Tumor growth instability and the onset of invasion

Abstract

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.

arXiv comment12 pages, 8 figures, revtex4

References in corpus (3)

• Phase-Field Model of Dendritic Sidebranching with Thermal Noise
• Growth Patterns of Microscopic Brain Tumors
• Morphological Instability and Dynamics of Fronts in Bacterial Growth Models with Nonlinear Diffusion

Cited by in corpus (7)

• Modeling tumor cell migration: from microscopic to macroscopic
• Dynamics and pattern formation in invasive tumor growth
• Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate
• Stability and roughness of interfaces in mechanically-regulated tissues
• Physical Aspects of Cancer Invasion
• Effect of heterogeneity and spatial correlations on the structure of tumor invasion front in cellular environments
• Geometrical approach to tumor growth