。数学分析有助于阐明内皮细胞迁移和增殖这两个独立过程对模型的具体贡献。
