Abstract
Pre- or post-operational chemo-radiotherapy have become one of the standard adjuvant therapies in recent years. Though both chemo- and radiotherapy protocols are standardized, the question about the order in which they should be applied, or concurrency, remains an open question. In this work we attempt to answer it with mathematical modeling and optimization of two-dimensional control that represents therapy in a control-theory based approach. In order to address this problem, two issues are discussed. First, two different ways of modeling tumor growth under therapy are compared. For each of them, the necessary conditions for optimal control representing the therapy are presented and discussed. Then, Kaplan-Meier survival curves are compared for standard therapy protocols used in clinics and different approaches to model tumor growth. Finally, a framework for analysis of treatment efficacy is presented, in which optimization and survival analysis are used sequentially.
The authors were supported by NCN grant (National Science Centre, Poland) DEC-2016/21/B/ST7/02241. Calculations were partially performed on the Ziemowit computational cluster (http://www.ziemowit.hpc.polsl.pl) created in the POIG.02.01.00-00-166/08 project (BIO-FARMA) and expanded in the POIG.02.03.01-00-040/13 project (Syscancer) and PBS3/B3/32/2015 project (Biotest).
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Acknowledgment
The Authors would like to thank Prof. Suwinski from the Maria Sklodowska-Curie Institute -Oncology Centre (MSCI), branch in Gliwice, for valuable comments on clinical applicability of the results obtained from modeling.
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Swierniak, A., Smieja, J., Mura, M., Bajger, P. (2020). Modeling and Optimization of Radio-Chemotherapy. In: Korbicz, J., Maniewski, R., Patan, K., Kowal, M. (eds) Current Trends in Biomedical Engineering and Bioimages Analysis. PCBEE 2019. Advances in Intelligent Systems and Computing, vol 1033. Springer, Cham. https://doi.org/10.1007/978-3-030-29885-2_20
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