Mathematical Modeling of Tumor Growth

Abstract

The main objective of this paper is to present a mathematical framework for modeling the tumor growth process by applying a state-decomposition-based formulation called SSDT, originally developed for multiphase flow in porous media. Computational models for tumor growth and its response to different therapeutic regimens play a fundamental role in improving prognosis and quality of life, given that an increase in cancer incidence is expected in the coming years, which will have a major social and economic impact. Based on the hypothesis that the variables that affect tumor growth may depend on the variation in phase pressures and nutrient concentration, pressure relationships between different cell types and an interstitial fluid are proposed, in addition to considering the extracellular matrix as the deformable structural component. By leveraging the analogy between the behavior of soft tissue and porous media, we establish pressure relationships that integrate the various components of the tumor system. Additionally, a nutrient phase is introduced that is updated with each loading cycle, allowing for a more realistic modeling of resource availability for tumor cells. Finally, the discretized system of equations is presented for resolution using the finite element method.