title: Mathematical modeling of efficient protocols to control glioma growth.
abstract: In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.
authors: CMUC & Polytechnic Institute of Coimbra, ISEC, DFM, Coimbra, Portugal. Electronic address: jrbranco@isec.pt.
authors: J R
authors: JR
authors: Branco
authors: CMUC & Department of Mathematics, University of Coimbra, Coimbra, Portugal. Electronic address: ferreira@mat.uc.pt.
authors: J A
authors: JA
authors: Ferreira
authors: CMUC & Department of Mathematics, University of Coimbra, Coimbra, Portugal. Electronic address: poliveir@mat.uc.pt.
authors: Paula
authors: P
authors: de Oliveira
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use; D001932:Brain Neoplasms / Q000473:pathology* / Q000503:physiopathology / Q000628:therapy; D049109:Cell Proliferation / Q000187:drug effects; D002985:Clinical Protocols; D003198:Computer Simulation; D004548:Elasticity; D005910:Glioma / Q000473:pathology* / Q000503:physiopathology / Q000628:therapy; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D009361:Neoplasm Invasiveness / Q000473:pathology / Q000517:prevention & control; D014783:Viscosity
chemical_list: D000970:Antineoplastic Agents
keywords: Chemotherapy; Glioma; Numerical simulation; Protocols; Viscoelastic behavior