Multi-objective optimal chemotherapy control model for cancer treatment

Abstract

This article presents an investigation into the development of a multi-objective optimal chemotherapy control model to reduce the number of cancer cells after a number of fixed treatment cycles with minimum side effects. Mathematical models for cancer chemotherapy are designed to predict the number of tumour cells and control the tumour growth during treatment. This requires an understanding of the system in the absence of treatment and a description of the effects of the treatment. In order to achieve multi-objective optimal control model, we used the proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin's model for drug concentration. To the best of our knowledge, this is the first PID/IPD-based optimal chemotherapy control model used to investigate the cancer treatment. The proposed control schemes are designed based on the optimal solution of three objective functions, which include (i) maximising tumour cell killing, for (ii) minimum toxicity, and (iii) tolerable drug concentration. Multi-objective genetic algorithm (MOGA) is used to find suitable parameters of controllers that trade-off among design objectives considered in this work. The results of the different optimal scheduling patterns of the proposed models are presented and discussed through a set of experiments. Finally, the observations are compared with the existing models in order to demonstrate the merits and capabilities of the proposed multi-objective optimisation models. It is noted that the proposed model offers best performance as compared to any models reported earlier.