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Controlling and stabilizing unpredictable behavior of metabolic reactions and carcinogenesis in biological systems

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Technical University, 2 Kyrpychova Str., Kharkiv, 61002, Ukraine

    Larysa Dzyubak

  2. Ascension All Saint Cancer Center, 3809 Spring Street, Racine, WI, 53405, USA

    Oleksandr Dzyubak

  3. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Str., 90-924, Lodz, Poland

    Jan Awrejcewicz

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  1. Larysa Dzyubak
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  2. Oleksandr Dzyubak
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  3. Jan Awrejcewicz
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Correspondence to Larysa Dzyubak.

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Dzyubak, L., Dzyubak, O. & Awrejcewicz, J. Controlling and stabilizing unpredictable behavior of metabolic reactions and carcinogenesis in biological systems. Nonlinear Dyn 97, 1853–1866 (2019). https://doi.org/10.1007/s11071-018-04737-1

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  • DOI: https://doi.org/10.1007/s11071-018-04737-1

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