Numerical simulation of inhibitory effects of endostatin on tumor angiogenesis

The inhibitory effects of anti-angiogenic drug Endostatinon tumor angiogenesis are simulated by adopting 2D and 3D discretemathematical models, which are used to describe the formation of capillarynetworks inside and outside the tumor. In the discrete mathematical models,five factors were mainly taken into account the influence of the migrationof endothelial cells: (i) proliferation and (ii) random motility of theendothelial cells; (iii) chemotaxis in response to tumor angiogenic factor(TAF) released by the tumor; (iv) haptotaxis in response to fibronectingradients in the extracellular matrix, especially the inhibitory action ofanti-angiogenic drug Endostatin, and (v) inhibitory effects of Endostatin.Meanwhile, spatiotemporal evolution of 2D and 3D tumor microvascularnetworks is performed. The simulation results indicate that anti-angiogenicdrug Endostatin obviously has the inhibitory effects on the rate of bloodvessels growth, the bifurcation amount and the development of themicrovascular network inside and outside the tumor. Furthermore, themicrovascular networks generated by the present mathematical models haverelatively realistic structure and morphology inside and outside the tumor.These results may provide beneficial information for anti-angiogenesistreatment of tumor and further clinical research.