To investigate tumor-induced angiogenesis under the influence of the mechanical environments inside and outside the tumor, mathematical model of tumor angiogenesis was developed. In the model, extra-cellular matrix (ECM) was treated as a thin plane. The displacement of ECM is obtained from the force balance equation consisted of the ECs traction, the ECM visco-elastic forces and the external forces. Simulation results show that a layered capillary network is obtained with a well vascularized region at the periphery of the tumor. The present model can be used as a valid theoretical method in the basic researches in tumorinduced angiogenesis.

To investigate the influence of anti-angiogenesis drug Endostatin on solid tumor angiogenesis, a mathematical model of tumor angiogenesis was developed with combined influences of local extra-cellular matrix mechanical environment, and the inhibiting effects of Angiostatin and Endostatin. Simulation results show that Angiostatin and Endostatin can effectively inhibit the process of tumor angiogenesis, and decrease the number of blood vessels in the tumor. The present model could be used as a valid theoretical method in the investigation of anti-angiogenic therapy of tumors.