Three-compartmental Model of a Cell Cycle and Drug Resistance in Chemotherapy Design

A. Swierniak and J. Smieja (Poland)

Keywords

Biomedical modelling, drug resistance, phase-specific chemotherapy.

Abstract

This paper presents an approach to modelling of the cancer cell population that takes into account phase specific chemotherapy and evolution of drug resistance stemming from gene amplification. It allows to analyse simultaneously these two aspects of chemotherapy that have been studied separately so far. The mathematical model is based on three compartments in the cell cycle and two drugs that are administered in different phases: a blocking and a killing agent. The task of finding the best chemotherapy protocol is given by an optimal control problem defined in l1 space, which aims at killing the greatest number of cancer cells while simultaneously trying to minimise side effects of the drugs.

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