A Tumor Growth Model with a „Butterfly” – Type Chaotic Time Attractor. Cancer Evolution Through a Traveling Waves-Type Mechanism

Butuc, Irina; Ghizdovăţ, Vlad; Rusu, Cristina-Marcela; Buzea, Călin Gheorghe

doi:10.2478/bipmf-2021-0014

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A Tumor Growth Model with a „Butterfly” – Type Chaotic Time Attractor. Cancer Evolution Through a Traveling Waves-Type Mechanism

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

Volume 67 (2021): Issue 3 (September 2021)

By: Irina Butuc, Vlad Ghizdovăţ, Cristina-Marcela Rusu and Călin Gheorghe Buzea

Open Access

|Mar 2022

Abstract

In this paper we propose a new tumor growth model, based on the original model developed by Anderson-Chaplain to which we attached Ivancevic’s “butterfly” time attractor. The chaotic behavior provides a more realistic perspective on tumor growth, with uncertainties and uncontrollable long term stochastic effects.

References

Anderson A.R.A., Chaplain M.A.J., Newman E.L., Steele R.J.C., Thompson A.M., Mathematical Modelling of Tumour Invasion and Metastasis, Computational and Mathematical Methods in Medicine 2, 129-154 (2000).10.1080/10273660008833042
Search in Google Scholar Back to article
Brahimi-Horn M.C., Pouyssegur J., Oxygen, a Source of Life and Stress, FEBS Letters 581, 19, 3582-3591 (2007).10.1016/j.febslet.2007.06.01817586500
Search in Google Scholar Back to article
Cuvier C., Jang A, Hill R.P., Exposure to Hypoxia, Glucose Starvation and Acidosis: Effect on Invasive Capacity of Murine Tumor Cells and Correlation with Cathepsin (L + B) Secretion, Clinical & Experimental Metastasis 15, 1, 19-25 (1997).10.1023/A:1018428105463
Search in Google Scholar Back to article
Ivancevic T.T., Bottema M.J., Jain L.C., A Theoretical Model of Chaotic Attractor in Tumor Growth and Metastasis, arXiv:0810.4580v1 (2008).
Search in Google Scholar Back to article
Kozusko F., Bourdeau M., A Unified Model of Sigmoid Tumour Growth Based on Cell Proliferation and Quiescence, Cell Proliferation 40, 6, 824-834 (2007).10.1111/j.1365-2184.2007.00474.x18021173
Search in Google Scholar Back to article
Liu C., Gao S., Zhang L., Tumor Microenvironment: Hypoxia and Buffer Capacity for Immunotherapy, Medical Hypotheses 69, 3, 590-595 (2007).10.1016/j.mehy.2006.12.05317360127
Search in Google Scholar Back to article
Marchant B.P., Norbury J., Sherratt J.A., Travelling Wave Solutions to a Haptotaxis-Dominated Model of Malignant Invasion, Nonlinearity 14, 1653-1671 (2001).10.1088/0951-7715/14/6/313
Search in Google Scholar Back to article
Perumpanani A.J., Norbury J., Sherratt J.A., Byrne H.M., Traveling Shock Waves Arising in a Model of Malignant Invasion, Physica D 126, 145-159 (1999).10.1016/S0167-2789(98)00272-3
Search in Google Scholar Back to article
Witz I.P., Levy-Nissenbaum O., The Tumor Microenvironment in the Post-PAGET Era, Cancer Letters 242, 1, 1-10 (2006).10.1016/j.canlet.2005.12.00516413116
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/bipmf-2021-0014 | Journal eISSN: 2537-4990

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Language: English

Page range: 31 - 41

Submitted on: Aug 3, 2021

Accepted on: Sep 7, 2021

Published on: Mar 17, 2022

Published by: Gheorghe Asachi Technical University of Iasi

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Related subjects:

Mechanical engineering,

Mechanics,

Materials sciences,

Materials sciences, other,

Physics,

Theoretical and mathematical physics,

Technical and applied physics

© 2022 Irina Butuc, Vlad Ghizdovăţ, Cristina-Marcela Rusu, Călin Gheorghe Buzea, published by Gheorghe Asachi Technical University of Iasi
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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