The Effect of Tumor Angiogenesis Agents on Tumor Growth Dynamics: A Mathematical Model

Ali  Mohseni; Mohammad  Pooyan; Somayeh  Raiesdana; Mohammad Bagher  Menhaj

doi:10.18502/fbt.v12i1.17743

Ali Mohseni Department of Biomedical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Mohammad Pooyan Department of Biomedical Engineering, Shahed University, Tehran, Iran
Somayeh Raiesdana Department of Biomedical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Mohammad Bagher Menhaj Faculty of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

DOI: https://doi.org/10.18502/fbt.v12i1.17743

Keywords: Chaos; Angiogenesis; Mathematical Model; Vascular Tumor; Tumor Angiogenesis Agents; Numerical Simulation.

Abstract

Purpose: Tumor-induced angiogenesis is a dangerous state of the tumor growth process in which solid tumors have a blood supply. Modeling has been a very important tool in studying tumor growth and angiogenesis. In this paper, we developed a cancer model by introducing tumor angiogenesis agents to better highlight the role of these chemical substances in tumor-induced vascularization. Our model can reconstruct the transition from a pre-angiogenic to a post-angiogenic state.

Materials and Methods: The proposed model comprises five variables: host cells (normal cells), immune cells, tumor cells, endothelial cells, and tumor angiogenesis agents. Chaotic behavior in the production of different populations of cells during vascular growth may confer survival advantages to tumors. Our model has a chaotic regime, which is an indication of tumor-induced angiogenesis dynamics. The fixed points are analyzed biologically, and stability analysis is performed via their eigenvalues. We analyzed the model dynamics via observability and bifurcation analysis.

Results: The numerical simulations illustrate biological and clinical findings about vascular tumors. The results show that the proposed model with the existence of tumor angiogenesis agents could capture both avascular and vascular stages of tumor growth. There is no effect of tumor cell killing rate via immune cells on the system dynamics. However, the increase of inhibitory factors of tumor angiogenesis agents leads to the termination of chaos.

Conclusion: Our results show the ineffectiveness of targeted treatments on the immune system, which has been confirmed by many negative treatment methods in immunotherapies. Tumor-secreted inhibitor factors are essential to regulating the angiogenesis process. However, increasing inhibitor factors via anti-angiogenic drugs would be a more effective therapeutic approach to eradicate metastasis.