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The invasive capability is fundamental in determining the malignancy of a solid tumor. In particular, tumor invasion fronts are characterized by different morphologies, which result both from cell-based processes (such as cell elasticity, adhesive properties and motility) and from subcellular molecular dynamics (such as growth factor internalization, ECM protein digestion and MMP secretion). Of particular relevance is the development of tumors with unstable fingered morphologies: they are in fact more aggressive and hard to be treated than smoother ones as, even if their invasive depth is limited, they are difficult to be surgically removed. The phenomenon of malignant fingering has been reproduced with several mathematical approaches. In this respect, we here present a qualitative comparison between the results obtained by an individual cell-based model (an extended version of the cellular Potts model) and by a measure-based theoretic method. In particular, we show that in both cases a fundamental role in finger extension is played by intercellular adhesive forces and taxis-like migration.

. Acad. Sci. 108 3749 3754 10.1073/pnas.1014480108 [27] E. Khain, M. Katakowski, N. Charteris, F. Jiang and M. Chopp. (2012), Migration of adhesive glioma cells: Front propagation and fingering. Phys. Rev. E, 86, 011904. 10.1103/PhysRevE.86.011904 Khain E. Katakowski M. Charteris N. Jiang F. Chopp M. 2012 Migration of adhesive glioma cells: Front propagation and fingering Phys. Rev. E 86 011904 10.1103/PhysRevE.86.011904 [28] E. Konukoglu, O. Clatz, P. Y. Bondiau, H. Delingette, N. Ayache. (2010), Extrapolating glioma invasion margin in brain magnetic resonance