Proposing optimal chemotherapy protocol for cancer treatment with metastasis by using SDRE based optimal control technique

Ghaffari, Ali; Bahmaie, Behnaz; Nazari, Motafa; Ghaffari, Bahareh; Daneshmand, Mitra

Proposing optimal chemotherapy protocol for cancer treatment with metastasis by using SDRE based optimal control technique

Authors

Ali Ghaffari ¹

Behnaz Bahmaie ²

Motafa Nazari ²

Bahareh ghaffari ³

Mitra Daneshmand ⁴

¹ K.N. Toosi university of technology

² K. N. T. university

³ Sharif university

⁴ K. N. T. University

Abstract

Although chemotherapy is one of the effective methods in cancer treatment its effects may be moderated due to drug resistance. The main objective of this paper is to propose optimal finite cancer treatment duration. In this paper, a mathematical model of tumor growth by adding radiotherapy, chemotherapy and metastasis of cancer cells terms is extended. Stability analysis shows that the tumor free equilibrium point is unstable. Hence, changing the dynamics of the system around this equilibrium point for achieving finite duration treatment method is essential. Therefore, the effects of chemotherapy drug are considered not only on cells populations but also on the dynamics of the system. For this purposes, State Dependent Riccati Equation (SDRE) based optimal control is used. So chemotherapy agent is used as the control input to the extended cancer nonlinear model. Then, in order to show the flexibility in design, two different types of input weighting matrices are selected. Moreover, the robustness of this control method is investigated by simulation. Results show that changing the dynamics of the system is necessary for finite duration cancer treatment method.

Keywords

Cancer

mathematical modeling

tumor growth

metastasis

SDRE control