Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics Blanco Besteiro, Beatriz Campos Rodríguez, Juan Juan, Melchor Soler Vizcaino, Juan Segundo Cell motility Flux-saturated Hele-Shaw model Mathematical modelling Mechanical feedback Numerical simulations Porous media Tumor dynamics What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms. 2021-07-05T10:30:19Z 2021-07-05T10:30:19Z 2021 info:eu-repo/semantics/article Blanco, B.; Campos, J.; Melchor, J; Soler, J. Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics. Mathematics 2021, 9, 1376. https://doi.org/10.3390/math9121376 http://hdl.handle.net/10481/69512 10.3390/math9121376 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI