Tumor growth instability and the onset of invasion

Details Tumor growth instability and the onset of invasion Tumor growth instability and the onset of invasion

2005-03-15

arxiv.org/abs/physics/0503127v1

Physics

Biological Physics

12 pages, 8 figures, revtex4

Scientific paper

10.1103/PhysRevE.72.041907

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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