An Optimal Control of Bone Marrow in Cancer Chemotherapy by Artificial Neural Networks H. Hosseinipour 1 , H. R. Sahebi 2 1 Department of Computer Science, Ashtian Branch, Islamic Azad University, Ashtian, Iran. hessamhosseinipour2@gmail.com 2 Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran. sahebi@aiau.ac.ir Abstract Although neural network models for cancer chemotherapy have been analyzed since the early seventies, less research has been done in actually formulating them as optimal control problems. In this paper an artificial neural networks-based method for optimal control of bone marrow in cell-cycle-specific chemotherapy is proposed. In this method, we use artificial neural networks for approximating the optimal control problem which maximizes both bone marrow mass and drug's dose at the same time. The corresponding model be transfer to Hamiltonian function and using Pontryagin principle we create the boundary conditions. After defining boundary conditions, we use the approximating property of artificial networks and put the boundary conditions in error functions to satisfy the limitations.. Keywords: Optimal control, Bone marrow, Cancer chemotherapy, Artificial neural networks. 1. Introduction Chemotherapy is a category of cancer treatment that uses chemical substances, especially one or more anti- cancer drugs (chemotherapeutic agents) that are given as part of a standardized chemotherapy regimen. Since two decades ago we have seen a lot of researches in terms of cancer chemotherapy [1-5]. Almost in most of them, administering drugs was their first priority. All of us know cancer is one of the biggest challenges which human has faced with it. This disease hurts a lot of part in the body, but maybe the most important one is bone marrow damaging. While biomedical research concentrates on new drugs and treatments, mathematicians analyze the models for the purpose of testing various treatment strategies and searching for the optimal ones. After early, simple structures were considered [6], classes of models which are cell-cycle-specific were developed. These so-called compartmental models, introduced in the nineties [7] and analyzed further recently [8, 9], divide the cell-cycle into clusters, called compartments, which allow to model drug applications at the stages where they are the most effective. The bone marrow produces blood cells which is containing both white and red globules. So defensing and oxygen transporting duties could be damaged by this matter. There are some treatments for facing this issue. One of these treatments is chemotherapy, which our focus is on the cell-cycle-specific kind of it, in which chemotherapies' drugs will act only in …. Phase of cell's life time. For reaching this purpose we use a known model. Pantta [10] and, Fister and Panetta [11] had introduced a model and then analyzed it. They used dynamical control system which includes both active and resting phases of cell-cycle to analyze the effect of cell-cycle-specific chemotherapy. This system is as:                ) ( ) ( ) ( ) ( ), ( ) ( )) ( ( ) ( t Q t p t Q t Q t X t su t X        (1) Where (.) p and (.) Q are the proliferating and quiescent cells mass in the bone marrow respectively, and bounded measurable function (.) u shows the drugs treatment which takes values in interval [0,1] and acts only on the proliferating cells. Moreover, the parameters are all considered constant, positive, and are defined as follows.  , cycling cells’ growth rate;  , transition rate from proliferating to resting;  , natural cell death;  , transition rate from resting to proliferating;  , cell differentiation- mature bone marrow cell leaving the bone marrow and entering the blood stream as various types of blood cells; and s, the strength or effectiveness of the treatment. Note that (.) u is control function and 0 ) (  t u means no drug is injected at time t while 1 ) (  t u means maximum rate is used. Noori Skandari et al [12] use Alamir and Cheyron constraint suggestion [11, 13] and exploit the following optimal control problem: ACSIJ Advances in Computer Science: an International Journal, Vol. 4, Issue 5, No.17 , September 2015 ISSN : 2322-5157 www.ACSIJ.org 138 Copyright (c) 2015 Advances in Computer Science: an International Journal. All Rights Reserved.