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A survey of optimization models on cancer chemotherapy treatment planning

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Abstract

While chemotherapy is an effective method for treating cancers such as colorectal cancer, its effectiveness may be dampened by the drug resistance and it may have significant side effects due to the destruction of normal cells during the treatment. As a result, there is a need for research on choosing an optimal chemotherapy treatment plan that minimizes the number of cancerous cells while ensuring that the total toxicity is below an allowable limit. In this paper, we summarize the mathematical models applied to the optimal design of the cancer chemotherapy. We first elaborate on a typical optimization model and classify relevant literature with respect to modeling methods: Optimal control model (OCM) and others. We further classify the OCM models with respect to the solution method used. We discuss the limitations of the existing research and provide several directions for further research in optimizing chemotherapy treatment planning.

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References

  • Agur, Z., Hassin, R., & Levy, S. (2006). Optimizing chemotherapy scheduling using local search heuristics. Operations Research, 54(5), 829–846.

    Article  Google Scholar 

  • Alagoz, O., Maillart, L. M., Schaefer, A. J., & Roberts, M. S. (2004). The optimal timing of living-donor liver transplantation. Management Science, 50(10), 1420–1430.

    Article  Google Scholar 

  • Alagoz, O., Maillart, L. M., Schaefer, A. J., & Roberts, M. S. (2007a). Determining the acceptance of cadaveric livers using an implicit model of the waiting list. Operation Research, 55(1), 24–36.

    Article  Google Scholar 

  • Alagoz, O., Maillart, L. M., Schaefer, A. J., & Roberts, M. S. (2007b). Choosing among living-donor and cadaveric livers. Management Science, 53(11), 1702–1715.

    Article  Google Scholar 

  • American Cancer Society (ACS) (2001–2008). Cancer facts and figures 2001–2008. http://www.cancer.org/docroot/STT/content/STT_1x_2001_Facts_and_Figures.pdf.asp. Accessed 5 Oct 2009.

  • American Cancer Society (ACS) (2009). Cancer facts and figures 2009. http://www.cancer.org/downloads/STT/500809web.pdf. Accessed Apr 21 2010.

  • Andre, T., Colin, P., Louvet, C., Gamelin, E., Bouche, O., Achille, E. et al. (2003). Semimonthly versus monthly regimen of fluorouracil and leucovorin administered for 24 or 36 weeks as adjuvant therapy in stage II and III colon cancer: Results of a randomized trial. Journal of Clinical Oncology, 21(15), 2896–2903.

    Article  Google Scholar 

  • Andre, T., Boni, C., Mounedji-Boudiaf, L., Navarro, M., Tabernero, J., Hickish, T. et al. (2004). Oxaliplatin, fluorouracil, and leucovorin as adjuvant treatment for colon cancer. New England Journal of Medicine, 350(23), 2343–2351.

    Article  Google Scholar 

  • Barbolosi, D., & Iliadis, A. (2001). Optimizing drug regimens in cancer chemotherapy: A simulation study using a PK-PD model. Computers in Biology and Medicine, 31(3), 157–172.

    Article  Google Scholar 

  • Birkhead, B. G., & Gregory, W. M. (1984). A mathematical model of the effects of drug resistance in cancer chemotherapy. Mathematical. Bioscience, 72, 59–69.

    Article  Google Scholar 

  • Butcher, J. C. (2003). Numerical methods for ordinary differential equations. New York: Wiley.

    Book  Google Scholar 

  • CancerHelp UK (2010). Which treatment for advanced bowel cancer. http://www.cancerhelp.org.uk/type/bowel-cancer/treatment/which-treatment-for-advanced-bowel-cancer#chemo.

  • Clare, S. E., Nakhlis, F., & Panetta, J. C. (2000). 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), 430–435.

    Article  Google Scholar 

  • Coldman, A. J., & Goldie, J. H. (1983). A model for the resistance of tumor cells to cancer chemotherapeutic agents. Mathematical Biosciences, 65(2), 291–307.

    Article  Google Scholar 

  • Coldman, A. J., & Goldie, J. H. (1986). A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bulletin of Mathematical Biology, 48(3/4), 279–292.

    Article  Google Scholar 

  • Coldman, A. J., & Murray, J. M. (2000). Optimal control for a stochastic model of cancer chemotherapy. Mathematical Biosciences, 168, 187–200.

    Article  Google Scholar 

  • Coldman, A. J., Goldie, J. H., & Ng, V. (1985). The effect of cellular differentiation on the development of permanent drug resistance. Mathematical Biosciences, 74(2), 177–198.

    Article  Google Scholar 

  • Coldman, A. J., Coppin, C. M. L., & Goldie, J. H. (1988). Models for dose intensity. Mathematical Biosciences, 92(1), 97–113.

    Article  Google Scholar 

  • Costa, M. I. S., & Boldrini, J. L. (1997). Chemotherapeutic treatments: A study of the interplay among drug resistance, toxicity and recuperation from side effects. Bulletin of Mathematical Biology, 59(2), 205–232.

    Article  Google Scholar 

  • d’Onofrio, A., Ledzewicz, U., Maurer, H., & Schattler, H. (2009). On optimal delivery of combination therapy for tumors. Mathematical Biosciences, 222(1), 13–26.

    Article  Google Scholar 

  • Day, R. S. (1986). Treatment sequencing, asymmetry, and uncertainty: Protocol strategies for combination. Cancer Research, 46, 3876–3885.

    Google Scholar 

  • de Gramont, A., Figer, A., Seymour, M., Homerin, M., Hmissi, A., Cassidy, J. et al. (2000). Leucovorin and fluorouracil with or without oxaliplatin as first-line treatment in advanced colorectal cancer. Journal of Clinical Oncology, 18(16), 2938–2947.

    Google Scholar 

  • Dua, P., Dua, V., & Pistikopoulos, E. N. (2008). Optimal delivery of chemotherapeutic agents in cancer. Computers & Chemical Engineering, 32, 99–107.

    Article  Google Scholar 

  • Feng, S.-S., & Chien, S. (2003). Chemotherapeutic engineering: Application and further development of chemical engineering principles for chemotherapy of cancer and other diseases. Chemical Engineering Science, 58(18), 4087–4114.

    Article  Google Scholar 

  • Floares, A., Floares, C., Cucu, M., & Lazar, L. (2003). Adaptive neural networks control of drug dosage regimens in cancer chemotherapy. In Proceedings of the international joint conference on neural networks, Portland (Vol. 1, pp. 154–159).

    Google Scholar 

  • Gardner, S. N. (2002). Modeling multi-drug chemotherapy: Tailoring treatment to individuals. Journal of Theoretical Biology, 214(2), 181–207.

    Article  Google Scholar 

  • Goldie, J. H., Coldman, A. J., & Gudauskas, G. A. (1982). Rationale for the use of alternating non-cross-resistant chemotherapy. Cancer Treatment Reports, 66, 439–449.

    Google Scholar 

  • Harrold, J. M. (2005). Model-based design of cancer chemotherapy treatment schedules. Ph.D. thesis, University of Pittsburgh, Pittsburgh.

  • Harrold, J. M., & Parker, R. S. (2009). Clinically relevant cancer chemotherapy dose scheduling via mixed-integer optimization. Computers & Chemical Engineering, 33(12), 2042–2054.

    Article  Google Scholar 

  • Horner, M. J., Ries, L. A. G., Krapcho, M., Neyman, N., Aminou, R., & Howlader, N. (2009). Seer cancer statistics review 1975–2006. http://seer.cancer.gov/csr/1975_2006/. Accessed 15 Oct 2009.

  • Hryniuk, W. M. (1988). The importance of dose intensity in the outcome of chemotherapy. Important Advances in Oncology, 121–141.

  • Iliadis, A., & Barbolosi, D. (2000). Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Computers and Biomedical Research, 33(3), 211–226.

    Article  Google Scholar 

  • Itik, M., Salamci, M. U., & Banks, S. P. (2009). Optimal control of drug therapy in cancer treatment. Nonlinear Analysis, 71(12), 1473–1486.

    Article  Google Scholar 

  • Jackson, T. L., & Byrne, H. M. (2000). A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Mathematical Biosciences, 164(1), 17–38.

    Article  Google Scholar 

  • Liang, Y., Leung, K.-S., & Mok, T. S. K. (2006). A novel evolutionary drug scheduling model in cancer chemotherapy. IEEE Transactions on Information Technology in Biomedicine, 10(2), 237–245.

    Article  Google Scholar 

  • Martin, R. B. (1992). Optimal control drug scheduling of cancer chemotherapy. Automatica, 28(6), 1113–1123.

    Article  Google Scholar 

  • Martin, R. B., & Teo, K. L. (1994). Optimal control of drug administration in cancer chemotherapy. World Scientific: Singapore.

    Google Scholar 

  • Martin, R. B., Fisher, M. E., Minchin, R. F., & Teo, K. L. (1990). A mathematical model of cancer chemotherapy with an optimal selection of parameters. Mathematical Biosciences, 99(2), 205–230.

    Article  Google Scholar 

  • Martin, R. B., Fisher, M. E., Minchin, R. F., & Teo, K. L. (1992a). Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy. Mathematical Biosciences, 110(2), 201–219.

    Article  Google Scholar 

  • Martin, R. B., Fisher, M. E., Minchin, R. F., & Teo, K. L. (1992b). Low-intensity combination chemotherapy maximizes host survival time for tumors containing drug-resistant cells. Mathematical Biosciences, 110(2), 221–252.

    Article  Google Scholar 

  • Matveev, A. S., & Savkin, A. V. (2000). Optimal control applied to drug administration in cancer chemotherapy: The case of several toxicity constraints. In Proceedings of the 39th IEEE conference on decision and control (Vol. 5, pp. 4851–4856).

    Google Scholar 

  • Meropol, N. J., & Schulman, K. A. (2007). Cost of cancer care: Issues and implications. Journal of Clinical Oncology, 25(2), 180–186.

    Article  Google Scholar 

  • Miller, B. E., Miller, F. R., & Heppner, G. H. (1989). Therapeutic perturbation of the tumor ecosystem in reconstructed heterogeneous mouse mammary tumors. Cancer Research, 49, 3747–3753.

    Google Scholar 

  • Murray, J. M. (1990). Some optimal control problems in cancer chemotherapy with a toxicity limit. Mathematical Biosciences, 100(1), 49–67.

    Article  Google Scholar 

  • Murray, J. M. (1994). Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle. Mathematical Biosciences, 123(2), 183–213.

    Article  Google Scholar 

  • Murray, J. M. (1997). The optimal scheduling of two drugs with simple resistance for a problem in cancer chemotherapy. IMA Journal of Mathematics Applied in Medicine & Biology, 14, 283–303.

    Article  Google Scholar 

  • Nanda, S., Moore, H., & Lenhart, S. (2007). Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Mathematical Biosciences, 210(1), 143–156.

    Article  Google Scholar 

  • NCI—National Cancer Institute (2007). Cancer trends progress report-2007 update. http://progressreport.cancer.gov/doc_detail.asp?pid=1&did=2007&chid=75&coid=726&mid. Accessed 5 Oct 2009.

  • Panetta, J. C. (1996). A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment. Bulletin of Mathematical Biology, 58(3), 425–447.

    Article  Google Scholar 

  • Panetta, J. C. (1998). A mathematical model of drug resistance: Heterogeneous tumors. Mathematical Biosciences, 147(1), 41–61.

    Article  Google Scholar 

  • Panetta, J. C., & Adam, J. (1995). A mathematical model of cycle-specific chemotherapy. Mathematical and Computer Modelling, 22(2), 67–82.

    Article  Google Scholar 

  • Parker, R. S., & Doyle, F. J. (2001). Control-relevant modeling in drug delivery. Advanced Drug Delivery Reviews, 48, 211–228.

    Article  Google Scholar 

  • Pereira, F. L., Pedreira, C. E., Pinho, M. R., Fernandes, M. H., & Sousa, J. B. (1990). An optimal control algorithm for multidrug cancer chemotherapy design. In Proceedings of the twelfth annual international conference of the IEEE engineering in medicine and biology society (pp. 1021–1022).

    Chapter  Google Scholar 

  • Pereira, F. L., Pedreira, C. E., & De Sousa, J. B. (1995). A new optimization based approach to experimental combination chemotherapy. Frontiers of Medical and Biological Engineering, 6(4), 257–268.

    Google Scholar 

  • Petrovski, A., & McCall, J. (2001). Multi-objective optimisation of cancer chemotherapy using evolutionary algorithms. Lecture Notes in Computer Science, 1993/2001, 531–545.

    Article  Google Scholar 

  • Petrovski, A., Shakya, S., & McCall, J. (2006). Optimising cancer chemotherapy using an estimation of distribution algorithm and genetic algorithms. Paper presented at: 8th annual conference on genetic and evolutionary computation.

  • Petrovski, A., Sudha, B., & McCall, J. (2004). Optimising cancer chemotherapy using particle swarm optimisation and genetic algorithms. Lecture Notes in Computer Science, 3242, 633–641.

    Article  Google Scholar 

  • Pillis, L. G. D., & Radunskaya, A. (2003). The dynamics of an optimally controlled tumor model: A case study. Mathematical and Computer Modelling, 37, 1221–1244.

    Article  Google Scholar 

  • Pillis, L. G. D., Gu, W., Fister, K. R., Head, T., Maples, K., Murugan, A. et al. (2007). Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls. Mathematical Biosciences, 209(1), 292–315.

    Article  Google Scholar 

  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1962). The mathematical theory of optimal processes. New York: Gordon & Breach.

    Google Scholar 

  • Powell, W. B. (2007). Approximate dynamic programming: Solving the curses of dimensionality. Hoboken: Wiley.

    Book  Google Scholar 

  • Retsky, M. W., Demicheli, R., Swartzendruber, D. E., Bame, P. D., Wardwell, R. H., Bonadonna, G. et al. (1997). Computer simulation of a breast cancer metastasis model. Breast Cancer Research and Treatment, 45(2), 193–202.

    Article  Google Scholar 

  • Schrag, D. (2004). The price tag on progress—chemotherapy for colorectal cancer. New England Journal of Medicine, 351(4), 317–319.

    Article  Google Scholar 

  • Skipper, H. E., Schabel, F. M., & Lloyd, H. (1979). Dose-response and tumor cell repopulation rate in chemotherapeutic trials. Advances in Cancer Chemotherapy, 1, 205–253.

    Google Scholar 

  • Sullivan, P. W., & Salmon, S. E. (1972). Kinetics of tumor growth and regression in IgG multiple myeloma. The Journal of Clinical Investigation, 51(7), 1697–1708.

    Article  Google Scholar 

  • Swan, G. W. (1984). Applications of the optimal control theory in biomedicine. New York: Dekker.

    Google Scholar 

  • Swan, G. W. (1987). Tumor growth models and cancer chemotherapy. In J. R. Thompson & B. Brown (Eds.), Cancer modeling (pp. 91–179). New York: Dekker.

    Google Scholar 

  • Swan, G. W. (1990). Role of optimal control theory in cancer chemotherapy. Mathematical Biosciences, 101(2), 237–284.

    Article  Google Scholar 

  • Swan, G. W., & Vincent, T. L. (1977). Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bulletin of Mathematical Biology, 39(3), 317–337.

    Article  Google Scholar 

  • Tan, K. C., Khor, E. F., Cai, J., Heng, C. M., & Lee, T. H. (2002). Automating the drug scheduling of cancer chemotherapy via evolutionary computation. Artificial Intelligence in Medicine, 25(2), 169–185.

    Article  Google Scholar 

  • Tse, S. M., Liang, Y., Leung, K.-S., Lee, K.-H., & Mok, T. S. K. (2007). A memetic algorithm for multiple-drug cancer chemotherapy schedule optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 37(1), 84–91.

    Article  Google Scholar 

  • U.S. Department of Health and Human Services Centers for Medicare and Medicaid Services (SCMMS) (1960–2007). National health expenditures by type of service and source of funds, calendar years 2007–1960. http://www.cms.hhs.gov/NationalHealthExpendData/02_NationalHealthAccountsHistorical.asp#TopOfPage.Social. Accessed 7 Oct 2009.

  • Villasana, M., & Ochoa, G. (2004). Heuristic design of cancer chemotherapies. IEEE Transactions on Evolutionary Computation, 8(6), 513–521.

    Article  Google Scholar 

  • Yu, P. L., & Leitmann, G. (1974). Nondominated decisions and cone convexity in dynamic multicriteria decision problems. Journal of Optimization Theory and Applications, 14(5), 573–584.

    Article  Google Scholar 

  • Zietz, S., Desaive, C., Grattarola, M., & Nicolini, C. (1980). Modeling to determine dose dependence of drug and cell kinetic parameters. Computers & Biomedical Research, 13(3), 297–305.

    Article  Google Scholar 

  • Zietz, S., & Nicolini, C. (1979). Mathematical approaches to optimization of cancer chemotherapy. Bulletin of Mathematical Biology, 41(3), 305–324.

    Article  Google Scholar 

  • Zitzler, E. (1999). Evolutionary algorithms for multi-objective optimization: Methods and applications. Swiss Federal Institute of Technology, Zurich.

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Authors and Affiliations

  1. Department of Industrial Engineering and Logistics Management, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jinghua Shi

  2. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Jinghua Shi & Oguzhan Alagoz

  3. Department of Management Sciences, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Fatih Safa Erenay

  4. School of Economics & Management, Tongji University, Shanghai, 200092, China

    Qiang Su

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  1. Jinghua Shi
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Correspondence to Oguzhan Alagoz.

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Shi, J., Alagoz, O., Erenay, F.S. et al. A survey of optimization models on cancer chemotherapy treatment planning. Ann Oper Res 221, 331–356 (2014). https://doi.org/10.1007/s10479-011-0869-4

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