Proposing a Finite Duration Cancer Treatment Using Multi-Objective Optimization

Document Type : Research Article

Authors

1 Faculty of Mechanical Engineering, K.N. Toosi University of technology.

2 K.N. Toosi University of Technology

3 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran.

Abstract

The main target of this paper is to propose an optimal method for eradicating cancer, such that it cannot be relapsed. The major issue is that the tumor-free equilibrium point at the end of chemotherapy is still unstable. Mathematically, it means that when the chemotherapy is stopped, the trajectory of the system moves away from the tumor-free equilibrium point and the tumor cells start increasing. To overcome this problem, we can either restart the process of chemotherapy or try to stabilize the equilibrium. In this article, the dynamics of the system is changed around the tumor-free equilibrium point using the vaccine therapy and the chemotherapy pushes the system to the domain of attraction of the desired point. In other words, some inputs have an effect on the parameters of the system. For optimal chemotherapy, two objective functions optimized simultaneously in order to minimize the size of the tumor as well as the side effects of the anticancer drug on the patients’ body. After removing the chemotherapy, cancer does not relapse due to the change in the dynamics of the system. Simulation results show that by applying this method, the cancer cells population approaches to zero even after the cessation of chemotherapy for a long time.

Keywords

Main Subjects

References

[1]  Y. Batmani, H. Khaloozadeh, Optimal drug regimens in cancer chemotherapy: A multi-objective approach, Computers in biology and medicine, 43(12) (2013) 2089-2095.
[2]  G.W. Swan, T.L. Vincent, Optimal control analysis in the chemotherapy of IgG multiple myeloma, Bulletin of mathematical biology, 39(3) (1977) 317-337.
[3]  G.W. Swan, Role of optimal control theory in cancer chemotherapy, Mathematical biosciences, 101(2) (1990) 237-284.
[4]  S.E. Clare, F. Nakhlis, J.C. Panetta, Molecular biology of breast metastasis The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer, Breast Cancer Research, 2(6) (2000) 430.
[5]  R.S. Parker, F.J. Doyle, Control-relevant modeling in drug delivery, Advanced drug delivery reviews, 48(2) (2001) 211-228.
[6]  S.-S. Feng, S. Chien, Chemotherapeutic engineering: application and further development of chemical engineering principles for chemotherapy of cancer and other diseases, Chemical Engineering Science, 58(18) (2003) 4087-4114.
[7] J.M. Harrold, Model--Based Design of Cancer Chemotherapy Treatment Schedules, University of Pittsburgh, 2005.
[8] L.G. de Pillis, W. Gu, K.R. Fister, T.a. Head, K. Maples, A. Murugan, T. Neal, K. Yoshida, Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls, Mathematical Biosciences, 209(1) (2007) 292-315.
[9] A. d’Onofrio, U. Ledzewicz, H. Maurer, H. Schättler, On optimal delivery of combination therapy for tumors, Mathematical biosciences, 222(1) (2009) 13- 26.
[10]  M. Engelhart, D. Lebiedz, S. Sager, Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function, Mathematical Biosciences, 229(1) (2011) 123-134.
[11]   J. Shi, O. Alagoz, F.S.  Erenay,  Q.  Su, A survey  of optimization models on cancer chemotherapy treatment planning, Annals of Operations Research, 221(1) (2014) 331-356.
[12]   V. Kumar, A.K. Abbas, J.C. Aster, Robbins Basic Pathology E-Book, Elsevier Health Sciences, 2017.
[13]  C.A. Klein, D. Hölzel, Systemic cancer progression and tumor dormancy: mathematical models meet single cell genomics, Cell cycle, 5(16) (2006) 1788- 1798.
[14]  O. Isaeva, V. Osipov, Different strategies for cancer treatment: mathematical modelling, Computational and Mathematical Methods in Medicine, 10(4) (2009) 253-272.
[15]  M. Nazari, A. Ghaffari, The effect of finite duration inputs on the dynamics of a system: Proposing a new approach for cancer treatment, International Journal of Biomathematics, 8(3) (2015) 1-19.
[16]  L.G. de Pillis, W. Gu, A.E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, Journal of theoretical biology, 238(4) (2006) 841-862.
[17] A. Ghaffari, M. Khazaee, Cancer dynamics for identical twin brothers, Theoretical Biology and Medical Modelling, 9(1) (2012) 4.
[18] F.S. Lobato, V.S. Machado, V. Steffen Jr, Determination of an optimal control strategy for  drug administration in tumor treatment using multi-objective optimization differential evolution, Computer methods and programs in biomedicine, 131 (2016) 51-61.
[19] J.D. Schaffer, Multiple objective optimization with vector evaluated genetic algorithms, in: Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1985, Lawrence Erlbaum Associates. Inc., Publishers, 1985.
[20]N. Srinivas, K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary computation, 2(3) (1994) 221-248.
[21] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE transactions on evolutionary computation, 6(2) (2002) 182-197.
[22] R.T. Marler, J.S. Arora, Survey of multi-objective optimization methods for engineering, Structural and multidisciplinary optimization, 26(6) (2004) 369-395.
[23] M.A. Branch, A. Grace, Optimization Toolbox: for Use with MATLAB: User’s Guide: Version 1, Math works, 1998.
[24]  A. Ghaffari, M. Nazari, F. Arab, Suboptimal mixed vaccine and chemotherapy in finite duration cancer treatment: state-dependent Riccati equation control, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37(1) (2015) 45-56.
[25]  M. Nazari, A. Ghaffari, F. Arab, Finite duration treatment of cancer by using vaccine therapy and optimal chemotherapy: state-dependent Riccati equation control and extended Kalman filter, Journal of Biological Systems, 23(01) (2015) 1-29.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 5
August 2020
Pages 1365-1376

Files

Share

How to cite

Statistics