This paper proposes a more realistic mathematical simulation method to investigate the dynamic process of tumour angio-genesis by fully coupling the vessel growth,tumour growth and associated blood perfusion.The tumour growth and angiogenesis are coupled by the chemical microenvironment and the cell-matrix interaction.The haemodynamic calculation is carried out on the new vasculature,and an estimation of vessel collapse is made according to the wall shear stress criterion.The results are consistent with physiological observations,and further confirm the application of the coupled model feedback mechanism.The model is available to examine the interactions between angiogenesis and tumour growth,to study the change in the dynamic process of chemical environment and the vessel remodeling.
Y.Cai,1,2 S.X.Xu,1,a) J.Wu,3 and Q.Long 2,b) 1) Department of Mechanics and Engineering Science,Fudan University,Shanghai 200433,China 2) Brunel Institute for Bioengineering,School of Engineering and Design,Brunel University,Uxbridge,Middlesex,UK 3) School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiaotong University,Shanghai 200240,China
A hybrid discrete-continuum model of tumor growth in the avascular phase considering capillary points is established. The influence of the position of capillary points on tumor growth is also studied by simulation. The results of the dynamic tumor growth and the distribution of oxygen, matrix-degrading enzymes, and extracellular matrixconcentration in the microenvironment with respect to time are shown by graphs. The relationships between diferent oxygenated environments and the numbers of surviving, dead, proliferative, and quiescent tumor cells are also investigated.
The effects of anti-angiogenesis treatment by angiostatin and endostatin on normalization of tumor microvasculature and microenvironment are investigated,based on mathematical modeling and numerical simulation of tumor anti-angiogenesis and tumor haemodynamics.The results show that after anti-angiogenesis treatment:(i) the proliferation,growth,and branching of neo-vessels are effectively inhibited,and the extent of vascularization in tumors is accordingly reduced.(ii) the overall blood perfusion inside of tumor is declined,the plateau of tumor interstitial fluid pressure(IFP) is relieved,the interstitial fluid oozing out from the tumor periphery into the surrounding normal tissue is reduced,the reduction of overall extravasation across vasculature to tumor interstium is much less than the decreased overall blood perfusion,due to the decline of IFP,the intravasations is remarkablely effected by the change,in some cases there are no intravasation flow appear.
To investigate the inhibiting effects of the anti-angiogenic factor andostatin and the anti-angiogenic drug endostatin on tumour angiogenesis and tumour cells, a coupled mathematical model of tumor angiogenesis with tumour growth and blood perfusion is developed. Simulation results show that angiostatin and endostatin can improve the abnormal microenvironment inside the tumour tissue by effectively inhibiting the process of tumor angiogenesis and decreasing tumour cells. The present model can be used as a valid theoretical method in the investigation of the tumour anti-angiogenic therapy.
