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

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Mathematical biosciences, ISSN: 1879-3134, Vol: 270, Issue: Pt A, Page: 10-29

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Holder, Andrew B; Rodrigo, Marianito R
Elsevier BV
Mathematics; Biochemistry, Genetics and Molecular Biology; Immunology and Microbiology; Agricultural and Biological Sciences; Engineering; Science and Technology Studies
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article description
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.