Blood perfusion and interstitial fluid transport in metastatic tumor microcirculation based on microvasculature response to angiostatin's inhibitory effect are investigated.Microvascular network model contains inhibitory effect of angiostatin,chemotaxis response of tumor angiogenic factors and random motility of endothelial cells.Blood flow,interstitial fluid transport and transvascular flow are described by extended Poiseuille's,Darcy's and Starling's law,respectively.It shows that angiostatin can decrease branching,anastomosis and proliferation of capillary sprouts and inhibit growth of a capillary network in metastatic tumor;Angiostatin can improve capacity of blood perfusion and material exchange within metastatic tumor microenvironment;Furthermore,angiostatin can increase convective flow out of vasculature and result in reduced difficulty of drug delivery and penetration within a metastatic tumor,which agree with experimental observed facts.It may provide theoretical references and foundation understandings for further clinical anti-angiogenic cancer therapy.

We present 2D and 3D discrete mathematical models for migratory response of endothelial cells inside and outside a metastasic tumor based on a physiological fact that some primary tumor can inhibit metastasic tumor growth quickly. In models we consider inhibitory effects of angiostatin excreted by primary tumor, chemotactic effects of TAF due to metastasic tumor and random movement of endothelial cells and simulate spatiotemporal evolution of microvascular network inside and outside the metastasic tumor. It shows that the angiostatin excreted by primary tumor has obviously inhibitory effects on vascular growth rates, bifurcation amount and development of microvascular network inside and outside the metastasic tumor. Inhibitory effects of angiostatin decrease revascularization of a metastasic tumor and suppress growth of the metastasic tumor in tumor therapy. It provides theoretical references for experimental research on clinical anti-angiogenesis.

Supersonic inviscid flows in missile propulsive jet are simulated numerically with discontinuous finite element method based on twodimensional conservation laws, which is developed to solve axlsymmetric Euler equations. Computational results show good agreement with experimental data. The method shows higher resolution at discontinuous points compared with TVD schemes. It exhibits high capability in capturing shocks without numerical oscillation and artificial viscosity near discontinuous points.