Mathematical modeling of efficient protocols to control glioma growth

被引：17

作者：

Branco, J. R. ^{[1
,2
]}

Ferreira, J. A. ^{[1
,3
]}

de Oliveira, Paula ^{[1
,3
]}

机构：

[1] CMUC, Coimbra, Portugal

[2] Polytech Inst Coimbra, DFM, ISEC, Coimbra, Portugal

[3] Univ Coimbra, Dept Math, Coimbra, Portugal

来源：

MATHEMATICAL BIOSCIENCES | 2014年 / 255卷

关键词：

Glioma; Viscoelastic behavior; Chemotherapy; Protocols; Numerical simulation; TUMOR; DIFFUSION; TRANSPORT; PROLIFERATION; CHEMOTHERAPY; MOTILITY; RIGIDITY; SYSTEM;

D O I：

10.1016/j.mbs.2014.07.002

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：83 / 90

页数：8

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