Mathematical Modeling of the Effect of Angiostatin on the Density of the Circular Tumor-Induced Microvascular Network

Angiogenesis is a connection bridge between the avascular and vascular growth phases of the tumor. The rate of tumor growth increases after angiogenesis. Anti-angiogenesis therapy is an effective method that is used in cancer treatment, especially in combination with other strategies such as chemotherapy and radiotherapy. Mathematical models are used for simulating different processes in cancer-related areas, such as angiogenesis and anti-angiogenesis. In this study, the formation of a capillary network from two parent vessels toward a circular tumor of different sizes is studied by considering the anti-angiogenic effects of angiostatin. The discrete model applied in previous studies of our group is developed in this paper to study the effect of angiostatin on the density of capillaries as a parameter that may represent anti-angiogenesis effectiveness. It is concluded that angiostatin decreases the rate of the spread of the parent vessels' sprouts into the tumor with a small non-dimensional size of 0.1. Moreover, it is shown that anti-angiogenesis normalizes the microenvironment of the tumor. Results show that the microvascular network is pruned by the anti-angiogenic agent, which results in a reduction of the microvascular density in all tumor sizes. Based on the findings of the present study, the reduction of neo-vessel density induced by angiostatin administration decreases with increasing tumor size, which can indicate the dependence of anti-angiogenic treatment performance on tumor size as a factor of tumor progression stage.