Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study

Mahya Mohammadi; M. Soltani; Cyrus Aghanajafi; Mohammad Kohandel; Mahya Mohammadi; M. Soltani; Cyrus Aghanajafi; Mohammad Kohandel

doi:10.3934/mbe.2023252

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 5448-5480. doi: 10.3934/mbe.2023252

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Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study

1.
Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran 19919-43344, Iran
2.
Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
3.
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
4.
School of Optometry and Vision Science, Faculty of Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
5.
Advanced Bioengineering Initiative Center, Multidisciplinary International Complex, K. N. Toosi University of Technology, Tehran 19697-64499, Iran
6.
Centre for Biotechnology and Bioengineering (CBB), University of Waterloo, Waterloo, ON N2L 3G1, Canada

Received: 30 September 2022 Revised: 21 December 2022 Accepted: 25 December 2022 Published: 13 January 2023

Anti-angiogenesis as a treatment strategy for normalizing the microvascular network of tumors is of great interest among researchers, especially in combination with chemotherapy or radiotherapy. According to the vital role that angiogenesis plays in tumor growth and in exposing the tumor to therapeutic agents, this work develops a mathematical framework to study the influence of angiostatin, a plasminogen fragment that shows the anti-angiogenic function, in the evolutionary behavior of tumor-induced angiogenesis. Angiostatin-induced microvascular network reformation is investigated in a two-dimensional space by considering two parent vessels around a circular tumor by a modified discrete angiogenesis model in different tumor sizes. The effects of imposing modifications on the existing model, i.e., the matrix-degrading enzyme effect, proliferation and death of endothelial cells, matrix density function, and a more realistic chemotactic function, are investigated in this study. Results show a decrease in microvascular density in response to the angiostatin. A functional relationship exists between angiostatin's ability to normalize the capillary network and tumor size or progression stage, such that capillary density decreases by 55%, 41%, 24%, and 13% in tumors with a non-dimensional radius of 0.4, 0.3, 0.2, and 0.1, respectively, after angiostatin administration.
- anti-angiogenesis,
- microvascular network,
- angiostatin,
- modified angiogenesis model,
- microvascular density
Citation: Mahya Mohammadi, M. Soltani, Cyrus Aghanajafi, Mohammad Kohandel. Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 5448-5480. doi: 10.3934/mbe.2023252

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Abstract

Anti-angiogenesis as a treatment strategy for normalizing the microvascular network of tumors is of great interest among researchers, especially in combination with chemotherapy or radiotherapy. According to the vital role that angiogenesis plays in tumor growth and in exposing the tumor to therapeutic agents, this work develops a mathematical framework to study the influence of angiostatin, a plasminogen fragment that shows the anti-angiogenic function, in the evolutionary behavior of tumor-induced angiogenesis. Angiostatin-induced microvascular network reformation is investigated in a two-dimensional space by considering two parent vessels around a circular tumor by a modified discrete angiogenesis model in different tumor sizes. The effects of imposing modifications on the existing model, i.e., the matrix-degrading enzyme effect, proliferation and death of endothelial cells, matrix density function, and a more realistic chemotactic function, are investigated in this study. Results show a decrease in microvascular density in response to the angiostatin. A functional relationship exists between angiostatin's ability to normalize the capillary network and tumor size or progression stage, such that capillary density decreases by 55%, 41%, 24%, and 13% in tumors with a non-dimensional radius of 0.4, 0.3, 0.2, and 0.1, respectively, after angiostatin administration.

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