In this paper, we propose a vascular tumor growth model that combines a phase-field tumor model with a phase-field angiogenesis model. By incorporating various tumor cell species, we capture the instabilities of the tumor in the presence of evolving neovasculature. The model not only considers different dynamics of tumor cell phase conversions, movement, and pressure effects but also provides a comprehensive representation of angiogenesis, encompassing chemotaxis of endothelial cells, sprouting, anastomoses, and blood flow in capillaries. This study evaluates the impact of chemotaxis on tumor cell movement in both avascular and vascular tumor growth scenarios. The results highlight the acceleration of tumor growth when angiogenesis is stimulated. Additionally, the investigation explores various initial distances of the tumor from neighboring vessels, revealing a critical threshold distance beyond which the angiogenesis factor fails to stimulate angiogenesis, resulting in the tumor maintaining a stable state. The integration of chemotaxis into the growth model induces instabilities, leading to increased nutrient availability and faster growth for the tumor. Furthermore, the study considers anti-angiogenesis therapy as an ideal approach, assuming complete inhibition of angiogenesis from the early stages. In this scenario, the tumor persists in a steady state, adhering to the avascular size limit in the absence of neovasculature. Conversely, when considering chemotaxis, anti-angiogenesis therapy loses efficiency, enabling unrestrained tumor growth towards neighboring vessels. This work sheds light on the intricate interplay among chemotaxis, angiogenesis, and anti-angiogenesis therapy in the context of vascular tumor growth, providing valuable insights for the development of targeted treatment strategies.

Soroosh Arshadi

Ahmadreza Pishevar

Mahdi Javanbakht

Shaghayegh Haghjooy Javanmard

Mathematical Biosciences

MATHEMATICAL BIOSCIENCES 发表使用数学模型提供新概念或对生物系统的新理解的工作，或可能适用于多个生物系统的方法论文章。预计论文将提出对生物科学或数学生物学具有广泛意义的重大研究发现。数学生物科学欢迎原创研究文章、信件、评论和观点。

The journal Mathematical Biosciences publishes research that uses mathematical models to provide new concepts or insights into biological systems, as well as methodological articles applicable to multiple biological systems. The journal expects submissions to present significant research findings that have broad implications for the biological sciences or mathematical biology. Mathematical Biosciences welcomes original research articles, letters, reviews, and perspectives.

《Mathematical Biosciences》期刊发表利用数学模型提供新概念或对生物系统的新理解的研究成果，以及适用于多个生物系统的方法论文章。期刊期待论文能够提出对生物科学或数学生物学具有广泛意义的重要研究发现。数学生物科学欢迎原创研究文章、信件、评论和观点。

Category	Quartile
数学	4
数学, 生物学	3
数学, 数学与计算生物学	3

Chemotaxis Effects on the Vascular Tumor Growth: Phase-field Model and Simulations

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