A mathematical model of tumor hypoxia targeting in cancer treatment and its numerical simulation

DOI10.1016/j.camwa.2017.08.019zbMath1398.92129OpenAlexW2751330155MaRDI QIDQ1672692

Wazir Muhammad, Peter Bastian, Muhammad Sabir, Ijaz Ali, Abdullah Shah

Publication date: 11 September 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.08.019

zbMATH Keywords

reaction-diffusion systemmathematical modelingnumerical discretizationDUNE-PDELabtumor hypoxia

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (4)

A two‐grid finite element method for the Allen‐Cahn equation with the logarithmic potential ⋮ Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations ⋮ A 2D mathematical model for tumor angiogenesis: the roles of certain cells in the extra cellular matrix ⋮ A fast time two-mesh algorithm for Allen-Cahn equation

Uses Software

• DUNE-FEM
• Plot Digitizer

Cites Work

• A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module
• Semigroups of linear operators and applications to partial differential equations
• A weakly nonlinear analysis of a model of avascular solid tumour growth
• A new mathematical model for avascular tumour growth
• Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies
• A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion
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