Solving an Optimal Control Problem of Cancer Treatment by Artificial Neural Networks

Abstract

Cancer is an uncontrollable growth of abnormal cells in any tissue of the body. Many researchers have focused on machine learning and artificial intelligence (AI) based on approaches for cancer treatment. Dissimilar to traditional methods, these approaches are efficient and are able to find the optimal solutions of cancer chemotherapy problems. In this paper, a system of ordinary differential equations (ODEs) with the state variables of immune cells, tumor cells, healthy cells and drug concentration is proposed to anticipate the tumor growth and to show their interactions in the body. Then, an artificial neural network (ANN) is applied to solve the ODEs system through minimizing the error function and modifying the parameters consisting of weights and biases. The mean square errors (MSEs) between the analytical and ANN results corresponding to four state variables are 1.54e-06, 6.43e-07, 6.61e-06, and 3.99e-07, respectively. These results show the good performance and efficiency of the proposed method. Moreover, the optimal dose of chemotherapy drug and the amount of drug needed to continue the treatment process are achieved.