Mathematical Analysis of Taxis in Angiogenesis with Application to the Study of Tumor Growth

Levine 9803992 研究人员和他的合作者开发了血管生成模型。 血管生成是响应于外部提供的化学刺激而从预先存在的脉管系统形成毛细血管芽的过程。 在内皮细胞迁移和有丝分裂的驱动下，芽生长并组织成树突状结构。 例如，在胚胎发生、伤口愈合、关节炎发展和实体瘤生长期间已经观察到血管生成。 该过程被认为分三个步骤发生：内皮细胞降解血管膜和间质基质，后者的迁移和增殖，最后是小管形成。 本项目主要研究肿瘤血管生成数学模型的构建和分析。 这些模型是基于强化随机游走结合非标准反应扩散机制的思想，以描述毛细血管芽如何形成以及内皮细胞如何迁移到间质细胞基质中。 特别地，建模包括通过从肿瘤发出的某些肿瘤血管生成因子的化学吸引和通过从内皮细胞分泌纤连蛋白的趋触性。 本研究的基本目标是提出毛细血管芽形成的可验证的假说，并了解吻合和毛细血管分支的机制。 我们的目标是使用模型提出的策略，从而可以阻碍毛细血管芽的生长，从而抑制毛细血管网络的蔓延。 通过阻止毛细血管树突状结构到达肿瘤，肿瘤将缺乏血液供应。 因此，将防止肿瘤细胞转移到身体的其他部位。 几年前，波士顿儿童医院的Judah Folkman博士提出了一个恶性肿瘤生长模型。 众所周知，无血管肿瘤（没有血液供应的肿瘤）只能生长到一定的大小，然后由于氧气不足而开始死亡。 福克曼认为，当它死亡时，它会发出一种化学信号，诱导身体产生第二种化学物质（称为肿瘤血管生成因子，TAF）。 TAF继而通过周围的身体组织扩散到附近的毛细血管，在毛细血管中其在毛细血管壁中产生开口。 排列在所有毛细血管壁上的（内皮）细胞然后能够通过这些开口泄漏，并沿着TAF留下的化学痕迹回到肿瘤，在它们去的时候形成新的毛细血管。 然后，这些次级毛细血管将氧气直接输送到肿瘤，使其能够比无血管状态下更快地生长。 为了抑制肿瘤生长，已经提出可能使用某些抗血管生成因子（抗原）来抑制TAF的作用，从而不仅通过防止这些次级毛细血管的生长来使肿瘤饥饿，而且还防止肿瘤细胞通过循环系统扩散到身体的其他部位。 研究人员和他的合作者的目标是通过开发一个既有描述性又有预测性的数学模型，将福克曼的机制建立在定量的基础上。 也就是说，该模型不仅有助于在基础科学水平上理解Folkman的思想，而且还可以用来建议毛细管生长受阻的策略，从而抑制毛细管网络的扩散。 该模型最终应该建议防止毛细血管到达肿瘤所需的抗原的最佳剂量，从而最大限度地降低肿瘤失去血液供应时患者的风险。 从更积极的方面来看，同样的模型也许也可以用来有效地模拟一种机制，通过这种机制，可以鼓励毛细血管萌芽的生长，例如在胚胎发育或伤口愈合中，通过分离那些鼓励这种生长的因素。

Levine 9803992 The investigator and his collaborators develop models of angiogenesis. Angiogenesis is a process whereby capillary sprouts from a pre-existing vasculature are formed in response to externally supplied chemical stimuli. The sprouts, driven by endothelial cell migration and mitosis, develop and organize themselves into a dendritic structure. Angiogenesis has been observed for example during embryogenesis, wound healing, arthritic development and during the growth of solid tumors. This process is thought to occur in three steps: the degradation of the vascular membrane and interstitial matrix by endothelial cells, the migration and proliferation of the latter, and finally tubulogenesis. This project is specifically directed at constructing and analyzing mathematical models of tumor angiogenesis. These models are based on the idea of reinforced random walks combined with nonstandard reaction-diffusion mechanisms to describe how capillary sprouts are formed and how endothelial cells migrate into the interstitial cellular matrix. In particular, the modeling includes chemo-attraction via certain tumor angiogenesis factors emitted from the tumors and haptotaxis via secretion of fibronectin from the endothelial cells. Fundamental objectives of the study are to suggest testable hypotheses for the capillary sprout formation and to understand the mechanisms for anastomosis and the branching of capillaries. The goal is to use the models to suggest strategies whereby capillary sprout growth can be impeded and consequently inhibit the spread of capillary networks. By preventing the capillary dendritic structure from reaching the tumor, the tumor will be starved of a blood supply. Consequently tumor cells will be prevented from metastasizing to other parts of the body. Several years ago, Dr. Judah Folkman of Children's Hospital, Boston, proposed a model for malignant tumor growth. It is known that an avascular tumor (a tumor without a blood sup ply) can only grow to a certain size before it begins to die because of oxygen insufficiency. Folkman suggested that as it dies, it sends out a chemical signal that induces the body to produce a second chemical (called a tumor angiogenic factor, TAF). TAF, in turn, diffuses through the surrounding body tissue to nearby capillary vessels where it creates openings in the capillary walls. The (endothelial) cells that line all capillary walls are then able to leak through these openings and follow the chemical trail left by the TAF back to the tumor, forming new capillaries as they go. These secondary capillaries then deliver oxygen directly to the tumor, enabling it to grow more rapidly than it could in the avascular state. In order to inhibit the tumor growth, it has been suggested that it might be possible to use certain anti-angiogenic factors (antigens) to inhibit the action of the TAF and thus not only starve the tumor by preventing the growth of these secondary capillaries but also prevent the spread of tumor cells to other parts of the body through the circulatory system. The investigator and his collaborators aim to put Folkman's mechanism on a quantitative footing by developing a mathematical model that is both descriptive and predictive. That is, the model will not only aid in the understanding of Folkman's ideas at a fundamental scientific level but can also be used to suggest strategies whereby capillary growth can be impeded and consequently inhibit the spread of capillary networks. The model should ultimately suggest optimal dosages of antigens needed to prevent capillaries from reaching the tumor, thus minimizing risk to the patient as the tumor is deprived of a blood supply. On a more positive note, the same models could perhaps also be used to effectively model a mechanism by which capillary sprout growth can be encouraged, such as in embryo development or wound healing, by isolating those factors that encourage such growth.