Optimal design of chemotherapy drug protocol for cancer treatment based on a new mathematical model

Cancer chemotherapy is the treatment of cancer using drug that kills the malignant cancer cells (tumours). In chemotherapy, the drug is delivered according to a schedule which specifies the cycles of application and rest time and the dosage of the drug which must be delivered. One of the major aims of chemotherapy is to eliminate the tumour cells after a fixed treatment with minimum adverse drug effects. This paper proposes an algorithm to design an optimal chemotherapy drug protocol. The target is to optimise the number of rests, the application course and the drug dosage. A new mathematical model is employed in the form of ordinary differential equations governing cancer growth on a cell population level. The model is modified by appending cumulative drug toxicity as an additional equation. An optimisation problem is formulated for optimal control with a set of dynamic equations in the state space form. A new objective function is considered to minimise the tumour size as well as drug toxicity under a set of constraints using a proposed genetic approach. Also, the drug resistant effect in the optimal treatment schedule is applied to the model as well. Finally, results are presented to demonstrate the efficiency of the proposed protocol in cancer treatment.