论文标题
综合差异主方程描述了血管生成中积极生长的血管
Integrodifference master equation describing actively growing blood vessels in angiogenesis
论文作者
论文摘要
我们研究了二维几何形状中的颗粒系统，该系统根据加强的随机行走移动，其过渡概率取决于基础磁场的反应扩散方程溶液。还考虑了出生过程和依赖历史的杀戮过程。该系统模拟了肿瘤诱导的血管生成，这是由肿瘤释放的生长因子诱导的血管形成过程。颗粒代表血管尖端细胞，其轨迹构成了增长的血管网络。新船在进化过程中可能与现有的船只融合。因此，通过跟踪活动尖端的密度来描述系统，该密度在随机过程的许多实现中计算为集成平均值。这样的密度满足了带有源和下沉项的新型离散主方程。水槽期限与空间依赖且适当合适的杀伤系数成正比。结果说明了两个有影响力的血管生成模型。
We study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.
