A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy.

*(English)*Zbl 0947.92013Summary: A mathematical model is developed that describes the reduction in volume of a vascular tumor in response to specific chemotherapeutic administration strategies. The model consists of a system of partial differential equations governing intratumoral drug concentration and cancer cell density. In the model the tumor is treated as a continuum of two types of cells which differ in their proliferation rates and their responses to the chemotherapeutic agent. The balance between cell proliferation and death within the tumor generates a velocity field which drives expansion or regression of the spheroid. Insight into the tumor’s response to therapy is gained by applying a combination of analytical and numerical techniques to the model equations.

##### MSC:

92C50 | Medical applications (general) |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

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\textit{T. L. Jackson} and \textit{H. M. Byrne}, Math. Biosci. 164, No. 1, 17--38 (2000; Zbl 0947.92013)

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