Ambrosi D, Gamba A, Serini G
Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy.
Bull Math Biol. 2004 Nov;66(6):1851-73. doi: 10.1016/j.bulm.2004.04.004.
In vertebrates, supply of oxygen and nutrients to tissues is carried out by the blood vascular system through capillary networks. Capillary patterns are closely mimicked by endothelial cells cultured on Matrigel, a preparation of basement membrane proteins. On the Matrigel surface, single randomly dispersed endothelial cells self-organize into vascular networks. The network is characterized by a typical length scale, which is independent of the initial mean density of deposed cells n over a wide range of values of n. We give here a detailed description of a mathematical model of the process which is able to reproduce several qualitative and quantitative features of in vitro vascularization experiments. Cell matter is basically modelled as an elastic fluid subjected to a specific force field depending on the concentration of a chemoattractant factor. Starting from sparse initial data, mimicking the initial conditions realized in laboratory experiments, numerical solutions reproduce characteristic network structures, similar to observed ones, whose average size is theoretically related to the finite range of chemoattractant diffusion. A possible area of application of the model is the design of properly vascularized artificial tissues.
在脊椎动物中，血液血管系统通过毛细血管网络为组织提供氧气和营养物质。在基质胶（一种基底膜蛋白制剂）上培养的内皮细胞能紧密模拟毛细血管模式。在基质胶表面，单个随机分散的内皮细胞会自我组织形成血管网络。该网络具有一个典型的长度尺度，在很宽的细胞沉积初始平均密度(n)值范围内，它与(n)无关。在此，我们详细描述了一个该过程的数学模型，它能够重现体外血管生成实验的几个定性和定量特征。细胞物质基本上被建模为一种弹性流体，受到一个取决于趋化因子浓度的特定力场作用。从稀疏的初始数据出发，模拟实验室实验中实现的初始条件，数值解能重现与观察到的相似的特征网络结构，其平均大小在理论上与趋化因子扩散的有限范围相关。该模型的一个可能应用领域是设计具有适当血管化的人工组织。
