Blanco, BeatrizCampos, JuanMelchor, JuanSoler, Juan2022-10-262022-10-262021-06-14Blanco B, Campos J, Melchor J, Soler J. Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics. Mathematics. 2021; 9(12):1376http://hdl.handle.net/10668/4285What 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.enAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Cell motilityFlux-saturatedHele-Shaw modelMathematical modelingMechanical feedbackNumerical simulationPorous mediaTumor dynamicsMovimiento celularModelos teóricosFloculadoresHomeostasisMedical Subject Headings::Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::PorosityMedical Subject Headings::Information Science::Information Science::Communication::Cybernetics::FeedbackMedical Subject Headings::Diseases::NeoplasmsMedical Subject Headings::Phenomena and Processes::Chemical Phenomena::Biochemical Phenomena::Biochemical Processes::Signal TransductionMedical Subject Headings::Phenomena and Processes::Physiological Phenomena::Physiological Processes::HomeostasisMedical Subject Headings::Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::ElasticityMedical Subject Headings::Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Epidemiologic Methods::Data Collection::Vital Statistics::Mortality::Cause of DeathMedical Subject Headings::Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Transdifferentiation::Epithelial-Mesenchymal TransitionMedical Subject Headings::Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Movementresearch articleAcceso abierto10.3390/math91213762227-7390