抗血管生成药物Endostantin作用下实体肿瘤血管生成的数值模拟:考虑基质力学环境及血管生成抑素的影响

为研究抗血管生成药物Endostatin作用下,肿瘤血管生成过程中基质力学环境及血管生成抑素的影响,考虑内皮细胞(EC)和细胞外基质(ECM)两相,耦合抗血管生成药物Endostatin和血管生成抑素Angiostatin的抑制效应,建立肿瘤内外血管生成的二维数值模型.抗血管生成因子Angiostatin和药物Endostatin耦合作用时,可明显降低肿瘤组织内的微血管密度,对肿瘤快速生长起到一定的抑制作用.所给出的模型,可以较好模拟基质力学环境影响下,肿瘤抗血管生成因子对内皮细胞迁移和增殖的抑制作用.     

血管抑素与内皮抑素作用下抗血管生成治疗对肿瘤微血管网与微环境影响的模拟研究

基于对血管抑素和内皮抑素作用下肿瘤抗血管生成及血液动力学的数学建模与数值模拟,研究抗血管生成治疗对肿瘤微血管网的影响及对微环境流动的改善作用．研究表明,抗血管生成治疗后:1） 新生血管的生长与分叉受到抑制,血管化程度降低;2） 血液灌注量减少,间质高压得到缓解,渗入宿主组织的间质液减少,负向跨壁流量大幅下降．     

二维离散数学模型模拟肿瘤内外血管生成

建立九点差分格式的二维离散数学模型,模拟肿瘤内外的血管生成,模型扩展了内皮细胞沿9个方向运动,考虑存在两根母血管的情况下,耦合内皮细胞在肿瘤内外不同力学环境下的随机、趋化和趋触性运动,数值生成了肿瘤内外异构的血管网.结果表明,该模型可以产生相对真实的具有接近肿瘤病理生理特性的血管网,可为临床研究提供有益的信息.     

Neuropilin-1与胃癌发生、发展及血管生成的关系

目的探讨胃癌组织中Neuropilin-1、VEGF的表达与胃癌生物学行为及血管生成的关系和意义.方法应用免疫组化ElivisionTM法检测正常胃黏膜、上皮内瘤变、胃癌组织中Neuropilin-1、VEGF、CD34的表达并测定MVD,回顾分析胃癌患者的临床病理资料.结果胃癌组织中Neuropilin-1、VEGF的表达及MVD高于正常胃黏膜和上皮内瘤变组织,且与胃癌淋巴结转移、浸润程度密切相关.Neuropilin-1、VEGF表达阳性组的MVD高于各自阴性组.两者表达呈正相关关系,联合表达时MVD增高.结论 Neuropilin-1、VEGF、血管生成参与了胃癌发生、浸润与转移;Neuropilin-1、VEGF参与了胃癌的血管生成;表达存在协同作用;联合表达时血管生成的效应增强.Neuropilin-1作为肿瘤抗血管治疗的靶点具有一定的价值.     

一种未血管化肿瘤生长模型整体解的证明

研究了一种未血管化肿瘤生长模型的自由边界问题,模型与此类其它模型有着明显的不同,它引入新的运动项来描述肿瘤内细胞的运动,反映了肿瘤内细胞运动的"接触抑制"性质.运用Banach不动点理论和抛物型方程的L~P理论,证明了模型存在唯一整体解.     

一个时滞肿瘤生长的自由边界问题

研究了一个时滞肿瘤生长自由边界问题,它来源于描述考虑了由于肿瘤细胞分裂速率变化引起肿瘤细胞生长环境的变化而引起的肿瘤细胞凋亡的肿瘤生长模型.在这个问题中考虑两种因素引起肿瘤细胞消亡:一种是肿瘤细胞度过固有的生命周期后自身的凋亡,另一种是肿瘤细胞的分裂速率变化引起生长环境的变化而引起的肿瘤细胞的凋亡,第二种消亡具有时滞.研究了该问题解的非负性,稳态解的存在唯一性和渐近性以及周期解的存在性.     

一个肿瘤生长自由边界问题的研究

本文研究一个描述肿瘤生长的自由边界问题.这个自由边界问题是对Byrne和Chaplain相应肿瘤生长模型的一个改进,研究了该问题解当t→∞时的渐近状况,证明了未血管化的肿瘤体积不会无限制地增大,它或者趋于消失,或者趋于一个休眠态,依营养物浓度的大小和抑制物浓度的大小而定.     

一个肿瘤生长自由边界问题的研究

本文研究一个描述肿瘤生长的自由边界问题.这个自由边界问题是对Byrne和Chaplain相应肿瘤生长模型的一个改进,研究了该问题解当t→∞时的渐近状况,证明了未血管化的肿瘤体积不会无限制地增大,它或者趋于消失,或者趋于一个休眠态,依营养物浓度的大小和抑制物浓度的大小而定.     

一个肿瘤生长自由边界问题解的渐近性态

该文研究根据Byrne和Chaplain的思想建立的一个描述抑制物作用下无坏死核肿瘤生长的数学模型, 这个模型是一个非线性反应扩散方程组的自由边界问题. 作者运用反应扩散方程理论中的上下解方法结合自由边界问题的迭代技巧, 研究了解的渐近性态, 在营养物消耗函数f、抑制物消耗函数g和肿瘤细胞繁衍函数S的一些一般条件下,证明当常数c₁,c₂(肿瘤细胞分裂速率和营养物、抑制物扩散速率的比值)都非常小时,在一定的初边值条件下肿瘤趋于消失,在另外一些初边值条件下肿瘤半径趋于一个常数,进而时变解将趋于一个稳态解.     

一种肿瘤生长自由边界问题整体解的存在唯一性

研究了一种肿瘤生长模型中自由边界问题，该肿瘤生长模型异于其它此类模型之处就在于采用了新的方式来描述繁衍细胞和休眠细胞的运动．运用抛物型方程的Lp理论和不动点原理，证明了该模型存在唯一的整体解．     

A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy

A model consisting of a system of five ordinary differential equations to simulate the interactions between normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent in tumour growth is developed. By a partial analysis of the cancer-free subspace, it is shown how the anti-angiogenic agent may help the chemotherapy agent in controlling the cancer. This is illustrated by numerical examples and bifurcation diagrams.     

Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments

A cell-population-based model for tumor growth under anti-angiogenic treatment, with the tumor volume and its variable carrying capacity as variables, is combined with the linear-quadratic model for damage done by radiation ionization. The resulting multi-input system is analyzed as an optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric constraints that limit the overall amounts of anti-angiogenic agents, respectively, the damage done to healthy tissue by radiotherapy. For various model formulations, explicit expressions for singular controls are derived for both the dosage of the anti-angiogenic therapeutic agent and the radiation dose schedule. Their role in the structure of optimal protocols is discussed.     

An analysis of a mathematical model describing acid‐mediated tumor invasion

We present a mathematical analysis of a reaction‐diffusion model describing acid‐mediated tumor invasion. The model describes the spatial distribution and temporal evolution of tumor cells, normal cells, and excess lactic acid concentration. The model assumes that tumor‐induced alteration of microenvironmental pH provides a simple but complete mechanism for cancer invasion. We provide results on the existence and uniqueness of a solution considering Neumann boundary condition and comments about the same results with Dirichlet boundary conditions. We also provide numerical simulations to the solutions considering both boundary conditions.     

A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation

An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.     

Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behavior of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.     

肿瘤免疫无标度网络模型平衡点存在性及应用

应用无标度网络,建立肿瘤-免疫网络模型,来刻画免疫效应细胞、肿瘤细胞与细胞因子相互作用的机理。研究了网络模型的肿瘤平衡点在免疫效应细胞与细胞因子度关联与度非关联两种情况下的存在条件.得到了根据所得到的肿瘤平衡点存在的临界值,根据临界值提出免疫途径与方法,为抑制或预测肿瘤生长提供的理论参考.     

Analysis of the Hopf bifurcation for the family of angiogenesis models

In this paper we study a family of models with delays describing the process of angiogenesis, that is a physiological process involving the growth of new blood vessels from pre-existing ones. This family includes the well-known models of tumour angiogenesis proposed by Hahnfeldt et al. and d?Onofrio-Gandolfi and is based on the Gompertz type of the tumour growth. As a consequence we start our analysis from the influence of delay onto the Gompertz model dynamics. The family of models considered in this paper depends on two time delays and a parameter α∈[0,1] which reflects how strongly the vessels dynamics depends on the ratio between tumour and vessels volume. We focus on the analysis of the model in three cases: one of the delays is equal to 0 or both delays are equal, depending on the parameter α. We study the stability switches, the Hopf bifurcation and the stability of arising periodic orbits for different α∈[0,1], especially for α=1 and α=0 which reflects the Hahnfeldt et al. and the d?Onofrio-Gandolfi models. For comparison we use also the value α=1/2.     

Optimal control synthesis in therapy of solid tumor growth

A mathematical model of tumor growth therapy is considered. The total amount of a drug is bounded and fixed. The problem is to choose an optimal therapeutic strategy, i.e., to choose an amount of the drug permanently affecting the tumor that minimizes the number of tumor cells by a given time. The problem is solved by the dynamic programming method. Exact and approximate solutions to the corresponding Hamilton-Jacobi-Bellman equation are found. An error estimate is proved. Numerical results are presented.