Article
A Glioblastoma PDE-ODE model including chemotaxis and vasculature
Author/s | Fernández Romero, Antonio
Guillén González, Francisco Manuel Suárez, Antonio |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2022-01-26 |
Deposit Date | 2022-07-01 |
Published in |
|
Abstract | In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma,
which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for
the (possible) solutions of the ... In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular, under some conditions on the parameters, we obtain that the system does not develop blow-up at finite time. In addition, we design a fully discrete finite element scheme for the model which preserves some pointwise estimates of the continuous problem. Later, we make an adimensional study in order to reduce the number of parameters. Finally, we detect the main parameters determining different width of the ring formed by proliferative and necrotic cells and different regular/irregular behaviour of the tumor surface. |
Citation | Fernández Romero, A., Guillén González, F.M. y Suárez, A. (2022). A Glioblastoma PDE-ODE model including chemotaxis and vasculature. ESAIM: Mathematical Modelling and Numerical Analysis, 56 (2), 407-431. |
Files | Size | Format | View | Description |
---|---|---|---|---|
A Glioblastoma PDE-ODE model ... | 1.174Mb | [PDF] | View/ | |