Medical Instrumentation School, Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China.
Periodicals Agency, Shanghai University, Shanghai, 200444, China.
PLoS One. 2016 Oct 4;11(10):e0163173. doi: 10.1371/journal.pone.0163173. eCollection 2016.
The processes governing tumor growth and angiogenesis are codependent. To study the relationship between them, we proposed a coupled hybrid continuum-discrete model. In this model, tumor cells, their microenvironment (extracellular matrixes, matrix-degrading enzymes, and tumor angiogenic factors), and their network of blood vessels, described by a series of discrete points, were considered. The results of numerical simulation reveal the process of tumor growth and the change in microenvironment from avascular to vascular stage, indicating that the network of blood vessels develops gradually as the tumor grows. Our findings also reveal that a tumor is divided into three regions: necrotic, semi-necrotic, and well-vascularized. The results agree well with the previous relevant studies and physiological facts, and this model represents a platform for further investigations of tumor therapy.
肿瘤生长和血管生成的过程是相互依存的。为了研究它们之间的关系，我们提出了一个耦合的混合连续-离散模型。在这个模型中，肿瘤细胞、它们的微环境（细胞外基质、基质降解酶和肿瘤血管生成因子）以及它们的血管网络，由一系列离散的点来描述。数值模拟的结果揭示了肿瘤生长和从无血管到血管形成阶段的微环境变化的过程，表明随着肿瘤的生长，血管网络逐渐发展。我们的发现还表明，肿瘤可以分为三个区域：坏死区、半坏死区和血管丰富区。研究结果与以前的相关研究和生理事实相符，该模型为进一步研究肿瘤治疗提供了一个平台。
