Optimal delivery of chemotherapeutic agents in cancer
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abstract
Cancer refers to a set of diseases where normal cells of the body lose mechanisms which are responsible for controlling their growth and motility. Chemotherapy aims to kill these abnormal or cancer cells, however normal cells and healthy tissues are also adversely affected. Systematic modelling and optimization approaches can be employed to obtain effective chemotherapeutic protocol that minimizes the tumour cell population while limiting the damage to the normal cells. In this paper, two models for cancer chemotherapy are considered and the effect of the time of drug administration on the final tumour size is analyzed. The first model is cell cycle non-specific and considers all the cancer cells as belonging to one compartment whereas the second model is cell cycle specific and takes into account the effect of the drugs that act on cells at certain specific stages of the cell cycle. An optimal control problem is also formulated and solved for both the models so as to obtain the chemotherapeutic schedule which minimizes the final tumour size while taking into account the constraints on drug resistance and toxicity. For the first model a mixed integer dynamic optimization problem and for the second model a dynamic optimization problem are solved. The optimal chemotherapeutic drug administration profiles and the variation of number of cells with time are obtained and analyzed in detail. 2007 Elsevier Ltd. All rights reserved.
