Towards Personalized Radio-Chemotherapy – Learning from Clinical Data vs. Model Optimization

  • Andrzej Świerniak
  • Jarosław Śmieja
  • Krzysztof Fujarewicz
  • Rafał Suwiński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12033)


We summarize results of our research studies on models of combined anticancer radio- and chemotherapy and their comparison with real clinical data. We use two mathematical techniques, which, to our knowledge, have not been applied simultaneously: optimal control theory and survival analysis. We recall results of analytical optimization of combined chemo-radio-therapy for a simple model of tumor growth with respect to the order, in which these two modes of treatment should be applied. Then we study both structural and parametric sensitivity of this model and related optimal control problem. Afterwards, we present results of survival analysis based on the Kaplan-Meier curves for different protocols of chemo-radio-therapy and compare them with real clinical data and results of optimal treatment protocols.


Therapy optimization Survival analysis 



The Authors would like to thank for financial support of their research. The study is partially supported by National Science Committee, Poland, Grant no. 2016/21/B/ST7/02241 and partially by Silesian University of Technology Grant no. 02/010/BK18/0102.


  1. 1.
    Świerniak, A., Kimmel, M., Smieja, J., Puszynski, K., Psiuk-Maksymowicz, K.: System Engineering Approach to Planning Anticancer Therapies. Springer, Cham (2016). Scholar
  2. 2.
    Schättler, H., Ledzewicz, U.: Optimal control for mathematical models of cancer therapies. IAM, vol. 42. Springer, New York (2015). Scholar
  3. 3.
    Geng, C., Paganetti, H., Grassberger, C.: Prediction of treatment response for combined chemo- and radiation therapy for non-small cell lung cancer patients using a bio-mathematical model. Sci. Rep. 7, 13542 (2017)CrossRefGoogle Scholar
  4. 4.
    Curran, W.J., et al.: Sequential vs concurrent chemoradiation for stage III nonsmall cell lung cancer: randomized phase III trial RTOG 9410. JNCI J. Natl Cancer Inst. 103(19), 1452–1460 (2011)CrossRefGoogle Scholar
  5. 5.
    Dolbniak, M., Kardynska, M., Smieja, J.: Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth. Discr. Continuous Dyn. Syst. Ser. B 23, 145–160 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dudley, W.N., Wickham, R., Coombs, N.: An introduction to survival statistics: kaplan-meier analysis. J. Adv. Pract. Oncol. 7(1), 91–100 (2016)Google Scholar
  7. 7.
    Bajgier, P., Fujarewicz, K., Swierniak, A.: Effects of pharmacokinetics and DNA repair on the structure of optimal controls in a simple model of radio-chemotherapy. In: Proceedings of the MMAR Conference, pp. 686–691 (2018)Google Scholar
  8. 8.
    Dolbniak, M., Smieja, J., Swierniak, A.: Structural sensitivity of control models arising in combined chemo-radiotherapy. In: Proceedings of the MMAR Conference, pp. 339–344 (2018)Google Scholar
  9. 9.
    Skipper, H.E., Schabel, F., Wilcox, W.: Experimental evaluation of potential anticancer agents. XIII. on the criteria and kinetics associated with curability of experimental leukemia. Cancer Chemother. Rep. 35, 1–111 (1964)Google Scholar
  10. 10.
    Fowler, J.F.: The linear-quadratic formula and progress in fractionated radiotherapy. Br. J. Radiol. 62, 679–694 (1989)CrossRefGoogle Scholar
  11. 11.
    Gerlee, P.: The model muddle in search of tumor growth laws. Cancer Res. 73(8), 2407–2411 (2013)CrossRefGoogle Scholar
  12. 12.
    Lee, J.Y., Kim, M.-S., Kim, E.H., Chung, N., Jeong, Y.K.: Retrospective growth kinetics and radiosensitivity analysis of various human xenograft models. Lab. Anim. Res. 32(4), 187–193 (2016). Scholar
  13. 13.
    Wolkowicz, S., et al.: Prediction of lung cancer patients’ response to combined chemo-radiotherapy using a personalized hybrid model. Mathematica Applicanda 47(2), 219–229 (2019)CrossRefGoogle Scholar
  14. 14.
    Bajger, P., Fujarewicz, K., Swierniak, A.: Optimal control in a model of chemotherapy-induced radiosensilization. Mathematica Applicanda 47(1), 81–91 (2019)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Radu-Emil, P., Radu-Codrut, D.: Nature-Inspired Optimization Algorithms for Fuzzy Controlled Servo Systems. Butterworth-Heinemann, Oxford (2019)Google Scholar
  16. 16.
    Król, D., Lasota, T., Trawiński, B., Trawiński, K.: Investigation of evolutionary optimization methods of TSK fuzzy model for real estate appraisal. Int. J. Hybrid Intell. Syst. 5(3), 111–128 (2008)CrossRefGoogle Scholar
  17. 17.
    Swierniak, A., Smieja, J., Mura, M., Bajger, P.: Modeling and optimization of radio-chemotherapy. Adv. Intell. Syst. Comput. 1033, 223–233 (2020)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Systems Biology and EngineeringSilesian University of TechnologyGliwicePoland
  2. 2.M. Sklodowska-Curie Memorial Cancer Center and Institute of OncologyGliwicePoland

Personalised recommendations