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 exter- nal 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.
Yan CaiKalkabay GulnarHongyi ZhangJinfeng CaoShixiong XuQuan Long
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.
A multi-scale continuous-discrete model based on the effects of the p27 gene control is built to simulate the avascular tumor growth. At the tissue level, the continuous Eulerian model is adopted to determine the distribution of the concentration of oxygen, the extracellular matrix （ECM）, and the matrix-degradative enzyme （MDE）. At the cellular level, the discrete Lagrangien model is adopted to determine the movement, the proliferation, and the death of single tumor cells （TCs）. At the genetic level, whether a cell is committed to mitosis is determined by solving a set of equations modeling the effects of the p27 gene control. The avascular morphological evolution of the solid tumor growth is simulated, including the radius the oxygen distribution over time, and the expression. of the solid tumor, the number of the TCs, inhibiting effect＇ of the up-regulating p27 gene
Yu ZHOUJia-wan CHENXiao-ning DAIYan CAIWei YAOShi-xiong XUQuan LONG
