Hypoxia tissue-vascular carbon dioxide exchange plays a key role in influencing the cerebral vascular. One of the tools to analyze the dynamics of hypoxia in tissue-vascular is a mathematical modeling. The current paper proposes perturbation iteration method to solve the mathematical model of hypoxia tissue-vascular carbon dioxide exchange. This method involves different order derivatives in Taylor series expansion. To test the efficiency of this method, the obtained solutions in the form of an infinite series are compared to ones from Euler method and Runge Kutta method. Using the data of a 30-year old woman performing three regular physical activities, that is walking, jogging and running fast, the validation of the mathematical model has been carried out through numerical simulation. The results are in good agreement with experimental data which demonstrate the role of physical activities in the recovery of patients suffering from cardiovascular-respiratory system related diseases such as hypoxia.

response, physical activity, hypoxic hypoxia, tissue, oxygen, perturbation iteration method, numerical simulation.

Received: November 15, 2023; Revised: November 25, 2023; Accepted: March 2, 2024; Published: March 20, 2024

How to cite this article: Mahamat Saleh DAOUSSA HAGGAR and Jean Marie NTAGANDA, Response of physical activity to the dynamics of hypoxia tissue-vascular carbon dioxide exchange using perturbation iteration method, Far East Journal of Dynamical Systems 37(1) (2024), 51-68. https://doi.org/10.17654/0972111824003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] A. Cymennan and P. B. Rock, Medical Problems in High Mountain Environments. A Handbook for Medical Officers, USARIEM Technical Note TN 94-2, 1994.
[2] G. Gutierrez, A Mathematical Model of Tissue-Blood Carbon Dioxide Exchange during Hypoxia, Am. J. Respir. Crit. Care Med. 169 (2004), 525-533.
[3] J. J. Tyson and B. Novak, Regulation of the eukariotic cell-cycle: molecular antagonism, hysteresis, and irreversible transitions, J. Theor. Biol. 210 (2001), 249-263.
[4] D. Gammack, H. M. Byrne and C. E. Lewis, Estimating the selective advantage of mutant p53 tumour cells to repeated rounds of hypoxia, Bull. Math. Biol. 63 (2001), 135-166.
[5] J. A. Dempsey, H. V. Forster and D. M. Ainsworth, Regulation of hyperpnea, hyperventilation, and respiratory muscle recruitment during exercise, In: J. A. Dempsey, A. I. Pack, editors, Regulation of Breathing, New York, Marcel Dekker; 1995, p. 1065-1133.
[6] B. Zhang, H. Ye and A. Yang, Mathematical modelling of interacting mechanisms for hypoxia mediated cell cycle commitment for mesenchymal stromal cells, BMC Syst. Biol. 12 (2018), 35. https://doi.org/10.1186/s12918-018-0560-3.
[7] E. P. Chen, R. S. Song and X. Chen, Mathematical model of hypoxia and tumor signaling interplay reveals the importance of hypoxia and cell-to-cell variability in tumor growth inhibition, BMC Bioinformatics 20 (2019), 507.
https://doi.org/10.1186/s12859-019-3098-5.
[8] G. Fiandaca, M. Delitala and T. Lorenzi, A mathematical study of the influence of hypoxia and acidity on the evolutionary dynamics of cancer, Bull. Math. Biol. 83 (2021), 83. https://doi.org/10.1007/s11538-021-00914-3.
[9] A. Ardaseva, R. A. Gatenby, A. R. A. Anderson, H. M. Byrne, P. K. Maini and T. Lorenzi, A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels, Bull. Math. Biol. 82(6) 81.
[10] S. Timischl, A global model for the cardiovascular and respiratory system, Ph. D. Thesis, Karl-Franzens-Universitaet Graz, 1998.
[11] S. Timischl, J. J. Batzel and F. Kappel, Modeling the human cardiovascular- respiratory control system: an optimal control application to the transition to non-REM sleep, Spezialforschungsbereich F-003 Technical Report 190, Karl- Franzens-Universitat, 2000.
[12] Y. Aksoy and M. Pakdemirli, New perturbation-iteration solutions for Bratu-type equations, Computers and Mathematics with Applications 59(8) (2010), 2802-2808.
[13] M. Pakdemirli, Y. Aksoy and H. Boyaci, A new perturbation-iteration approach for first order differential equations, Mathematical and Computational Applications 16(4) (2011), 890-899.
[14] M. Pakdemirli, Review of the perturbation-iteration method, Mathematical and Computational Applications 18(3) (2013), 139-151.
[15] Jean Marie Ntaganda and Benjamin MAMPASSI, Modelling blood partial pressures of the human cardiovascular/respiratory system, Applied Mathematics and Computation 187 (2007), 1100-1108.