Traveling waves and free boundaries arising in tumor angiogenesis

  • Antonio Fasano

    Università degli Studi di Firenze; FIAB SpA, Vicchio; CNR, Roma, Italy
  • Carmela Sinisgalli

    Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” - CNR, Roma, Italy
Traveling waves and free boundaries arising in tumor angiogenesis cover
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Abstract

In a paper appeared in 2021, a mathematical model was developed for tumor invasion with vessel cooption, including a fine analysis of angiogenesis driven by chemotaxis. Numerical solutions in spherical symmetry revealed that a traveling wave sets in. Results were in agreement with experimental data. In the present paper, we introduce some nontrivial changes in the model and we further analyze the structure of the solutions as well as their dependence on some critical biological parameters, emphasizing for instance which are the most active zones where angiogenesis takes place. Moreover, we propose an alternative model characterized by the presence of a free boundary (playing the role of the invasion front), showing that the new formulation (which is advantageous from the computational point of view) matches the results of the previous model for some biologically significant range of the parameters.

Cite this article

Antonio Fasano, Carmela Sinisgalli, Traveling waves and free boundaries arising in tumor angiogenesis. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023), no. 1, pp. 175–194

DOI 10.4171/RLM/1003