Abstract
In this paper, we investigate the employment of evolutionary algorithms as a search mechanism in a decision support system for designing chemotherapy schedules. Chemotherapy involves using powerful anti-cancer drugs to help eliminate cancerous cells and cure the condition. It is given in cycles of treatment alternating with rest periods to allow the body to recover from toxic side-effects. The number and duration of these cycles would depend on many factors, and the oncologist would schedule a treatment for each patient’s condition. The design of a chemotherapy schedule can be formulated as an optimal control problem; using an underlying mathematical model of tumour growth (that considers interactions with the immune system and multiple applications of a cycle-phase-specific drug), the objective is to find effective drug schedules that help eradicate the tumour while maintaining the patient health’s above an acceptable level. A detailed study on the effects of different objective functions, in the quality and diversity of the solutions, was performed. A term that keeps at a minimum the tumour levels throughout the course of treatment was found to produce more regular treatments, at the expense of imposing a higher strain on the patient’s health, and reducing the diversity of the solutions. Moreover, when the number of cycles was incorporated in the problem encoding, and a parsimony pressure added to the objective function, shorter treatments were obtained than those initially found by trial and error.
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Notes
Notice that 3 h corresponds to 0.125 as a fraction of a day, however, we decided to round this value to 0.2, as 0.125 was found to be too small to provide visible differences in our simulations.
According to the oncologists consulted during Dr. Villasana’s doctorate degree (personal cominucation).
References
Chuang, L., Lotzova, E., Cook, K., Cristoforoni, P., Morris, M., Wharton, T.: Effect of new investigational drug taxol on oncolytic activity and stimulation of human lymphocytes. Gynecol. Oncol. 49, 291–298 (1993)
de Pillis, L., Radunskaya, A.: The dynamics of an optimally controlled tumor model: a case study. Math. Comput. Model. 37(11), 1221–1244 (2003)
de Pillis, L., Radunskaya, A.: A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. J. Theor. Med. 3, 79–100 (2001)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)
Hansen, N., Ostermeier, A.: (1996) Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation, pp. 312–317. IEEE Press, Piscataway, NJ
Hardman, J., Linbird, L.: Goodman and Gilman’s the pharmacological basis of therapeutics, 9th edn. McGraw-Hill, New York (1996)
Luus, R.: Iterative dynamic programming, monographs and surveys in pure and applied mathematics, vol. 110. Chapman and Hall, New York (2000)
Morrison, R.W., De Jong K.A.: Measurement of population diversity. In: Hartmanis, J., Goos, G., van Leeuwnen, J. (eds) Proceedings of Artificial Evolution: 5th International Conference, Evolution Artificielle (EA 2001), LNCS, vol. 2310, pp. 31–41. Springer, Berlin (2002)
Panetta, J.C., Adam, J.: A mathematical model of cycle-specific chemotherapy. Math. Compt. Model. 22(2), 67–82 (1995)
Petrovski, A., McCall, J.: Multi-objective optimisation of cancer chemotherapy using evolutionary algorithms. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello C. A., Corne D. (eds.) Proceedings of Evolutionary Multi-Criterion Optimization, First International Conference, EMO 2001, LNCS, vol. 1993, pp. 531–545. Springer, Berlin (2001)
Petrovski. A., Shakya, S., McCall, J.: Optimising cancer chemotherapy using an estimation of distribution algorithm and genetic algorithms. In: Cattolico, M. (ed.) Genetic and Evolutionary Computation Conference, GECCO 2006, vol. 1, pp. 413–418. ACM Press, Washington (2006)
Petrovski, A., Sudha, B., McCall, J.: Optimising cancer chemotherapy using particle swarm optimisation and genetic algorithms. In: Yao, X., Burke, E. K., Lozano, J.A., Smith, J., Merelo Guervós, J. J., Bullinaria, J. A., Rowe, J. E., Tiño, P., Kabán, A., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature-PPSN VIII, LNCS, vol. 3242, pp. 633–641. Springer, Berlin (2004)
Sear, J.: Clinics in anaesthesiology, vol. 2. Intravenous anaesthesiology, no. 1, ch. 12, p. 223. W. B. Saunders, Philadelphia (1984)
Villasana, M.: A delay differential equation model for tumor-immune system interactions, Ph.D. thesis, Claremont Graduate University (2001)
Villasana, M., Ochoa, G.: Heuristic design of cancer chemotherapy, IEEE trans. Evol. Comput. 8(6), 513–521 (2004)
Villasana, M., Radunskaya, A.: A delay differential equation model for tumor growth. J. Math. Biol. 47, 270–294 (2003)
Wheldon, T.: Mathematical models in cancer research. Adam Hilger, Bristol, Philadelphia (1998)
Zoli, W., Flamigni, A., Frassineti, G., Bajorko, P., De Paola, F., Milandri, C., Amadori, D., Gasperi-Campani, A.: In vitro activitity of taxol and toxotere in comparison with doxorubicin and cisplatin on primary cell cultures of human breast cancers. Breast Cancer Res. Treat. 34, 63–69 (1995)
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Ochoa, G., Villasana, M. & Burke, E.K. An evolutionary approach to cancer chemotherapy scheduling. Genet Program Evolvable Mach 8, 301–318 (2007). https://doi.org/10.1007/s10710-007-9041-y
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DOI: https://doi.org/10.1007/s10710-007-9041-y