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Model for acid-mediated tumour invasion with chemotherapy intervention II: spatially heterogeneous populations

Journal Article


Abstract


  • This paper extends the model for acid-mediated tumour invasion with chemotherapy intervention examined in part I. The model presented in part I considers the interaction between tumour cells, normal cells, acid and drug in a well mixed (i.e. spatially homogeneous) setting, which is governed by a system of nonlinear differential equations. The model examined here removes the assumption that the populations are spatially homogeneous resulting in a system of nonlinear partial differential equations. Numerical simulations of this model are presented for different treatment methods displaying several possible behaviours. Asymptotic approximations are also derived for a special case of the treatment method and set of parameter values. This analysis then allows us to draw conclusions about the effectiveness of treating acid-mediated tumours with chemotherapy.

Publication Date


  • 2015

Citation


  • Holder, A. B. & Rodrigo, M. R. (2015). Model for acid-mediated tumour invasion with chemotherapy intervention II: spatially heterogeneous populations. Mathematical Biosciences, 270 10-29.

Scopus Eid


  • 2-s2.0-84947569636

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5303

Number Of Pages


  • 19

Start Page


  • 10

End Page


  • 29

Volume


  • 270

Abstract


  • This paper extends the model for acid-mediated tumour invasion with chemotherapy intervention examined in part I. The model presented in part I considers the interaction between tumour cells, normal cells, acid and drug in a well mixed (i.e. spatially homogeneous) setting, which is governed by a system of nonlinear differential equations. The model examined here removes the assumption that the populations are spatially homogeneous resulting in a system of nonlinear partial differential equations. Numerical simulations of this model are presented for different treatment methods displaying several possible behaviours. Asymptotic approximations are also derived for a special case of the treatment method and set of parameter values. This analysis then allows us to draw conclusions about the effectiveness of treating acid-mediated tumours with chemotherapy.

Publication Date


  • 2015

Citation


  • Holder, A. B. & Rodrigo, M. R. (2015). Model for acid-mediated tumour invasion with chemotherapy intervention II: spatially heterogeneous populations. Mathematical Biosciences, 270 10-29.

Scopus Eid


  • 2-s2.0-84947569636

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5303

Number Of Pages


  • 19

Start Page


  • 10

End Page


  • 29

Volume


  • 270