抗血管生成治疗肿瘤的数值模拟
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摘要
肿瘤是严重威胁人类健康与生命的一类疾病。肿瘤治疗仍是医药学界面临的一大难题，探索和研究新的策略、方法、途径对解决这一难题至关重要。抗血管生成作为肿瘤治疗的新视野，已迅速发展为重要的抗癌策略，并成为肿瘤治疗领域的研究热点。抗血管生成治疗以血管内皮细胞为靶点，通过对抗肿瘤血管生成，切断肿瘤血液和营养供应，从而遏制肿瘤生长和转移。其方法主要包括抑制或中和血管生成因子、调节或改变肿瘤微循环和应用血管生成抑制剂攻击肿瘤血管内皮细胞等。本论文针对抗血管生成治疗肿瘤的特点和途径，数值模拟肿瘤血管生成、肿瘤微循环血液动力学以及抗血管生成因子和药物对肿瘤血管生成过程中选择性的抑制作用，为抗血管生成治疗肿瘤的临床研究提供相应的理论参考和信息依据。
本文主要研究工作
肿瘤血管生成的研究
对肿瘤血管生成模型，从计算方法、影响条件和生理因素等不同角度进行改进，并且建立宏观尺度上肿瘤动态生长与微观尺度上血管生成耦合的模型，生成肿瘤内外微血管网。
(1)建立肿瘤血管生成的二维九点差分格式数学模型。本模型的特点是，将现有文献报道的内皮细胞沿五个方向直线运动扩展为沿九个方向运动；耦合了内皮细胞在肿瘤内外不同力学环境影响下的随机、趋化和趋触性运动；数值生成肿瘤内外异构的血管网和肿瘤内部的分层网络结构。
(2)在模型(1)的基础上，建立肿瘤血管可以沿任意方向生长的模型，模拟微血管系统的生成过程，并且与血管沿直角方向生长和模型(1)的生长进行对比。
(3)考虑宏观尺度上肿瘤自身向外浸润式生长的动态变化对微观尺度上肿瘤微血管生成过程产生的影响，建立耦合的“肿瘤组织生长动力学—血管生成”二维离散数学模型，模拟血管生成过程。
(4)将力学环境影响下的二维离散数学模型扩展到三维，生成肿瘤内外异构的微血管网。
血液动力学的研究
(1)采用图像处理方法重新构建微血管网，探索研究各向异性间质水力传导性对肿瘤微循环内血液动力学的影响。
(2)采用数值生成的二维肿瘤内外微血管网，将宿主血管和微血管网内的流动相结合，建立肿瘤“微血管网—微血管网跨壁交换—间质流动”耦合模型，分析宿主血管入口雷诺数、微血管壁渗透性以及间质水力传导性等动力学因素对肿瘤微循环内流体流动的影响，获得与生理现象相符的结果。
(3)采用九点差分格式数值生成的肿瘤内外微血管网，扩展耦合的“微血管网—微血管网跨壁交换—间质流动”模型，考虑间质流动阻力和跨壁流动阻力的影响，模拟微血管网和组织间质空间内流体流动。
抗血管生成因子和药物对肿瘤血管生成影响的研究
建立抗血管生成因子和药物与促血管生成因子(TAFs)共同作用下内皮细胞运动的二维、三维离散数学模型，研究抗血管生成因子Angiostatin和药物Endostatin对肿瘤内外血管生成的影响。
(1)针对某些原发性肿瘤能抑制远处转移性肿瘤和继发性肿瘤的快速生长，建立抗血管生成因子Angiostatin与TAFs共同作用下内皮细胞迁移的二维、三维离散数学模型，模拟肿瘤内外血管生成。给出一种可能的解释：某些转移性肿瘤快速生长的抑制依赖于转移细胞局部的抑制因子和生长因子的水平。
(2)建立抗血管生成药物Endostatin对肿瘤血管生成抑制效应的二维、三维离散数学模型，耦合内皮细胞的扩散、趋化和趋触性运动，特别是内皮细胞自身的增殖，模拟Endostatin作用下肿瘤内外微血管网的生长过程。
(3)耦合抗血管生成因子Angiostatin和药物Endostatin对内皮细胞运动的抑制效应、细胞的增殖、凋亡和TAFs诱导下内皮细胞的随机、趋化和趋触性运动，建立二维模型生成肿瘤内外微血管网。比较全面的分析和研究了肿瘤血管生成不同时期和抑制因子间不同耦合情况下Angiostatin和Endostatin对血管生成的综合抑制效应。
本文工作在相应的研究领域中有以下几方面的新进展
(1)首次实现了以Chaplain为首的欧洲科学家们提出的肿瘤血管生成沿任意方向生长的思想，并且把采用Euler-Lagrange观点描述血管生成的数学模型与肿瘤组织生长动力学模型耦合，数值生成了肿瘤内外微血管网。
(2)根据现有的国际文献报道，迄今为止，基于数值生成的血管网研究肿瘤微循环时，均考虑血管网内的流动，未涉及间质流动及跨壁交换。本文建立了“微血管网—跨微血管壁交换—间质流动”模型，分析了肿瘤微血管网、跨血管壁及间质内的耦合流动。
(3)抗血管生成抑制剂Angiostatin和Endostatin对肿瘤血管生成影响的数值模拟已有研究，但利用血管形态学直接给出其抑制效果，目前尚未见报道。本文第一次基于数值生成的微血管网，利用血管形态学数值分析研究了Angiostatin和Endostatin对肿瘤血管生成的抑制影响。
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 works
Tumor angiogenesis study
The 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 angiogenesis
By 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.
本文主要研究工作
肿瘤血管生成的研究
对肿瘤血管生成模型，从计算方法、影响条件和生理因素等不同角度进行改进，并且建立宏观尺度上肿瘤动态生长与微观尺度上血管生成耦合的模型，生成肿瘤内外微血管网。
(1)建立肿瘤血管生成的二维九点差分格式数学模型。本模型的特点是，将现有文献报道的内皮细胞沿五个方向直线运动扩展为沿九个方向运动；耦合了内皮细胞在肿瘤内外不同力学环境影响下的随机、趋化和趋触性运动；数值生成肿瘤内外异构的血管网和肿瘤内部的分层网络结构。
(2)在模型(1)的基础上，建立肿瘤血管可以沿任意方向生长的模型，模拟微血管系统的生成过程，并且与血管沿直角方向生长和模型(1)的生长进行对比。
(3)考虑宏观尺度上肿瘤自身向外浸润式生长的动态变化对微观尺度上肿瘤微血管生成过程产生的影响，建立耦合的“肿瘤组织生长动力学—血管生成”二维离散数学模型，模拟血管生成过程。
(4)将力学环境影响下的二维离散数学模型扩展到三维，生成肿瘤内外异构的微血管网。
血液动力学的研究
(1)采用图像处理方法重新构建微血管网，探索研究各向异性间质水力传导性对肿瘤微循环内血液动力学的影响。
(2)采用数值生成的二维肿瘤内外微血管网，将宿主血管和微血管网内的流动相结合，建立肿瘤“微血管网—微血管网跨壁交换—间质流动”耦合模型，分析宿主血管入口雷诺数、微血管壁渗透性以及间质水力传导性等动力学因素对肿瘤微循环内流体流动的影响，获得与生理现象相符的结果。
(3)采用九点差分格式数值生成的肿瘤内外微血管网，扩展耦合的“微血管网—微血管网跨壁交换—间质流动”模型，考虑间质流动阻力和跨壁流动阻力的影响，模拟微血管网和组织间质空间内流体流动。
抗血管生成因子和药物对肿瘤血管生成影响的研究
建立抗血管生成因子和药物与促血管生成因子(TAFs)共同作用下内皮细胞运动的二维、三维离散数学模型，研究抗血管生成因子Angiostatin和药物Endostatin对肿瘤内外血管生成的影响。
(1)针对某些原发性肿瘤能抑制远处转移性肿瘤和继发性肿瘤的快速生长，建立抗血管生成因子Angiostatin与TAFs共同作用下内皮细胞迁移的二维、三维离散数学模型，模拟肿瘤内外血管生成。给出一种可能的解释：某些转移性肿瘤快速生长的抑制依赖于转移细胞局部的抑制因子和生长因子的水平。
(2)建立抗血管生成药物Endostatin对肿瘤血管生成抑制效应的二维、三维离散数学模型，耦合内皮细胞的扩散、趋化和趋触性运动，特别是内皮细胞自身的增殖，模拟Endostatin作用下肿瘤内外微血管网的生长过程。
(3)耦合抗血管生成因子Angiostatin和药物Endostatin对内皮细胞运动的抑制效应、细胞的增殖、凋亡和TAFs诱导下内皮细胞的随机、趋化和趋触性运动，建立二维模型生成肿瘤内外微血管网。比较全面的分析和研究了肿瘤血管生成不同时期和抑制因子间不同耦合情况下Angiostatin和Endostatin对血管生成的综合抑制效应。
本文工作在相应的研究领域中有以下几方面的新进展
(1)首次实现了以Chaplain为首的欧洲科学家们提出的肿瘤血管生成沿任意方向生长的思想，并且把采用Euler-Lagrange观点描述血管生成的数学模型与肿瘤组织生长动力学模型耦合，数值生成了肿瘤内外微血管网。
(2)根据现有的国际文献报道，迄今为止，基于数值生成的血管网研究肿瘤微循环时，均考虑血管网内的流动，未涉及间质流动及跨壁交换。本文建立了“微血管网—跨微血管壁交换—间质流动”模型，分析了肿瘤微血管网、跨血管壁及间质内的耦合流动。
(3)抗血管生成抑制剂Angiostatin和Endostatin对肿瘤血管生成影响的数值模拟已有研究，但利用血管形态学直接给出其抑制效果，目前尚未见报道。本文第一次基于数值生成的微血管网，利用血管形态学数值分析研究了Angiostatin和Endostatin对肿瘤血管生成的抑制影响。
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 works
Tumor angiogenesis study
The 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 angiogenesis
By 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.
引文
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