title: Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion.
abstract: This work studies a general reaction-diffusion model for acid-mediated tumor invasion, where tumor cells produce excess acid that primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleared by vasculature, and the healthy and tumor cells are viewed as two species following logistic growth with mutual competition. A key feature of this model is the density-limited diffusion for tumor cells, reflecting that a healthy tissue will spatially constrain a tumor unless shrunk. Under appropriate assumptions on model parameters and on initial data, it is shown that the unique heterogeneous state is nonlinearly stable, which implies a long-term coexistence of the healthy and tumor cells in certain parameter space. Our theoretical result suggests that acidity may play a significant role in heterogeneous tumor progression.
authors.affiliation: Department of Applied Mathematics, Dong Hua University, Shanghai 200051, China. email:taoys@dhu.edu.cn.
authors.forename: Youshan
authors.initials: Y
authors.lastname: Tao
authors.forename: J Ignacio
authors.initials: JI
authors.lastname: Tello
mesh_terms: D000818:Animals; D002465:Cell Movement; D003198:Computer Simulation; D006801:Humans; D006863:Hydrogen-Ion Concentration; D019344:Lactic Acid / Q000737:chemistry / Q000378:metabolism*; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D009369:Neoplasms / Q000737:chemistry / Q000378:metabolism* / Q000473:pathology*; D017711:Nonlinear Dynamics; D059016:Tumor Microenvironment
chemical_list: D019344:Lactic Acid