Abstract
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.
Highlights
This paper seeks to address the analysis of the interaction among pressure, growth and cell migration in avascular tumors
We propose a thermodynamically consistent approach that links the theory of finite growth with a novel migration term based on flow-saturated mechanisms that allows controlling the dispersion front of the tumor, both from a qualitative point of view defining the characteristics of the front, and quantitatively since the speed of the tumor can be regulated from experimental data
We have proposed how internal pressure, proliferation, and dispersal migration play a relevant role as competitors regulating the reorganization of tumor cell density in its evolution
Summary
This paper seeks to address the analysis of the interaction among pressure, growth and cell migration in avascular tumors. We propose a thermodynamically consistent approach that links the theory of finite growth with a novel migration term based on flow-saturated mechanisms that allows controlling the dispersion front of the tumor, both from a qualitative point of view defining the characteristics of the front, and quantitatively since the speed of the tumor can be regulated from experimental data. Cancer is the leading cause of death worldwide. Some papers [2,3,4,5,6] highlight the challenges surrounding the dynamics of cancer and review mathematical models that attempt to respond to these concerns. Research has been focused, on a large degree, on models that control growth and treatments through biochemical interactions that identify morphogens and target genes involved in deregulation and growth associated with tumor processes [4,7]
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