Controlling and stabilizing unpredictable behavior of metabolic reactions and carcinogenesis in biological systems
- 35 Downloads
Developing new designs and optimization of the cancer treatment is extremely important task. In this work, the nonlinear multi-scale diffusion cancer invasion model that describes the interactions of the tumor cells, matrix-metalloproteinases, matrix-degradative enzymes and oxygen is studied. The conditions under which the cancerous biological system exhibits chaotic behavior were obtained by means of the method based on wandering trajectories analysis. Regions of parameters leading to carcinogenesis in the biological system studied were found in control parameter planes ‘number of tumor cells versus diffusion saturation level.’ Significant influence of the biological system initial state to carcinogenesis was ascertained and illustrated by regions in phase planes of initial conditions. Evolution of all regions obtained is presented depending on glucose level.
KeywordsTumor Metabolic reactions Carcinogenesis Chaotic attractors Phase spaces Control parameters
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest concerning the publication of this manuscript.
- 7.Baumann, M., Petersen, C.: TCP and NTCP: a basic introduction. Rays 30(2), 99–104 (2005)Google Scholar
- 8.Baumann, M., Petersen, C., Krause, M.: TCP and NTCP in preclinical and clinical research in Europe. Rays 30(2), 121–126 (2005)Google Scholar
- 13.Zhu, J., Li, R., Tiselius, E., et al.: Immunotherapy (excluding checkpoint inhibitors) for stage I to III non-small cell lung cancer treated with surgery or radiotherapy with curative intent. Cochrane Database Syst Rev. 12, CD011300 (2017). https://doi.org/10.1002/14651858.CD011300.pub2 Google Scholar
- 17.Ivancevic, T.T., Bottema, M.J., Jain, L.C.: A theoretical model of chaotic attractor in tumor growth and metastasis. Cornell University Library’s arXiv: 0807.4272, pp. 1–17 (2008)
- 18.Harney, M., Yim, W.: Chaotic attractors in tumor growth and decay: a differential equation model. In: Vlamos P., Alexiou A. (eds.) GeNeDis 2014. Advances in Experimental Medicine and Biology, vol. 820, pp. 193–206. Springer, Cham (2014)Google Scholar
- 28.Berezovoj, V.P., Bolotin, Y.L., Dzyubak, O.P., et al.: Stochastic resonance in a periodically modulated dissipative nuclear dynamics. Fermilab Report, Jan 2001 FERMILAB-CONF-01-009-T. http://lss.fnal.gov/archive/2001/conf/Conf-01-009-T.pdf
- 35.Watson, J.D., Baker, T.A., Bell, S.P., Gann, A., Levine, M., Losick, R.: Molecular Biology of the Gene. Pearson, New York (2014)Google Scholar
- 36.Prigogine, I., Stengers, I.: Order Out of Chaos. Heinemann, London (1984)Google Scholar