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

莱文，9803992，这位研究员和他的合作者开发了血管生成的模型。血管生成是指对外界提供的化学刺激作出反应，从已有的血管系统中形成毛细血管萌芽的过程。在内皮细胞迁移和有丝分裂的驱动下，萌芽发育并组织成树枝状结构。血管生成在胚胎发生、伤口愈合、关节炎发育和实体瘤生长等过程中被观察到。这一过程被认为包括三个步骤：血管内皮细胞降解血管膜和间质基质，后者迁移和增殖，最终形成小管。本项目专门针对构建和分析肿瘤血管生成的数学模型。这些模型基于强化随机行走的思想，结合非标准的反应扩散机制来描述毛细血管芽是如何形成的，以及内皮细胞如何迁移到间质细胞基质中。具体地说，该模型包括通过从肿瘤释放的某些肿瘤血管生成因子来进行化学吸引，以及通过从内皮细胞分泌纤维连接蛋白来实现趋化性。这项研究的基本目标是为毛细血管芽的形成提出可检验的假说，并了解毛细血管吻合和分支的机制。目标是使用这些模型来建议可以阻止毛细血管萌芽生长的策略，从而抑制毛细血管网络的扩散。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，肿瘤细胞将被阻止转移到身体的其他部位。几年前，波士顿儿童医院的朱达·福克曼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，然后才会因为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)。转而，Taf通过周围的身体组织扩散到附近的毛细血管，在那里它在毛细血管壁上形成开口。然后，排列在所有毛细血管壁上的(内皮)细胞能够通过这些开口泄漏，并跟随TAF留下的化学痕迹回到肿瘤部位，在它们前进的过程中形成新的毛细血管。然后，这些次级毛细血管直接向肿瘤输送氧气，使其比无血管状态下生长得更快。为了抑制肿瘤的生长，有人建议使用某些抗血管生成因子(抗原)来抑制TAF的作用，从而不仅通过阻止这些次级毛细血管的生长来饥饿肿瘤，而且还可以防止肿瘤细胞通过循环系统扩散到身体的其他部位。这位研究人员和他的合作者的目标是通过开发一个既具有描述性又具有预测性的数学模型，将福克曼的机制建立在量化的基础上。也就是说，该模型不仅有助于在基础科学水平上理解福克曼的思想，而且还可以用来提出阻止毛细血管生长从而抑制毛细血管网络扩散的策略。该模型最终应该建议最佳的抗原剂量，以防止毛细血管到达肿瘤，从而将患者面临的风险降至最低，因为肿瘤失去了血液供应。从更积极的方面来看，同样的模型也可能被用来有效地模拟一种机制，通过分离那些促进毛细血管萌芽生长的因素，可以鼓励这种生长，例如在胚胎发育或伤口愈合过程中。

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.