Numerical Simulation Of The Tumor Anti-angiogenic Therapy

Tumor poses a great threat to human health and life. The novel therapeutic strategy, method and approache play a crucial role in the therapy of tumor because cancer therapy is still a big challenge in medical and pharmacal field. However, as a promising new field of tumor treatment, anti-angiogenic therapy has been developed quickly as a powerful anti-cancer strategy and become a focus research to cancel therapy in the world. Therapeutic targeting of anti-angiogenesis is the endothelial cell. The rationale of developing anti-angiogenic therapy is that blocking the tumors' blood and the nutrition supply could starve tumors thus inhibiting tumor growth and transfer. According to tumor anti-angiogenesis, the approaches mainly include the inhibition or neutralization of angiogenesis factors, the adjustment and change of tumor microcirculation, and the application of angiogenesis inhibitors for attacking the endothelial cell. Based on the characteristics and approaches of tumor anti-angiogenic therapy, we studied the tumor angiogenesis, the hemodynamics in the microcirculation and simulated numerically the selective inhibition as a function of the anti-angiogenesis factor and drug during the tumor angiogenesis. These researches may provide some theoretical references and foundational understandings for further clinical experimental research.The main worksTumor angiogenesis studyThe mathematical models of tumor angiogenesis are extended from the computing method, the influence condition and the physiological factor to generate tumor vascular network. Furthermore, a coupled "macroscopical tumor growth—microscopic vessel formation" model is developed to describe tumor vessel growth.(1) A 2D discrete mathematical model of nine-point finite difference scheme is built to simulate tumor angiogenesis. The model includes random motility, chemotaxis and haptotaxis of endothelial cell under different mechanical environments and extends an individual endothelial cell moving along nine directions. The results show the heterogeneous distribution and the different architecture of tumor vascular network.(2) The process of angiogenesis moving along random direction is simulated and the results are compared with vascular network generated from the models with five and nine growth directions.(3) A coupled "macroscopical tumor growth—microscopic vessel formation" mathematical model is built to simulate physiological process of tumor angiogenesis.(4) A 3D discrete mathematical model of tumor angiogenesis under different mechanical environments is developed and relatively realistic tumor microvascular network is generated.Hemodynamics study(1) The effect of the anisotropic interstitial hydraulic conductivity on the hemodynamics in tumor microcirculation is studied based on the microvascular network which is generated from image manipulation.(2) Simulation of hemodynamics under the combined effects of both the host blood vessel and the microvascular network, which is generated from a discrete model of tumor angiogenesis, is performed systemically. A "microvascular network—transport across microvascular wall—flow in interstitium" model is developed to analyze the effects of the variations of the inlet Reynolds number in the host blood vessel, the hydraulic conductivity of the microvascular wall, and the interstitial hydraulic conductivity on the fluid flow in tumor microcirculation. The results are in agreement with physiological observed facts.(3) A coupled intravascular—transvascular—interstitial fluid flow model is developed to study the influences of interstitial and transvascular flow resistances on the blood flow and interstitial fluid flow in tumor microcirculation based on a microvascular network, which is generated from a 2D nine-point discrete mathematical model of tumor-induced angiogenesis.Inhibition of anti-angiogenic factor and drug to tumor angiogenesisBy coupling the angiogenic inhibitor and the angiogenic factor, the 2D and 3D discrete mathematical models of endothelial cell motion are developed to investigate the influence of the anti-angiogenic factor angiostatin and the drug endostatin on vascular formation inside and outside tumor.(1) Some primary tumor can inhibit the quick growth of secondary or metastatic tumor, thus 2D and 3D discrete mathematical models of coupling anti-angiogenic factor angiostatin and TAFs are presented to describe the tumor angiogenesis. A possible explanation for this suppression of secondary or metastatic tumor by the primary tumor is given in terms of the migratory response of endothelial cells to anti-angiogenic inhibitor and angiogenesis factor. (2) The 2D and 3D discrete models of coupling endostatin suppression, endothelial cell random, chemotactic and haptotatic movement, especially the proliferation of endothelial cell, are developed to simulate the spatiotemporal evolution of microvascular network inside and outside tumor.(3) To investigate the synthetic effect of angiogenic inhibitors angiostatin and endostatin on tumor induced angiogenesis. A 2D mathematical model of coupling proliferation, degradation, random motility, chemtaxis, haptotaxis of endothelial cell and inhibitions of angiostatin and endostatin, is developed to describe microvascular network structure at different stage of tumor vessel growth.In this paper,(1) We firstly realize the idea of tumor vessel moving along random direction with the numerical method, which is proposed by Prof Chaplain et al in European. Furthermore, the model of vascular growth, which is described by using Euler-Lagrange viewpoint, and the model of tumor growth are combined to generate tumor microvascular network.(2) The current investigations for tumor microcirculation based on vascular network generated from numerical simulation include the description of the blood flow through the capillary network, but transvascular fluid exchange and interstitial fluid flow in tumor are not calculated according to the reports in the present international documents and literatures. In this paper, we have developed a "blood flow through the microvascular network—transport across microvascular wall—interstitial fluid flow" model for analyzing the coupled flow problem about capillary network, transvascular wall and interstitial fluid flow.(3) Numerical simulation about the influence of angiogenic inhibitors angiostatin and endostatin on tumor vascular growth has been carried out. However, at present, there are no any published reports on analyzing the inhibition effects to the vessel growth by using vessel morphological character. The present paper firstly studied inhibition effects of angiostatin and endostatin to tumor angiogenesis based on microvascular network which is generated from discrete mathematical model by using morphological structure.