肿瘤生长的不稳定性和侵袭的开始
Tumor growth instability and the onset of invasion
摘要：
受实验观察的启发，我们开发了一个化学导向肿瘤生长的数学模型。我们提出了一个分析研究的模型，以及一个数值。数学分析表明：（i）肿瘤细胞增殖本身不能产生实验观察到的侵入性分支行为，（ii）异型趋化性提供了一种导致肿瘤侵袭发作的不稳定机制，（iii）同型趋化性不提供这种不稳定机制，但提高了肿瘤表面的平均速度。数值结果不仅支持进行数学分析所需的假设，而且还提供了（i），（ii）和（iii）的证据。最后，无论是分析研究和数值工作与实验现象一致。
英文摘要：
Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell proliferation by itself cannot generate the invasive branching behaviour observed experimentally, (ii) heterotype chemotaxis provides an instability mechanism that leads to the onset of tumor invasion and (iii) homotype chemotaxis does not provide such an instability mechanism but enhances the mean speed of the tumor surface. The numerical results not only support the assumptions needed to perform the mathematical analysis but they also provide evidence of (i), (ii) and (iii). Finally, both the analytical study and the numerical work agree with the experimental phenomena.
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