Spatiotemporal dynamics of angiogenesis in tumor vasculature under treatment - Islam, M. Rashedul; Haque, M. Mozammelul; Kabir, Muhammad Humayun (Fırat Evirgen, 2026)
Cancer remains a major global health challenge, and mathematical modeling is frequently used to understand tumor progression and angiogenesis mechanisms. In this study, a reaction–diffusion model of angiogenesis-driven tumor growth is developed to investigate the effects of key parameters on tumor dynamics under both spatially homogeneous and non-homogeneous settings. The model is analyzed qualitatively and numerically. In the absence of diffusion, the endothelial progenitor cell (EPC) population in the bone marrow initially increases and then approaches a steady state, while the circulating cell population remains nearly constant. Under these conditions, the nonlinear growth of the tumor mass is observed. The system is found to evolve toward spatially uniform stable states when diffusion is included, demonstrating the stabilizing influence of diffusion on the system. Additionally, the influence of treatment is assessed using a control parameter, and increasing treatment intensity leads to a significant reduction in tumor mass. Important insights into the dynamics of tumor angiogenesis are obtained, and the potential role of treatment strategies in controlling tumor growth is highlighted. The proposed model is expected to contribute to a better understanding of tumor behavior and to support the development of more effective therapeutic approaches.
Keywords: Biological Mathematics; Biyolojik Matematik